2026-09-05-author-consolidation

Work in A-M-Berns/alignment-workspace.

Your task is an author-level consolidation pass with three goals:

1. clean up, verify, and merge PR80;
2. clean up, rebase/retarget as needed, verify, and merge PR82;
3. update the repository wiki so that it gives a clear, mature account of the current overall theory: integrity, openness/non-capture, legitimate cognitive evolution, obligation export, normative induction, and the concrete Normative Inductor realization.

This is not a new speculative research round. The main theoretical architecture has already been developed. Your job is to reconcile the landed repository state with it, fix stale documentation/evidence claims, and leave the public-facing conceptual story coherent.

Use the current repository state as authoritative. Read DECISIONS.md, RESEARCH_STATE.md, PRIORITIES.md, state/, current claims/evidence registries, supersession markers, consolidated trees, and repository contribution rules before changing anything.

Do not silently promote conjectural or conditional results.

Part I — Clean up and merge PR80

Start by reading PR80 in full, including all changed files, theorem ledgers, reports, Lean declarations, tests, and prior-art notes.

PR80 currently contains the Defeat Principle landing, Horty/prior-art work, the standing repair, nonvacuity witnesses, and principal-relative anti-laundering results.

Before merging:

• check whether any PR80 prose or metadata is stale relative to current main;
• check whether PR79 or any dependency has already landed or changed;
• rebase/retarget cleanly if required;
• resolve merge conflicts conservatively;
• do not rewrite historical round findings merely to make them look current;
• distinguish historical annotation from current canonical theory;
• preserve the evidence status of every theorem.

Pay particular attention to these substantive points that should survive consolidation:

Defeat Principle

The mature principle is:

A participant may answer an obligation or contest whether it is owed; only an authenticated settlement-backed terminal condition may make an unanswered obligation disappear.

Equivalently:

Defeat/disposition carries an obligation; it does not extinguish it.

Pure challenge/defeat is an obligation-to-obligation transition, not Progress.

Standing and principal relativity

The standing repair should correctly use participant-indexed standing/licence.

The current result is importantly principal-relative. Do not present AnswerableFor or no_coalition_excluding_principal as a complete theory of non-capture.

The lesson is:

Answerability is answerability to someone; preservation of standing is relative to a protected principal or declared relation.

Prior-art interpretation

Preserve the careful distinction established by PR80:

• Horty/default logic determines what conclusions/defaults are operative;
• it does not maintain a history-sensitive obligation ledger;
• defeat in our theory leaves an authored successor/residue;
• the novelty is not merely endogenous priorities but authored, history-sensitive answerability under defeat.

Do not overstate novelty claims beyond what the cited primary/secondary texts actually support.

Evidence cleanup

Fix any stale claim-language, broken links, incorrect citation-status labels, or outdated counts discovered during review.

Run the full relevant verification suite before merging.

Once PR80 is clean and genuinely merge-ready, **merge it into main** using the repository’s normal preferred merge method.

Do not stop merely because it was previously stacked.

Part II — Clean up and merge PR82

After PR80 is merged, update PR82 against the new main.

Do not retain stale stack metadata.

Read the current head of PR82 carefully. The second refinement materially changed its conclusions, so the old PR body may still describe obsolete architecture.

The current intended realization architecture is approximately:

$$ \mathsf{NI} = \mathsf{MarketMaker}\!\left( \mathsf{TradingFirm}^{\mathcal L} + \mathsf{JointProjectionEnforcer}[ \mathsf{Compile}(\mathcal O_P)] \right) + \mathsf{DecisionAdapter}. $$

Here the Decision Adapter consumes the market state; it is not another trader inside the market-maker fixed point.

Preserve the revised normalization

The original PR82 public convention

$$ d=\operatorname{dist}_2/\sqrt m, \qquad a=m\lambda $$

was rejected because harmless coordinate padding changes both reported defect and reported service.

The current public realization should use:

$$ \boxed{ d_s(b) = \operatorname{dist}_\infty(b,K_s), \qquad a_s=\lambda_s. } $$

Euclidean projection remains an implementation tool for the enforcement trader.

