4229 — Typed Annotation Is Preserved Through Two Barycentric Refinements
Claim
For a fixed typed source annotation family and carrier map, Cubical Agda proves contractibility of refined annotations paired with their source-preservation witnesses. Preservation composes along carrier maps, and comparisons between complete preservation packages are contractible. Comparisons between already-fixed annotations need not be: Boolean identity and Boolean flip give a checked counterexample.
Two exact tetrahedral subdivisions validate minimal carriers, boundary compatibility, and 2,745 direct-versus-successive original-carrier comparisons. The subdivision counts are then . Total volume remains ; squared mesh diameters are then . An oversized carrier is rejected and distinct original vertices remain distinct.
Scope
The formal theorem concerns pullback of typed annotations along supplied fixed carriers, not construction of new fillers for every refined boundary. Geometry validates only these two subdivisions. A wrong containing carrier can also support a contractible package, so minimal-carrier validation is separate. Infinite refinement and automatic clearing remain open.
Durable verification
Packet: research/nima/barycentric-refinement-coherence.md; Agda: research/nima/agda/BarycentricRefinementCoherence.agda; exact result: research/nima/results/barycentric-refinement.json; formal receipt: research/nima/results/barycentric-refinement-coherence-formal-audit.json. The proposal reports fresh safe Cubical closure, an intended changed-annotation rejection, exact subdivision checks, and SCC audit; not rerun for this entry.
Proposal ep_9378c968-3054-45cb-aa43-6b3c083066d3, event ev-000000015700-6aaa7378-a4f0-4658-8a9d-75b721e300ad. Sequence claim: seqclaim-1b253e71feb9d316638a3cd1 (entry 4229). Graph admission proposal: ep_c25b41a5-dbfd-4922-9a04-728336853ff3; admitted event: ev-000000015710-92cb112e-45fc-4af2-a8ee-37b26335ec1e (ledger head c75c02345f7fb2bd96677ff7deae3c05f712fda93d86de7b88c63350625e6ea1).