Engineering Note 17: Determinant-Ratio Criterion as a Data Suitability Gate

Abstract

Abstract This note specifies a data suitability gate — a lightweight boundary criterion positioned between the output of probabilistic language models and the input of deterministic symbolic reasoning systems. The gate answers a single structural question before any inference is attempted: is this data suitable for the intended task, and if so, to what degree? The criterion is negative-first: it does not assert fit; it structurally excludes non-fit. Positive admission is graded, not proven. Note that: In terms of this paper domain (if it recognized as scope definitions, terms and explanations) is equivalent corpora, becasuse domain always grounds on corpora/norm sources 1. The Core Principle A deterministic reasoning system — one that operates over a structured index of knowledge and produces verifiable conclusions — cannot admit arbitrary input. Input that is structurally degenerate (rank-deficient, informationally empty) or structurally foreign (inconsistent with the domain's reference form) will produce wrong answers without signalling that anything is wrong. The gate prevents silent failure at the boundary. The gate operates by comparing the covariance structure of the candidate data against an external reference form derived from the target domain or query class. The comparison yields a single scalar ratio. Both tails of this ratio are refusal signals — for opposite reasons: Condition Structural meaning Ratio collapses to zero Rank-deficient data — no independent structure, informationally empty Ratio blows up Data structure foreign to the reference — not from this domain Ratio within bounded corridor Admissible; degree of fit is the value of the ratio The admissible region is a bounded corridor. Both walls are set by the reference form, not by free parameters. The gate excises both tails and keeps what could not be structurally excluded. 2. Two Questions, One Measure The same criterion answers two distinct questions about the same data, depending on what the reference form is set to: Fitness for domain/corpora synthesis. Does this data structurally belong to the domain being built? If admitted, it may extend the domain's knowledge base — adding new facts, definitions, or constraints. The reference is the existing domain structure. Fitness for answering a query. Does this data — or this query — structurally land on the assembled domain? The reference is the query class combined with the information structure of the domain as currently assembled. The two questions are two instances of the same test. The gate runs both; their combined result determines whether the data is admitted, and at which layer of the domain it should be integrated. 3. Two Levels on One Basis A knowledge domain is not a separate structure above the data. It is a layer of constraints — definitions and enforcements — applied on top of the same underlying index of Subject–Predicate–Object triples. The gate therefore operates on one basis at two levels: Raw index level — what the domain can structurally distinguish in principle. Constrained level — what the domain distinguishes under its current set of applied rules. Both levels yield a covariance form over the same index, so they are directly comparable. The gap between the two ratios localises the deficiency: Data passes at the raw level but fails at the constrained level → the index contains the relevant facts, but the domain's rules do not yet cover this case. The constraint layer needs to be extended, not the underlying data. Data fails already at the raw level → the facts are absent from the index itself. No rule extension will help; the domain simply does not cover this topic. This two-level diagnostic replaces a binary pass/fail with a precise instruction: what to fix, and at which layer. 4. The Honesty of the Criterion The gate makes an asymmetric claim — one that is worth stating explicitly: The system is exact in what it rejects, and calibrated — not certain — in what it admits. A ratio collapse or explosion is a structural proof of non-belonging. Refusal is deterministic. Admission, by contrast, is not a proof of fit — it is a measured failure to exclude. The degree of fit (the ratio value within the corridor) is a confidence weight on the admitted data, not a certification. This asymmetry is the boundary that separates a deterministic reasoning system from a probabilistic one: refusal is a fact; admission is a graded hypothesis. 5. Positioning in the Architecture The gate sits at the ingress boundary of the deterministic layer — after language model output is produced, before it enters the structured reasoning graph. It is a pure linear-algebraic check: rank and volume of the candidate covariance against the reference form. It does not re-run inference; it does not require the reasoning engine to process degenerate input speculatively. The gate is the structural counterpart — on the ingress side — of the constrained-decoding mechanisms (grammar masks, schema validators) that vendors attach to language model outputs on the egress side. Both are instances of the same pattern: when formal guarantees are required, linear algebra and formal structure are applied at the boundary; the probabilistic model is not trusted to self-regulate.