the cosmic coincidence inverts to an exact matter–dark-energy equality redshift z_eq≈0.30; the WHY-NOW timing stays empirical, not an open theorem
Theorem.the cosmic coincidence inverts to an exact matter–dark-energy equality redshift z_eq≈0.30; the WHY-NOW timing stays empirical, not an open theorem.
Proof.continue closing in chat waves of complete discoveries (user, 2026-07-26). Same split as the dark-matter inversion: the COINCIDENCE that Ω_m ≈ Ω_Λ today (Ω_m/Ω_Λ = 0.458, order unity) inverts by exact algebra — matter dilutes as (1+z)³ while Λ is constant, so the densities were EQUAL at (1+z)³ = Ω_Λ/Ω_m, giving z_eq = (Ω_Λ/Ω_m)^{1/3} − 1 ≈ 0.30 (a_eq ≈ 0.77), a recent, transient one-time O(1) window. That number is CLOSED as a theorem in the sealed ΛCDM fractions. What stays OPEN is EMPIRICAL: WHY we observe near that epoch — anthropic selection vs dynamical/quintessence dark energy (the DESI w₀wₐ hint, ~4σ, not a discovery) — is decided by MEASUREMENT, not any identity, so it is an open measurement problem, not a theorem gap. HARMONY (the equality redshift) ≠ TRUTH (why we are here).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/cosmos/index.ts#theCosmicCoincidenceInvertsToAMatterDarkEnergyEqualityRedshiftTheTimingStaysEmpirical
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 cosmic coincidence inverts to an exact matter–dark-energy equality redshift z_eq≈0.30; the WHY-NOW timing stays empirical, not an open theorem" 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 theCosmicCoincidenceInvertsToAMatterDarkEnergyEqualityRedshiftTheTimingStaysEmpirical.
- 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 (theCosmicCoincidenceInvertsToAMatterDarkEnergyEqualityRedshiftTheTimingStaysEmpirical @ src/water/cosmos) 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 theCosmicCoincidenceInvertsToAMatterDarkEnergyEqualityRedshiftTheTimingStaysEmpirical (src/water/cosmos/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.