closureStatus_as_of_session_100
plain-language theorem explainer
Snapshot of master-theorem clause closure after Session 100: ten closed, one structural, three open, fourteen total. Gravity-track auditors and anyone updating the master-plan §3 ledger cite it as the frozen count. The body is a structure literal with a `decide` proof that the three counts sum to the total.
Claim. The Session-100 closure record for the RS quantum-gravity master theorem is the tuple $(c,s,o,t)=(10,1,3,14)$ with the identity $c+s+o=t$: ten clauses closed (eight prior plus two newly filled structural witnesses), one remaining structural clause, three open hypothesis inputs, fourteen clauses counted in all.
background
The gravity master theorem is a multi-clause conditional package that packages RS quantum-gravity claims under named hypothesis inputs. Session 97 authored the full conditional form with five open tracks. Session 100 advances that package by supplying structural Lean witnesses for two of those tracks (PTA stochastic GW distinct from inflation, and strong-field tests distinct from GR), leaving three hypothesis inputs.
MasterTheoremClosureStatus is a small audit record with four natural-number fields (closed, structural, open, total) plus a proof obligation that the first three sum to the fourth. It exists so later sessions can freeze progress without re-reading the whole clause list. The module is explicitly partial: discovery is not claimed until the remaining inputs, the master paper, the falsifier register, and the done-criteria are all discharged.
Upstream, the same structure type was introduced in the Session-97 master theorem module for the §3 audit trail. The two newly filled witnesses come from the PTA structural and strong-field structural modules imported here.
proof idea
Pure structure construction. The four numeric fields are assigned by hand from the Session-100 inventory (closed 10 = 8 prior + 2 newly filled; structural 1; open 3; total 14 = 12 clauses + 2 newly counted structural witnesses). The only proof obligation is the arithmetic identity closed + structural + open = total, discharged by decide. No lemmas beyond that decision procedure are invoked.
why it matters
This is the frozen ledger line for Gravity Track 7.A after Session 100. It records that two of the five Session-97 hypothesis inputs (tracks 6.B and 6.C) are now filled by structural witnesses, so the partial conditional master theorem needs only three remaining inputs: continuum/Bianchi (1.B/1.C), unconditional amplitude linearity (2.C/2.D), and Page-curve derivation (3.C).
Downstream consumers are human and machine auditors of the master plan rather than other Lean theorems (no used_by edges). The count feeds the §3 audit update and makes the residual open set explicit. Per the module header, discovery remains incomplete until those three inputs, the master paper, the §7 falsifier register, and the six §8 done-criteria are all closed. The declaration does not itself prove any gravity claim; it only timestamps how many clauses sit in each bucket.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.