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Created refined investigation script for Erdős–Gyárfás conjecture where previous test found no power-of-two cycles (conjecture holds: False). Refinements: - Regular graph construction (all vertices same degree) - Exhaustive DFS cycle detection - More samples per n (5 instead of 3) - Extended n values [8, 10, 12, 14, 16] Goal: Determine if previous negative result was due to random graph construction or if regular graphs with exhaustive cycle detection find power-of-two cycles. Script created: investigate_erdos_gyarfas_refined.py Execution canceled by user - awaiting further instructions.
44 lines
1.7 KiB
Text
44 lines
1.7 KiB
Text
created: 20260507101500000
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modified: 20260507101500000
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tags: ResearchStack Erdos Diagnostics FourPrimitives ConjectureAudit
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title: Erdos Four Primitive Diagnostics
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type: text/vnd.tiddlywiki
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! Erdos Four Primitive Diagnostics
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This index records Erdős-style conjecture experiments as diagnostic packets, not theorem claims.
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!! Active Cards
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* [[Erdos Gyarfas Detector Anomaly]] — power-of-two cycle test must emit a verified Γ_fail packet before any counterexample claim is trusted.
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* [[Erdos Selfridge Finite Smoke Test]] — finite generated covering-system samples found no odd-moduli violation, but this is not a proof of the full conjecture.
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!! Four-Primitive Reading
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The accurate framework claim is:
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> The four primitives provide a diagnostic coordinate system over Erdős-style objects: field density, spectral structure, shear balance, and packetized obstruction witnesses.
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For graph-cycle problems:
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* `ρ(x)` = edge and degree density.
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* `C = UΛU^T` = adjacency spectral structure.
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* `G = A^T A` = graph rigidity or degree deformation.
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* `Γ_i` = cycle packet, missing-cycle residual, and counterexample certificate.
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For covering-system problems:
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* `ρ(x)` = residue/modulus coverage density.
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* `C = UΛU^T` = covering overlap spectrum.
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* `G = A^T A` = even/odd modulus balance.
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* `Γ_i` = covering-system packet plus violation witness.
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!! Local Evidence
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* `4-Infrastructure/shim/test_erdos_gyarfas_4primitive_results.json`
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* `4-Infrastructure/shim/test_erdos_selfridge_4primitive_results.json`
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* `4-Infrastructure/shim/investigate_erdos_gyarfas_refined.py`
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!! Rule
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Do not promote an Erdős experiment from diagnostic to result unless the packet primitive carries a reproducible witness, a receipt hash, and an independent verifier result.
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