All Elementary Functions from a Single Operator (AEFSO)

We evaluated whether the AEFSO operator eml(x,y) = exp(x) − ln(y) could serve as a TOE core component — a single binary primitive sufficient to reconstruct all elementary functions. Assessed via SPAR paper review, fhval validation, and 4 dogfood runs. Result: SPAR ACCEPT WITH BOUNDS. Classified as OPTIONAL_REPRESENTATION_LAYER — approved for symbolic normalization and IR research, not promoted to core. Key contribution: missing-link IR discovery.

OpenAI Erdős Conjecture Disproof: Equation (2.2) Executable Reproduction

In May 2026, an OpenAI reasoning model proved that Erdős' discrete geometry conjecture is false, publishing a crucial exponent excess equation (2.2). Naive computer floats collapse this value to zero due to catastrophic cancellation. This project builds an independent Python artifact using arbitrary-precision math to successfully reproduce and verify the published numerical results. Result: The computation is fully reproduced to 0.014% relative error, locally CI-verified, and published on Zenodo.

LOGOS-to-TOE Intake Governance Gate Verification

We evaluated whether the offline reasoning sidecar pipeline could safely ingest theoretical math solver candidates without bypassing mandatory governance review. The system was presented with an incomplete research dossier lacking a concrete algebraic model candidate. Result: The intake contract engine correctly identified the gaps, issued a hard 'BLOCK' recommendation to inhibit candidate promotion, and successfully protected the ledger registry.

Reasoning Model Sidecar Pipeline & Namespace Integrity Scan

We audited active Python environment variables, package search hierarchies, and potential import path collisions between standalone and embedded reasoning APIs in local workspaces. Result: Mapped import-latency causes, defined explicit adapter targets, and established safe namespace isolation guidelines with 'Degraded Sidecar Only' status.

Fluid Dynamics GTE Pedagogy Hypothesis

We evaluated the hypothesis that the General Transport Equation (GTE) is the universal pedagogical foundation for fluid dynamics, unifying Mass, Momentum, Energy, and Scalar transport via φ-substitution — sourced from expert LinkedIn academic discussion. Result: Gate REJECTED. While core mathematics is internally sound, the universality claim is invalid — GTE applies only to incompressible Newtonian flow. SPAR score 73/100, Omega 0.697 AMBER. Minor revision required.

TOE-TEST Foundational Runs (0001 ~ 0051)

The foundational Flamehaven-TOE experiment series that preceded the active EQA ledger (0052+): string-theory / topology physics, quantum-biology and protein spin-qubit studies, and the verification-methodology layers themselves. Each entry opens the verbatim source report in the Ledger Inspector (local-workspace paths sanitized; report content unedited). Ordered most-recent first.

Click any run above to open its verbatim report and provenance in the Ledger Inspector.