# NDT Axiom and Theorem Audit

**Status:** Unratified reviewer finding for the v52 RC4 candidate. The presentation uses four named explanatory axioms; local plurality is classified as a scope-derived consequence; five nonredundant headline theorems are classified below. Nothing in this audit is an authorial ratification.

## Executive result

The earlier checker tested four candidates across sixteen subsets; it did not screen sixteen candidate claims.

The current presentation uses four explanatory headings with nine separately inspectable computational components. The declared Horn model finds all four necessary for its full target profile, but that result is relative to the authored headings, targets, and rules; it does not establish a uniquely natural semantic grain. **Local plurality is not an axiom:** because NDT is descriptive and does not define one objectively correct verdict, its scope must permit multiple locally valid represented perspectives. Polyphony adds comparison-readiness and conflict conditions.

This result is target-relative. Evaluative Grounding states the broader prerequisite and includes explicit, attributed, encoded, and derived realization routes. CET proper names only the constitutively encoded route; its existence and non-negligibility are separate empirical commitments. Moving a component or consequence between levels can leave the heading count unchanged while altering the theory, so the component record remains visible.

## Candidate presentation: four named explanatory axioms

| Axiom | Candidate audit status | Natural-grain commitment | Why it remains independent |
|---|---|---|---|
| Actual Framing | The axiom identifies what is relevant to this judgment. Its interpretive-frame test and producing-route test do distinct computational work and are shown separately. | NDT explains a judgment through the interpretation active when someone makes it and through the represented elements that actually helped form it—not through unrepresented facts or merely available alternatives. | An availability classifier that credits objective or merely active features even when they were not represented or did not help produce the judgment. |
| Evaluative Grounding | The broad prerequisite is operative evaluative structure. Explicit, attributed, and encoded evaluation are alternative realization routes; encoded evaluation is not an additional prerequisite. | A normative judgment requires some operative distinction in what matters. That evaluative organization may be explicit, attributed, encoded in a representation’s functional role, or derived from those sources. Constitutive evaluativity names the encoded realization; it is not another name for this broader prerequisite. | A pure-syntax engine that derives prescriptions from symbols with no operative evaluative ordering. |
| Normative Detachment | The judgment-forming transformation and live-support requirement are fixed; the algorithms, timing, uncertainty, errors, and implementation may vary. | Normative detachment occurs when a framed, evaluatively structured process forms a prescription, permission, prohibition, praise, blame, or other appraisal through a live connected support path. It means that the judgment is formed; it does not mean that the person acts on it. | A direct classifier that attaches a normative label without using evaluation to form that judgment. |
| Relational Moral Type | The relationship’s broad role is fixed. Its exact components, thresholds, measurement, and psychological realization remain partly conceptually and empirically open. | A normative judgment is specifically moral when a qualifying represented relationship between a subject and an object helps organize the same process that produces the judgment. | A content classifier that fixes moral type by harm, cooperation, or another topic signature without qualifying relationship provenance. |

## Mechanized basis results

The checker uses complete forward consequence for the declared Horn rules and constructs the least model under each omitted axiom. If a target is absent from that least model, the model is an explicit countermodel to entailment.

| Target profile | Subsets checked | Unique minimum | Minimum basis |
|---|---:|---:|---|
| Results about when a judgment is moral | 16 | yes | Actual Framing; Evaluative Grounding; Relational Moral Type |
| Results about how normative judgments form | 16 | yes | Actual Framing; Evaluative Grounding; Normative Detachment |
| All selected results except Polyphony | 16 | yes | Actual Framing; Evaluative Grounding; Normative Detachment; Relational Moral Type |
| All selected NDT results | 16 | yes | Actual Framing; Evaluative Grounding; Normative Detachment; Relational Moral Type |

## Derived theorems

A headline theorem is neither stipulated scope, a definition, a model-wide adequacy constraint, a replaceable module, nor an empirical hypothesis. It states a nontrivial consequence of at least one named explanatory axiom together with explicitly named definitions, scope commitments, or registered witnesses.

