IndisputableMonolith.NumberTheory.HonestPhaseAdmissibility
The module defines honest phase admissibility as the condition that realized sampled families carry finite total annular J-cost. Researchers assembling the Riemann hypothesis from Recognition Composition Law data would cite it as the required bridge predicate. The module consists of predicate definitions together with equivalence theorems linking admissibility to charge-zero and zero-free criteria, all built on the imported analytic trace infrastructure.
claimHonest phase data is admissible when the total annular J-cost of its realized sampled family is finite: $J$-cost sum over annuli $< 1$. Equivalences hold between this predicate, charge-zero conditions, and zero-free criteria on the phase data.
background
Recognition Science uses the J-function $J(x) = (x + x^{-1})/2 - 1$ (equivalently cosh(log x) - 1) to quantify recognition cost; the Recognition Composition Law governs its additive properties under multiplication and division. The upstream AnalyticTrace module supplies the axiom-free analytic infrastructure, including contour winding numbers, that replaces earlier axioms for the RH bridge. This module introduces the admissibility predicate for honest phase data in that setting and records the equivalences to charge zero.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the admissibility condition required by the parent assembly in RH_From_RCL. Downstream documentation states that this is the final assembly where the only remaining nontrivial datum is BoundaryTransportCert, the explicit form of the RS physical bridge that transports realized annular collapse to the T1-bounded Euler ledger boundary. It therefore closes the link from RCL data to the Riemann Hypothesis.
scope and limits
- Does not prove finiteness of the J-cost sum for any concrete data set.
- Does not construct the BoundaryTransportCert object.
- Does not perform numerical checks on the alpha inverse band.
- Does not extend the argument beyond the eight-tick octave and D=3 setting.
used by (1)
depends on (1)
declarations in this module (14)
-
structure
HonestPhaseAdmissible -
theorem
charge_zero_of_honestPhaseAdmissible -
theorem
honestPhaseAdmissible_iff_charge_zero -
structure
HonestPhaseAdmissibilityBridge -
def
chargeZeroBridge_of_admissibilityBridge -
def
admissibilityBridge_of_chargeZeroBridge -
theorem
honestPhaseAdmissibilityBridge_iff_chargeZeroBridge -
def
zeroFreeCriterion_of_honestPhaseAdmissibility -
theorem
direct_rh_from_honestPhaseAdmissibility -
structure
WitnessedHonestPhaseAdmissibilityBridge -
theorem
witnessed_rh_from_honestPhaseAdmissibility -
def
witnessedHonestPhaseAdmissibilityBridge_of_rh -
theorem
witnessedHonestPhaseAdmissibilityBridge_iff_rh -
theorem
direct_rh_from_witnessedAdmissibilityBridge