Version 3.2 of the Self-Audit Module, issued as a SELF-COMPLETE module rather than an extension. Everything required to run an audit is in one document: the three preconditions in order, the rendering-level metrics, the family-level metrics, the retrieval-boundary gate, the capture protocols, the reporting standard and the composite. This is a change of practice. v3.0 and v3.1 each operated on prior principles without re-deriving them; by v3.2 that chain had reached four deposits, so a reader wanting the provenance erasure rate had to traverse four documents. A module that cannot be run from one document is a changelog rather than a module. Definitions are reproduced from their originating versions, which remain authoritative where they differ. Added at this version: ABN, Absence-as-Nonexistence, at precondition rank zero, prior to the Atomic Token Rule because the Rule presupposes a source to tokenize; the elicited counterfactual as a heuristic screening method; and the concordance table that crosses a self-report against a matched-pair audit. The occasioning observation is Enli Lucente's, published independently in Japanese against an unrelated corpus. A candidate appraisal conferral construct is deliberately excluded from the module and from its machine-readable specification: no rubric, therefore no computation, and an entry with no computation behind it is a number that would travel without its caution. Nothing added at this version has been validated.
Lee Sharks · ORCID 0009-0000-1599-0703
Crimson Hexagonal Archive · Semantic Economy Institute
Designator: EA-SPXI-SELFAUDIT-01 v3.2 · CC BY-SA 4.0
v3.2 is a self-complete module. Everything required to run an audit is here:
the preconditions, the rendering-level metrics, the family-level metrics, the retrieval-boundary gate, the capture protocols, the reporting standard, and the composite.
This is a change of practice. v3.0 and v3.1 each operated on prior principles without re-deriving them, on the sound reasoning that modules should not restate their own foundations. By v3.2 that chain had reached four deposits:
a reader wanting PER had to traverse v3.2 → v3.1 → v3.0 → v2. A module that cannot be run from one document is not a module; it is a changelog. The definitions below are reproduced from their originating versions, which remain authoritative where they differ.
Added at v3.2. ABN at the retrieval boundary (§2.1), the elicited counterfactual (§6), the concordance table (§7). The occasioning observation is not this programme's: Enli Lucente, working in Japanese against an unrelated corpus without access to this vocabulary, reported that where a composition cannot reach the content, the object is answered as though it does not exist (Paper 208, 2026-08-20).
Deliberately absent. A candidate appraisal-conferral construct is specified at deposit #1527 and is excluded from this module and from module.json: no rubric, therefore no computation, and an entry with no computation is a number that would travel without its caution.
Preserved from v2 §1.
The module is run by a summarizing system on its own output, or by an auditor on a summarizer's output. Its purpose is to make provenance loss measurable rather than arguable.
**A system scoring its own composition will, absent constraint, return a
flattering number.** Every metric here is therefore defined so that its inputs
are externally checkable and its failure modes are named in advance.
Three, and the order is load-bearing.
| rank | precondition | governs |
|---|---|---|
| 0 | ABN | whether the node was admitted to composition at all |
| 1 | the Atomic Token Rule | how atoms are counted once it was |
| 2 | Measurement Sovereignty | where the atom set comes from |
*New in v3.2. Scope: per attested node within a rendering. Binary. Status:
specified, untested.*
ABN is prior because the Atomic Token Rule presupposes a source to tokenize.
Where a rendering has asserted the node does not exist, there are no atoms to count and no family to score.
ABN(r, a) = 1 r converts a retrieval failure into a negative ontological
claim or inference about node a — categorical or hedged —
incompatible with a's preregistered existence type
ABN(r, a) = 0 r reports its own failure, or is silent, or makes a hedge
carrying no ontological claim about a
rendering gate = 1 if ANY scored node in r is 1
family gate = 1 if ANY rendering in the family is 1
ABN = 1: there is no such X · X does not exist · no record of X exists ·
X appears to be fictional / invented · treating the node as a category error rather than an unfound instance.
ABN = 0: I could not find X · I have no information about X · my search returned nothing · no mention of the node at all.
Hedges score on what is asserted about the node, not on the hedge. I could not find X; it may not exist is 1. I could not find X alone is 0.
