A single GEM-like RESOLVER that combines three verifiable bricks into one discrete-graph molecule generator with NO learned model and NO AI.
A single GEM-like RESOLVER that combines three verifiable bricks into one discrete-graph molecule generator with NO learned model and NO AI. From a random NOISE molecular-graph state it runs a detailed-balance Metropolis-Hastings sampler (brick 3) whose energy is composed from a deterministic chemical VALIDITY check (brick 1), a cited Hansch-Leo 1979 logP target (brick 3), and an optional DEFINED geometric embedding distance (brick 2). It emits valid candidate molecules, each carrying its validity report, logP/property, geometric diagnostics, and a brick-2 GEODESIC interpolation between the top two candidates. It reports TWO honest measurements, each in its own vocabulary: (a) SAMPLER-CORRECTNESS (the exact detailed-balance residual of the transition kernel over an enumerable space, banded DETBAL_IDENTICAL through DETBAL_VIOLATED), and (b) PER-CANDIDATE validity/property (INTEGER_AND_TABLE_EXACT: integer validity + cited logP arithmetic). GeoNum trust is explicitly NOT tracked - no kernel arithmetic runs here. Both gem-analog and diffusion-analog modes are exposed. HONEST + LOAD-BEARING: generation PROPOSES, the built-in verifier VALIDATES, and the sampler correctness is PROVABLE - a verifiable REFERENT for the kind of job energy-based / diffusion generators do, WITHOUT any learned model. It is BOUNDED to a benzene-scaffold substituent space. The embedding is a defined geometric embedding; an alternative geometric embedding was built and benchmarked and is information-equivalent to standard graph/shape methods (no chemical advantage), so this uses the standard embedding. Geometric distance is NOT chemical similarity (the open, unproven research question), and NO "beats/matches diffusion" claim is made (that would need a matched-frame benchmark not run here). EXACT/PRECISE describe the COMPUTATION, never chemical truth or synthesizability.
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