{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp09_archetype_breadth150_20260804","cell_id":"preimage_set_characterization__accounting_auditing","arm":"BREADTH_PROBE_ONE_SHOT","candidate_id":"preimage_set_characterization__accounting_auditing__P1","proposal_index":1,"version":0,"title":"Zero-Residual Configuration Audit for Bank Reconciliations","problem":"A completed monthly bank reconciliation reports a zero difference, and reviewers treat that output as evidence that the ledger and bank activity have one uniquely correct transaction-level explanation. Yet distinct configurations—such as two offsetting amount errors, an omission paired with an unsupported adjustment, duplicate postings on opposite sides, or compensating cutoff errors—can produce the same zero residual. The independently recognizable problem is false assurance from a balanced reconciliation whose many-to-one aggregation hides materially different underlying states.","actors":["Bank-reconciliation preparer","Controller or accounting manager","Internal or external audit lead","Audit analyst","Owner of the cash-disbursement and receipt controls"],"observable_state":"For a specified bank account and accounting period, the approved reconciliation has a residual of zero or falls within the approved tolerance, while the review artifact does not identify the complete bounded set of transaction and adjustment configurations that would also yield that result. Manual adjustments, ambiguous matches, or cutoff items may be present even though the displayed output is identical.","consequence":"Reviewers may close the reconciliation without examining offsetting discrepancies, allowing an unsupported adjustment, posting error, duplicate, omission, or control failure compatible with the zero output to remain unresolved. Preimage membership alone would not establish that any such configuration actually occurred.","affected_objective":"Reliable audit assurance over cash completeness, accuracy, cutoff, and the operating effectiveness of the reconciliation control.","intervention":"Freeze and version the reconciliation mapping, including matching rules, sign conventions, cutoff treatment, approved adjustments, and tolerance. Define the target output as a zero residual or the exact approved tolerance band. Bound the input domain to the account, period, source transactions, ledger entries, reconciling items, and finite discrepancy states under review. Write a reproducible membership predicate: a candidate transaction-level configuration belongs only if applying the frozen mapping produces the target residual. Use a Constraint-Solver Backsolve to enumerate or symbolically characterize satisfying configurations, then use a Collision Analysis Matrix and witness/counterexample set to expose distinct configurations that collapse to the same output. Report completeness only for the declared finite domain and search limits, register boundary cases, and prohibit conclusions about actual error, responsibility, or fraud without independent evidence.","structural_mapping":[{"archetype_element":"Mapping Under Review","domain_realization":"The versioned transformation from bank transactions, ledger postings, matches, cutoff rules, and reconciling adjustments to the displayed reconciliation residual."},{"archetype_element":"Output Condition or Target Value","domain_realization":"A residual equal to zero, or within the explicitly approved currency tolerance."},{"archetype_element":"Input Domain Boundary","domain_realization":"One named bank account, one closed accounting period, its frozen bank and ledger populations, recorded reconciling items, and a declared finite set of possible discrepancy states."},{"archetype_element":"Preimage Membership Rule","domain_realization":"Include a configuration exactly when replaying it through the frozen reconciliation mapping yields the target residual without violating declared accounting constraints."},{"archetype_element":"Candidate Input Enumeration","domain_realization":"Enumerated or symbolic configurations of omissions, duplicates, amount differences, cutoff shifts, misclassifications, and manual adjustments within the declared search bound."},{"archetype_element":"Collision and Multiplicity Check","domain_realization":"Identify distinct transaction-level configurations that yield the same zero residual and record their count or symbolic family."},{"archetype_element":"Completeness Evidence","domain_realization":"Solver coverage logs, finite-state counts, tested constraints, excluded-state register, and explicit labeling of any unsearched region."},{"archetype_element":"Boundary Case Register","domain_realization":"Items exactly at tolerance, transactions straddling period cutoff, many-to-one matches, foreign-currency rounding, and unresolved source-record differences."},{"archetype_element":"Projection Loss Note","domain_realization":"The scalar reconciliation residual preserves net difference but discards the composition, identity, and provenance of offsetting discrepancies."},{"archetype_element":"Action or Interpretation Policy","domain_realization":"A satisfying configuration is a compatible explanation requiring targeted evidence; it is not proof that the configuration occurred or that a person is responsible."}],"mechanism_mapping":[{"mechanism_slug":"constraint_solver_backsolve","role":"Backsolve from the target residual to all discrepancy configurations satisfying the frozen rules within the declared finite domain or express the remaining family symbolically.","counterfactual_removal":"Without the backsolve, reviewers would retain only hand-imagined examples and could not distinguish a searched set from an exhaustive bounded preimage."},{"mechanism_slug":"collision_analysis_matrix","role":"Compare distinct omission, duplication, adjustment, amount, and cutoff configurations that collapse to the same reconciliation output.","counterfactual_removal":"Without collision analysis, the zero residual could continue to appear uniquely reversible even when multiple configurations satisfy it."},{"mechanism_slug":"witness_and_counterexample_set","role":"Store concrete satisfying witnesses and near-identical counterexamples that fail the residual or accounting constraints.","counterfactual_removal":"Without witnesses and counterexamples, reviewers could not inspect whether the membership predicate draws the intended boundary."},{"mechanism_slug":"coverage_completeness_audit","role":"Reconcile searched states against the declared domain, constraints, exclusions, and search limits before any completeness statement.","counterfactual_removal":"Without the coverage audit, a partial search could be presented as the full set of configurations compatible with the zero residual."