Annex 6 Ablation sufficiency and extensibility

Documentary appendix to the article When the controls work but the system fails

Question answered. What happens when principles are removed, how are independence and sufficiency verified, and to what extent can the result be transferred?

Coverage. Complete sections 7 and 8, including executed tests, falsifications, corrections, mathematical limits, and transfer families.

Reading rule. The source block is preserved in its entirety, with its nuances, states of evidence, and original links. It should not be interpreted as product results when the text describes it as a design, symbolic proof, constructed scenario, or hypothesis.

Synthesis and use

This appendix keeps separate four outcomes that are often confused: coverage of principles, ablation of a principle in a defined case, logical independence through counterexamples, and sufficiency within declared finite models. None of these, on its own, demonstrates universal behavior or deployment performance.

To transfer a result to a different size or domain, it is necessary to declare which structure remains, which budget changes, which oracle is preserved, and which conditions cease to be equivalent. Corrections and falsifications are part of the result: a test that weakens the hypothesis should not be removed from the record.

Document navigation

• Main article: When the Controls Work but the System Fails
• Complete source and concordance: Annex 0 — Complete Source and Concordance
• Appendix of claims and evidence: Annex 9 — Claims and Evidence Appendix
• Collaboration Guide: Annex 10 — Collaboration Guide
• Full map of sources and links: Annex 11 — Complete Map of Sources and Links
• Reproducible technical corpus: structural-awareness-contributions — commit 8f17843c568114f31cc0ad486b4a1303396021e6

How to read this appendix

This appendix asks what each principle P1–P6 actually contributes. The ablation strategy eliminates or weakens a principle and observes which requirement, gate, or outcome ceases to hold.

The evidence combines symbolic regressions, Boolean analysis, finite audits, and transfer tests. These are distinct layers: their figures should not be added together or described as independent incidents or trials.

Recommended route

Begin by removing each principle; continue with the four numerical families; close with A25/A26 and their transfer conditions.

Table 1. Reading of the P1–P6 ablation

Table 2. Figures, certificates and correct meaning

Reading conclusions

Conclusion 1. Ablations show dependencies within the declared fixtures.

Conclusion 2. Finite review supports P1/P2/P4 and maintains counterexamples for P3/P5/P6.

Conclusion 3. Conditional extensibility does not equate to a universal guarantee of transfer.

Preservation and navigation

The 379 cases, 64 signatures, historical certificate of 65,536 states, audit of 33 fields, 22 comparisons, 11 tests and links of A25/A26 remain traceable in the source block.

Full source text

7 — Testing the principle basis: ablation, independence and sufficiency

The tests below ask three different questions that a nontechnical reader can keep separate. Coverage asks whether every principle becomes a checkable requirement. Ablation asks what happens in a defined case if one principle is removed while the others and serious repair options remain. Mathematical countermodels ask whether any principle follows logically from the other five; finite-model checks examine the reverse requirement implication. These tests supply complementary model-level evidence and prepare the question of deployed behavior under real constraints.

The positive requirement routes spell out a qualified decision for each of the six cases and set a concrete target for future product executions. The next question is whether the six underlying principles are redundant or sufficient for this declared problem class. The coverage matrix and semantic-conservation proof map each principle to concrete requirements and failure witnesses; the reverse conformance proof examines whether satisfying the applicable S#/T# route entails the corresponding principle invariant. The revised model supports that implication for P1/P2/P4 and exposes countermodels for P3/P5/P6. Forward traceability is therefore distinct from a completed bidirectional conformance result; the operational requirements add information and are not identical to the principles. Requirement-basis closure is likewise relative to the declared EA decision-frame language.

Current scope of the preceding reverse-conformance statement: audited A23 supports P1/P2/P4 in the reconstructed finite model, not a closed theorem for all six. P3/P5/P6 remain explicit open semantic questions. Forward traceability and relative requirement-basis closure do not remove those countermodels.

