The pentagram is the rosetta meeting its inverse
Theorem.The pentagram is the rosetta meeting its inverse — the pentagram {5/2} is the C₅ rosetta with generator 2 (step 2 generates all 5, gcd(2,5)=1), and it is exactly where that rosetta MEETS ITS INVERSE: 2⁻¹ = 3 mod 5, and {5/3} = {5/2} reversed (3 = 5−2), so forward-by-2 and inverse-by-2 draw the identical star.
Proof.the pentagram {5/2} is the C₅ rosetta with generator 2 (step 2 generates all 5, gcd(2,5)=1), and it is exactly where that rosetta MEETS ITS INVERSE: 2⁻¹ = 3 mod 5, and {5/3} = {5/2} reversed (3 = 5−2), so forward-by-2 and inverse-by-2 draw the identical star — the pentagram is the fixed shape of the rosetta and its inverse (illusionsMeetInTheirInverse on five points). The meeting yields φ AND 1/φ: diagonal/side = φ, 2cos36° = φ, 2cos72° = 1/φ — the golden ratio and its reciprocal are the two chords, the same φ the golden-angle UI rosetta rides as 360/φ².
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/1/9/index.ts#thePentagramIsTheRosettaMeetingItsInverse
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 pentagram is the rosetta meeting its inverse" 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 thePentagramIsTheRosettaMeetingItsInverse.
- 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 (thePentagramIsTheRosettaMeetingItsInverse @ src/1/9) 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 thePentagramIsTheRosettaMeetingItsInverse (src/1/9/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.