the rosetta 42 is the CRT product — ℤ₄₂ ≅ ℤ₆ × ℤ₇
Theorem.the rosetta 42 is the CRT product — ℤ₄₂ ≅ ℤ₆ × ℤ₇ — ROSETTA_AREAS = ROSETTA_SIX × ROSETTA_SEVEN; gcd(6,7)=1 so CRT gives ℤ/42 ≅ ℤ/6 × ℤ/7 by exhaustive residue enumeration (all 42 (ray,unit) pairs distinct);.
Proof.ROSETTA_AREAS = ROSETTA_SIX × ROSETTA_SEVEN; gcd(6,7)=1 so CRT gives ℤ/42 ≅ ℤ/6 × ℤ/7 by exhaustive residue enumeration (all 42 (ray,unit) pairs distinct); inverse 7×6 transpose same 42. Finite-complete · pair crt/rosetta · claySolved via theorem.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/digit/index.ts#theRosettaConstantsAreTheoremsSevenBySixIsFortyTwoByCrtTenIsTheDecad
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 rosetta 42 is the CRT product — ℤ₄₂ ≅ ℤ₆ × ℤ₇" 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 theRosettaConstantsAreTheoremsSevenBySixIsFortyTwoByCrtTenIsTheDecad.
- 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 (theRosettaConstantsAreTheoremsSevenBySixIsFortyTwoByCrtTenIsTheDecad @ src/water/digit) 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 theRosettaConstantsAreTheoremsSevenBySixIsFortyTwoByCrtTenIsTheDecad (src/water/digit/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.