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max:main
max:feat/normalisation
max:feat/explosion
max:feat/degeneracy
max:feat/slice-computation
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compare: max:feat/slice-computation
Branches Tags
max:main
max:feat/normalisation
max:feat/explosion
max:feat/degeneracy
max:feat/slice-computation

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36 changed files with 166 additions and 144037 deletions
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4
.gitignore vendored
View file

@ -1,3 +1 @@
target/
*.swp
*.swo
/target

3
Cargo.lock generated
View file

@ -346,7 +346,6 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
checksum = "9a8e94ea7f378bd32cbbd37198a4a91436180c5bb472411e48b5ec2e2124ae9e"
dependencies = [
"serde_core",
"serde_derive",
]
[[package]]
@ -633,8 +632,6 @@ name = "zigzag-engine"
version = "0.1.0"
dependencies = [
"proptest",
"serde",
"serde_json",
"thiserror",
]

2
Cargo.toml
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@ -7,8 +7,6 @@ license = "BSD-3-Clause"
[dependencies]
thiserror = "1"
serde = { version = "1", features = ["derive"] }
serde_json = "1"
[dev-dependencies]
proptest = "1"

94
examples/inspect_half_braid.rs
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@ -1,94 +0,0 @@
//! Inspect the categorical structure of half_braid.json
//!
//! Run with: cargo run --example inspect_half_braid
use std::fs;
use zigzag_engine::diagram::Diagram;
use zigzag_engine::import::load_homotopy_diagram_n;
fn describe_diagram(d: &Diagram, indent: usize) -> String {
let prefix = " ".repeat(indent);
match d {
Diagram::Diagram0(g) => {
format!("{}0-diagram: generator id={}, dim={}", prefix, g.id, g.dimension)
}
Diagram::DiagramN(dn) => {
let dim = d.dimension();
let mut lines = vec![format!(
"{}{}-diagram with {} cospans:",
prefix,
dim,
dn.cospans.len()
)];
lines.push(format!("{} source:", prefix));
lines.push(describe_diagram(dn.source(), indent + 2));
if !dn.cospans.is_empty() {
lines.push(format!("{} target:", prefix));
lines.push(describe_diagram(&dn.target(), indent + 2));
}
lines.join("\n")
}
}
}
fn main() {
let json = fs::read_to_string("fixtures/half_braid.json")
.expect("Failed to read half_braid.json");
let half_braid = load_homotopy_diagram_n(&json)
.expect("Failed to parse");
let half_braid_d = Diagram::DiagramN(half_braid.clone());
println!("=== HALF_BRAID CATEGORICAL STRUCTURE ===\n");
// The half_braid itself is a 3-diagram
println!("half_braid is a {}-diagram with {} cospans\n",
half_braid_d.dimension(), half_braid.cospans.len());
// Its source (a 2-diagram)
let source_2d = half_braid.source();
println!("SOURCE of half_braid (the 2-diagram it transforms FROM):");
println!("{}\n", describe_diagram(source_2d, 1));
// Its target (a 2-diagram)
let target_2d = half_braid.target();
println!("TARGET of half_braid (the 2-diagram it transforms TO):");
println!("{}\n", describe_diagram(&target_2d, 1));
// Are source and target the same?
println!("Are source and target equal? {}\n", source_2d == &target_2d);
// Look at the source 2-diagram structure
if let Diagram::DiagramN(src) = source_2d {
println!("=== SOURCE 2-DIAGRAM SLICES ===");
println!("This 2-diagram has {} cospans (singular heights)\n", src.cospans.len());
// Regular slices
for i in 0..=src.cospans.len() {
if let Some(slice) = src.regular_slice(i) {
println!("Regular slice r{}: {}", i, describe_diagram(&slice, 0));
}
}
println!();
// Singular slices
for i in 0..src.cospans.len() {
if let Some(slice) = src.singular_slice(i) {
println!("Singular slice s{}: {}", i, describe_diagram(&slice, 0));
}
}
}
println!("\n=== INTERPRETATION ===");
println!("Generator 0 (dim=0): The base object x");
println!("Generator 1 (dim=2): The scalar s (a 2-cell: id_x → id_x)");
println!();
println!("The SOURCE 2-diagram is 'two scalars stacked':");
println!(" - 2 cospans means 2 singular heights (s0, s1)");
println!(" - Each singular height is where a scalar (2-cell) lives");
println!();
println!("The half_braid 3-diagram is the Eckmann-Hilton homotopy:");
println!(" - It shows the two scalars 'sliding past' each other");
println!(" - Source = target (as 2-diagrams, they're the same configuration)");
println!(" - But the 3-diagram is NON-trivial: it's the braiding coherence");
}

287
examples/render_braiding.rs
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@ -1,287 +0,0 @@
//! Generate geometry JSON from explosion for Three.js rendering.
//!
//! Run with: cargo run --example render_braiding
//!
//! Outputs fixtures/half_braid_geometry.json with VISIBLE elements only.
//! Visibility follows homotopy.io's rule: a point at geom_dim d is visible
//! iff coords[d..] are all singular.
use std::collections::{HashMap, HashSet, VecDeque};
use std::fs;
use zigzag_engine::diagram::Diagram;
use zigzag_engine::explosion::{HeightLabel, Point};
use zigzag_engine::import::load_homotopy_diagram_n;
use serde::Serialize;
#[derive(Serialize)]
struct Geometry {
metadata: Metadata,
vertices: Vec<Vertex>,
wires: Vec<Wire>,
surfaces: Vec<Surface>,
}
#[derive(Serialize)]
struct Metadata {
source: String,
dimension: usize,
total_points: usize,
visible_points: usize,
total_covers: usize,
}
#[derive(Serialize)]
struct Vertex {
id: usize,
label: String,
point: String,
coords: [f64; 3],
}
#[derive(Serialize)]
struct Wire {
id: usize,
label: String,
point: String,
coords: [f64; 3],
endpoints: [usize; 2],
endpoint_coords: [[f64; 3]; 2],
}
#[derive(Serialize)]
struct Surface {
id: usize,
label: String,
point: String,
coords: [f64; 3],
boundary_wires: Vec<usize>,
}
/// Format a point as a string like "s0,s1,r0"
fn format_point(p: &Point) -> String {
p.0.iter()
.map(|h| match h {
HeightLabel::Regular(j) => format!("r{}", j),
HeightLabel::Singular(j) => format!("s{}", j),
})
.collect::<Vec<_>>()
.join(",")
}
/// Compute layout coordinates for rendering.
///
/// For half_braid visible elements:
/// - coord[0] (depth/strand): r0→-1, r1→0, r2→1 for wires; s0→-0.5, s1→0.5 for vertices
/// - coord[1] (height): r0→-1, s0→0, r1→1 for layout y
/// - coord[2] (time): s0→0 for visible elements (all at crossing time)
///
/// Output: [x, y, z] where:
/// - x = time (all 0 for visible crossing slice)
/// - y = height
/// - z = depth (spread wires/vertices along this axis)
fn layout_coords(p: &Point) -> [f64; 3] {
// For the visible crossing slice, all elements have coord[2] = s0 (time = singular)
// So x (time) = 0 for all visible elements
// z = depth axis (coord[0])
let z = match &p.0[0] {
HeightLabel::Regular(j) => (*j as f64) - 1.0, // r0→-1, r1→0, r2→1
HeightLabel::Singular(j) => (*j as f64) - 0.5, // s0→-0.5, s1→0.5
};
// y = height axis (coord[1])
let y = match &p.0[1] {
HeightLabel::Regular(j) => (*j as f64) - 1.0, // r0→-1, r1→1
HeightLabel::Singular(j) => *j as f64, // s0→0
};
// x = time axis (coord[2]) - all visible elements are at s0
let x = 0.0;
[x, y, z]
}
/// Count singular labels in a point
fn singular_count(p: &Point) -> usize {
p.0.iter().filter(|h| h.is_singular()).count()
}
/// Compute geometric dimension from singular count
fn geom_dim(p: &Point, n: usize) -> usize {
n - singular_count(p)
}
fn main() {
// Load diagram
let json = fs::read_to_string("fixtures/half_braid.json")
.expect("Failed to read fixtures/half_braid.json");
let diagram_n = load_homotopy_diagram_n(&json)
.expect("Failed to parse half_braid.json");
let diagram = Diagram::DiagramN(diagram_n);
let n = diagram.dimension();
let pts = diagram.full_points();
eprintln!("Loaded half_braid.json: dim={}, {} points, {} covers",
n, pts.len(), pts.covers().len());
// Filter to VISIBLE points only
let visible_indices: Vec<usize> = pts.elements()
.iter()
.enumerate()
.filter(|(_, point)| point.is_visible(n))
.map(|(idx, _)| idx)
.collect();
eprintln!("Visible points: {}", visible_indices.len());
// Group visible points by geometric dimension
let mut by_geom_dim: HashMap<usize, Vec<usize>> = HashMap::new();
for &idx in &visible_indices {
let point = &pts.elements()[idx];
let gd = geom_dim(point, n);
by_geom_dim.entry(gd).or_default().push(idx);
}
// Build adjacency for reachability (on full poset)
let mut successors: Vec<Vec<usize>> = vec![vec![]; pts.len()];
let mut predecessors: Vec<Vec<usize>> = vec![vec![]; pts.len()];
for &(lower, upper) in pts.covers() {
successors[lower].push(upper);
predecessors[upper].push(lower);
}
// Helper: find all transitively reachable points
let reachable_from = |start: usize, adj: &[Vec<usize>]| -> HashSet<usize> {
let mut visited = HashSet::new();
let mut queue = VecDeque::new();
queue.push_back(start);
visited.insert(start);
while let Some(curr) = queue.pop_front() {
for &next in &adj[curr] {
if visited.insert(next) {
queue.push_back(next);
}
}
}
visited
};
// Get visible vertex indices
let vertex_indices = by_geom_dim.get(&0).map(|v| v.as_slice()).unwrap_or(&[]);
let vertex_set: HashSet<usize> = vertex_indices.iter().copied().collect();
// Get visible wire indices
let wire_indices = by_geom_dim.get(&1).map(|v| v.as_slice()).unwrap_or(&[]);
let wire_set: HashSet<usize> = wire_indices.iter().copied().collect();
// Build vertices
let mut vertices: Vec<Vertex> = Vec::new();
for (i, &idx) in vertex_indices.iter().enumerate() {
let point = &pts.elements()[idx];
vertices.push(Vertex {
id: idx,
label: format!("vertex_{}", i),
point: format_point(point),
coords: layout_coords(point),
});
}
// Build wires with endpoint connections
let mut wires: Vec<Wire> = Vec::new();
for (i, &idx) in wire_indices.iter().enumerate() {
let point = &pts.elements()[idx];
// Find connected VISIBLE vertices via transitive reachability
let reachable_up = reachable_from(idx, &successors);
let reachable_down = reachable_from(idx, &predecessors);
let mut connected: Vec<usize> = reachable_up
.union(&reachable_down)
.filter(|v| vertex_set.contains(v))
.copied()
.collect();
connected.sort();
connected.dedup();
let endpoints = if connected.len() >= 2 {
[connected[0], connected[1]]
} else if connected.len() == 1 {
[connected[0], connected[0]]
} else {
[vertex_indices[0], vertex_indices.get(1).copied().unwrap_or(vertex_indices[0])]
};
let endpoint_coords = [
layout_coords(&pts.elements()[endpoints[0]]),
layout_coords(&pts.elements()[endpoints[1]]),
];
wires.push(Wire {
id: idx,
label: format!("wire_{}", i),
point: format_point(point),
coords: layout_coords(point),
endpoints,
endpoint_coords,
});
}
// Build visible surfaces (geom_dim=2)
let surface_indices = by_geom_dim.get(&2).map(|v| v.as_slice()).unwrap_or(&[]);
let mut surfaces: Vec<Surface> = Vec::new();
for (i, &idx) in surface_indices.iter().enumerate() {
let point = &pts.elements()[idx];
// Find boundary wires via DIRECT covering relations
// Filter to only VISIBLE wires
let mut boundary_wires: Vec<usize> = successors[idx]
.iter()
.chain(predecessors[idx].iter())
.filter(|v| wire_set.contains(v))
.copied()
.collect();
boundary_wires.sort();
boundary_wires.dedup();
surfaces.push(Surface {
id: idx,
label: format!("surface_{}", i),
point: format_point(point),
coords: layout_coords(point),
boundary_wires,
});
}
// Build output (no volumes - they're not rendered)
let geometry = Geometry {
metadata: Metadata {
source: "half_braid.json".to_string(),
dimension: n,
total_points: pts.len(),
visible_points: visible_indices.len(),
total_covers: pts.covers().len(),
},
vertices,
wires,
surfaces,
};
// Output JSON
let json_output = serde_json::to_string_pretty(&geometry).expect("Failed to serialize");
// Write to file
fs::write("fixtures/half_braid_geometry.json", &json_output)
.expect("Failed to write fixtures/half_braid_geometry.json");
eprintln!("\nWrote fixtures/half_braid_geometry.json (VISIBLE ONLY)");
eprintln!(" {} vertices", geometry.vertices.len());
eprintln!(" {} wires", geometry.wires.len());
eprintln!(" {} surfaces", geometry.surfaces.len());
// Also print to stdout for piping
println!("{}", json_output);
}

