didericis
81a9e1fef3
- Generalize Phase 1 to include even interior faces as optional flip
candidates and allow the source-triangle break in $L_0$ to be skipped;
generalize Phase 2 so even outer-incident cycles may have at most one
outer-face edge flipped (odd cycles still must have one).
- Define "simple level resolution" as a triangulation $G'$ obtained from
some $(G, S)$ via the algorithm with bipartite parity subgraphs
(Definition 5.4).
- Add Conjecture 5.7 (simple-resolution md4 surjectivity) and
Observation 5.6: every minimum-degree-4 plane triangulation iso-class
on $n \in \{6, ..., 11\}$ vertices is reached as a simple level
resolution. Counts: 1, 1, 2, 5, 12, 34. The md4 restriction is
necessary -- specific non-md4 iso-classes (iso 5 at n=8; iso 25, 183
at n=10) are not reachable.
- Add experiments/simple_level_resolution_coverage.py implementing the
branched algorithm and coverage check, plus supporting scripts for
Phase 1 cycling debugging, Phase 2 gap diagnosis, inductive-lift
scaffolding (inductive_lift_check.py for the route-1 proof strategy),
and visualizations of the unreached n=10 iso-classes and the original
Phase 2 gap example.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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</usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi6.pfb></
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usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></us
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r/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.pfb></usr/
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local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/lo
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cal/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/local
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/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/local/te
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xlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/local/tex
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live/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy5.pfb></usr/local/texli
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ve/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy6.pfb></usr/local/texlive
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/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/local/texlive/2
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022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/local/texlive/20
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22/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb></usr/local/texlive/2022
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/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb></usr/local/texlive/2022/
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texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb></usr/local/texlive/2
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022/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb>
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Output written on paper.pdf (8 pages, 258447 bytes).
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PDF statistics:
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281 PDF objects out of 1000 (max. 8388607)
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232 compressed objects within 3 object streams
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60 named destinations out of 1000 (max. 500000)
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145 words of extra memory for PDF output out of 10000 (max. 10000000)
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