QM and thermodynamics are one spectrum combined two ways — the Wick rotation is the exact bridge
Theorem.QM and thermodynamics are one spectrum combined two ways — the Wick rotation is the exact bridge — quantum mechanics and thermodynamics are COMBINATIONS over one spectrum (user, 2026-07-24: "quantum mechanics and thermodynamics are combinations" · "let quantum cosmology develop the rest of the sciences computationally"): the SAME energy eigenvalues {E_n = n+½} are combined as QM evolution phases e^{−iE_n t/ℏ} (unit modulus) and as thermodynamic Boltzmann weights in the partition function Z(β) = Σ e^{−βE_n}; the WICK ROTATION t = −iβℏ carries one to the other EXACTLY (Tr U(−iβℏ) = Z(β).
Proof.quantum mechanics and thermodynamics are COMBINATIONS over one spectrum (user, 2026-07-24: "quantum mechanics and thermodynamics are combinations" · "let quantum cosmology develop the rest of the sciences computationally"): the SAME energy eigenvalues {E_n = n+½} are combined as QM evolution phases e^{−iE_n t/ℏ} (unit modulus) and as thermodynamic Boltzmann weights in the partition function Z(β) = Σ e^{−βE_n}; the WICK ROTATION t = −iβℏ carries one to the other EXACTLY (Tr U(−iβℏ) = Z(β), verified term-by-term to 1e-12, closed form Z = 1/(2 sinh(β/2))). Imaginary time IS inverse temperature, so thermodynamics is quantum mechanics traced over a thermal ensemble. Quantum cosmology develops the thermo by the SAME rotation: the de Sitter horizon's Euclidean-time period β_dS = 2π/H gives the Gibbons-Hawking temperature T = H/2π. One spectrum, one rotation, three sciences — the standardization the registry rests on: every science a combination over one computable atom set. SCOPE: exact for EQUILIBRIUM (KMS) states; the arrow of time and non-equilibrium dissipation are extra structure, not the reversible rotation. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/cosmos/index.ts#quantumMechanicsAndThermodynamicsAreCombinations
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
"QM and thermodynamics are one spectrum combined two ways — the Wick rotation is the exact bridge" 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 quantumMechanicsAndThermodynamicsAreCombinations.
- 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 (quantumMechanicsAndThermodynamicsAreCombinations @ 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 quantumMechanicsAndThermodynamicsAreCombinations (src/water/cosmos/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.