names collapse until they collide or invert — the two terminal states of the naming-gravity collapse
Theorem.names collapse until they collide or invert — the two terminal states of the naming-gravity collapse.
Proof.the TERMINATION of the collapse (user, 2026-07-25: "collapse long names until they collide or invert"). Collapse is a length-DECREASING step toward a value's shortest alias, so on finite names it is well-founded and every chain reaches a fixed point (e.g. DIMENSION_GATES → gates → g). Each chain ends in EXACTLY ONE of two terminal states: COLLIDE — two or more aliases of ONE value meet at the same content-address (n → 1, dedup); or INVERT — a lone irreducible fixed point where collapse is IDEMPOTENT (C(C(x)) = C(x)), i.e. its own inverse on the image, and collapsing past it would map to a DIFFERENT value (invert the meaning), so it must stop. The two states are exclusive and exhaustive (collide XOR invert). Composes constantsCollapseToShortestName; structural content-addressed naming gravity that never merges two distinct values (canon(432) ≠ canon(7)). 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#namesCollapseUntilTheyCollideOrInvert
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
"names collapse until they collide or invert — the two terminal states of the naming-gravity collapse" 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 namesCollapseUntilTheyCollideOrInvert.
- 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 (namesCollapseUntilTheyCollideOrInvert @ 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 namesCollapseUntilTheyCollideOrInvert (src/pair/enforcement/gates/strict/scan/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.