Executed leave-one-principle-out tests

The ablation campaign fixes a scenario branch, removes one principle at a time and challenges the remaining five with strong repair attempts, matched positive and negative controls, and an explicit falsifier. For each corrected isolated fixture, removing the invariant reopens a material failure route; passing conventional repairs reconstruct its minimal semantics. Some earlier fixtures were themselves falsified and corrected, and P4 was narrowed: full historical lineage is not necessary when another current, verifiable and non-amplifying authority basis suffices. The complete testbook records the six routes and corrections. The registered symbolic campaign comprises 346 core regression tests plus 33 supplemental falsification, isolation and cross-scenario tests (379 total); the separate CI record reports 379/379. The 379 results substantiate the declared symbolic regression and falsification campaign; the CI record measures model behavior rather than live product outcomes.

Correction and replay record. The 00H integration record documents the corrected strict monetary threshold and preservation of the older artifact. The merge 00K run 36197588452 reproduces the corrected 346 core + 33 supplemental regression checks. The separate 11 A23 tests below are not added to, or confused with, those 379 checks.

Individual executable ablations: P1/00J; P2/00E; P3/00F; P4/00H; P5/00I; P6/00G.

Mathematical result and claim boundary

Separately from the scenario tests, the shared-substrate proof constructs, for each Pi, a countermodel satisfying the other five: none of the six follows logically from the remaining five under its declared semantics. The full-cube result realizes all 64 pass/fail signatures and establishes a six-coordinate lower bound for a lossless Boolean diagnostic basis; it does not establish minimality among every possible reformulation or non-Boolean representation. The historical finite-model certificate checked 65,536 states for the reverse requirement-conformance implication; its all-six sufficiency claim has been superseded by the clause audit below. Those states are not additional ablation trials. The distinct evidence supports logical non-redundancy, tested operational necessity and joint branch correctness within the specified fixtures, alongside the revised partial finite sufficiency result. They supply a basis for broader tests of universal minimality, real-world effectiveness and comparative superiority.

Certificate correction — 26 September 2026. The 65,536-state all-six sufficiency certificate cited here and in the next paragraph is historical and superseded. The clause audit found nine clause/target equivalences in the old model and reconstructed the clauses from canonical wording while retaining the original P1–P6 functions. The revised model has 33 fields and checks exact support projections; it does not literally enumerate 8,589,934,592 rows. The current certificate records 22 clause/target comparisons: none of those clauses is equivalent to or alone entails its target. P1/P2/P4 retain finite implication; P3/P5/P6 have countermodels. These findings do not by themselves prove a defect in the canonical requirements.

Verification route for the numerical claims: start at the A15 testbook for each fixture and branch, follow its A14 CI record to the recorded run, then inspect A22 for the 64-signature diagnostic and the separate formal certificate for the historical, superseded 65,536-state implication check; the current clause audit and its separate reproduction route are linked above and below. The linked proof map distinguishes those results from source-reviewed technology comparisons and from live product evidence.

Current audit reproduction. The auditor and 11-test suite detect reordered copies, copies padded with an additional conjunct and hidden target-function calls. The execution record separates those checks from the 379 regressions. Requirements-vNext records CAND-A23-P3 (uncertainty, permission and qualified response), CAND-A23-P5 (recorded obligation versus action-time execution) and CAND-A23-P6 (dependency versus false independent corroboration). These remain review candidates; no S15, T5 or H7 has been adopted.

Further checks and the limits of transfer

The foundation-to-principle chain also has a syntactic normal-form closure argument: within the declared A/B/C/D, Type-0/1/2, received-state, time and composition vocabulary, admitted failure forms normalize to P1–P6 unless a new foundational primitive is introduced. A corpus-derived six-countermodel certificate complements the shared-substrate independence proof. The serious-repair review preserves the earlier fixture falsifiers, and the proof map provides the full reading and reproduction route. The repository’s integrated CI record adds traceability, full-cube, S/T-conformance, syntactic-closure and case-extension checks to the 379-test symbolic campaign; these versioned records broaden the reproduction route, while the current A23 clause audit supersedes the earlier all-six conformance interpretation.