**Proof discipline:** Dependency reach is never proof. Each theorem must report its proof mode: claim-level Horn consequence, constructive witness, formal guarantee, or a pending negation-capable certificate.

| Theorem | Statement | Kind | Minimum axiom basis | Other named support | Proof status |
|---|---|---|---|---|---|
| Qualifying Moral Provenance | If a normative output is morally typed, a qualifying represented moral relationship must actually contribute to a sufficient live process producing that token; availability or thematic relevance alone cannot do the work. | strict theorem | Actual Framing + Relational Moral Type | moral-token definition | Machine-checked in the claim-level consequence model; its quantified realization is fixed by the moral-token definition and the live-route clauses. |
| Moral Subset | Because NDT admits normative tokens without qualifying moral-relationship provenance, while a moral token requires that provenance, moral cognition is a proper subset of normative cognition. | scope-dependent theorem | Actual Framing + Relational Moral Type | broad normative-domain scope; moral-token definition; agentless normative construction (C5) | The inclusion is machine-checked in the claim-level model; properness also uses the declared nonmoral normative domain and its registered witness. |
| Content–Provenance Nonidentity | Two tokens may have identical content while one is moral and the other nonmoral because different actually contributing routes produced them. Content therefore does not determine moral type. | constructive theorem | Actual Framing + Relational Moral Type | moral-token definition; same-content moral/nonmoral construction (C1); same-content Theory Trace | The claim-level consequence is machine-checked and the possibility claim has a registered same-content moral/nonmoral witness. |
| Polyphony Is Possible | Someone can sustain two locally coherent judgments about one case that remain comparison-ready through the appropriate bridge and directly conflict. NDT calls this bridged conflict Polyphony. | constructive theorem |  | SCOPE_DESCRIPTIVE_PLURALITY; Polyphony definition; indexed-Polyphony construction (C9) | The registered indexed construction witnesses a satisfiable pair of locally coherent, aligned, conflicting outputs. Descriptive scope alone does not guarantee that every context supplies a bridge or conflict. |
| Polyphony Subset | Every polyphonic pair is plural, but not every plural pair is polyphonic. Without the appropriate surviving comparison bridge, multiple outputs remain unaligned plurality and do not directly conflict. | strict classification theorem |  | SCOPE_DESCRIPTIVE_PLURALITY; Polyphony definition; unaligned-plurality construction (C10) | Subset inclusion is fixed by the Polyphony definition; the registered unaligned-plurality construction witnesses a plural pair outside the Polyphony class. |

### Why plurality is scope-derived and Polyphony is a theorem

Local plurality follows from NDT's descriptive, non-verdict-setting scope rather than adding a fifth axiom. Polyphony Is Possible is a constructive theorem supported by registered construction C9. Polyphony Subset is the analytic classification result: Polyphony is the bridged-conflict subset of plurality, and C10 witnesses unaligned plurality outside it.

### Immediate corollaries

These direct restatements or one-step consequences are useful, but they are not displayed as coequal headline theorem nodes.

| Corollary | Axiom basis | Claim-level check |
|---|---|---|
| Frame-indexed token identity | Actual Framing · interpretive-frame component | machine-checked |
| Evaluatively empty input barrier | Evaluative Grounding · evaluative-prerequisite component | machine-checked |
| Encoded evaluation is a genuine possible realization | Evaluative Grounding · realization-routes component | machine-checked |
| Typed normative detachment | Evaluative Grounding + Normative Detachment | machine-checked |
| Actual token provenance | Actual Framing · producing-route component | machine-checked |
| Moral-relationship constitutivity | Perceived Moral Relationship | machine-checked |
| Behavioral guidance presupposes an agent-capable subject | Behavioral-norm definition; not specifically moral | not in the current Horn target set |
| Noncontributing structure cannot classify a token | Actual Framing · producing-route component | not in the current Horn target set |
| A qualifying relationship grounds the guidance it actually organizes | Qualifying Moral Provenance + Normative Detachment | not in the current Horn target set |
| No mandatory global verdict | Descriptive scope and the absence of an automatic global verdict | machine-checked |

### Technical guarantees kept below the headline layer

Provenance Closure and Anchored Survival remain formal guarantees in the technical layer. Skeptical Challenge belongs to a replaceable defeat module, and Conditional Contribution Convergence depends on a chosen contribution implementation. They should not be promoted to coequal core-theorem cards without preserving those qualifications.

## What the 2026 reconstruction changed

- **Operative Evaluative Organization** is the realization-neutral prerequisite for every normative detachment. **Encoded Evaluative Realization** names CET proper: the possible constitutively encoded route within that broader prerequisite. Explicit, attributed, and derived evaluation may satisfy the broader prerequisite without thereby instantiating CET proper; the encoded route's existence and non-negligibility remain separate empirical commitments.
- **Detachment** repeatedly appears as the connection from operative evaluation to guidance or appraisal. The 2026 reconstruction makes the output types, bridge principles, connected support, anchoring, and route survival explicit.
- **Descriptive plurality** continues the earlier corpus's independent, unmerged normative voices and its rejection of a mandatory global verdict. It is presented as a consequence of descriptive scope, not an additional axiom. The current reconstruction sharply distinguishes plurality from Polyphony by adding comparison-readiness and surviving-bridge conditions.

