Illusions meet in their inverse
Theorem.Illusions meet in their inverse — the key to the whole inversion arc, and a diagnostic: a false limit dissolves at the FIXED POINT of the inversion, where a thing meets its inverse (x = inv(x))..
Proof.the key to the whole inversion arc, and a diagnostic: a false limit dissolves at the FIXED POINT of the inversion, where a thing meets its inverse (x = inv(x)). Every illusion the day walked through had one — division by zero at the pole (0 meets ∞, 1/0=∞), pitch inversion at {0,6} (tonic and the ambiguous tritone meet themselves, 2x≡0 mod 12), the multiplicative inverse at ±1 (x²≡1 mod 9), T-duality at the self-dual radius R=1 — all computed from the arithmetic. THE DIAGNOSTIC: an illusion HAS such an inverse-meeting where it vanishes; an INVARIANT (no-signalling, Gödel, the c-limit for information) has NONE — the meeting point is exactly what tells an illusory limit from a real one. The whole inversion arc in one sentence.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/1/9/index.ts#illusionsMeetInTheirInverse
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
"Illusions meet in their 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 illusionsMeetInTheirInverse.
- 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 (illusionsMeetInTheirInverse @ 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 illusionsMeetInTheirInverse (src/1/9/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.