strongFieldRung
plain-language theorem explainer
The strong-field gravitational rung is fixed at the integer 44. It is the half-area address of stellar-mass black-hole horizons on the φ-ladder and equals the absolute baryon-asymmetry rung. Gravity and cosmology channels that need a common strong-field scale cite this constant. The body is a bare integer assignment.
Claim. The strong-field rung is the integer $44$. Equivalently, if the horizon cell count satisfies $A_{\mathrm{horizon}}/\ell_{\mathrm{sub}}^{2}\approx\varphi^{88}$, the half-area rung is $s=44$, and this coincides with $|\eta_{B\text{-rung}}|=44$.
background
This module derives φ-powers for quantum-gravity falsifier channels (PTA, EHT, S-star, Cassini, ringdown) from the rung address of each observable. The substrate assigns to a length $L$ the rung $r(L)=\log_\varphi(L/\ell_{\mathrm{sub}})$; recognition corrections then scale as $\varphi^{-r}$ relative to the Planck-scale value.
For an astrophysical black hole the horizon cell count is $N=A/\ell_{\mathrm{sub}}^{2}$. On the φ-ladder this is written $\varphi^{2s}$ for a strong-field rung $s$. The half-area rung (the address at which half the horizon information has been processed) is $s=44$. The same integer appears in the baryon asymmetry $\eta_B=\varphi^{-44}$; the module treats the match as structural rather than accidental.
Sibling facts in the file record that this constant equals the absolute baryon-asymmetry rung and lies on the φ-ladder used by the channel predictions.
proof idea
Definitional constant: the body is the integer literal $44$ at type $\mathbb{Z}$. No lemmas or tactics are involved. Downstream equalities such as the channel-rung-pair theorem discharge by reflexivity against this assignment.
why it matters
Every strong-field D5 channel correction is built from this rung. PTA strain, S-star periapsis residual, EHT shadow shift ($2\cdot\varphi^{-44}$), and Cassini Shapiro delay ($3\cdot\varphi^{-44}$) all exponentiate $-\mathrm{strongFieldRung}$. The channel-rung-pair theorem records that the five corrections use only two rungs: $44$ (strong field) and $1$ (self-similar step), with geometric prefactors $1,2,3$ independent of the rung.
In the Recognition ladder this is the same address that appears in $\eta_B=\varphi^{-44}$, linking baryogenesis to strong-field gravitational-wave injection. The module status is structural (zero sorry, no RS-internal axiom): fixing the integer here closes the scale address for the whole channel table.
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