rs_pta_stochastic_phi_signature
plain-language theorem explainer
The RS PTA stochastic gravitational-wave background signature is the positive scale φ^{-44} on the golden-ratio ladder. Gravity and cosmology bridge work cites it as the algebraic discriminator against a pure-inflation zero baseline. The definition is a direct integer power of the RS constant φ at rung 44; no further proof content.
Claim. The Recognition Science PTA stochastic-background signature is the real number $\varphi^{-44}$, where $\varphi$ is the golden-ratio self-similar fixed point of the Recognition Composition Law.
background
Track 6.B of the gravity stack isolates the algebraic half of a PTA stochastic-background discriminator. Pulsar timing arrays constrain a nanohertz stochastic GW background; the RS side of the comparison is not a fitted spectrum but a single positive scale on the $\varphi$-ladder.
That scale is rung 44: $\varphi^{-44}$. The same rung appears elsewhere in the gravity/cosmology bridge. The module pairs it with an explicit zero proxy for pure inflation, so positivity alone already separates the two structural predictions.
Constants come from the RS native bundle (c = 1, $\hbar = \varphi^{-5}$, etc.). The module imports the $\varphi$-rung ladder and the gravity master theorem so this number can inhabit the master input PTAStochasticGWDistinctFromInflation. No PTA dataset is attached here.
proof idea
Pure definition: the real is defined as Constants.phi raised to the integer power $-44$. There is no tactic proof, no lemma application, and no reduction beyond the power notation on the RS constant $\varphi$.
why it matters
This constant is the structural inhabitant every Track 6.B discriminator builds on. Downstream, positivity (0 < φ^{-44}), inequality with the inflation zero baseline, the band predicate centered on half-to-three-halves of the signature, and the one-statement theorem all quote it by name.
It feeds PTAStructuralCert and pta_structural_one_statement, which package the master-theorem hypothesis PTAStochasticGWDistinctFromInflation. The module doc is explicit: dataset sensitivity and channel-specific spectral fitting remain empirical falsifier work; Lean only supplies the algebraic, theorem-grade scale.
Framework landmark: the $\varphi$-ladder forced at T6, reused here at rung 44 as a gravity/cosmology bridge scale rather than a particle mass rung.
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