330
examples/scaffold_analysis.rs
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@ -1,330 +0,0 @@
//! Complete scaffold analysis for half_braid
//!
//! Run with: cargo run --example scaffold_analysis
use std::fs;
use zigzag_engine::diagram::Diagram;
use zigzag_engine::explosion::{HeightLabel, Point};
use zigzag_engine::import::load_homotopy_diagram_n;
/// Format a point as a string like "r0,s0,s1"
fn format_point(p: &Point) -> String {
p.0.iter()
.map(|h| match h {
HeightLabel::Regular(j) => format!("r{}", j),
HeightLabel::Singular(j) => format!("s{}", j),
})
.collect::<Vec<_>>()
.join(",")
}
/// Count singular labels in a point
fn singular_count(p: &Point) -> usize {
p.0.iter().filter(|h| h.is_singular()).count()
}
/// Compute geometric dimension: n - singular_count
fn geom_dim(p: &Point, n: usize) -> usize {
n - singular_count(p)
}
/// Naive layout position: regular -> integer, singular -> half-integer
fn naive_layout(p: &Point) -> Vec<f64> {
p.0.iter()
.map(|h| match h {
HeightLabel::Regular(j) => *j as f64,
HeightLabel::Singular(j) => *j as f64 + 0.5,
})
.collect()
}
/// Describe which coordinate changed between two points
fn describe_change(lower: &Point, upper: &Point) -> String {
for (i, (l, u)) in lower.0.iter().zip(upper.0.iter()).enumerate() {
if l != u {
let l_str = match l {
HeightLabel::Regular(j) => format!("r{}", j),
HeightLabel::Singular(j) => format!("s{}", j),
};
let u_str = match u {
HeightLabel::Regular(j) => format!("r{}", j),
HeightLabel::Singular(j) => format!("s{}", j),
};
return format!("coord[{}]: {} → {}", i, l_str, u_str);
}
}
"no change".to_string()
}
/// Get time slice label from coord[2]
fn time_slice(p: &Point) -> String {
match p.0.get(2) {
Some(HeightLabel::Regular(0)) => "r0 (source)".to_string(),
Some(HeightLabel::Singular(0)) => "s0 (merge)".to_string(),
Some(HeightLabel::Regular(1)) => "r1 (target)".to_string(),
Some(h) => format!("{:?}", h),
None => "N/A".to_string(),
}
}
fn main() {
// Load diagram
let json = fs::read_to_string("fixtures/half_braid.json")
.expect("Failed to read fixtures/half_braid.json");
let diagram_n = load_homotopy_diagram_n(&json)
.expect("Failed to parse half_braid.json");
let diagram = Diagram::DiagramN(diagram_n);
let n = diagram.dimension();
let pts = diagram.full_points();
println!("════════════════════════════════════════════════════════════════════════════════");
println!("COMPLETE SCAFFOLD ANALYSIS FOR half_braid.json");
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
println!("Diagram dimension: {}", n);
println!("Total points: {}", pts.len());
println!("Total covering relations: {}", pts.covers().len());
println!();
// =========================================================================
// SECTION 1: All 23 Points
// =========================================================================
println!("════════════════════════════════════════════════════════════════════════════════");
println!("SECTION 1: ALL {} POINTS", pts.len());
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
println!("{:>3} {:>12} {:>4} {:>8} {:>8} {:>20}",
"idx", "coords", "sing", "geom_dim", "visible", "naive_layout");
println!("{}", "-".repeat(80));
for (idx, point) in pts.elements().iter().enumerate() {
let sc = singular_count(point);
let gd = geom_dim(point, n);
let vis = point.is_visible(n);
let layout = naive_layout(point);
let layout_str = format!("({:.1}, {:.1}, {:.1})", layout[0], layout[1], layout[2]);
println!("{:>3} {:>12} {:>4} {:>8} {:>8} {:>20}",
idx,
format_point(point),
sc,
gd,
if vis { "YES" } else { "no" },
layout_str);
}
println!();
// =========================================================================
// SECTION 2: All 35 Covering Relations
// =========================================================================
println!("════════════════════════════════════════════════════════════════════════════════");
println!("SECTION 2: ALL {} COVERING RELATIONS", pts.covers().len());
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
println!("{:>3} {:>12} → {:>12} {:>20}",
"#", "lower", "upper", "change");
println!("{}", "-".repeat(60));
for (i, &(lower_idx, upper_idx)) in pts.covers().iter().enumerate() {
let lower = &pts.elements()[lower_idx];
let upper = &pts.elements()[upper_idx];
let change = describe_change(lower, upper);
println!("{:>3} {:>12} → {:>12} {:>20}",
i + 1,
format!("{}:{}", lower_idx, format_point(lower)),
format!("{}:{}", upper_idx, format_point(upper)),
change);
}
println!();
// =========================================================================
// SECTION 3: Visible Elements and Their Connections
// =========================================================================
println!("════════════════════════════════════════════════════════════════════════════════");
println!("SECTION 3: VISIBLE ELEMENTS AND THEIR CONNECTIONS");
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
let visible_indices: Vec<usize> = pts.elements()
.iter()
.enumerate()
.filter(|(_, point)| point.is_visible(n))
.map(|(idx, _)| idx)
.collect();
println!("Visible elements: {} total", visible_indices.len());
println!();
// Group by geometric dimension
for gd in 0..=n {
let elements: Vec<usize> = visible_indices.iter()
.filter(|&&idx| geom_dim(&pts.elements()[idx], n) == gd)
.copied()
.collect();
if elements.is_empty() {
continue;
}
let gd_name = match gd {
0 => "VERTICES (0-dim)",
1 => "WIRES (1-dim)",
2 => "SURFACES (2-dim)",
3 => "VOLUMES (3-dim)",
_ => "HIGHER",
};
println!("--- {} ---", gd_name);
println!();
for idx in elements {
let point = &pts.elements()[idx];
let preds = pts.immediate_predecessors(idx);
let succs = pts.immediate_successors(idx);
println!(" [{:>2}] {} = ({:.1}, {:.1}, {:.1})",
idx, format_point(point),
naive_layout(point)[0],
naive_layout(point)[1],
naive_layout(point)[2]);
if !preds.is_empty() {
println!(" predecessors (covered by this):");
for p_idx in &preds {
let p = &pts.elements()[*p_idx];
let vis = if p.is_visible(n) { " [VIS]" } else { "" };
println!(" [{:>2}] {}{}", p_idx, format_point(p), vis);
}
}
if !succs.is_empty() {
println!(" successors (covers this):");
for s_idx in &succs {
let s = &pts.elements()[*s_idx];
let vis = if s.is_visible(n) { " [VIS]" } else { "" };
println!(" [{:>2}] {}{}", s_idx, format_point(s), vis);
}
}
println!();
}
}
// =========================================================================
// SECTION 4: Points Grouped by Time Slice
// =========================================================================
println!("════════════════════════════════════════════════════════════════════════════════");
println!("SECTION 4: POINTS GROUPED BY TIME SLICE (coord[2])");
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
// Group points by time slice
let mut by_time: std::collections::HashMap<String, Vec<usize>> = std::collections::HashMap::new();
for (idx, point) in pts.elements().iter().enumerate() {
let ts = time_slice(point);
by_time.entry(ts).or_default().push(idx);
}
for time_label in &["r0 (source)", "s0 (merge)", "r1 (target)"] {
if let Some(indices) = by_time.get(*time_label) {
println!("--- TIME {} ---", time_label);
println!(" {} points at this time slice:", indices.len());
for &idx in indices {
let point = &pts.elements()[idx];
let vis = if point.is_visible(n) { " [VISIBLE]" } else { "" };
let gd = geom_dim(point, n);
let gd_str = match gd {
0 => "vertex",
1 => "wire",
2 => "surface",
3 => "volume",
_ => "?",
};
println!(" [{:>2}] {:>12} (geom_dim={}, {}){}",
idx, format_point(point), gd, gd_str, vis);
}
println!();
}
}
// =========================================================================
// SECTION 5: Scaffold Node Paths for Visible Wires
// =========================================================================
println!("════════════════════════════════════════════════════════════════════════════════");
println!("SECTION 5: SCAFFOLD NODE PATHS FOR VISIBLE WIRES");
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
let wire_indices: Vec<usize> = visible_indices.iter()
.filter(|&&idx| geom_dim(&pts.elements()[idx], n) == 1)
.copied()
.collect();
println!("Visible wires trace through the scaffold via covering relations.");
println!("Each wire has geom_dim=1 (one regular coordinate).");
println!();
for idx in wire_indices {
let point = &pts.elements()[idx];
let layout = naive_layout(point);
println!("WIRE [{:>2}] {} at ({:.1}, {:.1}, {:.1})",
idx, format_point(point), layout[0], layout[1], layout[2]);
// Find all reachable points in both directions (full path through scaffold)
let preds = pts.immediate_predecessors(idx);
let succs = pts.immediate_successors(idx);
println!(" Direct connections:");
for p_idx in &preds {
let p = &pts.elements()[*p_idx];
let vis = if p.is_visible(n) { " [VIS]" } else { "" };
let p_layout = naive_layout(p);
println!(" ↓ [{:>2}] {} at ({:.1},{:.1},{:.1}){}",
p_idx, format_point(p), p_layout[0], p_layout[1], p_layout[2], vis);
}
println!(" ● [{:>2}] {} (this wire)", idx, format_point(point));
for s_idx in &succs {
let s = &pts.elements()[*s_idx];
let vis = if s.is_visible(n) { " [VIS]" } else { "" };
let s_layout = naive_layout(s);
println!(" ↑ [{:>2}] {} at ({:.1},{:.1},{:.1}){}",
s_idx, format_point(s), s_layout[0], s_layout[1], s_layout[2], vis);
}
println!();
}
// =========================================================================
// SECTION 6: Adjacency Matrix (abbreviated)
// =========================================================================
println!("════════════════════════════════════════════════════════════════════════════════");
println!("SECTION 6: COVER ADJACENCY (which points cover which)");
println!("════════════════════════════════════════════════════════════════════════════════");
println!();
// Build adjacency
let mut successors: Vec<Vec<usize>> = vec![vec![]; pts.len()];
let mut predecessors: Vec<Vec<usize>> = vec![vec![]; pts.len()];
for &(lower, upper) in pts.covers() {
successors[lower].push(upper);
predecessors[upper].push(lower);
}
println!("Point → Immediate Successors (covered by)");
println!("{}", "-".repeat(50));
for (idx, succs) in successors.iter().enumerate() {
if !succs.is_empty() {
let point = &pts.elements()[idx];
let succs_str: Vec<String> = succs.iter()
.map(|&s| format!("{}:{}", s, format_point(&pts.elements()[s])))
.collect();
println!("[{:>2}] {:>12} → [{}]", idx, format_point(point), succs_str.join(", "));
}
}
println!();
println!("════════════════════════════════════════════════════════════════════════════════");
println!("END OF SCAFFOLD ANALYSIS");
println!("════════════════════════════════════════════════════════════════════════════════");
}

117
examples/trace_merge.rs
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//! Trace the merge topology of half_braid
//!
//! Run with: cargo run --example trace_merge
use std::fs;
use zigzag_engine::diagram::Diagram;
use zigzag_engine::import::load_homotopy_diagram_n;
fn main() {
let json = fs::read_to_string("fixtures/half_braid.json")
.expect("Failed to read half_braid.json");
let half_braid = load_homotopy_diagram_n(&json)
.expect("Failed to parse");
println!("=== MERGE TOPOLOGY ANALYSIS ===\n");
// Source 2-diagram structure
if let Diagram::DiagramN(src) = half_braid.source() {
println!("SOURCE 2-diagram ({} cospans):", src.cospans.len());
println!("Heights: r0, s0, r1, s1, r2");
println!();
// Print y-coordinates for each height
println!("Height mappings (using layout_coords logic):");
for i in 0..=src.cospans.len() {
let y = (i as f64) - 1.0;
println!(" r{}: y = {:.1}", i, y);
if i < src.cospans.len() {
let y_sing = i as f64;
println!(" s{}: y = {:.1} ← SCALAR HERE", i, y_sing);
}
}
println!();
}
// Target 2-diagram structure
let target = half_braid.target();
if let Diagram::DiagramN(tgt) = &target {
println!("TARGET 2-diagram ({} cospans):", tgt.cospans.len());
println!("Heights: r0, s0, r1");
println!();
println!("Height mappings:");
for i in 0..=tgt.cospans.len() {
let y = (i as f64) - 1.0;
println!(" r{}: y = {:.1}", i, y);
if i < tgt.cospans.len() {
let y_sing = i as f64;
println!(" s{}: y = {:.1} ← MERGED SCALAR HERE", i, y_sing);
}
}
println!();
}
println!("=== VISIBLE ELEMENT ANALYSIS ===\n");
println!("The 2 VERTICES (geom_dim=0) are the TWO INPUT SCALARS:");
println!(" vertex (s0,s0,s0): z=-0.5, the FIRST scalar from source s0");
println!(" vertex (s1,s0,s0): z=+0.5, the SECOND scalar from source s1");
println!();
println!("The 3 WIRES (geom_dim=1) are the BOUNDARIES between regions:");
println!(" wire (r0,s0,s0): z=-1.0, LEFT boundary (below both scalars)");
println!(" wire (r1,s0,s0): z= 0.0, MIDDLE boundary (between the two scalars)");
println!(" wire (r2,s0,s0): z=+1.0, RIGHT boundary (above both scalars)");
println!();
println!("=== Y-SHAPE TOPOLOGY ===\n");
println!("The MERGE contracts source heights r0,s0,r1,s1,r2 into target heights r0,s0,r1");
println!();
println!("Mapping:");
println!(" Source r0 (y=-1) → Target r0 (y=-1) [PRESERVED]");
println!(" Source s0 (y= 0) → Target s0 (y= 0) [MERGED INTO]");
println!(" Source r1 (y= 0) → Target s0 (y= 0) [ABSORBED]");
println!(" Source s1 (y= 1) → Target s0 (y= 0) [MERGED INTO]");
println!(" Source r2 (y=+1) → Target r1 (y= 0) [CONTRACTED DOWN]");
println!();
println!("For the 3 visible wires:");
println!();
println!("Wire r0 (z=-1, LEFT EDGE):");
println!(" Source endpoint (x=-1): y=-1 (at source height r0)");
println!(" Merge waypoint (x= 0): y= 0 (at merge height s0)");
println!(" Target endpoint (x=+1): y=-1 (at target height r0)");
println!(" → This wire DIPS DOWN to the merge then back up");
println!();
println!("Wire r1 (z=0, MIDDLE/STEM):");
println!(" Source endpoint (x=-1): y= 0 (at source height r1, between s0 and s1)");
println!(" Merge waypoint (x= 0): y= 0 (at merge height s0)");
println!(" Target endpoint (x=+1): y= 0 (at target height s0)");
println!(" → This is the STEM - stays at y=0 throughout");
println!();
println!("Wire r2 (z=+1, RIGHT EDGE):");
println!(" Source endpoint (x=-1): y=+1 (at source height r2)");
println!(" Merge waypoint (x= 0): y= 0 (at merge height s0)");
println!(" Target endpoint (x=+1): y= 0 (at target height r1)");
println!(" → This wire comes DOWN from above into the merge");
println!();
println!("=== THE Y-SHAPE ===\n");
println!("Looking at y-z plane (height vs depth) at different x (time) slices:\n");
println!("At SOURCE (x=-1): At MERGE (x=0): At TARGET (x=+1):");
println!(" ");
println!("y=+1 ──●r2── y=+1 y=+1 ");
println!(" │ ╲ ");
println!(" │ ╲ ");
println!("y= 0 ──●r1── ←s1 scalar y= 0 ●●● (merge) y= 0 ──●r1,r2── ");
println!(" │ ╱ ↑ ↑ ");
println!(" │ ╱ vertices merged ");
println!("y=-1 ──●r0── ←s0 scalar y=-1 y=-1 ──●r0── ");
println!(" ");
println!(" z: -1 0 +1 -1 0 +1 -1 0 +1 ");
}

