canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as the real number φ − 3/2, with φ the golden-ratio fixed point of Recognition Science. Cosmology and ladder-mass arguments cite it as the comparison value against domain cost when placing the inflaton on the φ-ladder. The body is a pure definitional abbreviation, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio self-similar fixed point of the Recognition cost.
background
The module derives a structural placement of the inflaton mass on the Recognition φ-ladder: $m_{\mathrm{inflaton}} = \varphi^k E_{\mathrm{coh}}$ with $E_{\mathrm{coh}} \approx 0.121,\mathrm{MeV}$. For rung $k \approx 57$ one recovers the conventional $\sim 10^{13},\mathrm{GeV}$ scale; nearby rungs give PeV-scale values. Status is structural (zero sorry, zero axiom).
φ itself is forced by the T6 self-similarity step of the unified forcing chain: it is the unique positive fixed point compatible with the J-cost $J(x) = (x+x^{-1})/2-1$ and the Recognition Composition Law. The threshold φ − 3/2 sits just below φ and is the natural comparison constant once a domain cost (a non-negative real built from J) is evaluated on the ladder.
Sibling material in the same file introduces that domain cost, proves it is non-negative, and packages an inhabited certificate that the inflaton mass sits above the threshold.
proof idea
Pure definitional abbreviation: the constant is introduced by the single equation canonicalThreshold := φ − 3/2. No tactics, no lemmas, and no reduction steps are required.
why it matters
Supplies the numerical cut that the surrounding InflatonMass3 certificate compares against domain cost. In the broader RS cosmology story the same φ-ladder that forces particle masses (yardstick · φ^{rung−8+gap(Z)}) is reused for the inflaton; the threshold φ − 3/2 marks the minimal cost excess needed for a viable slow-roll scale near 10^{13} GeV. It therefore sits downstream of T5–T6 (J-uniqueness and φ-forcing) and upstream of any later claim that the inflaton rung is occupied. No open scaffold remains: the module is already zero-sorry.
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