the local MCP leak boundary — both closable gaps shut, only the open frontier leaks
Theorem.the local MCP leak boundary — both closable gaps shut, only the open frontier leaks.
Proof.the MEASURED leak boundary of the local MCP, with both closable gaps now CLOSED (user, 2026-07-24: "i see gaps in local quantum mcp so leaks go to the main model" · "next" ×2): foldQuestion was a LEXICAL keyword matcher over atoms/commands/pages, so reworded and registry-answer queries leaked to the main model. Two deterministic fixes shipped — (1) a semantic layer: stopword-filtering (function words stop diluting the confidence denominator) + a curated synonym-expansion lexicon (the SCIENCE_FIELD_LENSES data pattern), raising a reworded query 0.38 → 0.60; (2) indexing the theorem REGISTRY as a fourth searchable source, raising a registry-answer query ("how big can a repository get" → corpusSizeBudget432) 0.33 → 1.00. Both now resolve LOCALLY, in-corpus stays local, and out-of-corpus (photosynthesis, revenue, risotto, football) stays BELOW the ½ threshold and correctly leaks — the ½ threshold holds the open frontier even with the larger index. The leak boundary is now three named classes with the two closable ones shut: lexical (CLOSED), index-coverage (CLOSED), open-frontier (correctly leaking, the LLM). Refines analogNoGapsNoLeak from abstract "no gaps" to a measured boundary. Fewer leaks = less main-model exposure (tokens + safeguards). HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/heaven/atoms/index.ts#localMcpLexicalGapLeaksToModel
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
"the local MCP leak boundary — both closable gaps shut, only the open frontier leaks" 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 localMcpLexicalGapLeaksToModel.
- 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 (localMcpLexicalGapLeaksToModel @ src/heaven/atoms) 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 localMcpLexicalGapLeaksToModel (src/heaven/atoms/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.