IndisputableMonolith.Gravity.QGChannelRungDerivation
Fixes the strong-field gravity rung at 44 on the φ-ladder, identified with both the stellar-mass black-hole half-area scale and the absolute baryon-asymmetry rung. Packages PTA, EHT, S*, Cassini, and ringdown channel corrections as explicit positive φ-powers of that rung. Gravity and cosmology workers cite it when matching strong-field observables to the RS ladder. Content is definitional equalities plus elementary positivity lemmas.
claimThe strong-field rung is $r_{\mathrm{sf}}=44$, equal to $|\eta_{B,\mathrm{rung}}|$, and is the half-area exponent for stellar-mass horizons: $A_{\mathrm{horizon}}/\ell_{\mathrm{sub}}^2\approx\varphi^{88}$ so half-rung $44$. Channel corrections (PTA, EHT, $S^*$, Cassini, ringdown) are positive values on the $\varphi$-ladder built from this rung.
background
Recognition Science places masses and scales on a discrete φ-ladder whose self-similar ratio is forced by the J-cost fixed point (T5–T6). The cosmology module records the baryon-asymmetry rung and its arithmetic through the eight-tick period; its absolute value is 44.
In the gravity sector the same integer appears as the half-area rung of stellar-mass black holes: the horizon area in sub-quantum units sits near $\varphi^{88}$, so the half-rung is 44. The module therefore treats one shared ladder index as the strong-field anchor.
Constants supply the RS-native tick $\tau_0=1$. Downstream channel amplitudes (pulsar-timing, Event Horizon Telescope, stellar orbits, Cassini, ringdown) are read off as φ-powers relative to this common rung.
proof idea
Definition module with thin lemmas. The strong-field rung is introduced as the constant 44 and identified with the absolute baryon rung by a one-line equality. Membership on the φ-ladder is recorded directly. Each named channel correction (PTA, EHT, S*, Cassini, ringdown) is a definitional φ-ladder value; positivity lemmas discharge the sign obligations by the standard positivity of φ-powers.
why it matters in Recognition Science
Gives the gravity side a single integer anchor that already appears in cosmology as $|\eta_B|$. That coincidence lets strong-field QG channel predictions sit on the same φ-ladder as the mass formula (yardstick times $\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$) and the eight-tick octave (T7). No downstream theorems are wired yet in the graph; the module is the definitional feedstock for later PTA/EHT/Cassini/ringdown bounds. It does not itself force D=3 or the J-uniqueness step; it consumes φ and the ladder arithmetic already fixed upstream.
scope and limits
- Does not derive rung 44 from Einstein equations or horizon thermodynamics.
- Does not prove observational bounds; only defines correction amplitudes and positivity.
- Does not identify which channel dominates any given dataset.
- Does not alter c, ħ, G, or the α band; those stay in Constants.
- Does not close any sorry; content is definitional plus elementary lemmas.
depends on (2)
declarations in this module (33)
-
def
strongFieldRung -
theorem
strongFieldRung_eq_abs_eta_B_rung -
theorem
strongFieldRung_in_ladder -
def
ptaCorrectionValue -
def
ehtCorrectionValue -
def
sStarCorrectionValue -
def
cassiniCorrectionValue -
def
ringdownCorrectionValue -
theorem
ptaCorrectionValue_pos -
theorem
ehtCorrectionValue_pos -
theorem
sStarCorrectionValue_pos -
theorem
cassiniCorrectionValue_pos -
theorem
ringdownCorrectionValue_pos -
theorem
golden_ratio_partition -
theorem
golden_ratio_complement -
theorem
channel_rung_pair -
theorem
pta_sstar_same_base -
theorem
eht_eq_two_times_pta -
theorem
cassini_eq_three_times_pta -
theorem
ringdown_is_one_rung -
structure
DerivedChannelPrediction -
def
ptaDerived -
def
ehtDerived -
def
sStarDerived -
def
cassiniDerived -
def
ringdownDerived -
def
derivedChannels -
theorem
derivedChannels_length -
theorem
all_derived_channels_pos -
theorem
four_channels_share_rung_44 -
theorem
ringdown_rung_eq_1 -
structure
QGChannelRungDerivationCert -
def
qgChannelRungDerivationCert