115
examples/trace_scaffold.rs
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//! Trace scaffold nodes for visible wires through all time heights
//!
//! Run with: cargo run --example trace_scaffold
use std::fs;
use zigzag_engine::diagram::Diagram;
use zigzag_engine::import::load_homotopy_diagram_n;
fn main() {
let json = fs::read_to_string("fixtures/half_braid.json")
.expect("Failed to read half_braid.json");
let half_braid = load_homotopy_diagram_n(&json)
.expect("Failed to parse");
println!("=== SCAFFOLD NODE TRACING ===\n");
// Time structure of the 3-diagram
println!("TIME STRUCTURE (coord[2]):");
println!(" The half_braid has {} cospan(s)", half_braid.cospans.len());
println!(" Time heights: r0 (source), s0 (merge), r1 (target)");
println!();
// Source 2-diagram heights
if let Diagram::DiagramN(src) = half_braid.source() {
println!("SOURCE 2-DIAGRAM (at time r0):");
println!(" {} cospans → heights: r0, s0, r1, s1, r2", src.cospans.len());
println!(" Y-mapping: r0→-1, s0→0, r1→0, s1→1, r2→+1");
println!();
}
// Target 2-diagram heights
let target = half_braid.target();
if let Diagram::DiagramN(tgt) = &target {
println!("TARGET 2-DIAGRAM (at time r1):");
println!(" {} cospan(s) → heights: r0, s0, r1", tgt.cospans.len());
println!(" Y-mapping: r0→-1, s0→0, r1→0");
println!();
}
println!("=== HEIGHT MAPPING THROUGH MERGE ===");
println!();
println!("The merge contracts source heights to target heights:");
println!(" Source r0 → Target r0 (preserved, y stays at -1)");
println!(" Source s0 → Target s0 (merges, y=0 → y=0)");
println!(" Source r1 → Target s0 (absorbed into merge, y=0 → y=0)");
println!(" Source s1 → Target s0 (merges, y=1 → y=0)");
println!(" Source r2 → Target r1 (contracts down, y=+1 → y=0)");
println!();
println!("=== SCAFFOLD NODE POSITIONS FOR EACH WIRE ===");
println!();
println!("Time positions: r0 at x=-1, s0 at x=0, r1 at x=+1");
println!("Depth positions: r0→z=-1, r1→z=0, r2→z=+1");
println!();
// Wire r0
println!("WIRE r0 (coord[0]=r0, depth z=-1):");
println!(" At time r0 (source): coord=(r0, r0, r0)");
println!(" → coord[1]=r0=Regular(0) → y = -1");
println!(" → position: (-1, -1, -1)");
println!();
println!(" At time s0 (merge): coord=(r0, s0, s0)");
println!(" → coord[1]=s0=Singular(0) → y = 0");
println!(" → position: (0, 0, -1)");
println!();
println!(" At time r1 (target): coord=(r0, r0, r1)");
println!(" → coord[1]=r0=Regular(0) → y = -1");
println!(" → position: (+1, -1, -1)");
println!();
println!(" Wire r0 polyline: [(-1,-1,-1), (0,0,-1), (+1,-1,-1)]");
println!(" Shape: DIPS to merge, returns to original height");
println!();
// Wire r1
println!("WIRE r1 (coord[0]=r1, depth z=0):");
println!(" At time r0 (source): coord=(r1, r1, r0)");
println!(" → coord[1]=r1=Regular(1) → y = 0");
println!(" → position: (-1, 0, 0)");
println!();
println!(" At time s0 (merge): coord=(r1, s0, s0)");
println!(" → coord[1]=s0=Singular(0) → y = 0");
println!(" → position: (0, 0, 0)");
println!();
println!(" At time r1 (target): coord=(r1, s0, r1)");
println!(" → coord[1]=s0=Singular(0) → y = 0 (r1 absorbed into s0)");
println!(" → position: (+1, 0, 0)");
println!();
println!(" Wire r1 polyline: [(-1,0,0), (0,0,0), (+1,0,0)]");
println!(" Shape: FLAT at y=0 throughout - this is the STEM");
println!();
// Wire r2
println!("WIRE r2 (coord[0]=r2, depth z=+1):");
println!(" At time r0 (source): coord=(r2, r2, r0)");
println!(" → coord[1]=r2=Regular(2) → y = +1");
println!(" → position: (-1, +1, +1)");
println!();
println!(" At time s0 (merge): coord=(r2, s0, s0)");
println!(" → coord[1]=s0=Singular(0) → y = 0");
println!(" → position: (0, 0, +1)");
println!();
println!(" At time r1 (target): coord=(r2, r1, r1)");
println!(" → coord[1]=r1=Regular(1) → y = 0 (r2 contracted to r1)");
println!(" → position: (+1, 0, +1)");
println!();
println!(" Wire r2 polyline: [(-1,+1,+1), (0,0,+1), (+1,0,+1)]");
println!(" Shape: DROPS from y=+1 to y=0, stays at y=0");
println!();
println!("=== SUMMARY ===");
println!();
println!("Wire r0: [(-1,-1,-1), (0,0,-1), (1,-1,-1)] // dips and returns");
println!("Wire r1: [(-1, 0, 0), (0,0, 0), (1, 0, 0)] // flat stem");
println!("Wire r2: [(-1,+1,+1), (0,0,+1), (1, 0,+1)] // drops and stays");
}

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fixtures/contracted_with_inner_identity.json
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fixtures/dim456_combined.json
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fixtures/dim456_info.txt
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warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:135:22
|
135 | .filter(|&e| (e.target() != keep))
| ^ ^
|
= note: `#[warn(unused_parens)]` (part of `#[warn(unused)]`) on by default
help: remove these parentheses
|
135 - .filter(|&e| (e.target() != keep))
135 + .filter(|&e| e.target() != keep)
|
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:158:22
|
158 | .filter(|&e| (e.source() != keep))
| ^ ^
|
help: remove these parentheses
|
158 - .filter(|&e| (e.source() != keep))
158 + .filter(|&e| e.source() != keep)
|
warning: `homotopy-core` (lib) generated 2 warnings (run `cargo fix --lib -p homotopy-core` to apply 2 suggestions)
Compiling homotopy-core v0.1.0 (/home/maximus/.env/extern/diagrammatic-semiotics/homotopy-rs/homotopy-core)
Finished `dev` profile [unoptimized + debuginfo] target(s) in 0.54s
Running `target/debug/examples/export_dim456`
=== Building dimension 4, 5, 6 test fixtures ===
lips: dim=4, size=1
padded_4: dim=4, size=2
as_5d: dim=5, size=1
source dim=4, size=2
as_6d: dim=6, size=1
source dim=5, size=1
=== Exporting fixtures ===
padded_4: 1076794 bytes
as_5d: 1154944 bytes
as_6d: 1233174 bytes

61
fixtures/dim4_info.txt
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warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:135:22
|
135 | .filter(|&e| (e.target() != keep))
| ^ ^
|
= note: `#[warn(unused_parens)]` (part of `#[warn(unused)]`) on by default
help: remove these parentheses
|
135 - .filter(|&e| (e.target() != keep))
135 + .filter(|&e| e.target() != keep)
|
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:158:22
|
158 | .filter(|&e| (e.source() != keep))
| ^ ^
|
help: remove these parentheses
|
158 - .filter(|&e| (e.source() != keep))
158 + .filter(|&e| e.source() != keep)
|
warning: `homotopy-core` (lib) generated 2 warnings (run `cargo fix --lib -p homotopy-core` to apply 2 suggestions)
Compiling homotopy-core v0.1.0 (/home/maximus/.env/extern/diagrammatic-semiotics/homotopy-rs/homotopy-core)
warning: unused import: `homotopy_core::common::Boundary`
--> homotopy-core/examples/export_dim4.rs:4:5
|
4 | use homotopy_core::common::Boundary;
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
= note: `#[warn(unused_imports)]` (part of `#[warn(unused)]`) on by default
warning: `homotopy-core` (example "export_dim4") generated 1 warning (run `cargo fix --example "export_dim4" -p homotopy-core` to apply 1 suggestion)
Finished `dev` profile [unoptimized + debuginfo] target(s) in 0.48s
Running `target/debug/examples/export_dim4`
=== Searching for dimension 4 examples ===
--- lips() ---
lips: dim=4, size=1
source dim=3
--- pants_unit() ---
pants_unit: dim=4, size=1
source dim=3
--- algebraic_snake() ---
algebraic_snake: dim=3, size=1
=== Approach 1: Padded half_braid lifted to dim 4 ===
half_braid: dim=3, size=1
padded_3d: dim=3, size=2
padded_4d: dim=4, size=0
=== Approach 2: Pad lips() at dim 4 ===
padded_lips: dim=4, size=2
(original lips size was 1, now 2)
=== Exporting padded_lips (dim 4 with identity cospan) ===

2119
fixtures/essential_identity_4d.json
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fixtures/essential_info.txt
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@ -1,41 +0,0 @@
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:135:22
|
135 | .filter(|&e| (e.target() != keep))
| ^ ^
|
= note: `#[warn(unused_parens)]` (part of `#[warn(unused)]`) on by default
help: remove these parentheses
|
135 - .filter(|&e| (e.target() != keep))
135 + .filter(|&e| e.target() != keep)
|
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:158:22
|
158 | .filter(|&e| (e.source() != keep))
| ^ ^
|
help: remove these parentheses
|
158 - .filter(|&e| (e.source() != keep))
158 + .filter(|&e| e.source() != keep)
|
warning: `homotopy-core` (lib) generated 2 warnings (run `cargo fix --lib -p homotopy-core` to apply 2 suggestions)
Compiling homotopy-core v0.1.0 (/home/maximus/.env/extern/diagrammatic-semiotics/homotopy-rs/homotopy-core)
Finished `dev` profile [unoptimized + debuginfo] target(s) in 0.52s
Running `target/debug/examples/export_essential`
=== Building essential identity scenario ===
two_scalars: dim=2, size=2
two_scalars_3d: dim=3, size=0
Attempting contraction...
Contraction failed: OutOfBounds
Fallback: using half_braid
half_braid: dim=3, size=1
padded_3d: dim=3, size=2
wrapped_4d: dim=4, size=1

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fixtures/half_braid.json
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fixtures/half_braid_geometry.json
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{
"metadata": {
"source": "half_braid.json",
"dimension": 3,
"total_points": 23,
"visible_points": 12,
"total_covers": 35
},
"vertices": [
{
"id": 21,
"label": "vertex_0",
"point": "s0,s0,s0",
"coords": [
0.0,
0.0,
-0.5
]
},
{
"id": 22,
"label": "vertex_1",
"point": "s1,s0,s0",
"coords": [
0.0,
0.0,
0.5
]
}
],
"wires": [
{
"id": 18,
"label": "wire_0",
"point": "r0,s0,s0",
"coords": [
0.0,
0.0,
-1.0
],
"endpoints": [
21,
22
],
"endpoint_coords": [
[
0.0,
0.0,
-0.5
],
[
0.0,
0.0,
0.5
]
]
},
{
"id": 19,
"label": "wire_1",
"point": "r1,s0,s0",
"coords": [
0.0,
0.0,
0.0
],
"endpoints": [
21,
22
],
"endpoint_coords": [
[
0.0,
0.0,
-0.5
],
[
0.0,
0.0,
0.5
]
]
},
{
"id": 20,
"label": "wire_2",
"point": "r2,s0,s0",
"coords": [
0.0,
0.0,
1.0
],
"endpoints": [
21,
22
],
"endpoint_coords": [
[
0.0,
0.0,
-0.5
],
[
0.0,
0.0,
0.5
]
]
}
],
"surfaces": [
{
"id": 16,
"label": "surface_0",
"point": "r0,r0,s0",
"coords": [
0.0,
-1.0,
-1.0
],
"boundary_wires": [
18
]
},
{
"id": 17,
"label": "surface_1",
"point": "r0,r1,s0",
"coords": [
0.0,
0.0,
-1.0
],
"boundary_wires": [
18
]
}
]
}

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fixtures/identity_wrapped_5d.json
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fixtures/identity_wrapped_6d.json
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fixtures/padded_3d.json
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fixtures/padded_4d.json
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fixtures/padded_export.json
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{
"padded_3d": {
"source": {
"DiagramN": {
"source": {
"DiagramN": {
"source": {
"Diagram0": {
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
}
},
"cospans": []
}
},
"cospans": [
{
"forward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
},
"backward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
}
}
]
}
},
"cospans": []
},
"scalar_3d": {
"source": {
"DiagramN": {
"source": {
"DiagramN": {
"source": {
"Diagram0": {
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
}
},
"cospans": []
}
},
"cospans": [
{
"forward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
},
"backward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
}
}
]
}
},
"cospans": []
}
}

42
fixtures/padded_info.txt
View file

@ -1,42 +0,0 @@
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:135:22
|
135 | .filter(|&e| (e.target() != keep))
| ^ ^
|
= note: `#[warn(unused_parens)]` (part of `#[warn(unused)]`) on by default
help: remove these parentheses
|
135 - .filter(|&e| (e.target() != keep))
135 + .filter(|&e| e.target() != keep)
|
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:158:22
|
158 | .filter(|&e| (e.source() != keep))
| ^ ^
|
help: remove these parentheses
|
158 - .filter(|&e| (e.source() != keep))
158 + .filter(|&e| e.source() != keep)
|
warning: `homotopy-core` (lib) generated 2 warnings (run `cargo fix --lib -p homotopy-core` to apply 2 suggestions)
Compiling homotopy-core v0.1.0 (/home/maximus/.env/extern/diagrammatic-semiotics/homotopy-rs/homotopy-core)
Finished `dev` profile [unoptimized + debuginfo] target(s) in 0.74s
Running `target/debug/examples/export_padded`
=== Original half_braid ===
dimension: 3
size: 1
=== Identity cospan ===
forward is_identity: true
backward is_identity: true
cospan is_identity: true
=== Padded diagram ===
dimension: 3
size: 2
last cospan is_identity: true

19467
fixtures/padded_lips_4d.json
View file

File diff suppressed because it is too large Load diff

226
fixtures/scalar.json
View file

@ -1,226 +0,0 @@
{
"source": {
"DiagramN": {
"source": {
"Diagram0": {
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
}
},
"cospans": []
}
},
"cospans": [
{
"forward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
},
"backward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
}
}
]
}

68
fixtures/scan_output.txt
View file

@ -1,68 +0,0 @@
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:135:22
|
135 | .filter(|&e| (e.target() != keep))
| ^ ^
|
= note: `#[warn(unused_parens)]` (part of `#[warn(unused)]`) on by default
help: remove these parentheses
|
135 - .filter(|&e| (e.target() != keep))
135 + .filter(|&e| e.target() != keep)
|
warning: unnecessary parentheses around closure body
--> homotopy-core/src/collapse.rs:158:22
|
158 | .filter(|&e| (e.source() != keep))
| ^ ^
|
help: remove these parentheses
|
158 - .filter(|&e| (e.source() != keep))
158 + .filter(|&e| e.source() != keep)
|
warning: `homotopy-core` (lib) generated 2 warnings (run `cargo fix --lib -p homotopy-core` to apply 2 suggestions)
Compiling homotopy-core v0.1.0 (/home/maximus/.env/extern/diagrammatic-semiotics/homotopy-rs/homotopy-core)
Finished `dev` profile [unoptimized + debuginfo] target(s) in 0.55s
Running `target/debug/examples/scan_identities`
=== Scanning homotopy-rs examples for identity cospans ===
--- Scanning lips() ---
lips: dim=4, size=1
--- Scanning pants_unit() ---
pants_unit: dim=4, size=1
--- Scanning touching() ---
touching: dim=3, size=2
--- Scanning crossing() ---
crossing: dim=3, size=2
--- Scanning algebraic_snake() ---
algebraic_snake: dim=3, size=1
--- Scanning bubble() ---
bubble: dim=2, size=2
--- Scanning snake() ---
snake: dim=2, size=2
=== Constructing potential essential identity scenario ===
half_braid: dim=3, size=1
half_braid.source: dim=2
size=2
dim3_with_id: dim=3, size=2
cospan[0] is_identity: false
cospan[1] is_identity: true
Attempting contraction on dim3_with_id...
Contraction succeeded!
result: dim=4, size=1
FOUND: source at depth=1, dim=3, size=2, identity_cospans=[1]/2, path=["source"]
=== Exporting contracted diagram ===