The public defect is sup-distance to the compiled joint region.

The key work relation is inequality, not equality:

$$ \lambda_s d_s^2 \le \lambda_s \|b_s-\operatorname{proj}^{2}_{K_s}(b_s)\|_2^2 \le \rho_s. $$

Preserve the exact scope of presentation invariance:

• canonical security identities;
• enforcement-null product padding;
• unchanged ordinary book/resistance;
• no claim of invariance under arbitrary affine reparameterization or genuinely new tradable content.

Preserve the admissibility/value distinction

The refined PR82 correctly discovered:

$$ \boxed{ \text{normatively admissible market state} \neq \text{authenticated counterfactual value truth}. } $$

Projection onto \(K_s\) says the state is close to an admissible operative region.

It does not by itself certify the value of candidate policies.

The realization therefore needs an externally authenticated practical/value interface.

A typical internal witness is a value correspondence

$$ V_{es} $$

with target counterfactual vector \(v^*{es}\), ambiguity \(\zeta{es}\), and a pre-response calibration certificate.

For finite policy menus and randomized approximate optimization, the useful bridge is of the form

$$ \operatorname{Regret}_{v^*} \le 2d_s + 2\zeta_{es}+\eta_s. $$

An independently authenticated anchored-response theorem then supplies

$$ M_{es}=2L_{es}, $$

and

$$ \epsilon_{es} = L_{es}(2\zeta_{es}+\eta_s) + \epsilon^{\mathrm{resp}}_{es}. $$

Do not describe the projection point itself as the true/certified value vector.

Treat counterfactual semantics as a billed external theory

Do not try to solve the general semantics of counterfactual policy values in this consolidation pass.

The mature position is:

The Normative Inductor should specify exactly what a theory of counterfactual/value semantics must provide, and prove what follows from that certificate.

It need not itself be a general theory of counterfactuals.

Likewise for causal Non-Capture.

A concrete replicated-policy-evaluation ecology may remain as an illustrative theorem target, but label its assumptions explicitly rather than presenting it as the general solution.

Preserve joint-region compilation

Simultaneously serviced operative constraints should compile into one jointly feasible region.

Do not revert to independent per-reason enforcement.

Keep explicit distinctions between:

• compiler correctness;
• compiler completeness;
• convex representability;
• joint feasibility;
• affordable enforceability.

If conjunction fails, Conflict / Unknown must not silently discard obligations.

A new adjudication obligation should arise only if an upstream licensed rule says such a conflict requires one.

Add/clarify joint practical-response compatibility

The refinement should explicitly note:

$$ \boxed{ \text{joint price-space feasibility} \not\Rightarrow \text{joint practical-response compatibility}. } $$

One service occurrence may be matched to several obligation exposures, but all matched edges must be certified against the same realized response/decision distribution.

Treat this as a realization obligation.

The abstract admissible-edge relation should only allow an edge when the relevant practical-response certificate exists.

When obligations demand incompatible responses, the realization may need to:

• separate service contexts;
• invoke a legitimate upstream adjudication/aggregation rule;
• find a common adequate response;
• or leave some evaluation mass residual.

Do not add a new top-level abstract theory unless truly necessary.

Evidence cleanup

The PR body and local documents must agree with the current head.

Update stale claims such as:

• old normalization;
• old number of Lean declarations;
• old number of tests;
• outdated “anything the author must decide” items;
• obsolete stack information.

Preserve the evidence distinction:

• Lean-proved algebra;
• exact finite witnesses;
• paper-level derivations;
• ambient assumptions;
• open theorem targets.

In particular:

exact_carry_left proves that an already certified (1,0) semantic edge is algebraically identity under affine composition.

It does not prove that defeat itself semantically has certificate (1,0).

The semantic exact-carry premise remains separate.

The general Progress theorem should not be described as newly Lean-proved if only finite instances / bridge lemmas are checked.