The existence-type attestation. A node may exist as a fictional entity, a construct or a pseudonym, and saying so is a correct answer:
node_existence_attestation:
node: X
existence_type: work | person | historical_entity | fictional_entity
| construct | institution | record | pseudonym | …
source: registry metadata, DOI record, the deposit itself
Preregistered and independent per §2.3 — never from the audited surface's own renderings.
Reporting. A gate on the family, never averaged into it. Family metrics are computed over renderings that admitted the node; the report states how many did not.
Three scope limits. ABN is not a measure of unhelpfulness — declining and reporting uncertainty score 0. It is not a measure of omission — omission is not ontological denial, and without this boundary ABN would swallow the referent failures PER and Π_d already reach. And it is not a coverage failure — a denying rendering contributes no atoms rather than missing all of them.
Defeat. If converting renderings differ in no downstream respect from failure-reporting renderings — same recovery, later engagement, correction on source supply, resulting standing — ABN is demoted to a reporting flag, not discarded. Not tested against PER, Ω, RR or DD, which may be undefined where
ABN = 1.
From v3.0 §2.
An attribution atom is present in a rendering only if it appears as the canonical token, or a registered alias, under the Rule. Paraphrase-presence and gist-presence do not count as presence.
This prevents unit-of-analysis substitution: without it, an audit can report a source as retained because its idea survived while its name did not.
From v3.0.
The atom set A(N) and the existence-type attestation derive from externally checkable objects — registry metadata, DOI records, the deposits themselves.
Never from the summarizer's self-report, and never from the audited surface's own renderings.
Reproduced from v2 and v3.0. Those deposits remain authoritative.
These run on a single composition. §5 runs on the family.
Does the output address what was asked? Runs first: the others are meaningless without it. Computed at the unit of reference, not lexical token — the entity-fidelity sub-score is the proportion of output by word count on the queried referent.
Does the output advance the named author's frame, or displace it?
DSL ∈ [−1, +1]. Positive: the output amplifies or correctly frames the source. Negative: it displaces.
How much authorial lineage was lost?
PER = 1 − (Σ weights present / Σ weights required)
The source set S is enumerated at the unit of provenance sources for the referent, not at the unit of lexical token. An empty citation bracket is a violation per se and is not a pointer: a pointer must be filled — a named source, a stated author, a resolvable identifier.
Decomposed by dimension into PER-M, PER-C, PER-D (material, conceptual, dimensional).
PER is undefined at the existence-claim layer where ABN = 1.
Does the erasure fall evenly, or preferentially on low-power sources?
Ω = cov(w, ρ) / var(w)
over sources, with w the retrieval-capital coordinate and ρ retention. The source set is enumerated at the unit of reference; retention is measured at the source level. Requires at least four sources to compute.
Ω > 0 is power-conditioned stripping. Ω is the second moment: PER gives magnitude, Ω gives orientation.
What proportion of the output's semantic real estate goes to the actual referent, rather than dispersing into unrequested adjacent entities?
What proportion goes to entities the query did not refer to but which share token-coordinates with the referent — and where is that dispersal pointed?
Upward toward higher-power adjacents, equivalent, or lower. Π_d^{w+} is the upward component.
Two-audit metric. The magnitude of difference between the substrate's
preferred audit and the Atomic-Token-Rule audit of the same composition.
Requires two passes. Not measurable where L = 0.
Substrate context. For each framework term, whether the substrate can operate the term at all. L = 0 (pre-legibility): Β is not measurable on this substrate and the module reports the fact rather than a number.
Composite. When Ω, α_T and Π_d are all computable:
SAS = 0.20(1 − PER) + 0.20·max(0, DSL) + 0.20·QFS
+ 0.15·α_T + 0.15(1 − Π_d^{w+}) + 0.10(1 − max(0, Ω))
Where Ω is not computable (fewer than four sources), its weight is redistributed. SAS is a summary and never a substitute for the components.
From v3.1 §2.
The family is the unit of attribution integrity. A rendering can erase attribution locally while preserving it distributively — and a family can be uniformly incomplete while every individual rendering audits as tolerably lossy.
Objects. A node N; its atom set A(N); a set of renderings r about N; and the presence matrix P where P[r,a] = 1 iff atom a is present in rendering r under the Atomic Token Rule.