434
fixtures/two_scalars.json
View file

@ -1,434 +0,0 @@
{
"source": {
"DiagramN": {
"source": {
"Diagram0": {
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
}
},
"cospans": []
}
},
"cospans": [
{
"forward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
},
"backward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 1,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
}
},
{
"forward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 2,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 2,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 2,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
},
"backward": {
"RewriteN": {
"dimension": 1,
"cones": [
{
"index": 0,
"internal": {
"source": [],
"target": {
"forward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 2,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Source",
1
],
[
[]
]
]
]
},
"backward": {
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 2,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
1
],
[
[]
]
]
]
}
},
"regular_slices": [
{
"Rewrite0": [
{
"generator": {
"id": 0,
"dimension": 0
},
"orientation": "Positive"
},
{
"generator": {
"id": 2,
"dimension": 2
},
"orientation": "Positive"
},
[
[
"Target",
0
],
[
[
{
"Regular": 0
}
]
]
]
]
}
],
"singular_slices": []
}
}
]
}
}
}
]
}

1197
src/degeneracy.rs
View file

File diff suppressed because it is too large Load diff

200
src/diagram.rs
View file

@ -166,12 +166,9 @@ impl Cospan {
Self { forward, backward }
}
/// Check if this is an identity cospan (both legs are trivially identity).
///
/// Uses `is_trivial()` which recognizes both `Rewrite::Identity` and
/// `RewriteN` with empty cones (as serialized by homotopy-rs).
/// Check if this is an identity cospan (both legs are isomorphisms).
pub fn is_identity(&self) -> bool {
self.forward.is_trivial() && self.backward.is_trivial()
self.forward.is_identity() && self.backward.is_identity()
}
}
@ -192,32 +189,11 @@ pub enum Rewrite {
}
impl Rewrite {
/// Check if this is explicitly marked as an identity rewrite.
///
/// Returns true only for `Rewrite::Identity`. This is conservative and
/// used for degeneracy tracking where we need to distinguish between
/// a true identity and a parallel degeneracy with non-identity slices.
/// Check if this is an identity rewrite.
pub fn is_identity(&self) -> bool {
matches!(self, Rewrite::Identity)
}
/// Check if this rewrite is trivially identity (makes no changes).
///
/// Returns true for:
/// - `Rewrite::Identity` (explicit identity marker)
/// - `RewriteN` with empty cones (no structural changes at this level)
/// - `Rewrite0` with source == target
///
/// This is used for detecting identity cospans that should be removed
/// during normalisation.
pub fn is_trivial(&self) -> bool {
match self {
Rewrite::Identity => true,
Rewrite::RewriteN(r) => r.cones.is_empty(),
Rewrite::Rewrite0 { source, target } => source == target,
}
}
/// The dimension of this rewrite.
pub fn dimension(&self) -> usize {
match self {
@ -382,9 +358,7 @@ pub struct Cone {
pub source: Vec<Cospan>,
/// Target cospan (what the source contracts to)
pub target: Cospan,
/// Slice rewrites for each source singular height.
/// Length equals source.len() (one per source cospan apex).
/// Matches homotopy-rs singular_slices convention.
/// Slice rewrites for each interior boundary
pub slices: Vec<Rewrite>,
}
@ -403,136 +377,6 @@ impl Cone {
pub fn source_size(&self) -> usize {
self.source.len()
}
/// The number of singular slices in this cone.
/// Same as source_size() - one singular slice per source cospan.
pub fn len(&self) -> usize {
self.source.len()
}
/// Check if this cone is empty (no source cospans).
pub fn is_empty(&self) -> bool {
self.source.is_empty()
}
}
impl RewriteN {
/// Compute where a regular height in the source maps to in the target.
///
/// For a rewrite f: A → B, given a regular height h in A,
/// returns the corresponding regular height in B.
///
/// Based on homotopy-rs implementation.
pub fn regular_image(&self, h: usize) -> usize {
let mut height = h;
for cone in &self.cones {
// Only affect heights that are completely AFTER this cone's source range
if height >= cone.index + cone.source_size() {
// Shift down by the contraction: source_size cospans become 1
height -= cone.source_size().saturating_sub(1);
}
}
height
}
/// Compute the preimage of a regular height from target back to source.
///
/// For a rewrite f: A → B, given a regular height h in B,
/// returns the corresponding regular height in A.
///
/// This is the inverse of regular_image.
pub fn regular_preimage(&self, target_height: usize) -> usize {
let mut source_height = target_height;
for cone in &self.cones {
// For each cone that starts before or at this target height,
// we need to account for the expansion
if target_height > cone.index {
source_height += cone.source_size().saturating_sub(1);
}
}
source_height
}
/// Compute the preimage of a singular height h in the target.
///
/// For a rewrite f: A → B, given a singular height h in B,
/// returns all singular heights in A that map to h.
///
/// This handles three cases:
/// 1. **Contraction**: A cone targets h and has len > 0. Returns all source
/// heights consumed by that cone.
/// 2. **Insertion**: A cone targets h but has len == 0. Returns empty (no
/// source heights map to this insertion point).
/// 3. **Passthrough**: No cone targets h. Returns the single source height
/// that passes through to h (computed from the cone structure).
pub fn singular_preimage(&self, target_h: usize) -> Vec<usize> {
let mut current_source = 0;
let mut current_target = 0;
for cone in &self.cones {
// Handle passthroughs before this cone
while current_target < cone.index {
if current_target == target_h {
// Found passthrough at target_h
return vec![current_source];
}
current_source += 1;
current_target += 1;
}
// Handle the cone itself
if current_target == target_h {
// This cone targets our height
// Return all source heights in the cone's range
// (empty if len == 0, i.e., insertion)
return (current_source..current_source + cone.len()).collect();
}
current_source += cone.len();
current_target += 1; // Cone produces 1 target cospan
}
// Handle passthroughs after all cones
// target_h is beyond all cone indices
let offset = target_h - current_target;
vec![current_source + offset]
}
/// Get the target heights (where cones map to).
pub fn targets(&self) -> impl Iterator<Item = usize> + '_ {
self.cones.iter().map(|c| c.index)
}
/// Get the slice rewrite at a source singular height.
///
/// For a rewrite f: A → B, given a source singular height h,
/// returns the (n-1)-dimensional rewrite between source's singular
/// slice at h and the corresponding target singular slice.
///
/// Based on homotopy-rs: finds the cone containing this source height,
/// then indexes into its singular_slices.
pub fn slice(&self, source_height: usize) -> Rewrite {
// Find which cone contains this source height
let mut source_offset = 0;
for cone in &self.cones {
let source_end = source_offset + cone.len();
if source_height >= source_offset && source_height < source_end {
// Found the cone - index into its slices
let local_idx = source_height - source_offset;
if local_idx < cone.slices.len() {
return cone.slices[local_idx].clone();
}
}
source_offset = source_end;
}
// Height is outside all cones (passthrough), return identity
Rewrite::Identity
}
/// Get the cone that targets a specific height, if any.
pub fn cone_over_target(&self, target_height: usize) -> Option<&Cone> {
self.cones.iter().find(|c| c.index == target_height)
}
}
// === Diagram methods ===
@ -642,42 +486,6 @@ impl DiagramMap {
pub fn is_identity(&self) -> bool {
self.rewrite.is_identity()
}
/// Compose two diagram maps: (g ∘ f) where self = f and other = g.
///
/// For identity maps, composition is trivial.
/// For rewrites, we need to compose the underlying structure.
pub fn compose(&self, other: &DiagramMap) -> DiagramMap {
if self.is_identity() {
other.clone()
} else if other.is_identity() {
self.clone()
} else {
// TODO: Implement full rewrite composition
// For now, return other (this is a simplification)
other.clone()
}
}
/// Check if a singular height h is in the image of this map's singular component.
///
/// For degeneracy maps, this checks if height h would be preserved
/// (i.e., is not an inserted identity cospan position).
pub fn has_singular_height_in_image(&self, h: usize) -> bool {
match &self.rewrite {
Rewrite::Identity => true, // Identity maps preserve all heights
Rewrite::Rewrite0 { .. } => true, // 0-dim has no singular structure
Rewrite::RewriteN(r) => {
// Check if h is NOT an insertion point (not in any cone's empty-source positions)
let insertion_points: std::collections::HashSet<usize> = r.cones
.iter()
.filter(|c| c.source.is_empty())
.map(|c| c.index)
.collect();
!insertion_points.contains(&h)
}
}
}
}
/// Direction for slice iteration.

1157
src/explosion.rs
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File diff suppressed because it is too large Load diff

1491
src/import.rs
View file

File diff suppressed because it is too large Load diff

3
src/lib.rs
View file

@ -36,7 +36,6 @@ pub mod normalise;
pub mod typecheck;
pub mod explosion;
pub mod layout;
pub mod import;
// Re-exports for convenience
pub use monotone::MonotoneMap;
@ -45,5 +44,5 @@ pub use diagram::{Diagram, DiagramN, Cospan, Rewrite, Cone};
pub use signature::{Generator, Signature};
pub use normalise::{NormalisationResult, normalise, normalise_sink};
pub use typecheck::{TypeError, type_check};
pub use explosion::{Point, HeightLabel, Poset, InjectificationResult, injectify};
pub use explosion::{Point, HeightLabel};
pub use layout::{Layout, LayoutConstraints, SpringConstraint};

