IndisputableMonolith.Gravity.MasterTheoremNonCircularityAudit
Audit module that packages non-circularity certificates for the gravity master theorem: each input clause (T0–T8 forcing, cost uniqueness, BMV, Lorentzian, Hawking, cRS) is either carried from an unconditional witness or closed as a named certificate. Gravity and foundations workers cite it to check that the master surface does not smuggle its own hypotheses. Structure is a conjunction of small hold/carried lemmas over the unconditional closure surface.
claimThe gravity master-theorem non-circularity audit asserts that the T0–T8 forcing-chain clause is the concrete conjunction of the T0-through-T8 theorem surface, that cost-uniqueness and BMV clauses are carried by unconditional witnesses, and that Lorentzian, Hawking, and $c_{\mathrm{RS}}$ clauses are closed certificates; the carried and closed clause bundles both hold.
background
Recognition Science derives physics from a single cost functional whose uniqueness and discrete geometry are forced along the T0–T8 chain: J-uniqueness with $J(x)=(x+x^{-1})/2-1$, the golden ratio $\varphi$ as self-similar fixed point, the eight-tick octave, and $D=3$ spatial dimensions. The older gravity master theorem was conditional on five named inputs.
The upstream module MasterTheoremUnconditional installs theorem-built witnesses for those inputs and supplies a zero-argument route through the conditional audit surface. This audit module sits one layer out: it does not reprove the physics, but records which clauses are carried from that unconditional surface versus which are already closed certificates, so a referee can see that the master statement is not circular.
Sibling names in the module track per-clause completeness and hold lemmas (T0–T8, cost uniqueness, BMV) plus certificate tags (Lorentzian, Hawking, $c_{\mathrm{RS}}$) and two aggregate hold statements for carried and closed bundles.
proof idea
Module-level argument, not a single proof. It imports the unconditional master-theorem closure surface and exposes a family of small lemmas: completeness/carried tags for the T0–T8, cost-uniqueness, and BMV clauses; certificate tags for Lorentzian, Hawking, and $c_{\mathrm{RS}}$; then two aggregate theorems that the carried bundle and the closed-certificate bundle both hold. The T0–T8 master clause is identified with the concrete conjunction of the T0-through-T8 theorem surface rather than a placeholder. No new analytic content; the work is bookkeeping that ties each master input to an already-proved witness or cert.
why it matters in Recognition Science
Without an explicit non-circularity audit, the gravity master theorem can be read as assuming what it concludes. This module is the ledger that separates carried unconditional witnesses from closed certificates, so the conditional master surface can be invoked with a transparent hypothesis budget. It sits directly on the unconditional closure surface and supports any downstream claim that the RS quantum-gravity master route is zero-argument and non-circular. Framework landmarks touched: the full T0–T8 forcing chain (including J-uniqueness, $\varphi$, eight-tick octave, $D=3$) as the concrete T0–T8 clause, plus cost uniqueness as a carried input to the gravity story.
scope and limits
- Does not reprove T0–T8, cost uniqueness, or BMV; only tags them as carried or complete.
- Does not derive Lorentzian, Hawking, or $c_{\mathrm{RS}}$ physics; only records certificate status.
- Does not replace the conditional master theorem; it audits inputs to that surface.
- Does not claim used-by edges; nothing downstream is recorded in the graph yet.
- Does not enlarge the physical hypothesis set beyond the unconditional witness module.
depends on (1)
declarations in this module (24)
-
theorem
t0t8_clause_is_complete_forcing_chain -
theorem
t0t8_clause_holds -
theorem
costUniqueness_clause_is_carried -
theorem
costUniqueness_clause_holds -
theorem
bmv_clause_is_carried -
theorem
bmv_clause_holds -
def
placeholderClauseCount -
theorem
lorentzian_clause_is_cert -
theorem
hawking_clause_is_cert -
theorem
cRS_clause_is_cert -
theorem
carried_clauses_hold -
theorem
closed_certs_hold -
def
inhabitedCertClauseCount -
theorem
d2_regge_field_is -
theorem
d2_bianchi_field_is -
theorem
d3_amplitude_field_is -
theorem
d4_page_field_is -
theorem
all_witness_fields_hold -
def
witnessFieldClauseCount -
theorem
d4_page_field_nondegenerate -
structure
ClauseClassification -
def
masterClauseClassification -
theorem
masterClauseClassification_total -
theorem
master_theorem_non_circularity_certificate