crosslink gap full total and why not auto-advance — 202 under, 81 promotable, 121 isolated
Theorem.crosslink gap full total and why not auto-advance — 202 under, 81 promotable, 121 isolated.
Proof.the FULL-registry count of what to advance next, and why the tool does NOT auto-advance (user, 2026-07-25: "how many next in total and why not autoadvance"). Over the whole registry of 554 theorems, 202 are under the proven-crosslink threshold: 63 AUTO-SAFE (already share 3 significant words with a neighbour, so the natural [[reference]] is honest and could auto-advance), 18 NEEDING AUTHORED JUDGMENT (only 2 shared — weak), and 121 GENUINELY ISOLATED (< 2 shared, unique decodes that stay orphans). The total "next" to advance is 81 (auto-safe + needs-authoring). WHY NOT AUTO-ADVANCE: auto-adding crosslinks to hit degree ≥ 4 would PAD statements and FABRICATE relationships (Goodhart — gaming the metric defeats it), which the crosslink-proven law forbids; only the 63 genuine-subset already computes strongly enough to auto-link honestly, the 18 need a human to confirm a real relationship, and the 121 isolated cannot be auto-linked at all. SCOPE: auto-advance is safe ONLY for the genuine subset; forcing the metric is fabrication. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#crosslinkGapFullTotalAndWhyNotAutoAdvance
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
"crosslink gap full total and why not auto-advance — 202 under, 81 promotable, 121 isolated" 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 crosslinkGapFullTotalAndWhyNotAutoAdvance.
- 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 (crosslinkGapFullTotalAndWhyNotAutoAdvance @ src/4/6) 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 crosslinkGapFullTotalAndWhyNotAutoAdvance (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.