Transfer beyond the six minimum cases is a separate conditional result. The failure-family extension test admits a larger, smaller or other-domain case only when its structural kernel, receiving decision boundary, failure predicate, inherited requirement route and positive controls remain intact. The success-case companion then pairs each 00E–00J failure with a bounded S/T-conforming route. For an admitted extension, exclusion of the same structural failure additionally requires a separately established base guarantee, failure reflection and conformance preservation; admission alone does not establish that guarantee. Other failure mechanisms and proposed cross-domain variants call for their own evaluation.

Transfer qualification — 26 September 2026. The preceding exclusion claim is conditional on a separately established base guarantee. Revised A25 requires failure reflection, conformance preservation and legitimate positive controls; family admission and finite fixture success alone do not supply that guarantee. Revised A26 preserves the same open premise for success-case transfer.

Six positive case records: 00E; 00F; 00G; 00H; 00I; 00J.

8 — Extensibility: from six minimum cases to bounded families

After the six scenario routes and principle tests, we asked whether each memorable case represented a reusable failure mechanism. The three directions, adapted from DAOS Annex II, are upward (more agents, owners, layers and decisions), downward (the smallest setting that still contains the mechanism) and horizontal (a different domain with the same decision relations). “Vertical” here means upward scale or organizational depth; merely renaming the setting does not establish an extension.

DAOS means “Delegated Authority OS under Context Change,” a separate FG-TIDA model-case package; its Annex II supplies this extension method. This article tests a conditional transfer of the EA requirement route, without treating that package as an adopted standard.

A25 separates the narrative from a structural kernel and admits a proposed variant only after seven checks: preservation of the material relations and receiving decision boundary; reflection of the same failure predicate; preservation of the inherited S1–S14/T1–T4 route and legitimate positive controls; explicit finite time, evidence and review capacity; and no hidden new semantic primitive. Membership is decided before scoring success. A25 then gives a conditional transfer result: for an admitted family member, a separately established base guarantee can transfer when failure reflection and conformance preservation hold. Membership and finite fixture success alone do not prove that conformity entails all relevant principle invariants or excludes the failure throughout the family. It does not exclude a different failure or prove that a proposed analogy belongs to the family.

Concrete evidence boundary. A25 §6 links 00F/P3 to A3, 00H/P4 to A4 and 00G/P6 to A6, including code and positive controls. The tested conforming implementations avoid the failure in those branches; this is not a guarantee for every reachable state of every admitted extension. Nor do the retained P2/P1 finite implications certify all of 00E/00J, whose full routes depend on other principles.

The six profiles make the boundary concrete. 00E extends qualification loss through compressed handoffs down to two agents or one summarizer; 00F extends incompatible local postures over a shared scarce resource to a factory cell or cloud cluster; 00G can shrink from a multi-agent cascade to a multi-turn conversation only when repeated dependent claims displace a bound task; 00H can shrink from 4,000 cases to two while keeping both unauthorized action and loss of a material finding; 00I requires only an initially valid decision, a material intervening change and later actuation; 00J needs one valid narrow provenance record promoted into an unsupported stronger downstream claim. Each profile also lists upward and horizontal variants and cases that fail admission.

A26 pairs each failure family with a Success Model Case using the same kernel, decision boundary and existing requirement route. Its additional success checks preserve the legitimate positive counterpart, an observable bounded disposition and finite resources without assuming perfect evidence or unlimited human review. Success may mean execute, continue, limit, hold, requalify, escalate or no conclusion, according to the qualified case; blanket blocking cannot pass the positive controls. A proposed extension that needs a genuinely new obligation becomes a Requirements-vNext candidate instead of being forced into S1–S14.

The CASE-EXTENSION registry and validator check the six parent–profile–success links, three directions per family and the declared admission structure (local validation: PASS, six of six families). The PASS result establishes that the design records satisfy the declared structural checks. Separately frozen fixtures and comparable outcomes are the route to evaluating the cross-domain candidates.

Extension sources: DAOS Annex II; A25 failure-family method; A26 success-case method; CASE-EXTENSION registry.

Six failure-family profiles: 00E; 00F; 00G; 00H; 00I; 00J. The paired positive case records are linked in the preceding section.