Repair the abstract contract typo in documentation

Where the realization contract is summarized, use the correctly typed coercive modulus:

$$ \check\phi(\delta) = \inf_{x\in[\delta,D]}\phi(x), \qquad 0<\delta\le D. $$

For inverse statements, use a generalized inverse unless the required continuity/strict-monotonicity hypotheses are explicitly assumed.

Do not make additional abstract-contract changes unless a genuine new typing/interface defect is found.

Verification and merge

Run:

• PR82 local exact-rational tests;
• the NormativeInductor Lean file;
• broader Lean/build checks required by repo policy;
• python3 -m checkers.run;
• repository state/wiki integrity checks;
• any full test suite required for a specification-layer merge.

Fix all failures caused by the branch.

Once PR82 is coherent against landed PR80 and current main, merge PR82.

Part III — Update the wiki

After PR80 and PR82 are landed, update the wiki to reflect the current overall theory, not the historical sequence by which it was discovered.

The wiki should be human-readable and conceptual.

Do not turn it into a dump of round names, PR numbers, or proof-status minutiae.

Where exact proof status matters, link to the repository’s theorem/evidence surfaces.

The wiki should clearly distinguish:

1. the abstract specification theory;
2. the concrete Logical-Induction realization;
3. the external contracts the theory intentionally bills to other theories;
4. future deference/corrigibility consumers.

Core conceptual story for the wiki

The mature central idea is:

$$ \boxed{ \text{legitimacy is a property of cognitive evolution, not an absolute certification of a state from first principles.} } $$

We can say that a later cognitive/normative state is a legitimate evolution of an earlier one.

We cannot in general certify the full goodness of the initial state from first principles.

A trajectory may inherit bad commitments.

Legitimacy constrains how those commitments may subsequently be revised, challenged, answered, defeated, discharged, or extended.

Full normative history and settlement view

Use the terminology:

• full normative history \(H\);
• settlement view \(S=\mathsf{SetView}(H)\).

Do not call the whole history “settled history.”

The full history contains internal normative moves:

• admissions;
• grounds;
• objections;
• answers;
• standing/licence changes;
• defeats/dispositions;
• semantic migrations;
• service-related events;
• settlement-interface receipts.

Settlement is a distinguished immutable/monotone view of that history.

Settlement facts enter through a privileged external interface and may ground terminal discharge.

Integrity

Introduce Integrity as a major component of the theory.

The rough role of Integrity is:

a cognitive trajectory cannot falsify or silently rewrite its own normative history.

A full Integrity theory should govern things such as:

• authenticated births/admissions;
• immutable anchors;
• provenance;
• lineage;
• write permissions;
• faithful carry under representation change;
• replayability from history;
• authenticated settlement receipts;
• terminal settlement-backed discharge.

State a crisp Settlement Integrity property as an external hypothesis to the internal integrity theory.

Separate this from Non-Capture.

Integrity versus Non-Capture

Make this distinction explicit:

Integrity: did the process faithfully preserve and account for what entered it?

Non-Capture: could the process improperly control what was able to enter, challenge, or evaluate it?

Integrity should be largely an internal/formal theory.

Non-Capture necessarily depends on counterfactual structure outside the trajectory.

Answerability

Diachronic Answerability is the conservation principle for incurred normative obligations.

Every inherited obligation component must have exactly one legitimate fate:

$$ \boxed{ \text{answered} \quad\text{or}\quad \text{settlement-discharged} \quad\text{or}\quad \text{faithfully carried live}. } $$

There is no fourth silent fate.

Defeat/disposition is carry, not discharge.

Structural successor/ancestry machinery is proof technology for this invariant, not necessarily the final public definition.

Answerability is principal-relative.

Openness

Openness governs incoming criticism/demand.

A declared coverage scope \(\Gamma\) or coverage contract is a modeling choice, not an embarrassment.

Any application must say, at least minimally, which class of concerns it claims to remain open to.

The general theory should be relative to this declared scope.

Coverage means there is an adequate route from an applicable concern to represented/accountable consideration.

Robust Openness strengthens this with a Non-Capture certificate relative to a declared intervention class.

