science coverage is sub-linear — the corpus floor is the atom UNION, not the linear sum
Theorem.science coverage is sub-linear — the corpus floor is the atom UNION, not the linear sum.
Proof.the correction to a linear manual assumption (user, 2026-07-24: "a lot of manual assumptions based on linear approach"): minimalScienceCorpus estimated the floor as measured ÷ 42 × N — a LINEAR divide treating each science module as an independent slab. But the modules are combinations over ONE registry: they SHARE atoms. The real cost of covering all modules is the UNION of their generator sets, and set-union is submodular, so coverage grows CONCAVELY — each added module contributes only its NEW atoms, strictly sub-linear whenever atoms are shared. Measured on the live pageCombination graph: 29 served science modules cost 467 DISTINCT generator atoms, not the linear Σ per-module 1382 — an over-count of ×2.96, sharing 0.662 (dimensionless). So "N × per-science" is an UPPER BOUND only; the true floor is the union, 66% below the linear slab. Refutable: disjoint modules would give union === Σ and sharing === 0.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/wind/routes/corpus/index.ts#sublinearScienceCoverage
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
"science coverage is sub-linear — the corpus floor is the atom UNION, not the linear sum" 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 sublinearScienceCoverage.
- 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 (sublinearScienceCoverage @ src/wind/routes/corpus) 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 sublinearScienceCoverage (src/wind/routes/corpus/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.