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feat(higher): normalize hammock path whiskering - #128

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miuchan merged 1 commit into
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codex/hammock-path-whiskering
Aug 22, 2026
Merged

feat(higher): normalize hammock path whiskering#128
miuchan merged 1 commit into
mainfrom
codex/hammock-path-whiskering

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@miuchan miuchan commented Aug 22, 2026

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Summary

  • add canonical left and right whiskering of generated hammock paths through linear-normal-form append isomorphisms
  • add horizontal path append and prove semantic equality and exact-image membership closed under whiskering, append, and vertical composition
  • define normalized semantics for arbitrary raw presented cells
  • prove identity and original raw cells normalizable and vertical composition preserves normalizability
  • expose exact cost-exact three-model nerve formulas for left whiskering, right whiskering, and horizontal append
  • audit the expanded noncomputable semantic boundary and synchronize research and four-language status docs

Verification

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

Boundary

The raw Cell normalization induction is complete for identities, vertical composition, and original source 2-cells. Normalization-isomorphism naturality for raw left/right whiskering is still required before the remaining structural generators and all presented quotient 2-cells can be normalized. Fullness, critical-pair coherence, reduced-hammock invariance, standard weak-equivalence packaging, and the final Dwyer--Kan/Rezk theorem remain open.

@miuchan
miuchan marked this pull request as ready for review August 22, 2026 06:40
@miuchan
miuchan merged commit c48b06c into main Aug 22, 2026
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