IndisputableMonolith.Cosmology.Baryon_Density_RS
Module packaging the RS-side baryon density certificate: a nonnegative domain cost, a positive canonical threshold, and an inhabited BaryonDensityCert record. Cosmology and constants auditors cite it when wiring baryon-fraction claims to the J-cost stack. Structure is definitional plus elementary positivity and equality lemmas, not a deep derivation.
claimIntroduce a domain cost $C$ on the RS cost stack, prove $C\ge 0$ and an evaluation identity, fix a canonical threshold $\theta>0$, and package an inhabited certificate $\mathrm{BaryonDensityCert}$ asserting the baryon-density side conditions used downstream in RS cosmology.
background
Recognition Science cosmology ties macroscopic abundance parameters to the same cost functional that forces the microphysical ladder. The Cost import supplies the J-cost infrastructure ($J(x)=(x+x^{-1})/2-1$ and its composition law); Constants supplies the RS-native tick and related units ($\tau_0=1$ tick).
This module sits in the Cosmology domain and does not re-derive $J$ or $\phi$. It introduces a domain-level cost functional (domainCost), records that the cost is nonnegative, and names a positive canonical threshold against which baryon-density claims are checked. The certificate type BaryonDensityCert is the bookkeeping object that later cosmology lemmas can assume or inhabit rather than re-proving local inequalities inline.
Sibling names indicate equality-at-a-point lemmas and an inhabitation witness (cert, cert_inhabited), so the module is a thin interface layer between Cost/Constants and any baryon-fraction or $\Omega_b$-style statements.
proof idea
Definition module with light lemma support. domainCost is introduced and tied to the Cost stack; domainCost_at_eq is an evaluation identity; domainCost_nonneg is nonnegativity, almost certainly by reduction to known nonnegativity of $J$ or a nonnegative combination thereof. canonicalThreshold is a named positive constant (canonicalThreshold_pos). BaryonDensityCert is a structure or Prop bundle; cert and cert_inhabited supply a concrete witness so downstream files can use the certificate without constructing it. No multi-step forcing-chain argument lives here.
why it matters in Recognition Science
Gives Cosmology a single place to hang baryon-density side conditions instead of scattering cost inequalities through abundance proofs. Feeds any parent development that needs an RS-native baryon-density certificate; the rendered used_by list is currently empty, so this is a leaf interface awaiting cosmology consumers (e.g. $\Omega_b$ or baryon-to-photon ratio bridges).
It does not itself force $D=3$, the eight-tick octave, or the $\alpha$ band (T7/T8 and related chain steps live elsewhere). Its role is infrastructural: connect Cost/Constants to baryon-density claims so later theorems can cite one inhabited cert rather than rebuild domain inequalities. Open question for auditors: whether the canonical threshold is numerically pinned to a paper value or left symbolic until a downstream match to observed $\Omega_b$.
scope and limits
- Does not derive observed $\Omega_b$ or baryon-to-photon ratio from first principles.
- Does not prove uniqueness of the canonical threshold or match it to a measured band.
- Does not re-prove J-uniqueness, $\phi$ forcing, or T0–T8 chain steps.
- Does not define mass-ladder rungs or lepton/baryon mass formulas.
- Does not assert observational cosmology fits beyond the certificate interface.