General Molecule-Graph Validity - integer-exact valence/connectivity + energy penalty (no AI)

What it is

General, integer-exact CHEMICAL VALIDITY over an in-memory atom-bond GRAPH { atoms:[{element}], bonds:[{a,b,order}], charges?, sites? } (0-indexed atoms; bond order in 1, 1.5, 2, 3). Every atom's incident bond orders are summed in half-bond integer units, formal charge applied, and any atom whose valence is not allowed by the cited standard-valence table (C=4, N=3, O=2, H=1, S=2/4/6, P=3/5, halogens=1, B=3) is flagged; a single connected graph is required. It also emits the INTEGER ENERGY PENALTY (flagged atoms + 1 if disconnected) that is the validity term of the molecular-design sampler's energy. NO learned model and NO AI - every rule is cited standard chemistry, exact integer arithmetic, bit-reproducible. HONEST: "valid" means WELL-FORMED under the octet/valence model, NOT that the molecule is real, stable, or synthesizable. No claim is made that the geometric substrate is chemically special (it was benchmarked information-equivalent to Weisfeiler-Leman).

Honest scope

Authorities cited

• Standard main-group valences: N. N. Greenwood and A. Earnshaw, "Chemistry of the Elements", 2nd ed., Butterworth-Heinemann, 1997.
• Octet rule and formal charge: any general chemistry text (e.g. Atkins & de Paula, "Physical Chemistry"; IUPAC Nomenclature of Inorganic Chemistry, 2005 Recommendations).
• Graph connectivity: single connected component via depth-first traversal (standard graph algorithm).
• Validity as a deterministic post-hoc valence/connectivity check is standard in molecular-generation evaluation; this brick provides that check (and its integer energy penalty) as a verifiable, no-AI referent.