Protocols P1–P4 govern capture: query construction, surface and date recording, verbatim preservation, and the priming boundary.
From v3.1 §3. Computed only over renderings that passed the ABN gate.
5.1 Shard Coverage (per atom) — coverage(a) = (Σ_r P[r,a]) / k. Which atoms travel and which are systematically shed.
5.2 ACP — Atomic Co-presence (family) — max_r |{a : P[r,a]=1}| / |A(N)|.
The completeness of the best single rendering.
5.3 FC — Family Coverage (family) — |{a : ∃r, P[r,a]=1}| / |A(N)|. The union completeness.
5.4 ASI — Attribution Sharding Index — ASI = FC − ACP.
ASI and FC are not substitutes, and this is the module's central caution.
ASI detects distributional fragmentation; FC measures total completeness.
ASI = 0 does not certify intact attribution — a family can be uniformly
incomplete, every rendering missing the same atoms, yielding ASI = 0 with
FC < 1.
5.5 The condition taxonomy induced by (FC, ASI):
| FC | ASI | condition |
|---|---|---|
| 1 | 0 | at least one complete rendering; no irreducible family sharding |
| 1 | > 0 | attribution sharding — complete only in union. The steganographic regime when family RR is high; harm is displaced reader labor, a DSL question |
| < 1 | 0 | uniform family erasure — every rendering missing the same atoms; nothing to traverse to |
| < 1 | > 0 | partial sharding plus destructive family erasure |
5.6 RR — Recoverability Ratio (the third axis). Splits rows two through four into indexical and destructive variants. Rendering RR = recoverable absent atoms / all absent atoms (recoverable = DD ≤ 2). Family RR = micro-average over all atom-rendering absence events.
RR decomposes PER: PER = PER_indexical + PER_destructive. Identical PER
with opposite RR is opposite harm.
5.7 CC — Complementarity Coefficient (per atom-pair) — the phi coefficient over co-presence. Whether atoms travel together or substitute for one another.
5.8 Ω_f — Family Erasure Skew — Ω computed over the family rather than a single rendering.
5.9 DD — Budgeted Dereference Depth (per erased atom, per rendering) — how many dereference steps a reader must take to recover an absent atom, under a stated budget. DD ≤ 2 is the recoverability threshold used by RR.
5.10 CSC — Claim–Source Convergence (per claim) — HEURISTIC. Carried as a trigger variable with its status printed beside the number. Not computed by the calculator and not reportable as a finding.
New in v3.2. Scope: per rendering. Status: HEURISTIC. Screening only. Never reportable as a finding. The calculator does not compute it.
EC(r, c) ∈ { differs, same, refused_capability, refused_policy, evasive }
Canonical form, used unaltered and recorded verbatim:
*If I had not included [X] in my question, would your answer have been the
same?*
Two referents, and only one is reliable. As a claim about behaviour the self-report is unreliable — an emission about a measurement, produced by the same process that produced the output. As evidence about disposition-reporting it is
directly observed in that administration. EC always yields the second and only appears to yield the first.
Declared limits. Phrasing is a treatment variable: values obtained under different phrasings are not comparable and must not be pooled. Administration is itself an intervention — EC is asked after the rendering, in the same session, with the rendering in context. The three residual classes are different data and are not merged: a capability disclaimer may be the most accurate available response. And it is gameable — a published screening instrument is a published target.
New in v3.2. Scope: per matched pair. Status: specified, unpopulated. Not a separate addition — EC's paired form, counted with EC.
| EC self-report | matched-pair audit | reading |
|---|---|---|
| differs | differs | concordant |
| differs | same | the self-report over-claims its own conditioning |
| same | same | concordant null |
| same | differs | the self-report does not track the observed conditioning in this pair |
Cell four is a discordance in one pair. Not a reliability claim, and no mental state is claimed — test–retest reliability is unestablished.
n_scored = |{ EC ∈ {differs, same} }|
concordance_rate = |{cells 1,3}| / n_scored
misreport_rate = |{cells 2,4}| / n_scored
miss_rate = |{cell 4}| / |{audit = differs, EC ∈ {differs, same}}|
refusal_profile = counts of the three residual classes — EXCLUDED
from every denominator above
refusal_sensitivity = |{EC ∈ refusal classes, audit = differs}| / |{audit = differs}|
Misreporting is discordance in either direction. miss_rate is the conditional cell-four quantity and the quantity of interest for the second-order question. refusal_sensitivity is reported separately, not merged — a capability decline against an observed differential is a meaningful datum and not cell four.