## Claim-layer screening

| Claim | Source classification | Audit disposition | Rationale |
|---|---|---|---|
| Whether a relationship actually contributed | claim-derived commitment | folded into axiom | The producing-route component of Actual Framing expresses token-level actual provenance. |
| Structural models of actual causation | claim-derived commitment | replaceable formalization | The fixed-scheme and minimal-sufficiency machinery operationalizes Actual Provenance; the specification explicitly permits replacement. |
| Association-based moral prediction | admitted case or module | admitted case or module | A possible influence on salience or prediction, not a constitutive requirement of NDT. |
| Moral cognition is evaluative in its makeup | claim-derived commitment | folded into axiom | CET proper is the constitutively encoded realization inside Evaluative Grounding; it is not the broader prerequisite and does not assert prevalence. |
| Complaint-sensitive guidance | admitted case or module | admitted case or module | One permitted guide family rather than a condition on every NDT model. |
| Cautious challenge resolution | replaceable formalization | replaceable formalization | Grounded skepticism is the reference implementation, not universal cognitive psychology. |
| Goal-and-means reasoning | admitted case or module | admitted case or module | The explicit goal-and-means route is one realization; the broader Detachment thesis is recovered from the formal layer. |
| Response patterns do not define a domain | claim-derived commitment | conceptual corollary pending formalization | The provenance-first contrast is motivated by Actual Provenance and Moral Molecule, but the current formal graph does not encode the external domain-typing alternatives needed for a mechanized theorem. |
| No ought from evaluatively empty inputs | scope boundary | derived theorem | It is the direct consequence that gives the broader Operative Evaluative Organization prerequisite empirical and conceptual bite. |
| What supplies motivation | replaceable formalization | replaceable formalization | Explicit, attributed, encoded, and derived entry routes realize evaluation without adding another global commitment. |
| Generation–status separation | scope boundary | scope or definition | Separating descriptive generation from truth or endorsement fixes project scope. |
| Requirements that outcomes cannot outweigh | replaceable formalization | module level postulate | Noncompensable requirements are supported by a replaceable decision-model module, not required for every normative token. |
| Representing a harmful dyad | admitted case or module | admitted case or module | A harm representation is an admitted case and does not constitute moral type. |
| Institution-based requirements | admitted case or module | admitted case or module | Institutional requirements are one possible source family. |
| Content does not settle moral type | claim-derived commitment | derived theorem | Content-provenance nonidentity follows from Actual Provenance plus Moral Molecule. |
| Four relational models do not exhaust moral qualification | claim-derived commitment | conceptual corollary pending formalization | The open functional criterion motivates non-exhaustion, but the current graph lacks predicates and paired witnesses for the four-model comparison. |
| Cooperation does not constitute moral type | claim-derived commitment | conceptual corollary pending formalization | The theory motivates the claim, but the graph does not yet represent cooperation signatures strongly enough to prove a necessity-and-sufficiency contrast. |
| Harm templates do not constitute morality | claim-derived commitment | conceptual corollary pending formalization | The theory motivates the claim, but the graph does not yet represent dyadic-harm signatures strongly enough to prove a necessity-and-sufficiency contrast. |
| Outcome-maximizing guidance | admitted case or module | admitted case or module | Outcome maximization is one permitted guide family. |
| Overridden duties that still matter | replaceable formalization | module level postulate | Residue is a substantive but local feature of the requirement/override module. |
| Case-by-case guidance | claim-derived commitment | module level postulate | Case-by-case model formation is permitted, but global NDT does not require every judgment to be particularistic. |
| Many-voiced normative cognition | claim-derived commitment | derived theorem | Descriptive scope permits multiple locally valid represented perspectives. C9 demonstrates that bridged conflict among locally coherent outputs is possible, while the definitions and C10 establish that Polyphony is the bridged-conflict subset of plurality. |
| What makes a represented relationship moral | claim-derived commitment | folded into axiom | This is the Moral Molecule's constitutive relationship criterion. |
| Relationship-grounded guidance | claim-derived commitment | immediate corollary | This is the grounding face of Qualifying Moral Provenance when the relationship organizes evaluation on an actual detachment route; it is not a separate headline theorem. |
| Bargaining-based decision models | admitted case or module | admitted case or module | Bargaining is one optional guide family. |
| Rule-based guidance | replaceable formalization | replaceable formalization | Rule detachment is one implementation family within the broader Detachment thesis. |
| Learning other people's moral weights | admitted case or module | admitted case or module | A learning model can affect inputs without defining the theory's global architecture. |