}],"causal_chain":["The reconciliation process projects transaction-level bank and ledger states into one scalar residual.","Several distinct discrepancy configurations can offset under that projection and produce the same zero output.","A conventional sign-off focused on the residual suppresses this multiplicity and encourages a unique-correct-state interpretation.","The intervention fixes the mapping, target output, domain, and membership predicate before conducting reverse search.","The backsolve constructs the bounded preimage, while collision analysis exposes transaction-level states lost in the scalar projection.","Completeness evidence separates exhaustively searched configurations from unknown or excluded regions.","Reviewers can then direct independent document and control testing toward compatible configurations without treating compatibility as proof of occurrence."],"baseline":"The preparer performs the standard reconciliation, a reviewer reperforms arithmetic and inspects listed reconciling items, and the auditor samples selected transactions or adjustments. This baseline validates the submitted reconciliation and examples but does not characterize the bounded set of other transaction-level configurations that would produce the same zero residual.","nearest_rivals":["Proof-of-cash or ordinary reconciliation reperformance, which checks agreement and arithmetic but need not enumerate alternative zero-producing configurations.","Exception reporting for unmatched transactions, which surfaces known failures but may omit combinations of individually matched or adjusted items that cancel in aggregate.","Audit sampling, which tests selected items but does not establish the full satisfying set within a declared domain.","Journal-entry testing, which targets risky postings but does not reverse-map a particular reconciliation output to every compatible bounded configuration."],"remaining_contrastive_claim":"The candidate's distinguishing claim is limited to method structure: it makes the bounded set of transaction-level configurations mapping to the specified reconciliation output the central audit object, with explicit multiplicity and completeness evidence. The nearest rivals primarily validate the submitted reconciliation, flag known exceptions, or test selected records without requiring that inverse-set characterization.","authority_safety":{"decision_authority":"The audit lead authorizes the reverse-analysis scope and decides whether independent evidence testing is warranted; the controller retains authority over accounting corrections, and neither the solver nor the analyst may post entries.","authorized_first_step":"An authorized audit analyst may run a read-only replay on a controlled copy of one closed reconciliation using only approved source records and synthetic perturbations.","excluded_actions":["Posting, reversing, or approving journal entries","Changing the production reconciliation or matching rules","Expanding access to bank or personnel data beyond the approved engagement scope","Treating a satisfying configuration as proof of error, fraud, intent, or responsibility","Closing or failing the control solely from solver output"],"halt_rollback":"Stop if the frozen mapping cannot reproduce the approved residual, source populations cannot be reconciled, required access exceeds authorization, or solver precision changes membership at the boundary. Preserve the original read-only snapshot, discard derived scenarios according to engagement retention rules, and make no production change."},"negative_tests":{"strongest_counterevidence":"Independent item-level evidence could show that the declared population is completely matched through authenticated one-to-one identifiers, every adjustment is separately substantiated, and the mapping is injective over all permitted states; under those conditions the zero residual would not conceal alternative admissible configurations in that domain.","problem_falsifier":"The problem is falsified for the tested reconciliation if a documented uniqueness proof establishes that exactly one admissible input configuration maps to the target residual across the complete declared domain, with no tolerance, cutoff, rounding, matching, or external-record unknowns.","intervention_falsifier":"The intervention is falsified as an adequate bounded audit aid if it fails to recover reviewer-designed zero-sum synthetic configurations, misclassifies known counterexamples, or cannot state which admissible states were searched and which remain unknown.","risks":["Combinatorial growth may force a narrower domain or symbolic characterization.","Omitted discrepancy types or external transactions may create a false completeness impression.","Incorrect sign, tolerance, cutoff, or matching rules may generate invalid membership results.","Currency rounding and solver precision may make boundary membership unstable.","Sensitive bank and ledger data may be exposed through derived scenarios.","Reviewers may mistake a logically compatible configuration for an observed error or allegation.","The frozen mapping may not represent undocumented manual steps in the actual reconciliation process."]},"next_evidence_step":"On a read-only copy of one closed month's reconciliation for one bank account, freeze the official rules and source populations; include all manual reconciling adjustments and no more than 25 items already classified as ambiguous or high-risk. Define finite discrepancy states and enumerate configurations containing at most two deviations. Test whether the solver reproduces the submitted configuration, detects three reviewer-designed synthetic zero-sum perturbations, rejects designed counterexamples, and reports searched versus excluded states. Record cardinality or symbolic families, boundary cases, runtime, and failures without posting entries or drawing a control conclusion.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Not assessed against prior proposals because runtime isolation prohibits inspecting them; this candidate is derived solely from the supplied archetype record and accounting-and-auditing domain card.","revision_record":{"parent_version":null,"progress_targets_addressed":["Initial one-shot construction of one complete accounting-and-auditing candidate preserving the preimage-set causal structure."],"conceptual_changes":["Not applicable; this is the initial version."],"operational_changes":["Not applicable; this is the initial version."],"evidence_changes":["Not applicable; prior art and external evidence remain unsearched."],"claim_changes":["No novelty, prevalence, demand, or effect-size claim is made."]}}