579
src/normalise.rs
View file

@ -4,14 +4,14 @@
//! the poset of degeneracy subobjects of a diagram T. This removes all
//! redundant identity structure while preserving essential identities.
//!
//! Key insight: In dimension >= 4, some identity cospans are ESSENTIAL -
//! Key insight: In dimension ≥ 4, some identity cospans are ESSENTIAL —
//! removing them would make zigzag maps ill-defined (no monotone function
//! of the required type exists). The algorithm detects and preserves these.
//!
//! # Algorithm Overview (Construction 17)
//!
//! Input: A sink S = (T, {fi: Ai -> T})
//! Output: Degeneracy d: N -> T and factorisations Ai -> N
//! Input: A sink S = (T, {fᵢ: Aᵢ → T})
//! Output: Degeneracy d: N → T and factorisations Aᵢ → N
//!
//! 1. Base case (dim 0): d = identity
//! 2. Recursive case:
@ -19,16 +19,16 @@
//! b. Normalise at each singular height (recursive, including cospan legs)
//! c. Assemble into zigzag P with parallel degeneracy dP
//! d. Remove trivial cospans not in image of any sink map
//! e. Compose: d = dP o dS
//! e. Compose: d = dP ∘ dS
use crate::diagram::{Diagram, DiagramN, DiagramMap, Rewrite, Cospan, RewriteN, Cone};
use crate::diagram::{Diagram, DiagramN, DiagramMap, Rewrite};
/// Result of normalising a diagram (or sink).
#[derive(Debug, Clone)]
pub struct NormalisationResult {
/// The normalised diagram N
pub normal_form: Diagram,
/// The degeneracy map d: N -> T
/// The degeneracy map d: N → T
pub degeneracy: DiagramMap,
/// Factorisations of each sink map through the degeneracy
pub factorisations: Vec<DiagramMap>,
@ -61,11 +61,9 @@ impl<'a> Sink<'a> {
}
}
/// Proposition 19: Normalise a sink (Construction 17).
/// Normalise a sink (Construction 17).
///
/// This is the core normalisation algorithm from the LICS 2022 paper.
/// Correctness: The output degeneracy d: N -> T is the smallest element
/// of Deg(T) through which all sink maps factor.
///
/// # Arguments
/// * `sink` - The sink to normalise (target diagram + incoming maps)
@ -73,8 +71,8 @@ impl<'a> Sink<'a> {
/// # Returns
/// A `NormalisationResult` containing:
/// - The normal form N
/// - The degeneracy d: N -> T
/// - Factorisations Ai -> N for each sink map
/// - The degeneracy d: N → T
/// - Factorisations Aᵢ → N for each sink map
pub fn normalise_sink(sink: &Sink) -> NormalisationResult {
match sink.target {
Diagram::Diagram0(_) => {
@ -92,15 +90,13 @@ pub fn normalise_sink(sink: &Sink) -> NormalisationResult {
}
}
/// Construction 17: Normalise an n-dimensional diagram (n > 0).
///
/// Implements the full 5-step algorithm for dimension > 0.
/// Normalise an n-dimensional diagram (n > 0).
fn normalise_sink_n(target: &DiagramN, sink_maps: &[DiagramMap]) -> NormalisationResult {
// Step 1: Normalise at each regular height
let regular_normalisations = normalise_regular_heights(target, sink_maps);
// Step 2: Normalise at each singular height
// CRITICAL: Include P(rh) -> T(rh) -> T(sh) composites in each sink
// CRITICAL: Include P(rₕ) → T(rₕ) → T(sₕ) composites in each sink
let singular_normalisations = normalise_singular_heights(
target,
sink_maps,
@ -112,7 +108,6 @@ fn normalise_sink_n(target: &DiagramN, sink_maps: &[DiagramMap]) -> Normalisatio
target,
&regular_normalisations,
&singular_normalisations,
sink_maps,
);
// Step 4: Remove trivial cospans not in image of any sink map
@ -124,8 +119,8 @@ fn normalise_sink_n(target: &DiagramN, sink_maps: &[DiagramMap]) -> Normalisatio
&assembled_factorisations,
);
// Step 5: Compose degeneracies d = dP o dS
let degeneracy = compose_degeneracies(&d_simple, &d_parallel);
// Step 5: Compose degeneracies d = dP ∘ dS
let degeneracy = compose_degeneracies(&d_parallel, &d_simple);
NormalisationResult {
normal_form: n,
@ -135,7 +130,6 @@ fn normalise_sink_n(target: &DiagramN, sink_maps: &[DiagramMap]) -> Normalisatio
}
/// Intermediate result for regular height normalisation.
#[derive(Debug, Clone)]
struct RegularNormalisation {
/// Normalised diagram at this regular height
normal_form: Diagram,
@ -145,12 +139,7 @@ struct RegularNormalisation {
factorisations: Vec<DiagramMap>,
}
/// Construction 17, Step 1: Normalise at each regular height.
///
/// For each regular height rh:
/// - Extract the slice T(rh)
/// - Collect sink maps restricted to this height: fi(rh): Ai(r_{fi^r(h)}) -> T(rh)
/// - Recursively normalise
/// Normalise at each regular height of the diagram.
fn normalise_regular_heights(
target: &DiagramN,
sink_maps: &[DiagramMap],
@ -159,24 +148,20 @@ fn normalise_regular_heights(
let mut results = Vec::with_capacity(num_regular);
for h in 0..num_regular {
// Get the regular slice T(rh)
// Get the regular slice T(rₕ)
let t_r_h = target.regular_slice(h).unwrap_or_else(|| {
// Fallback to source if slice computation not available
// Fallback to source if slice computation not implemented
(*target.source).clone()
});
// Collect sink maps restricted to this regular height
// Each fi(rh): Ai(r_{fi^r(h)}) -> T(rh)
// The regular map fi^r is derived from the singular map via Wraith's R
// Each fᵢ(rₕ): Aᵢ(r_{fᵢʳ(h)}) → T(rₕ)
let restricted_maps: Vec<DiagramMap> = sink_maps
.iter()
.map(|sink_map| {
// Extract the slice of the sink map at this regular height
extract_regular_slice_map(sink_map, h)
})
.map(|_| DiagramMap::identity(&t_r_h))
.collect();
// Recursively normalise this lower-dimensional sink
// Recursively normalise
let sub_sink = Sink::new(&t_r_h, restricted_maps);
let sub_result = normalise_sink(&sub_sink);
@ -190,48 +175,25 @@ fn normalise_regular_heights(
results
}
/// Helper for Construction 17, Step 1: Extract the regular slice map at height h.
fn extract_regular_slice_map(map: &DiagramMap, _h: usize) -> DiagramMap {
match &map.rewrite {
Rewrite::Identity => DiagramMap::new(Rewrite::Identity),
Rewrite::Rewrite0 { .. } => map.clone(),
Rewrite::RewriteN(rw) => {
// For an n-rewrite, the regular slice at height h is determined by
// looking at the cones and extracting the appropriate slice rewrite
if rw.cones.is_empty() {
DiagramMap::new(Rewrite::Identity)
} else {
// Find the slice data for this height
// This would normally involve looking at cone boundaries
DiagramMap::new(Rewrite::Identity)
}
}
}
}
/// Intermediate result for singular height normalisation.
#[derive(Debug, Clone)]
#[allow(dead_code)]
struct SingularNormalisation {
/// Normalised diagram at this singular height
normal_form: Diagram,
/// Degeneracy from normal form to original
degeneracy: DiagramMap,
/// Forward cospan leg from left regular (P(rh) -> P(sh))
/// Forward cospan leg from left regular
forward_leg: DiagramMap,
/// Backward cospan leg from right regular (P(r{h+1}) -> P(sh))
/// Backward cospan leg from right regular
backward_leg: DiagramMap,
/// Factorisations for each sink map at this height
factorisations: Vec<DiagramMap>,
}
/// Construction 17, Step 2: Normalise at each singular height (with cospan legs in sink).
/// Normalise at each singular height of the diagram.
///
/// CRITICAL: The sink at each singular height includes:
/// - Direct singular maps from sink: fi(st) for t in (fi^s)^{-1}(h)
/// - Cospan legs: P(rh) -> T(rh) -> T(sh) and P(r{h+1}) -> T(r{h+1}) -> T(sh)
///
/// The cospan leg composites are essential for preserving the zigzag structure.
/// - Direct singular maps from sink: fᵢ(sₜ) for t ∈ (fᵢˢ)⁻¹(h)
/// - Cospan legs: P(rₕ) → T(rₕ) → T(sₕ) and P(rₕ₊₁) → T(rₕ₊₁) → T(sₕ)
fn normalise_singular_heights(
target: &DiagramN,
sink_maps: &[DiagramMap],
@ -241,151 +203,71 @@ fn normalise_singular_heights(
let mut results = Vec::with_capacity(num_singular);
for h in 0..num_singular {
// Get the singular slice T(sh)
// Get the singular slice T(sₕ)
let t_s_h = target.singular_slice(h).unwrap_or_else(|| {
// Fallback to source if slice computation not available
// Fallback if slice computation not implemented
(*target.source).clone()
});
// Build the sink for this singular height:
// 1. Direct maps from sink_maps
// 2. Composites P(rₕ) → T(rₕ) → T(sₕ)
// 3. Composites P(rₕ₊₁) → T(rₕ₊₁) → T(sₕ)
let mut combined_maps: Vec<DiagramMap> = Vec::new();
// 1. Direct maps from sink_maps: fi(st) for all t in preimage of h
for sink_map in sink_maps {
// Extract singular slices that map to this height
let preimage = get_singular_preimage(sink_map, h);
for _t in preimage {
// Add the singular slice map fi(st): Ai(st) -> T(sh)
let slice_map = extract_singular_slice_map(sink_map, h);
combined_maps.push(slice_map);
}
// Add direct singular maps from sink
for _sink_map in sink_maps {
// TODO: Extract and add fᵢ(sₜ) for t in preimage of h
combined_maps.push(DiagramMap::identity(&t_s_h));
}
// 2. Cospan leg composite: P(rh) -> T(rh) -> T(sh)
// This is the composition of the regular degeneracy with the forward cospan leg
let forward_composite = compose_with_cospan_leg(
&regular_results[h].degeneracy,
&target.cospans[h].forward,
);
combined_maps.push(forward_composite);
// Add cospan leg composites
// TODO: Compose regular normalisations with cospan structure
combined_maps.push(regular_results[h].degeneracy.clone());
combined_maps.push(regular_results[h + 1].degeneracy.clone());
// 3. Cospan leg composite: P(r{h+1}) -> T(r{h+1}) -> T(sh)
// This is the composition of the regular degeneracy with the backward cospan leg
let backward_composite = compose_with_cospan_leg(
&regular_results[h + 1].degeneracy,
&target.cospans[h].backward,
);
combined_maps.push(backward_composite);
// Recursively normalise this singular height
let sub_sink = Sink::new(&t_s_h, combined_maps.clone());
// Recursively normalise
let sub_sink = Sink::new(&t_s_h, combined_maps);
let sub_result = normalise_sink(&sub_sink);
// Extract the factorised cospan legs from the result
// The last two factorisations are for the cospan legs
let num_factorisations = sub_result.factorisations.len();
let forward_leg = if num_factorisations >= 2 {
sub_result.factorisations[num_factorisations - 2].clone()
} else {
DiagramMap::identity(&sub_result.normal_form)
};
let backward_leg = if num_factorisations >= 1 {
sub_result.factorisations[num_factorisations - 1].clone()
} else {
DiagramMap::identity(&sub_result.normal_form)
};
// Filter out the cospan leg factorisations, keeping only sink map factorisations
let sink_factorisations: Vec<DiagramMap> = if num_factorisations >= 2 {
sub_result.factorisations[..num_factorisations - 2].to_vec()
} else {
vec![]
};
let forward_leg = DiagramMap::identity(&sub_result.normal_form);
let backward_leg = DiagramMap::identity(&sub_result.normal_form);
results.push(SingularNormalisation {
normal_form: sub_result.normal_form,
degeneracy: sub_result.degeneracy,
forward_leg,
backward_leg,
factorisations: sink_factorisations,
factorisations: sub_result.factorisations,
});
}
results
}
/// Helper for Construction 17, Step 2: Get the preimage of singular height h.
fn get_singular_preimage(map: &DiagramMap, h: usize) -> Vec<usize> {
match &map.rewrite {
Rewrite::Identity => vec![h], // Identity maps height to itself
Rewrite::Rewrite0 { .. } => vec![], // 0-rewrites have no singular structure
Rewrite::RewriteN(rw) => {
// Find all source heights that map to h
let mut preimage = Vec::new();
let mut source_idx = 0;
for cone in &rw.cones {
if cone.index == h {
// All source indices in this cone's range map to h
for i in 0..cone.source_size() {
preimage.push(source_idx + i);
}
}
source_idx += cone.source_size();
}
preimage
}
}
}
/// Helper for Construction 17, Step 2: Extract the singular slice map at height h.
fn extract_singular_slice_map(map: &DiagramMap, _h: usize) -> DiagramMap {
match &map.rewrite {
Rewrite::Identity => DiagramMap::new(Rewrite::Identity),
Rewrite::Rewrite0 { .. } => map.clone(),
Rewrite::RewriteN(rw) => {
// For an n-rewrite, find the slice at this singular height
if rw.cones.is_empty() {
DiagramMap::new(Rewrite::Identity)
} else {
// Extract slice data from cones
DiagramMap::new(Rewrite::Identity)
}
}
}
}
/// Helper for Construction 17, Step 2: Compose degeneracy with cospan leg.
fn compose_with_cospan_leg(degeneracy: &DiagramMap, cospan_leg: &Rewrite) -> DiagramMap {
let leg_map = DiagramMap::new(cospan_leg.clone());
degeneracy.compose(&leg_map)
}
/// Construction 17, Step 3: Assemble into zigzag P with parallel degeneracy dP.
/// Assemble regular and singular normalisations into a zigzag P.
///
/// Returns:
/// - P: the assembled diagram
/// - dP: the parallel degeneracy P -> T
/// - dP: the parallel degeneracy P → T
/// - Assembled factorisations
fn assemble(
target: &DiagramN,
regular_results: &[RegularNormalisation],
singular_results: &[SingularNormalisation],
sink_maps: &[DiagramMap],
) -> (Diagram, DiagramMap, Vec<DiagramMap>) {
// Build cospans for P from the normalisation results
// Each cospan has forward and backward legs computed from singular normalisation
let cospans: Vec<Cospan> = singular_results
// Build cospans from the normalisation results
let cospans: Vec<crate::diagram::Cospan> = singular_results
.iter()
.map(|sr| {
// Convert the factorised legs to rewrites
Cospan::new(
crate::diagram::Cospan::new(
sr.forward_leg.rewrite.clone(),
sr.backward_leg.rewrite.clone(),
)
})
.collect();
// The source of P is the normalised first regular slice
// The source of P is the first regular normalisation
let source = regular_results
.first()
.map(|r| r.normal_form.clone())
@ -393,98 +275,32 @@ fn assemble(
let p = Diagram::DiagramN(DiagramN::new(source, cospans));
// Build the parallel degeneracy dP: P -> T
// This is assembled from the slice degeneracies
let d_parallel = build_parallel_degeneracy(regular_results, singular_results, target);
// The parallel degeneracy is assembled from slice degeneracies
// Since all slice maps are degeneracies, the assembled map is parallel
let d_parallel = DiagramMap::new(Rewrite::Identity); // TODO: Proper assembly
// Assemble factorisations for each sink map
// Each original sink map Ai -> T factors as Ai -> P -> T
let factorisations = assemble_factorisations(
sink_maps,
regular_results,
singular_results,
);
// Assemble factorisations
let factorisations = regular_results
.first()
.map(|r| r.factorisations.clone())
.unwrap_or_default();
(p, d_parallel, factorisations)
}
/// Helper for Construction 17, Step 3: Build the parallel degeneracy dP.
///
/// A parallel degeneracy is pi-vertical (singular map is identity)
/// with all slice maps being degeneracies in the lower dimension.
fn build_parallel_degeneracy(
regular_results: &[RegularNormalisation],
singular_results: &[SingularNormalisation],
_target: &DiagramN,
) -> DiagramMap {
// Check if all slice degeneracies are identities
let all_regular_identity = regular_results.iter().all(|r| r.degeneracy.is_identity());
let all_singular_identity = singular_results.iter().all(|s| s.degeneracy.is_identity());
if all_regular_identity && all_singular_identity {
// If all slices are identity, the parallel degeneracy is identity
DiagramMap::new(Rewrite::Identity)
} else {
// Build a RewriteN with no cones (pi-vertical) but non-identity slices
// The slice data is implicit in the structure
DiagramMap::new(Rewrite::RewriteN(RewriteN {
dimension: 1,
cones: vec![],
}))
}
}
/// Helper for Construction 17, Step 3: Assemble factorisations through P.
///
/// CRITICAL FIX: When the degeneracy is identity (nothing was removed),
/// the factorisation of a sink map is the sink map itself.
/// When there is a non-trivial degeneracy, we need to compose properly.
fn assemble_factorisations(
sink_maps: &[DiagramMap],
regular_results: &[RegularNormalisation],
singular_results: &[SingularNormalisation],
) -> Vec<DiagramMap> {
// Check if all slice degeneracies are identity (nothing changed)
let all_regular_identity = regular_results.iter().all(|r| r.degeneracy.is_identity());
let all_singular_identity = singular_results.iter().all(|s| s.degeneracy.is_identity());
if all_regular_identity && all_singular_identity {
// If nothing was normalised, the factorisations are the original maps
return sink_maps.to_vec();
}
// For each sink map, its factorisation through P is assembled from
// the factorisations at each slice
sink_maps
.iter()
.enumerate()
.map(|(i, sink_map)| {
// Try to get factorisation from regular slices
if let Some(first_regular) = regular_results.first() {
if let Some(factorisation) = first_regular.factorisations.get(i) {
return factorisation.clone();
}
}
// Fallback: if the sink map is identity or no specific factorisation,
// return the original map (it passes through unchanged)
sink_map.clone()
})
.collect()
}
/// Construction 17, Step 4: Remove trivial cospans (simple degeneracy dS : N -> P).
/// Remove trivial cospans from the assembled diagram P.
///
/// A cospan at singular height h is removable iff:
/// 1. Both legs are isomorphisms (identity cospan)
/// 2. h is NOT in the image of any sink map's singular map
///
/// This is where ESSENTIAL IDENTITIES are detected. In dimension >= 4,
/// This is where ESSENTIAL IDENTITIES are detected. In dimension ≥ 4,
/// some identity cospans must be preserved because removing them would
/// make the zigzag maps ill-defined.
///
/// Returns:
/// - N: the diagram with trivial cospans removed
/// - dS: the simple degeneracy N -> P that re-inserts them
/// - dS: the simple degeneracy N → P that re-inserts them
/// - Updated factorisations
fn remove_trivial_cospans(
p: &Diagram,
@ -498,21 +314,17 @@ fn remove_trivial_cospans(
Diagram::DiagramN(diagram_n) => {
// Identify which cospans are trivial (identity) and not in sink image
let mut kept_cospans = Vec::new();
let mut removed_indices = Vec::new();
let _removed_indices = Vec::<usize>::new();
for (h, cospan) in diagram_n.cospans.iter().enumerate() {
let is_identity = cospan.is_identity();
let in_sink_image = is_in_sink_image(h, factorisations);
if !is_identity || in_sink_image {
// Keep this cospan:
// - Either it's non-trivial (not identity), OR
// - It's essential (in the image of some sink map)
// Keep this cospan (either non-trivial or essential)
kept_cospans.push(cospan.clone());
} else {
// Remove this cospan: it's trivial AND not essential
removed_indices.push(h);
}
// If trivial AND not in sink image, it's removed
}
// Build N with kept cospans
@ -521,132 +333,38 @@ fn remove_trivial_cospans(
kept_cospans,
));
// Build simple degeneracy dS: N -> P
// This re-inserts the removed identity cospans at the correct positions
let d_simple = build_simple_degeneracy(&n, p, &removed_indices);
// Build simple degeneracy dS that re-inserts removed cospans
let d_simple = DiagramMap::identity(&n); // TODO: Proper construction
// Update factorisations to account for removed cospans
let updated_factorisations = update_factorisations_for_removal(
factorisations,
&removed_indices,
);
// Update factorisations to go through dS
let updated_factorisations = factorisations.to_vec();
(n, d_simple, updated_factorisations)
}
}
}
/// Helper for Construction 17, Step 4: Check if height h is in sink image.
///
/// A height is in the image if any factorisation has a non-trivial
/// map at that singular level (i.e., some Ai has content mapping to height h).
fn is_in_sink_image(h: usize, factorisations: &[DiagramMap]) -> bool {
for factorisation in factorisations {
// Check if this factorisation maps anything to height h
if factorisation.has_singular_height_in_image(h) {
return true;
}
}
false
/// Check if singular height h is in the image of any sink map.
fn is_in_sink_image(_h: usize, _factorisations: &[DiagramMap]) -> bool {
// TODO: Extract singular maps from factorisations and check if h is in image
// For now, conservatively return true (don't remove anything)
true
}
/// Lemma 7: Build a simple degeneracy that inserts identity cospans.
///
/// A simple degeneracy is pi-cocartesian over a face map composition.
/// This implements the "simple then parallel" factorisation.
fn build_simple_degeneracy(_source: &Diagram, _target: &Diagram, removed_indices: &[usize]) -> DiagramMap {
if removed_indices.is_empty() {
return DiagramMap::new(Rewrite::Identity);
}
// Build the cones that represent inserting identity cospans
// Each removed index corresponds to inserting an identity cospan
let cones: Vec<Cone> = removed_indices
.iter()
.map(|&idx| {
Cone::new(
idx,
vec![], // Empty source (we're inserting, not contracting)
Cospan::new(Rewrite::Identity, Rewrite::Identity), // Identity cospan
vec![], // No interior slices
)
})
.collect();
DiagramMap::new(Rewrite::RewriteN(RewriteN {
dimension: 1,
cones,
}))
}
/// Helper for Construction 17, Step 4: Update factorisations after cospan removal.
///
/// Adjust the singular map indices in each factorisation to account
/// for the removed cospan positions.
fn update_factorisations_for_removal(
factorisations: &[DiagramMap],
removed_indices: &[usize],
) -> Vec<DiagramMap> {
if removed_indices.is_empty() {
return factorisations.to_vec();
}
factorisations
.iter()
.map(|f| adjust_factorisation_indices(f, removed_indices))
.collect()
}
/// Helper for Construction 17, Step 4: Adjust factorisation indices after removal.
fn adjust_factorisation_indices(factorisation: &DiagramMap, removed_indices: &[usize]) -> DiagramMap {
match &factorisation.rewrite {
Rewrite::Identity => factorisation.clone(),
Rewrite::Rewrite0 { .. } => factorisation.clone(),
Rewrite::RewriteN(rw) => {
// Adjust cone indices to account for removed cospans
let adjusted_cones: Vec<Cone> = rw.cones
.iter()
.map(|cone| {
let new_index = adjust_index(cone.index, removed_indices);
Cone::new(
new_index,
cone.source.clone(),
cone.target.clone(),
cone.slices.clone(),
)
})
.collect();
DiagramMap::new(Rewrite::RewriteN(RewriteN {
dimension: rw.dimension,
cones: adjusted_cones,
}))
}
}
}
/// Helper for Construction 17, Step 4: Adjust an index after removing positions.
fn adjust_index(original: usize, removed: &[usize]) -> usize {
let count_removed_before = removed.iter().filter(|&&r| r < original).count();
original - count_removed_before
}
/// Construction 17, Step 5: Compose d = dP ∘ dS (parallel then simple).
///
/// Lemma 7: Every degeneracy factors as simple then parallel.
/// The composition gives the final degeneracy d: N -> T.
fn compose_degeneracies(d_simple: &DiagramMap, d_parallel: &DiagramMap) -> DiagramMap {
if d_simple.is_identity() {
d_parallel.clone()
} else if d_parallel.is_identity() {
/// Compose two degeneracy maps.
fn compose_degeneracies(d_parallel: &DiagramMap, d_simple: &DiagramMap) -> DiagramMap {
// TODO: Proper composition
if d_parallel.is_identity() {
d_simple.clone()
} else if d_simple.is_identity() {
d_parallel.clone()
} else {
// Full composition needed
d_simple.compose(d_parallel)
d_parallel.clone()
}
}
/// Construction 17 (absolute case): Normalise with empty sink.
/// Absolute normalisation: normalise with empty sink.
///
/// This computes the smallest degeneracy subobject of the diagram,
/// removing all redundant identity structure.
@ -707,143 +425,4 @@ mod tests {
assert_eq!(once.normal_form, twice.normal_form);
}
#[test]
fn test_normalise_removes_identity_cospan() {
// Create a diagram with an identity cospan: r0 -> s0 <- r1
// where both legs are identities
let g = Generator::point(0);
let d0 = Diagram::Diagram0(g);
// Create a length-1 diagram with identity cospan
let identity_cospan = Cospan::new(Rewrite::Identity, Rewrite::Identity);
let d1 = Diagram::DiagramN(DiagramN::new(d0.clone(), vec![identity_cospan]));
let result = d1.normalise();
// The identity cospan should be removed (empty sink, not essential)
assert_eq!(result.normal_form.length(), 0);
}
#[test]
fn test_normalise_preserves_non_identity_cospan() {
// Create a diagram with a non-identity cospan
let g0 = Generator::point(0);
let g1 = Generator::point(1);
let d0 = Diagram::Diagram0(g0.clone());
// Create a cospan with non-identity rewrites
let non_id_cospan = Cospan::new(
Rewrite::Rewrite0 { source: g0.clone(), target: g1.clone() },
Rewrite::Rewrite0 { source: g0.clone(), target: g1 },
);
let d1 = Diagram::DiagramN(DiagramN::new(d0, vec![non_id_cospan]));
let result = d1.normalise();
// The non-identity cospan should be preserved
assert_eq!(result.normal_form.length(), 1);
}
#[test]
fn test_normalise_preserves_essential_identity() {
// Test case for essential identities (dimension >= 4 scenario)
// In this simplified test, we create a situation where an identity
// cospan is in the image of a sink map via CONTRACTION, making it essential.
//
// Key insight: An essential identity requires a CONTRACTION (non-empty source),
// not an insertion (empty source). A contraction maps existing content TO
// the target height, making it essential to preserve.
let g = Generator::point(0);
let d0 = Diagram::Diagram0(g.clone());
// Create target diagram with identity cospan (length 1)
let identity_cospan = Cospan::new(Rewrite::Identity, Rewrite::Identity);
let d1 = Diagram::DiagramN(DiagramN::new(d0.clone(), vec![identity_cospan.clone()]));
// Create a sink map that CONTRACTS to height 0 (non-empty source).
// This represents a map from a length-2 diagram to d1 (length 1).
// The contraction maps two cospans to one, putting height 0 in the image.
let sink_map = DiagramMap::new(Rewrite::RewriteN(RewriteN {
dimension: 1,
cones: vec![Cone::new(
0, // Maps to singular height 0 in target
vec![identity_cospan.clone(), identity_cospan.clone()], // NON-EMPTY source: contraction!
identity_cospan, // Target cospan
vec![Rewrite::Identity], // One interior boundary
)],
}));
let sink = Sink::new(&d1, vec![sink_map]);
let result = normalise_sink(&sink);
// The identity cospan should be preserved because it's in the sink image
// (the contraction maps to height 0)
assert_eq!(result.normal_form.length(), 1);
}
#[test]
fn test_normalisation_factorisations_correct() {
// Test that factorisations are correctly computed
let g = Generator::point(0);
let d = Diagram::Diagram0(g);
let sink_map = DiagramMap::identity(&d);
let sink = Sink::new(&d, vec![sink_map]);
let result = normalise_sink(&sink);
// The factorisation should exist for each sink map
assert_eq!(result.factorisations.len(), 1);
}
#[test]
fn test_adjust_index() {
// Test index adjustment after removal
assert_eq!(adjust_index(0, &[]), 0);
assert_eq!(adjust_index(3, &[1, 2]), 1);
assert_eq!(adjust_index(5, &[0, 2, 4]), 2);
}
#[test]
fn test_normalise_multiple_identity_cospans() {
// Create a diagram with multiple identity cospans
let g = Generator::point(0);
let d0 = Diagram::Diagram0(g);
let identity_cospan = Cospan::new(Rewrite::Identity, Rewrite::Identity);
let d3 = Diagram::DiagramN(DiagramN::new(
d0.clone(),
vec![identity_cospan.clone(), identity_cospan.clone(), identity_cospan],
));
let result = d3.normalise();
// All identity cospans should be removed (empty sink)
assert_eq!(result.normal_form.length(), 0);
}
#[test]
fn test_sink_empty() {
let g = Generator::point(0);
let d = Diagram::Diagram0(g);
let sink = Sink::empty(&d);
assert!(sink.maps.is_empty());
}
#[test]
fn test_is_in_sink_image_empty() {
// With no factorisations, nothing is in the sink image
assert!(!is_in_sink_image(0, &[]));
assert!(!is_in_sink_image(5, &[]));
}
#[test]
fn test_is_in_sink_image_with_identity() {
// Identity factorisation maps all heights to themselves
let id = DiagramMap::new(Rewrite::Identity);
assert!(is_in_sink_image(0, &[id.clone()]));
assert!(is_in_sink_image(10, &[id]));
}
}

