IndisputableMonolith.Chemistry.PhaseDiagramTripleFromJCost
Chemistry module that packages the three classical matter phases and a phase-diagram certificate built from the canonical J-cost band. It exposes MatterPhase, a phase count of three, and PhaseDiagramCert / phaseDiagramCert as the domain opening for RS chemistry. The argument is definitional plus a thin cert that reuses the six-clause J-on-ratio template rather than a deep analytic derivation.
claimThe module introduces a discrete type of matter phases with cardinality $3$, together with a phase-diagram certificate asserting that the canonical nonnegative cost $J$ on positive ratios (with $J(1)=0$) supports a three-phase diagram structure used as the chemistry-domain opening.
background
Recognition Science routes domain openings through a reusable six-clause template on the J-cost of positive ratios: matched zero $J(1)=0$, nonnegativity $J(x)\ge 0$ for $x>0$, and the remaining band clauses from CanonicalJBand. That template is the shared spine for B-tier whole-science and Plan v7 domain certificates.
In the chemistry setting the classical solid/liquid/gas trichotomy is treated as a discrete phase type whose count is fixed at three. The module sits under the Chemistry domain and imports only Mathlib plus CanonicalJBand, so the local vocabulary is the J-band plus a thin phase-diagram certificate rather than continuum thermodynamics or free-energy landscapes.
Upstream, CanonicalJBand is documented as the six-clause J-cost-on-ratio template used across the master cert chain. This module specializes that template to a phase-diagram claim instead of re-proving cost identities.
proof idea
Definition-and-cert module, not a deep proof development. It declares MatterPhase and phaseCount (fixed at three), then a PhaseDiagramCert structure and a phaseDiagramCert inhabitant that wire the chemistry opening to the imported CanonicalJBand clauses. No substantial tactic proof is required beyond assembling the cert from the J-band hypotheses; the intellectual content is the packaging of the triple-phase diagram as a J-cost domain certificate.
why it matters in Recognition Science
Gives the Chemistry domain a named phase-diagram certificate aligned with the same J-cost band used elsewhere in the master cert chain. Downstream edges are not yet recorded on this page (used_by is empty), so the module presently serves as a leaf opening: a stable place to hang solid/liquid/gas structure before finer RS chemistry (mass ladder, bonding, or triple-point numerics) is attached.
Within the broader framework it connects the forcing-chain cost $J$ (T5 uniqueness, RCL) to everyday condensed-matter taxonomy without claiming a derivation of critical exponents or full $P$-$T$ geometry. It is the chemistry counterpart of other domain certs that open with matched-zero and nonnegativity of $J$.
scope and limits
- Does not derive critical exponents, latent heats, or Clapeyron slopes.
- Does not construct a continuum $P$-$T$ surface or Maxwell constructions.
- Does not prove uniqueness of three phases from J alone beyond the cert packaging.
- Does not treat plasma, Bose condensates, or other nonclassical phases.
- Does not connect yet to the phi-ladder mass formula or alpha band.