created: 20260507101500000
modified: 20260507101500000
tags: ResearchStack Erdos Diagnostics FourPrimitives ConjectureAudit
title: Erdos Four Primitive Diagnostics
type: text/vnd.tiddlywiki

! Erdos Four Primitive Diagnostics

This index records Erdős-style conjecture experiments as diagnostic packets, not theorem claims.

!! Active Cards

* [[Erdos Gyarfas Detector Anomaly]] — power-of-two cycle test must emit a verified Γ_fail packet before any counterexample claim is trusted.
* [[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.

!! Four-Primitive Reading

The accurate framework claim is:

> The four primitives provide a diagnostic coordinate system over Erdős-style objects: field density, spectral structure, shear balance, and packetized obstruction witnesses.

For graph-cycle problems:

* `ρ(x)` = edge and degree density.
* `C = UΛU^T` = adjacency spectral structure.
* `G = A^T A` = graph rigidity or degree deformation.
* `Γ_i` = cycle packet, missing-cycle residual, and counterexample certificate.

For covering-system problems:

* `ρ(x)` = residue/modulus coverage density.
* `C = UΛU^T` = covering overlap spectrum.
* `G = A^T A` = even/odd modulus balance.
* `Γ_i` = covering-system packet plus violation witness.

!! Local Evidence

* `4-Infrastructure/shim/test_erdos_gyarfas_4primitive_results.json`
* `4-Infrastructure/shim/test_erdos_selfridge_4primitive_results.json`
* `4-Infrastructure/shim/investigate_erdos_gyarfas_refined.py`

!! Rule

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.