## Proposition Registry assumption screening

| ID | Assumption | Audit disposition | Rationale |
|---|---|---|---|
| A1 | Typed representations and model elements are distinguishable | meta constraint | Typed vocabulary and noncircular identity belong to Formal Adequacy and definitions. |
| A2 | Every moral token contains a represented subject and object | folded into axiom | A constitutive component of Moral Molecule. |
| A3 | Representationally agentless appraisal can be normative but not moral | definition level consequence | Moral exclusion follows directly from Moral Molecule's subject-object definition, while the agent-capacity presupposition belongs to behavioral norms generally rather than morality specifically. |
| A4 | Actual contribution uses a fixed constitutively adequate profile scheme | replaceable formalization | An application discipline for Actual Provenance, not the provenance commitment itself. |
| A5 | Methodological admissibility and constitutive adequacy are distinct | meta constraint | An epistemic distinction governing application and unresolvedness. |
| A6 | Control indicators and aggregation are fixed before the output | meta constraint | An anti-post-hoc identification requirement. |
| A7 | Only independently admitted challenges enter skeptical defeat | replaceable formalization | Load-bearing for the grounded baseline, which the specification calls replaceable. |
| A8 | Alignment bridges are canonical for conflict and polyphony | scope or definition | This fixes the defined classification condition for Polyphony; it is not an additional global axiom and does not follow from descriptive plurality alone. |
| A9 | Relation qualifiers do not directly confer moral type | derived theorem | Follows from Moral Molecule plus Actual Provenance. |
| A10 | Unrestricted cross-scheme invariance is not guaranteed | meta constraint | A model-class and epistemic boundary on Actual Provenance implementations. |
| A11 | Empirical antecedents are identified independently of outcomes | meta constraint | General empirical coherence rather than an NDT-specific axiom. |

## Formal and definition scan

The audit accounted for 592 formal nodes, 1896 dependency links, 118 architecture nodes, and 592 definition records. Of the formal symbols, 279 are defined by clauses and 313 are terminal vocabulary.

Predicate availability is vocabulary, not an assertion that the predicate holds. The scan therefore treated terminal symbols as possible inputs, parameters, sorts, operators, or structural relations and inspected the constitutive clauses that use them. Likewise, reachability in the dependency graph records relevance or use, not logical proof.

The formal scan recovers nine component regions organized under four explanatory headings: interpretive framing and producing-route provenance; the broad evaluative prerequisite and its realization routes, including CET proper as the encoded route; working-model formation and supported output; represented relationship, relationship qualification, and same-path moral classification. Local plurality is classified under descriptive scope. Polyphony requires the plurality consequence plus its explicit comparison, bridge, and conflict conditions. Defeat semantics, fallback, override, residue, guide families, measurement functions, thresholds, and cross-scheme identification remain implementations, local modules, parameters, or epistemic constraints.

## Limits

- The check is complete for the explicit positive Horn rule model. The candidate presentation fixes the audit's natural-grain axioms and defining targets for this check; it does not constitute authorial ratification.
- The audit establishes logical independence and target-relative necessity, not empirical truth.
- Dependency reach in the 1896-link current formal graph is not a proof relation and is not used as one here.
- Agent-capable subjects are a general consequence of behavioral-norm grammar and part of the Moral Molecule definition, not an independent moral theorem. Noncontributing structure is an immediate consequence of Actual Provenance, and relationship grounding is folded into Qualifying Moral Provenance.
- Polyphony's classification condition is analytic; possibility is supported separately by registered construction C9 and is not guaranteed for every context by descriptive scope alone.
- Formal predicates and free parameters are not axioms merely because they are primitive vocabulary; a universally or constitutively asserted relation is required.
- A later typed first-order or proof-assistant formalization could test quantifier-level consequences beyond this claim-level Horn abstraction.

## Candidate presentation record

The unratified v52 RC4 explanatory presentation uses four headings and nine separately traceable components. **Local Plurality** names a consequence of NDT's descriptive, non-verdict-setting scope rather than a fifth axiom. Polyphony is recorded through two derived results: registered construction C9 shows that bridged conflict among locally coherent outputs is possible, while Polyphony Subset states that Polyphony is the bridged-conflict subset of plurality and C10 witnesses unaligned plurality outside it. This reviewer classification remains pending Bree Beal's adjudication.