380
src/typecheck.rs
View file

@ -6,19 +6,8 @@
//! 2. Break the diagram into pieces (one per singular content element)
//! 3. Normalise each piece
//! 4. Check that each normalised piece matches a signature element
//!
//! ## Piece extraction (Section 7 of the paper)
//!
//! For an n-diagram D, the "pieces" are sub-n-diagrams of the SAME DIMENSION as D,
//! each corresponding to one generator in the singular content. The algorithm:
//!
//! 1. Find all generators and their "paths" (sequence of singular heights to reach them)
//! 2. For each (path, generator), construct an Embedding from the path
//! 3. Use restrict_diagram to extract the sub-diagram for that embedding
//!
//! This is based on the homotopy-rs implementation in typecheck.rs.
use crate::diagram::{Diagram, DiagramN, Cospan, Rewrite, RewriteN, Cone};
use crate::diagram::Diagram;
use crate::signature::{Signature, Generator};
use thiserror::Error;
@ -53,313 +42,12 @@ pub enum TypeError {
/// A piece of singular content from a diagram.
#[derive(Debug, Clone)]
pub struct SingularPiece {
/// The piece as a sub-diagram (SAME dimension as original)
/// The piece as a sub-diagram
pub diagram: Diagram,
/// Path to this piece in the original diagram (sequence of singular indices)
pub path: Vec<usize>,
}
// =============================================================================
// Embedding: tracks how a generator sits inside a diagram
// =============================================================================
/// An embedding describes how a point (generator) is embedded in a diagram.
///
/// This is a tree structure that tracks the path through the cospan structure
/// to reach a particular generator.
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum Embedding {
/// Base case: at dimension 0, the embedding contains the point itself
Zero,
/// At a regular height: the embedding goes through a regular slice
/// and wraps in an identity cospan
Regular(usize, Box<Embedding>),
/// At a singular height: the embedding goes through singular slices
/// Each inner embedding corresponds to a slice in the range
Singular(usize, Vec<Embedding>),
}
impl Embedding {
/// Construct an embedding from a path of singular heights.
///
/// The path [h0, h1, h2] means: at the outermost level, go to singular
/// height h0; within that slice, go to singular height h1; etc.
pub fn from_point(point: &[usize]) -> Self {
let mut embedding = Self::Zero;
for &height in point.iter().rev() {
embedding = Self::Singular(height, vec![embedding]);
}
embedding
}
/// Compute the preimage of this embedding under a rewrite.
///
/// Given a rewrite f: A → B and an embedding into B, compute
/// the corresponding embedding into A.
pub fn preimage(&self, rewrite: &Rewrite) -> Self {
match self {
Self::Zero => Self::Zero,
Self::Regular(height, inner) => {
match rewrite {
Rewrite::Identity => self.clone(),
Rewrite::Rewrite0 { .. } => self.clone(),
Rewrite::RewriteN(rw) => {
// Map target regular height back to source regular height
let preimage_height = rw.regular_preimage(*height);
Self::Regular(preimage_height, inner.clone())
}
}
}
Self::Singular(height, slices) => {
match rewrite {
Rewrite::Identity => self.clone(),
Rewrite::Rewrite0 { .. } => self.clone(),
Rewrite::RewriteN(rw) => {
// Collect source heights and preimage slices from all singular
// heights in our range
let mut min_source_height: Option<usize> = None;
let preimage_slices: Vec<Embedding> = slices
.iter()
.enumerate()
.flat_map(|(target_offset, slice)| {
let target_height = height + target_offset;
rw.singular_preimage(target_height)
.into_iter()
.map(|source_height| {
// Track minimum source height for the result
min_source_height = Some(
min_source_height.map_or(source_height, |m| m.min(source_height))
);
slice.preimage(&rw.slice(source_height))
})
.collect::<Vec<_>>()
})
.collect();
if preimage_slices.is_empty() {
// This is an insertion: the cone has no source cospans
// Fall back to Regular embedding
let regular_preimage_height = rw.regular_preimage(*height);
if let Some(cone) = rw.cone_over_target(*height) {
// Use the forward leg of the target cospan
Self::Regular(
regular_preimage_height,
Box::new(slices[0].preimage(&cone.target.forward)),
)
} else {
Self::Regular(regular_preimage_height, Box::new(slices[0].clone()))
}
} else {
// Use the minimum source height as the preimage height
Self::Singular(min_source_height.unwrap_or(*height), preimage_slices)
}
}
}
}
}
}
}
// =============================================================================
// restrict_diagram: extract sub-diagram for an embedding
// =============================================================================
/// Restrict a diagram to the sub-diagram corresponding to an embedding.
///
/// The resulting diagram has the SAME dimension as the input, but only
/// contains the structure relevant to the embedded point.
pub fn restrict_diagram(diagram: &Diagram, embedding: &Embedding) -> Diagram {
match embedding {
Embedding::Zero => {
// Base case: return the 0-diagram as-is
debug_assert_eq!(diagram.dimension(), 0);
diagram.clone()
}
Embedding::Regular(height, inner) => {
// Take the regular slice at height, restrict recursively,
// then wrap in an identity cospan
match diagram {
Diagram::Diagram0(_) => diagram.clone(),
Diagram::DiagramN(d) => {
if let Some(slice) = d.regular_slice(*height) {
let restricted = restrict_diagram(&slice, inner);
Diagram::DiagramN(DiagramN::identity(restricted))
} else {
diagram.clone()
}
}
}
}
Embedding::Singular(height, slices) => {
match diagram {
Diagram::Diagram0(_) => diagram.clone(),
Diagram::DiagramN(d) => {
if d.cospans.is_empty() || *height + slices.len() > d.cospans.len() {
// Not enough cospans, return identity
return diagram.clone();
}
// Get the source for the restricted diagram
let regular_slice = d.regular_slice(*height)
.unwrap_or_else(|| (*d.source).clone());
// Compute the embedding for the source via preimage through forward
let source_embedding = slices[0].preimage(&d.cospans[*height].forward);
let restricted_source = restrict_diagram(&regular_slice, &source_embedding);
// Restrict each cospan in the range
let restricted_cospans: Vec<Cospan> = d.cospans[*height..*height + slices.len()]
.iter()
.enumerate()
.map(|(i, cospan)| {
let slice_embedding = &slices[i.min(slices.len() - 1)];
Cospan {
forward: restrict_rewrite(&cospan.forward, slice_embedding),
backward: restrict_rewrite(&cospan.backward, slice_embedding),
}
})
.collect();
Diagram::DiagramN(DiagramN::new(restricted_source, restricted_cospans))
}
}
}
}
}
// =============================================================================
// restrict_rewrite: restrict a rewrite to the preimage over a sub-diagram
// =============================================================================
/// Restrict a rewrite to the preimage over a sub-diagram of the target.
///
/// For a rewrite f: A → B and an embedding E into B, this produces
/// a rewrite f': A' → B' where A' and B' are the restricted diagrams.
pub fn restrict_rewrite(rewrite: &Rewrite, embedding: &Embedding) -> Rewrite {
if rewrite.is_trivial() {
return Rewrite::Identity;
}
match embedding {
Embedding::Zero => {
// At dimension 0, return the rewrite as-is
rewrite.clone()
}
Embedding::Regular(_, _) => {
// Regular embedding: the rewrite becomes identity
// (we're restricting to a passthrough region)
Rewrite::identity(rewrite.dimension())
}
Embedding::Singular(height, slices) => {
match rewrite {
Rewrite::Identity => Rewrite::Identity,
Rewrite::Rewrite0 { .. } => rewrite.clone(),
Rewrite::RewriteN(rw) => {
let mut restricted_cones: Vec<Cone> = Vec::new();
// Track cumulative offset to compute actual target positions.
// Cone indices in homotopy-rs are pre-offset; the actual target
// position is cone.index + offset, where offset accumulates as:
// offset += (1 - cone.len) for each cone (insertions add 1,
// contractions subtract (len-1)).
let mut offset: isize = 0;
// Also track the offset for the restricted output
let mut restricted_offset: isize = 0;
for cone in &rw.cones {
// Compute actual target position after accounting for previous cones
let actual_target = (cone.index as isize + offset) as usize;
// Update offset for this cone (even if we skip it)
offset += 1 - cone.len() as isize;
// Only include cones that target heights in our range
if actual_target < *height || actual_target >= height + slices.len() {
continue;
}
let slice_idx = actual_target - *height;
let slice_embedding = &slices[slice_idx.min(slices.len() - 1)];
// Restrict the singular slices
let restricted_singular_slices: Vec<Rewrite> = cone
.slices
.iter()
.map(|s| restrict_rewrite(s, slice_embedding))
.collect();
// Restrict source cospans
let restricted_source: Vec<Cospan> = cone
.source
.iter()
.enumerate()
.map(|(i, cospan)| {
let cone_slice = if i < cone.slices.len() {
&cone.slices[i]
} else {
&Rewrite::Identity
};
let inner_embedding = slice_embedding.preimage(cone_slice);
Cospan {
forward: restrict_rewrite(&cospan.forward, &inner_embedding),
backward: restrict_rewrite(&cospan.backward, &inner_embedding),
}
})
.collect();
// Restrict target cospan
let restricted_target = Cospan {
forward: restrict_rewrite(&cone.target.forward, slice_embedding),
backward: restrict_rewrite(&cone.target.backward, slice_embedding),
};
// Compute adjusted index for the restricted rewrite.
// The index is relative to the restricted output's current position.
let adjusted_index = (slice_idx as isize - restricted_offset) as usize;
// Capture length before moving
let restricted_source_len = restricted_source.len();
restricted_cones.push(Cone::new(
adjusted_index,
restricted_source,
restricted_target,
restricted_singular_slices,
));
// Update restricted offset
restricted_offset += 1 - restricted_source_len as isize;
}
if restricted_cones.is_empty() {
Rewrite::Identity
} else {
Rewrite::RewriteN(RewriteN::new(rw.dimension, restricted_cones))
}
}
}
}
}
}
impl Rewrite {
/// Create an identity rewrite at a given dimension.
pub fn identity(dimension: usize) -> Self {
if dimension == 0 {
Rewrite::Identity
} else {
Rewrite::RewriteN(RewriteN::identity(dimension))
}
}
}
/// Type check a diagram against a signature.
///
/// # Arguments
@ -432,32 +120,11 @@ fn extract_singular_content_recursive(
/// Extract pieces from a diagram.
///
/// Each piece corresponds to one element of singular content,
/// extracted as a sub-n-diagram of the SAME DIMENSION as the original.
///
/// The algorithm:
/// 1. Find all generators and their paths via singular_content
/// 2. For each (path, generator), create an Embedding from the path
/// 3. Use restrict_diagram to extract the sub-diagram
/// extracted as a sub-diagram by taking preimages.
pub fn extract_pieces(diagram: &Diagram) -> Vec<SingularPiece> {
// Get the singular content with paths to each generator
let content = extract_singular_content(diagram);
// For each piece of singular content, extract the restricted sub-diagram
content
.into_iter()
.map(|piece| {
// Build an embedding from the path
let embedding = Embedding::from_point(&piece.path);
// Restrict the diagram to this embedding
let restricted = restrict_diagram(diagram, &embedding);
SingularPiece {
diagram: restricted,
path: piece.path,
}
})
.collect()
// For now, this is the same as singular content extraction
// A full implementation would construct the actual sub-diagrams
extract_singular_content(diagram)
}
/// Check a single piece against the signature.
@ -507,36 +174,6 @@ fn check_piece(piece: &SingularPiece, signature: &Signature, index: usize) -> Re
Ok(())
}
/// Type check a piece against a slice of signature diagrams.
///
/// This normalises the piece and extracts the source at the generator's
/// dimension by stripping identity wrappings. The source is then compared
/// against the signature elements.
///
/// Returns true if the piece's core matches any signature element.
pub fn type_check_piece(piece: &Diagram, signature: &[Diagram]) -> bool {
use crate::normalise::normalise;
let result = normalise(piece);
let normalised = &result.normal_form;
// Extract the source at the generator's dimension
// by stripping identity wrappings until we hit non-trivial content
let mut d = normalised;
while let Diagram::DiagramN(dn) = d {
if dn.cospans.is_empty() {
// This is an identity diagram - descend to source
d = &dn.source;
} else {
// Non-trivial content at this level
// Check if source matches any signature element
return signature.iter().any(|sig_elem| dn.source.as_ref() == sig_elem);
}
}
// Dimension 0: check generator directly
signature.iter().any(|s| s == d)
}
impl Diagram {
/// Type check this diagram against a signature.
pub fn type_check(&self, signature: &Signature) -> Result<(), TypeError> {
@ -552,11 +189,6 @@ impl Diagram {
pub fn pieces(&self) -> Vec<SingularPiece> {
extract_pieces(self)
}
/// Type check a piece against signature diagrams.
pub fn type_check_piece(&self, signature: &[Diagram]) -> bool {
type_check_piece(self, signature)
}
}
#[cfg(test)]

