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Filter axiom-5 bisectors by paper incidence before requiring toward #66

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opened 2026-07-05 00:15:28 +00:00 by toph · 0 comments
toph commented 2026-07-05 00:15:28 +00:00
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The kite base errors today:

--diag = map .b onto .d
@map --(.d .a) onto --diag    ; bisector is ambiguous; add `toward .p`

The two lines meet at corner a; only one of the two bisectors crosses the paper — the other touches it in a single point and folds nothing. Requiring toward here means disambiguating between a fold and a non-fold.

Proposal: when toward is omitted, clip both candidates against the paper, drop those without a positive-length segment, and only error if two remain (0 → "no fold lands on the paper"). Fits ADR 0014 (empty bundle ≠ crease) and ADR 0016 (metric selection only where incidence cannot discriminate).

Design note with geometry, doctrine fit, and open questions (clip region after folds, generalising to axioms 6/7): notes/2026-07-05-axiom5-paper-incidence.md.

The kite base errors today: ``` --diag = map .b onto .d @map --(.d .a) onto --diag ; bisector is ambiguous; add `toward .p` ``` The two lines meet at corner `a`; only one of the two bisectors crosses the paper — the other touches it in a single point and folds nothing. Requiring `toward` here means disambiguating between a fold and a non-fold. Proposal: when `toward` is omitted, clip both candidates against the paper, drop those without a positive-length segment, and only error if two remain (0 → "no fold lands on the paper"). Fits ADR 0014 (empty bundle ≠ crease) and ADR 0016 (metric selection only where incidence cannot discriminate). Design note with geometry, doctrine fit, and open questions (clip region after folds, generalising to axioms 6/7): `notes/2026-07-05-axiom5-paper-incidence.md`.
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toph/beloch#66
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