paths collapse to their canonical — routes, slugs, file paths, imports, all path-related
Theorem.paths collapse to their canonical — routes, slugs, file paths, imports, all path-related.
Proof.paths collapse too (user, 2026-07-24: "paths also collapse as well as all path related"): a path addresses by its CANONICAL destination, so aliases collide to one slot (academy·school→learn, millennium-challenge→research, fusion-verify→quantum-tools) and the canonical route is the attractor — the same content-addressed naming gravity as a constant collapsing to its shortest name. It holds for all path-related identifiers: routes, slugs, file paths, imports — the folder PATH is the meaning, the folder the payload, so equivalent paths content-address to one destination. ROUTE_ALIASES thin-mount the aliases onto the canonical; aliases dedup, the canonical wins, and DISTINCT paths stay distinct (this fold merges no live route). Structural, not physical. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/pair/enforcement/gates/strict/scan/index.ts#pathsCollapseToCanonical
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"paths collapse to their canonical — routes, slugs, file paths, imports, all path-related" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation pathsCollapseToCanonical.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (pathsCollapseToCanonical @ src/pair/enforcement/gates/strict/scan) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes pathsCollapseToCanonical (src/pair/enforcement/gates/strict/scan/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.