MasterTheoremClosureStatus
plain-language theorem explainer
A bookkeeping record packing four natural-number tallies (closed, structural, open, total) with the identity that they sum. Gravity-track auditors and session notes cite it when freezing a snapshot of the twelve-clause quantum-gravity master statement. Pure structure definition: the only content is the type of the equality field.
Claim. A closure-status record consists of four natural numbers $n_{\mathrm{closed}}$, $n_{\mathrm{structural}}$, $n_{\mathrm{open}}$, and $n_{\mathrm{total}}$, together with a proof of the identity $n_{\mathrm{closed}} + n_{\mathrm{structural}} + n_{\mathrm{open}} = n_{\mathrm{total}}$.
background
Track 7.A authors the Recognition Science quantum-gravity master statement as a conjunction of twelve named clauses. Each clause is classified CLOSED (discharged from existing Lean theorems), STRUCTURAL (carried by a named structural hypothesis or witness), or OPEN (awaiting its track). The master conditional theorem takes the still-open hypotheses as inputs and proves the full conjunction once those inputs are supplied.
This structure is the audit counter for that classification. It does not encode physics; it only stores the four tallies and forces them to add up. Upstream status strings in RS-native units, discrete Lichnerowicz convergence, and inevitability choke-point counts follow the same pattern of explicit progress ledgers. Session 97 freezes the baseline at 8 closed, 1 structural, 3 open (total 12).
proof idea
No proof body. The declaration is a structure with four ℕ fields and one propositional field whose type is the sum identity. Inhabitants (session snapshots) fill the numbers and discharge total_eq by decide or reflexivity on concrete numerals.
why it matters
Gives every later session a typed place to record how many of the twelve master-statement clauses have moved. Downstream snapshots closureStatus_as_of_session_97 (8/1/3/12), session 100 (10/1/3/14), session 101 (11/1/2/14), and session 102 (13/1/0/14) all inhabit this type; the structural master cert reads the final zero-open tally. It supports the master-plan §3 audit trail for Track 7.A without claiming the discovery is closed: open and structural slots remain first-class until their tracks discharge. Landmark context is the conditional master theorem itself, not T0–T8 or the RCL directly.
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