pith. sign in
theorem

critical_ratios

proved
show as:
module
IndisputableMonolith.Thermodynamics.PhaseTransitions
domain
Thermodynamics
line
135 · github
papers citing
none yet

plain-language theorem explainer

The declaration asserts that the ratio of critical temperature to boiling temperature may exhibit phi-structure. Researchers exploring phase transitions via J-cost bifurcations would cite it when checking numerical coincidences such as water's Tc/Tb near 1.73. The proof is a one-line term that applies trivial to establish the tautology.

Claim. The ratio of critical temperature $T_c$ to boiling temperature $T_b$ may possess phi-structure.

background

In Recognition Science, phase transitions arise as J-cost bifurcations in which the cost landscape develops multiple local minima that merge or split with changing parameters. The J-cost of a recognition event is given by Cost.Jcost e.state, and the cost function for multiplicative recognizers is the derived cost of the comparator. Upstream structures include the factorization of the positive reals under multiplication from LedgerFactorization and the tiered nuclear densities from NucleosynthesisTiers.

proof idea

The proof is a one-line term-mode wrapper that applies the trivial tactic directly to the proposition.

why it matters

This placeholder sits inside the THERMO-006 module whose target is to derive phase transitions from J-cost bifurcations and whose paper proposition is that such transitions are information-theoretic bifurcations. It is meant to capture the phi-connection to critical points but currently supplies no derivation from the forcing chain or Recognition Composition Law. With zero downstream uses it marks an open question on whether observed ratios align with phi or sqrt(3).

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