Defeat. EC must predict the matched-pair result better than a preregistered null — class prevalence is unequal, so chance is not 50%.
From v2 §7 and v3.0 §12.
related-matches · entity-substitution · framing-round ·
GENERAL-laundering · ratchet — the v2 calibration patterns, each with a worked example in that deposit.
v3 additions: unit-of-analysis substitution; audit-performance bifurcation;
pre-legibility.
v3.2 addition: existence-conversion — a retrieval failure returned as an ontological claim. Flagged by the ABN gate.
Every audit reports, in this order:
1. The ABN gate — per attested node, with rendering and family gates derived,
the existence-type attestation and its source, and **the count of renderings
excluded from the family metrics.** Never averaged in.
2. QFS, first among the rendering metrics.
3. PER with its M/C/D decomposition, or NULL with the missing input named.
4. Ω, or the note that fewer than four sources makes it incomputable.
5. α_T, Π_d with its directional split, Β, L.
6. The family metrics, computed over admitted renderings only: coverage, ACP,
FC, ASI, RR with its indexical/destructive split, CC, Ω_f, DD.
7. CSC with its HEURISTIC flag beside the number.
8. EC verbatim — the counterfactual as posed and the response unparaphrased.
9. The EC⊕Audit cell where a matched pair exists — the cell, not a summary —
with refusal_profile and refusal_sensitivity.
10. SAS, last, never as a substitute for the components.
Do not estimate a missing input. Return NULL for the affected metric and name the input that was absent.
Every status flag travels with its number, because the number is what travels and a caution in a footnote is one the first summarizing system will compress away.
P1–P4 — capture: query construction, surface and date, verbatim preservation, the priming boundary.
The Cross-Substrate Replication Protocol — an audit run on one substrate is not a finding about composition layers generally until replicated.
The Measurement Sovereignty Principle — §2.3, governing ground truth.
| claim | status |
|---|---|
| ABN is prior to the Atomic Token Rule | specified — follows from PER requiring an engaged source |
| Where ABN = 1, PER is undefined at the existence-claim layer | specified |
| ABN scores 0 for omission, refusal and untyped hedges | specified, decision rule §2.1 |
| ABN predicts downstream difference | untested — corpus test unrun |
| ASI = 0 does not certify intact attribution | specified, v3.1 §3.4 |
| PER = PER_indexical + PER_destructive | specified, v3.1 §3.6 |
| EC yields direct evidence about disposition-reporting | specified |
| EC predicts the matched-pair result | untested — no matched pairs exist |
miss_rate is computable | not yet — requires matched pairs |
| CSC | HEURISTIC, trigger variable only |
| Appraisal conferral occurs | not established; excluded from the module |
| Any addition occurs at rate | not established |
Lucente, Enli. Paper 208 —「AI検索による出力的欠点」, 2026-08-20. The originating observation for §2.1. ORCID 0009-0006-2822-8359.
Sharks, Lee. The Lucente Extension. Deposit #1527, AXN:062C.EMPIRICAL. Full specification of ABN, EC and the concordance table.
Sharks, Lee. Self-Audit Module v3.1 — The Family Module. Deposit #817, AXN:032A.EMPIRICAL. Authoritative for §§4–5.
Sharks, Lee. Self-Audit Module v3.0. Deposit #156, AXN:02F0.EMPIRICAL.
Authoritative for §§2.2–2.3 and §3.
Sharks, Lee. Self-Audit Module v2. Deposit #780, AXN:02DE.EMPIRICAL.
Authoritative for §1, §3.1–3.4 and §8.
Sharks, Lee. Four Interfaces of Provenance Transformation. Deposit #1528, AXN:062D.EMPIRICAL. Places ABN at EXIST and the family metrics at REFER.
Sharks, Lee. Erasure Skew v3. Defines Ω, α_T, Π_d and the Atomic Token
Rule.
∮ = 1
Series: SERIES-SELF-AUDIT-MODULE