numerology is phase-blind: it does NOT recognise the angle-change of dividing by 0
Theorem.numerology is phase-blind: it does NOT recognise the angle-change of dividing by 0.
Proof.does numerology recognise the angle-change of dividing by 0? (user, 2026-07-25: "does numerology recognise the angle changes dividing 0?"). Answer: NO. The digital root is a forgetful reduction ℤ → ℤ/9ℤ — non-invertible (dr(5)=dr(14)=dr(23)), so it discards the winding/angle and has no pole, no 1/0, no phase. The angle-change of dividing by 0 is the Möbius inversion z → 1/z sending 0 → ∞ (the point at infinity), an involution — invertible and angle-carrying — belonging to the C₆ inversion group (pole/60°/prime/cipher), computed by the project as PHASE. The 9-gon steps 360/9 = 40°, C₆ steps 360/6 = 60°. Numerology sees only magnitude. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#numerologyIsPhaseBlindToAngleThroughZero
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
"numerology is phase-blind: it does NOT recognise the angle-change of dividing by 0" 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 numerologyIsPhaseBlindToAngleThroughZero.
- 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 (numerologyIsPhaseBlindToAngleThroughZero @ src/4/6) 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 numerologyIsPhaseBlindToAngleThroughZero (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.