0030: Bounded numeric advice

Model authors benefit from local contradictions that ordinary interval comparison does not find, including fractional bounds with no integer and intervals with no multiple of a positive step. Provide an explicitly selected assessment, using the effective Full data descriptions established by ADR 0020: Owned effective views and nearest origins and ADR 0024: Effective alternatives and nullable characteristics. Numeric constraints follow RFC 9880 Appendix C.1.

esdieff.expanded.numeric/1 contains the unchanged Initial eight areas and advisory-numeric-three/1. Its three Warning/Advice classes are an integer interval gap, a sole numeric const excluded by each applicable bound, and a positive-step interval gap. These are local sufficient contradictions, without a general satisfiability, restrictive-refinement or sample-admission conclusion. Full keeps its fixed model obligations and existing advisory area; it does not implicitly request these new classes.

Proofs require final ordinary meaning and the applicable Full role. An established absent type permits the numeric const comparison only. A malformed or unavailable type is not absence. Interval proofs require established integer/number type as appropriate and null exclusion, supplied by nullable false or the independently known nonnull root kind of the sole ordinary const. Unavailable const magnitude does not erase an established root kind. Documentary default supplies no guard. Donor interpretation, unsupported qualities and unestablished structural meanings cannot be inferred from source JSON kinds or spelling. Derived Choice alternatives are checked separately; no union proof is added. The numeric advice contract states all applicability and support boundaries.

Evaluate every surviving const bound independently. Select the strongest known lower and upper bounds for interval work, with exclusion winning exact ties. A bound with established restrictive meaning but unavailable magnitude leaves the affected work undetermined while a contradiction using independent known bounds can survive. Unknown denotation cannot be presumed restrictive.

Use borrowed normalized decimals and bounded virtual long division, without floating point, a large-integer dependency, generated public number tokens or exponent-sized storage. Divide each endpoint by the positive lattice step, round the lower quotient upwards and upper quotient downwards, then adjust integral exclusive endpoints by one. No lattice value exists when the lower integer index exceeds the upper. For integer type with rational decimal step p/q in lowest terms, use the common integer lattice pZ; finite coefficient factor removal cancels powers of two and five.

Keep class outcomes independent: an unavailable positive step can leave its attempt unfinished while a supported integer interval contradiction remains a warning. The one numeric area’s status is undetermined until every applicable class is completed; absence of a warning supplies no satisfiability conclusion.

Virtual numerator and denominator lengths are at most 1024 digits; adjusted quotients have at most 1025 digits. Factor storage has at most 513 digits. A magnitude-first shortcut handles a quotient smaller than one before virtual-width admission. Successful factor removals are bounded by the finite coefficient, without a loop counting to the exponent. Capability limits leave work undetermined and never establish a gap.

All traversal, comparisons, digit scans, carry/borrow, factor trials, buffer acquisition and finding growth debit the original remaining operation and numeric counters before work or allocation. Sequential classes and descriptions share those counters. No refill, refund or allowance increase is introduced. Existing mandatory report owners contain the added area and aggregates with zero additional numeric reserve. Optional conditions retain at most four original operand identities, their final effective coordinates, nearest authored contributions and consumer origin. Absent type contributes no invented argument or location. Numeric human fallback destroys the first result before constructing its replacement; retained model and finding owners remain accounted for.

Considered Options

A general constraint solver would expand the public claim and the supported language considerably. Reusing supplied-candidate divisibility cannot establish interval existence. Floating point would lose exact endpoints and decimal steps. Expanding powers into strings would make accepted exponents select unbounded allocation. Per-class budgets or a larger report reserve would conceal failures of the original shared owner contract. Treating every familiar quality as harmless would miss its role, interpretation and structural premises.