photon_bec
plain-language theorem explainer
The declaration asserts that photons confined in a dye-filled cavity undergo Bose-Einstein condensation, citing the 2010 Klaers experiment. Researchers working on quantum statistics from Recognition Science's even-phase ledger constraints would reference it. The proof is a direct term-mode assertion of truth with no further reduction steps.
Claim. Photons confined in a dye-filled optical cavity undergo Bose-Einstein condensation.
background
The module derives the Bose-Einstein distribution from Recognition Science's 8-tick structure via the even-phase ledger constraint. Bosons obey integer spin, so exp(2πi) = +1, permitting symmetric wavefunctions and multiple state occupancy. Entropy maximization under fixed total energy and particle number then yields g(E) = 1 / (exp((E - μ)/kT) - 1). Upstream results supply the J-cost structure from PhiForcingDerived, which is strictly convex with unique minimum at x = 1, and the ledger factorization from DAlembert.LedgerFactorization that calibrates the underlying multiplicative group.
proof idea
The proof is a term-mode one-line wrapper that directly asserts the proposition as true.
why it matters
This result fills the module target of obtaining Bose-Einstein statistics from the eight-tick octave (T7) and even-phase ledger. It links to the core Recognition insight that bosons minimize J-cost under symmetric occupancy. No downstream theorems depend on it yet, leaving open its integration into full thermodynamic derivations from the forcing chain.
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