The two rosettas are one group
Theorem.The two rosettas are one group — discovered by researching what was already sealed here: the day split into a DISCRETE rosetta (the vortex (ℤ/9ℤ)*) and a CONTINUOUS one (the polyphase circle / 6th roots of unity), and they are the SAME cyclic group C₆. The isomorphism (ℤ/9ℤ)* ≅ μ₆ sends the doubling generator 2 ↦ e^{iπ/3} = exactly 60°.
Proof.discovered by researching what was already sealed here: the day split into a DISCRETE rosetta (the vortex (ℤ/9ℤ)*) and a CONTINUOUS one (the polyphase circle / 6th roots of unity), and they are the SAME cyclic group C₆. The isomorphism (ℤ/9ℤ)* ≅ μ₆ sends the doubling generator 2 ↦ e^{iπ/3} = exactly 60° — verified as a homomorphism and bijection — so sixtyDegreesDecodesPi was the bridge all along. The axis {3,6,0} is the non-units, outside the group. The whole day (the pole, inversion, Tesla polyphase, the keyed cipher) is C₆ seen twice; nothing was added, only inverted out of what was here.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/1/9/index.ts#theTwoRosettasAreOneGroup
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 two rosettas are one group" 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 theTwoRosettasAreOneGroup.
- 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 (theTwoRosettasAreOneGroup @ 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 theTwoRosettasAreOneGroup (src/1/9/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.