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feat(higher): normalize marked pair cells - #131

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

feat(higher): normalize marked pair cells#131
miuchan merged 1 commit into
mainfrom
codex/hammock-marked-pair-normalization

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@miuchan miuchan commented Aug 22, 2026

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Summary

  • prove generic normalization formulas between an empty word and any closed two-atomic-step word
  • use unitor equality and right-whiskering semantics to identify both directions exactly
  • specialize the formulas to marked unit, inverse unit, counit, and inverse counit
  • prove all four marked generators normalize exactly to their executable pair insertion/deletion refinements
  • remove the four marked fields from StructuralGeneratorNormalizable, reducing the remaining basis from ten fields to six
  • extend the cost-exact normalization core and synchronize audits and four-language boundaries

Verification

  • lake build Ript.ForMathlib.CategoryTheory.Bicategory.MarkedZigzagAlignedHammock
  • lake build Ript.Higher.CostExactZigzagMappingSpace
  • ./scripts/check-axioms.sh
  • ./scripts/quality-gate.sh

Boundary

Six unconditional structural normalization fields remain: associator and inverse, plus left/right unitors and inverses. All-cell normalization, semantic fullness, critical-pair coherence, reduced-hammock invariance, standard weak-equivalence packaging, and the final Dwyer--Kan/Rezk theorem remain open.

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miuchan marked this pull request as ready for review August 22, 2026 09:08
@miuchan
miuchan merged commit b23791d into main Aug 22, 2026
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