ClosureEntry
plain-language theorem explainer
A closure entry packages a proposition with a proof that it holds, as one named slot in the Delta-native strong closure certificate. Auditors of the Primitive Recognition Calculus closure registry cite this carrier when wiring certified layers. It is a bare dependent pair (Prop, proof); no tactics or lemmas are involved.
Claim. A closure entry is a pair $(P, h)$ where $P$ is a proposition and $h$ is a proof that $P$ holds.
background
The module builds a Delta-native strong closure certificate: a registry whose fields point at existing theorem heads asserting that successive layers of the Primitive Recognition Calculus are closed. Parameterized layers are stored as functions that return such entries.
Upstream holography defines ledger closure concretely. On a plaquette, four vertex bits XOR to zero (even parity), so a closed recognition loop posts a balanced zero-sum ledger around the face. On a glued domino, both unit faces must post balanced loops (left face even parity and right face even parity).
This structure is the bookkeeping atom for those claims inside the certificate: it names the closedness proposition and holds the proof witness, without itself choosing which layer or which holographic predicate is meant.
proof idea
Pure structure definition. Two fields: a proposition closed and a dependent proof of that proposition. No tactics, no lemmas, no computation. Downstream entryOf is the one-line constructor that packs an arbitrary proposition with its witness into this pair.
why it matters
This is the field type of StrongClosureCertificate, which collects Delta-real, generable-carrier, certified-analytic, transformer, and FRS-carrier closure heads (plus parameterized layers as functions into entries). entryOf builds instances. Without a uniform named proof entry, the certificate could not store heterogeneous theorem heads under one schema.
In the Recognition framework this sits in Foundation, packaging ledger-style closedness (balanced recognition loops) so later forcing and calibration layers can cite a single strong-closure object rather than ad hoc hypotheses. It does not itself advance T5–T8; it is infrastructure for the Delta-native closure claim those layers rely on.
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