IndisputableMonolith.Physics.SoundSpeedRatioFromPhi
Packages the RS derivation of a sound-speed ratio from the golden-ratio fixed point φ. Introduces a domain cost, its equilibrium value, a positive canonical threshold, and a SoundSpeedCert that the φ-derived ratio meets the bound. Continuum and condensed-matter readers of the eight-tick ledger would cite it. Structure is definitional plus elementary nonnegativity and positivity lemmas.
claimThe module defines a domain cost $C$, records $C$ at equilibrium and $C\ge 0$, a canonical threshold $T>0$ built from $\varphi$, and a inhabited certificate that the sound-speed ratio extracted from $\varphi$ clears $T$.
background
Recognition Science forces the cost $J(x)=(x+x^{-1})/2-1$ (T5) and the self-similar fixed point $\varphi$ (T6). Continuum transport coefficients are read off the same cost on the $\varphi$-ladder, with the eight-tick octave (T7) setting the discrete clock ($\tau_0=1$ tick in RS-native units from Constants).
This physics module sits on Cost and Constants. It treats sound speed as a ratio controlled by a domain cost relative to a canonical threshold fixed by $\varphi$, rather than as an independent material parameter. Equilibrium is the reference point where the cost is evaluated for the ratio.
Sibling objects name the pieces: domain cost, nonnegativity, equilibrium evaluation, positive canonical threshold, and a SoundSpeedCert bundle with an inhabited instance.
proof idea
Definition-first module, not a single deep theorem. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas; equilibrium evaluation is a one-line specialization. SoundSpeedCert packages the ratio-versus-threshold claim, and cert_inhabited supplies a witness. No long tactic scripts; the argument is assembly of Cost/Constants facts into a named certificate.
why it matters in Recognition Science
Gives a named home for the claim that sound speed in RS units is a $\varphi$-derived ratio checked against a cost threshold, aligning continuum acoustics with the forcing chain (T5–T7) rather than free parameters. Downstream used_by edges are empty in the mirror graph so far; the natural parents are later continuum or materials theorems that need a certified $c_s/c$ (or analogue) bound. Closes a scaffolding gap between abstract $J$-cost and a concrete transport coefficient certificate.
scope and limits
- Does not predict laboratory numerical sound speeds in SI units.
- Does not derive bulk modulus or density from microphysics.
- Does not prove uniqueness of the threshold beyond the stated defs.
- Does not connect to electromagnetic $c=1$; acoustic ratio only.
- Does not discharge open continuum limits outside this certificate.