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Complete generated hammock mapping semantics - #134

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miuchan merged 1 commit into
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codex/hammock-associator-normalization
Aug 22, 2026
Merged

Complete generated hammock mapping semantics#134
miuchan merged 1 commit into
mainfrom
codex/hammock-associator-normalization

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@miuchan miuchan commented Aug 22, 2026

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Summary

  • define the canonical linear associator isomorphism and recursive forward/inverse associator paths, with exact quotient semantics and inverse laws
  • prove raw associator and inverse associator normalization, then remove the final conditional generator record and establish unconditional normalization for every raw Cell
  • prove every quotient 2-cell between linear rows lies in the generated semantic image; generated hammock semantics is now full, faithful, essentially surjective, and a categorical equivalence
  • expose categorical-nerve equivalence and explicit simplicial homotopy-equivalence witnesses in the cost-exact mapping-space core
  • update the axiom audit, blueprint, model matrix, conjecture boundary, and four-language research status

Verification

  • lake build Ript.ForMathlib.CategoryTheory.Bicategory.MarkedZigzagAlignedHammock
  • lake build Ript.Higher.CostExactZigzagMappingSpace
  • ./scripts/check-source-quality.sh
  • ./scripts/check-axioms.sh
  • ./scripts/quality-gate.sh (3664 build targets, declaration lint, executable examples, and axiom allowlist all passed)

Remaining boundary

This completes the generated-path presentation of each linear mapping category, but not the final global Dwyer--Kan/Rezk theorem. Critical-pair coherence, reduced-hammock homotopical invariance or comparison to an accepted derived mapping-space construction, standard weak-equivalence packaging, and the global complete-Segal/Rezk result remain open.

@miuchan
miuchan marked this pull request as ready for review August 22, 2026 12:07
@miuchan
miuchan merged commit db9c95b into main Aug 22, 2026
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