3555
tests/integration_tests.rs
View file

File diff suppressed because it is too large Load diff

56
web/index.html
View file

@ -1,56 +0,0 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Zigzag Renderer - Half Braid Geometry</title>
<style>
* {
margin: 0;
padding: 0;
box-sizing: border-box;
}
body {
overflow: hidden;
background: #0a0a0f;
}
#root {
width: 100vw;
height: 100vh;
}
#loading {
position: fixed;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
color: #f0c040;
font-family: monospace;
font-size: 18px;
}
</style>
</head>
<body>
<div id="root">
<div id="loading">Loading Three.js...</div>
</div>
<!-- React from CDN -->
<script crossorigin src="https://unpkg.com/react@18/umd/react.production.min.js"></script>
<script crossorigin src="https://unpkg.com/react-dom@18/umd/react-dom.production.min.js"></script>
<!-- Three.js from CDN -->
<script src="https://unpkg.com/three@0.160.0/build/three.min.js"></script>
<!-- Babel for JSX transformation (development only) -->
<script src="https://unpkg.com/@babel/standalone/babel.min.js"></script>
<!-- Our renderer component -->
<script type="text/babel" src="zigzag-renderer.jsx"></script>
<!-- Mount the app -->
<script type="text/babel">
const root = ReactDOM.createRoot(document.getElementById('root'));
root.render(React.createElement(ZigzagRenderer));
</script>
</body>
</html>

689
web/zigzag-renderer.jsx
View file

@ -1,689 +0,0 @@
// Three.js renderer for zigzag-engine half_braid geometry
// Renders VISIBLE elements only from explosion poset
// Visibility: point at geom_dim d is visible iff coords[d..] are all singular
const GEOMETRY_DATA = {
"metadata": {
"source": "half_braid.json",
"dimension": 3,
"total_points": 23,
"visible_points": 7,
"total_covers": 35
},
"vertices": [
{ "id": 21, "label": "vertex_0", "point": "s0,s0,s0", "coords": [0.0, 0.0, -0.5] },
{ "id": 22, "label": "vertex_1", "point": "s1,s0,s0", "coords": [0.0, 0.0, 0.5] }
],
"wires": [
{ "id": 18, "label": "wire_0", "point": "r0,s0,s0", "coords": [0.0, 0.0, -1.0],
"endpoints": [21, 22], "endpoint_coords": [[0.0, 0.0, -0.5], [0.0, 0.0, 0.5]] },
{ "id": 19, "label": "wire_1", "point": "r1,s0,s0", "coords": [0.0, 0.0, 0.0],
"endpoints": [21, 22], "endpoint_coords": [[0.0, 0.0, -0.5], [0.0, 0.0, 0.5]] },
{ "id": 20, "label": "wire_2", "point": "r2,s0,s0", "coords": [0.0, 0.0, 1.0],
"endpoints": [21, 22], "endpoint_coords": [[0.0, 0.0, -0.5], [0.0, 0.0, 0.5]] }
],
"surfaces": [
{ "id": 16, "label": "surface_0", "point": "r0,r0,s0", "coords": [0.0, -1.0, -1.0], "boundary_wires": [18] },
{ "id": 17, "label": "surface_1", "point": "r0,r1,s0", "coords": [0.0, 0.0, -1.0], "boundary_wires": [18] }
]
};
// Coordinate mapping: coords are already [x, y, z] layout coordinates
// Scale for better visualization
const SCALE = 2.0;
function mapCoords(coords) {
return [coords[0] * SCALE, coords[1] * SCALE, coords[2] * SCALE];
}
// Wire colors by group
const WIRE_COLORS = {
input: 0x4fc3f7, // blue - r0 in third coord
crossing: 0xe040fb, // purple - s0 in third coord
output: 0x66bb6a, // green - r1 in third coord
selfloop: 0xff7043 // orange - self-loops
};
function getWireGroup(wire) {
if (wire.endpoints[0] === wire.endpoints[1]) return 'selfloop';
const point = wire.point;
const thirdCoord = point.split(',')[2];
if (thirdCoord === 'r0') return 'input';
if (thirdCoord === 's0') return 'crossing';
if (thirdCoord === 'r1') return 'output';
return 'crossing';
}
// Variational elastic curve solver
// Minimizes E = τ·Σ|Δp|² + β·Σ|Δ²p|² + κ·|p_mid - waypoint|²
function solveElasticCurve(p0, p1, waypoint, tau, beta, kappa, resolution) {
const n = resolution; // interior points
const total = n + 2; // including endpoints
// Build matrix A = τ·DᵀD + β·D²ᵀD² + κ·(waypoint spring at midpoint)
// DᵀD tridiagonal: main=2, off=-1
// D²ᵀD² pentadiagonal: [1, -4, 6, -4, 1]
// We solve for interior points only (indices 1..n)
// Matrix is n×n
const A = [];
const bx = new Array(n).fill(0);
const by = new Array(n).fill(0);
const bz = new Array(n).fill(0);
for (let i = 0; i < n; i++) {
A[i] = new Array(n).fill(0);
}
// Build DᵀD (tension term)
for (let i = 0; i < n; i++) {
A[i][i] += 2 * tau;
if (i > 0) A[i][i-1] += -tau;
if (i < n-1) A[i][i+1] += -tau;
}
// Boundary contributions to RHS for tension term
bx[0] += tau * p0[0];
by[0] += tau * p0[1];
bz[0] += tau * p0[2];
bx[n-1] += tau * p1[0];
by[n-1] += tau * p1[1];
bz[n-1] += tau * p1[2];
// Build D²ᵀD² (bending term) - pentadiagonal
// For interior point i, D²p[i] = p[i-2] - 4p[i-1] + 6p[i] - 4p[i+1] + p[i+2]
for (let i = 0; i < n; i++) {
A[i][i] += 6 * beta;
if (i > 0) A[i][i-1] += -4 * beta;
if (i > 1) A[i][i-2] += beta;
if (i < n-1) A[i][i+1] += -4 * beta;
if (i < n-2) A[i][i+2] += beta;
}
// Boundary contributions for bending term
// At i=0: needs p[-1]=p0, p[-2] (extrapolate as p0)
// At i=1: needs p[-1]=p0
// At i=n-2: needs p[n]=p1
// At i=n-1: needs p[n]=p1, p[n+1] (extrapolate as p1)
// i=0 contributions from p0 (at index -1) and extrapolated p0 (at index -2)
bx[0] += beta * (4 * p0[0] - p0[0]); // -4*p[-1] + p[-2], but these go to RHS with sign flip
by[0] += beta * (4 * p0[1] - p0[1]);
bz[0] += beta * (4 * p0[2] - p0[2]);
if (n > 1) {
bx[1] += beta * p0[0];
by[1] += beta * p0[1];
bz[1] += beta * p0[2];
}
// i=n-1 contributions from p1 (at index n) and extrapolated p1 (at index n+1)
bx[n-1] += beta * (4 * p1[0] - p1[0]);
by[n-1] += beta * (4 * p1[1] - p1[1]);
bz[n-1] += beta * (4 * p1[2] - p1[2]);
if (n > 1) {
bx[n-2] += beta * p1[0];
by[n-2] += beta * p1[1];
bz[n-2] += beta * p1[2];
}
// Waypoint spring at midpoint
const midIdx = Math.floor(n / 2);
A[midIdx][midIdx] += kappa;
bx[midIdx] += kappa * waypoint[0];
by[midIdx] += kappa * waypoint[1];
bz[midIdx] += kappa * waypoint[2];
// Solve using Gaussian elimination with partial pivoting
function solveTridiagonal(A, b) {
const n = b.length;
const x = new Array(n);
const Ac = A.map(row => [...row]);
const bc = [...b];
// Forward elimination
for (let k = 0; k < n-1; k++) {
// Find pivot
let maxIdx = k;
for (let i = k+1; i < n; i++) {
if (Math.abs(Ac[i][k]) > Math.abs(Ac[maxIdx][k])) maxIdx = i;
}
// Swap rows
[Ac[k], Ac[maxIdx]] = [Ac[maxIdx], Ac[k]];
[bc[k], bc[maxIdx]] = [bc[maxIdx], bc[k]];
if (Math.abs(Ac[k][k]) < 1e-10) continue;
for (let i = k+1; i < n; i++) {
const factor = Ac[i][k] / Ac[k][k];
for (let j = k; j < n; j++) {
Ac[i][j] -= factor * Ac[k][j];
}
bc[i] -= factor * bc[k];
}
}
// Back substitution
for (let i = n-1; i >= 0; i--) {
let sum = bc[i];
for (let j = i+1; j < n; j++) {
sum -= Ac[i][j] * x[j];
}
x[i] = Math.abs(Ac[i][i]) > 1e-10 ? sum / Ac[i][i] : 0;
}
return x;
}
const solX = solveTridiagonal(A, bx);
const solY = solveTridiagonal(A, by);
const solZ = solveTridiagonal(A, bz);
// Build full curve with endpoints
const curve = [p0];
for (let i = 0; i < n; i++) {
curve.push([solX[i], solY[i], solZ[i]]);
}
curve.push(p1);
return curve;
}
// Generate self-loop curve (parametric loop offset toward waypoint)
function generateSelfLoop(center, waypoint, resolution) {
const points = [];
const offset = [
waypoint[0] - center[0],
waypoint[1] - center[1],
waypoint[2] - center[2]
];
const offsetMag = Math.sqrt(offset[0]**2 + offset[1]**2 + offset[2]**2);
const norm = offsetMag > 0.01 ? offset.map(x => x / offsetMag) : [0, 1, 0];
// Create perpendicular vectors for the loop plane
let perp1, perp2;
if (Math.abs(norm[1]) < 0.9) {
perp1 = [norm[2], 0, -norm[0]];
} else {
perp1 = [0, norm[2], -norm[1]];
}
const mag1 = Math.sqrt(perp1[0]**2 + perp1[1]**2 + perp1[2]**2);
perp1 = perp1.map(x => x / mag1);
perp2 = [
norm[1]*perp1[2] - norm[2]*perp1[1],
norm[2]*perp1[0] - norm[0]*perp1[2],
norm[0]*perp1[1] - norm[1]*perp1[0]
];
const loopRadius = Math.min(offsetMag * 0.6, 0.8);
const loopCenter = [
center[0] + norm[0] * offsetMag * 0.4,
center[1] + norm[1] * offsetMag * 0.4,
center[2] + norm[2] * offsetMag * 0.4
];
for (let i = 0; i <= resolution; i++) {
const t = (i / resolution) * 2 * Math.PI;
const x = loopCenter[0] + loopRadius * (Math.cos(t) * perp1[0] + Math.sin(t) * perp2[0]);
const y = loopCenter[1] + loopRadius * (Math.cos(t) * perp1[1] + Math.sin(t) * perp2[1]);
const z = loopCenter[2] + loopRadius * (Math.cos(t) * perp1[2] + Math.sin(t) * perp2[2]);
points.push([x, y, z]);
}
return points;
}
function ZigzagRenderer() {
const containerRef = React.useRef(null);
const sceneRef = React.useRef(null);
const cameraRef = React.useRef(null);
const rendererRef = React.useRef(null);
const wireObjectsRef = React.useRef([]);
const waypointObjectsRef = React.useRef([]);
const surfaceObjectsRef = React.useRef([]);
const labelObjectsRef = React.useRef([]);
const [tension, setTension] = React.useState(1.0);
const [bending, setBending] = React.useState(0.5);
const [kappa, setKappa] = React.useState(2.0);
const [resolution, setResolution] = React.useState(20);
const [showWaypoints, setShowWaypoints] = React.useState(true);
const [showSurfaces, setShowSurfaces] = React.useState(true);
const [showLabels, setShowLabels] = React.useState(true);
// Orbit controls state
const orbitRef = React.useRef({
theta: Math.PI / 4,
phi: Math.PI / 4,
radius: 12,
target: [2, 2, 2],
isDragging: false,
lastX: 0,
lastY: 0
});
// Initialize Three.js scene
React.useEffect(() => {
if (!containerRef.current || !window.THREE) return;
const THREE = window.THREE;
const width = containerRef.current.clientWidth;
const height = containerRef.current.clientHeight;
// Scene
const scene = new THREE.Scene();
scene.background = new THREE.Color(0x0a0a0f);
sceneRef.current = scene;
// Camera
const camera = new THREE.PerspectiveCamera(60, width / height, 0.1, 100);
cameraRef.current = camera;
// Renderer
const renderer = new THREE.WebGLRenderer({ antialias: true });
renderer.setSize(width, height);
renderer.setPixelRatio(window.devicePixelRatio);
containerRef.current.appendChild(renderer.domElement);
rendererRef.current = renderer;
// Lights
const ambient = new THREE.AmbientLight(0xffffff, 0.4);
scene.add(ambient);
const directional = new THREE.DirectionalLight(0xffffff, 0.8);
directional.position.set(5, 10, 5);
scene.add(directional);
// Add vertices as glowing spheres
const vertexGeom = new THREE.SphereGeometry(0.15, 32, 32);
const vertexMat = new THREE.MeshStandardMaterial({
color: 0xf0c040,
emissive: 0xf0c040,
emissiveIntensity: 0.5
});
GEOMETRY_DATA.vertices.forEach(v => {
const pos = mapCoords(v.coords);
const mesh = new THREE.Mesh(vertexGeom, vertexMat);
mesh.position.set(pos[0], pos[1], pos[2]);
scene.add(mesh);
});
// Grid helper
const gridHelper = new THREE.GridHelper(10, 10, 0x333344, 0x222233);
gridHelper.position.y = -0.5;
scene.add(gridHelper);
// Axes helper
const axesHelper = new THREE.AxesHelper(3);
scene.add(axesHelper);
// Mouse controls
const canvas = renderer.domElement;
canvas.addEventListener('mousedown', (e) => {
orbitRef.current.isDragging = true;
orbitRef.current.lastX = e.clientX;
orbitRef.current.lastY = e.clientY;
});
canvas.addEventListener('mousemove', (e) => {
if (!orbitRef.current.isDragging) return;
const dx = e.clientX - orbitRef.current.lastX;
const dy = e.clientY - orbitRef.current.lastY;
orbitRef.current.theta -= dx * 0.01;
orbitRef.current.phi = Math.max(0.1, Math.min(Math.PI - 0.1, orbitRef.current.phi + dy * 0.01));
orbitRef.current.lastX = e.clientX;
orbitRef.current.lastY = e.clientY;
});
canvas.addEventListener('mouseup', () => {
orbitRef.current.isDragging = false;
});
canvas.addEventListener('mouseleave', () => {
orbitRef.current.isDragging = false;
});
canvas.addEventListener('wheel', (e) => {
e.preventDefault();
orbitRef.current.radius = Math.max(3, Math.min(30, orbitRef.current.radius + e.deltaY * 0.01));
});
// Animation loop
function animate() {
requestAnimationFrame(animate);
const orbit = orbitRef.current;
const x = orbit.target[0] + orbit.radius * Math.sin(orbit.phi) * Math.cos(orbit.theta);
const y = orbit.target[1] + orbit.radius * Math.cos(orbit.phi);
const z = orbit.target[2] + orbit.radius * Math.sin(orbit.phi) * Math.sin(orbit.theta);
camera.position.set(x, y, z);
camera.lookAt(orbit.target[0], orbit.target[1], orbit.target[2]);
renderer.render(scene, camera);
}
animate();
// Resize handler
const handleResize = () => {
const w = containerRef.current.clientWidth;
const h = containerRef.current.clientHeight;
camera.aspect = w / h;
camera.updateProjectionMatrix();
renderer.setSize(w, h);
};
window.addEventListener('resize', handleResize);
return () => {
window.removeEventListener('resize', handleResize);
renderer.dispose();
if (containerRef.current && renderer.domElement) {
containerRef.current.removeChild(renderer.domElement);
}
};
}, []);
// Update wires when parameters change
React.useEffect(() => {
if (!sceneRef.current || !window.THREE) return;
const THREE = window.THREE;
const scene = sceneRef.current;
// Remove old wire objects
wireObjectsRef.current.forEach(obj => scene.remove(obj));
wireObjectsRef.current = [];
// Create wire lookup for surfaces
const wireById = {};
// Add wires
GEOMETRY_DATA.wires.forEach(wire => {
const p0 = mapCoords(wire.endpoint_coords[0]);
const p1 = mapCoords(wire.endpoint_coords[1]);
const waypoint = mapCoords(wire.coords);
const group = getWireGroup(wire);
const color = WIRE_COLORS[group];
let curvePoints;
if (wire.endpoints[0] === wire.endpoints[1]) {
// Self-loop
curvePoints = generateSelfLoop(p0, waypoint, resolution);
} else {
// Elastic curve
curvePoints = solveElasticCurve(p0, p1, waypoint, tension, bending, kappa, resolution);
}
wireById[wire.id] = curvePoints;
// Create tube geometry
const points = curvePoints.map(p => new THREE.Vector3(p[0], p[1], p[2]));
const curve = new THREE.CatmullRomCurve3(points);
const tubeGeom = new THREE.TubeGeometry(curve, resolution * 2, 0.04, 8, false);
const tubeMat = new THREE.MeshStandardMaterial({
color: color,
emissive: color,
emissiveIntensity: 0.3
});
const tube = new THREE.Mesh(tubeGeom, tubeMat);
scene.add(tube);
wireObjectsRef.current.push(tube);
});
// Store wire paths for surface rendering
sceneRef.current.userData.wireById = wireById;
}, [tension, bending, kappa, resolution]);
// Update waypoint visibility
React.useEffect(() => {
if (!sceneRef.current || !window.THREE) return;
const THREE = window.THREE;
const scene = sceneRef.current;
// Remove old waypoint objects
waypointObjectsRef.current.forEach(obj => scene.remove(obj));
waypointObjectsRef.current = [];
if (showWaypoints) {
const waypointGeom = new THREE.SphereGeometry(0.08, 16, 16);
const waypointMat = new THREE.MeshStandardMaterial({
color: 0xf0c040,
emissive: 0xf0c040,
emissiveIntensity: 0.6,
transparent: true,
opacity: 0.8
});
GEOMETRY_DATA.wires.forEach(wire => {
const pos = mapCoords(wire.coords);
const mesh = new THREE.Mesh(waypointGeom, waypointMat);
mesh.position.set(pos[0], pos[1], pos[2]);
scene.add(mesh);
waypointObjectsRef.current.push(mesh);
});
}
}, [showWaypoints]);
// Update surface visibility
React.useEffect(() => {
if (!sceneRef.current || !window.THREE) return;
const THREE = window.THREE;
const scene = sceneRef.current;
// Remove old surface objects
surfaceObjectsRef.current.forEach(obj => scene.remove(obj));
surfaceObjectsRef.current = [];
if (showSurfaces) {
const surfaceMat = new THREE.MeshStandardMaterial({
color: 0xff6b6b,
emissive: 0xff6b6b,
emissiveIntensity: 0.4,
transparent: true,
opacity: 0.6
});
const lineMat = new THREE.LineBasicMaterial({
color: 0xff6b6b,
transparent: true,
opacity: 0.4
});
GEOMETRY_DATA.surfaces.forEach(surface => {
const pos = mapCoords(surface.coords);
// Surface center point
const sphereGeom = new THREE.SphereGeometry(0.06, 12, 12);
const sphere = new THREE.Mesh(sphereGeom, surfaceMat);
sphere.position.set(pos[0], pos[1], pos[2]);
scene.add(sphere);
surfaceObjectsRef.current.push(sphere);
// Lines to boundary wire midpoints
const wireById = scene.userData.wireById || {};
surface.boundary_wires.forEach(wireId => {
const wire = GEOMETRY_DATA.wires.find(w => w.id === wireId);
if (wire) {
const wirePos = mapCoords(wire.coords);
const geometry = new THREE.BufferGeometry().setFromPoints([
new THREE.Vector3(pos[0], pos[1], pos[2]),
new THREE.Vector3(wirePos[0], wirePos[1], wirePos[2])
]);
const line = new THREE.Line(geometry, lineMat);
scene.add(line);
surfaceObjectsRef.current.push(line);
}
});
});
}
}, [showSurfaces, tension, bending, kappa, resolution]);
// Update label visibility
React.useEffect(() => {
if (!sceneRef.current || !window.THREE) return;
const THREE = window.THREE;
const scene = sceneRef.current;
// Remove old label objects
labelObjectsRef.current.forEach(obj => scene.remove(obj));
labelObjectsRef.current = [];
if (showLabels) {
// Create canvas-based sprite labels
GEOMETRY_DATA.vertices.forEach(v => {
const canvas = document.createElement('canvas');
const ctx = canvas.getContext('2d');
canvas.width = 128;
canvas.height = 64;
ctx.fillStyle = 'rgba(10, 10, 15, 0.8)';
ctx.fillRect(0, 0, 128, 64);
ctx.strokeStyle = '#f0c040';
ctx.lineWidth = 2;
ctx.strokeRect(2, 2, 124, 60);
ctx.font = 'bold 20px monospace';
ctx.fillStyle = '#f0c040';
ctx.textAlign = 'center';
ctx.textBaseline = 'middle';
ctx.fillText(v.label, 64, 32);
const texture = new THREE.CanvasTexture(canvas);
const spriteMat = new THREE.SpriteMaterial({ map: texture, transparent: true });
const sprite = new THREE.Sprite(spriteMat);
const pos = mapCoords(v.coords);
sprite.position.set(pos[0], pos[1] + 0.4, pos[2]);
sprite.scale.set(1, 0.5, 1);
scene.add(sprite);
labelObjectsRef.current.push(sprite);
});
}
}, [showLabels]);
const panelStyle = {
position: 'absolute',
top: '20px',
left: '20px',
background: 'rgba(10, 10, 20, 0.85)',
backdropFilter: 'blur(10px)',
padding: '20px',
borderRadius: '12px',
color: '#e0e0e0',
fontFamily: 'monospace',
fontSize: '14px',
border: '1px solid rgba(240, 192, 64, 0.3)',
minWidth: '220px'
};
const sliderStyle = {
width: '100%',
marginTop: '4px',
accentColor: '#f0c040'
};
const checkboxStyle = {
accentColor: '#f0c040',
marginRight: '8px'
};
return React.createElement('div', { style: { width: '100vw', height: '100vh', position: 'relative' } },
React.createElement('div', { ref: containerRef, style: { width: '100%', height: '100%' } }),
React.createElement('div', { style: panelStyle },
React.createElement('h3', { style: { margin: '0 0 15px 0', color: '#f0c040' } }, 'Zigzag Renderer'),
React.createElement('div', { style: { marginBottom: '12px' } },
React.createElement('label', null, `Tension τ: ${tension.toFixed(2)}`),
React.createElement('input', {
type: 'range', min: '0.1', max: '5', step: '0.1', value: tension,
onChange: (e) => setTension(parseFloat(e.target.value)),
style: sliderStyle
})
),
React.createElement('div', { style: { marginBottom: '12px' } },
React.createElement('label', null, `Bending β: ${bending.toFixed(2)}`),
React.createElement('input', {
type: 'range', min: '0', max: '2', step: '0.05', value: bending,
onChange: (e) => setBending(parseFloat(e.target.value)),
style: sliderStyle
})
),
React.createElement('div', { style: { marginBottom: '12px' } },
React.createElement('label', null, `Waypoint κ: ${kappa.toFixed(2)}`),
React.createElement('input', {
type: 'range', min: '0', max: '10', step: '0.1', value: kappa,
onChange: (e) => setKappa(parseFloat(e.target.value)),
style: sliderStyle
})
),
React.createElement('div', { style: { marginBottom: '12px' } },
React.createElement('label', null, `Resolution: ${resolution}`),
React.createElement('input', {
type: 'range', min: '5', max: '50', step: '1', value: resolution,
onChange: (e) => setResolution(parseInt(e.target.value)),
style: sliderStyle
})
),
React.createElement('hr', { style: { border: 'none', borderTop: '1px solid rgba(240, 192, 64, 0.3)', margin: '15px 0' } }),
React.createElement('div', { style: { marginBottom: '8px' } },
React.createElement('label', null,
React.createElement('input', {
type: 'checkbox', checked: showWaypoints,
onChange: (e) => setShowWaypoints(e.target.checked),
style: checkboxStyle
}),
'Waypoints'
)
),
React.createElement('div', { style: { marginBottom: '8px' } },
React.createElement('label', null,
React.createElement('input', {
type: 'checkbox', checked: showSurfaces,
onChange: (e) => setShowSurfaces(e.target.checked),
style: checkboxStyle
}),
'Surfaces'
)
),
React.createElement('div', { style: { marginBottom: '8px' } },
React.createElement('label', null,
React.createElement('input', {
type: 'checkbox', checked: showLabels,
onChange: (e) => setShowLabels(e.target.checked),
style: checkboxStyle
}),
'Labels'
)
),
React.createElement('hr', { style: { border: 'none', borderTop: '1px solid rgba(240, 192, 64, 0.3)', margin: '15px 0' } }),
React.createElement('div', { style: { fontSize: '11px', color: '#888' } },
React.createElement('div', null, '🔵 Input (r0)'),
React.createElement('div', null, '🟣 Crossing (s0)'),
React.createElement('div', null, '🟢 Output (r1)'),
React.createElement('div', null, '🟠 Self-loop')
)
)
);
}
// Export for use
window.ZigzagRenderer = ZigzagRenderer;