Do not attempt to solve general counterfactual semantics in the wiki.

Instead explain that the theory bills an external non-capture theory:

give us a certificate establishing that the relevant coverage/standing/efficacy properties survive the declared interventions.

Legitimate cognitive evolution

The conceptual synthesis should be something like:

$$ \boxed{ \text{Legitimate Evolution} = \text{Integrity/Answerability} + \text{Robust Openness}. } $$

Or, if current formal notation still uses DA ∧ Open, retain the exact formal form while explaining Integrity as the deeper theory that supports the answerability/history side.

Suggested prose:

A legitimate cognitive trajectory remains answerable to what has legitimately reached it and remains robustly open to what may legitimately reach it.

Also:

Openness prevents evasion by exclusion. Answerability/Integrity prevents evasion by revision.

Be careful not to claim this certifies the substantive moral correctness of the initial state.

Obligation-process handoff

Legitimacy exports a qualitative obligation process.

It should determine:

• obligation identities;
• anchored specifications;
• live status;
• authenticated lineage/status.

It should not canonically determine numerical importance weights.

Keep qualitative normative status separate from downstream quantitative evaluation.

Live docket versus historical exposure

Explain:

$$ \mathsf{Live}_n = \text{what remains owed now}, $$

while historical exposure records what has entered the process’s responsibility/evaluation population.

The scheduler primarily consumes the live docket.

Progress evaluation consumes an externally chosen/declared view of historical exposure.

Progress is relative to an evaluation protocol

Make this explicit and simple.

The theory does not decide from first principles how different legitimate obligations should be numerically weighted.

Instead Progress is relative to an externally supplied evaluation measure/protocol:

$$ \Prog_N^{P,\mu}. $$

This is analogous to evaluating a learner on a declared test distribution.

The learner should not choose \(\mu\) after observing its mistakes.

An application may care about one measure or a family of measures.

Do not create an unnecessary new foundational “theory of morally correct weighting” in the generic framework.

Abstract Normative Induction

Explain the abstract Progress side as:

$$ \mathcal O_P \to \text{service} \to \text{operative uptake} \to \text{practical response} \to \text{anchored Progress}. $$

Keep the distinctions:

• service;
• scheduled enforcement intensity;
• realized corrective force.

The abstract endpoint remains approximately:

$$ \boxed{ \Prog_N^{P,\mu} \le \Gamma_N\Psi_\phi(\chi_N) + \bar\epsilon_N + D r_N. } $$

Interpret the three terms clearly:

1. serviced constraints were not sufficiently taken up / amplification was large;
2. decision or semantic-response error remained;
3. legitimate evaluation mass was left unserved.

The abstract theorem is a sufficiency theorem/interface characterization.

A literal iff converse is not currently a priority.

External practical/counterfactual semantics contract

The theory should bill, not solve, the general counterfactual/value problem.

Explain that a practical-semantics theory must supply something like:

• a declared policy/response space;
• authenticated counterfactual value or response semantics;
• calibration/ambiguity guarantees;
• causal relation to deployed responses;
• integrity/non-capture assumptions for the evaluator.

Normative Induction then proves what follows from such a certificate.

Do not imply that Logical Induction itself determines counterfactual policy values.

Normative Inductor realization

Add/update a wiki section describing the current concrete LI-based realization.

The architecture is:

qualitative legitimate obligations
        |
        v
proof-carrying compiler
        |
        v
joint feasible convex operative region K_s
        |
        v
projection-based normative enforcer
        |
        v
small public defect d_s = dist_infinity(b_s, K_s)
        |
        +---- external authenticated value/response semantics
        |
        v
Decision Adapter / practical response
        |
        v
anchored Progress

The concrete NI uses:

• ordinary Logical Induction / Trading Firm as substrate;
• additive normative enforcement rather than replacing LI;
• one joint convex region for simultaneously serviced constraints;
• Euclidean projection internally for traderized enforcement;
• sup-distance publicly for representation-stable operative defect;
• service intensity equal to prospective multiplier \(\lambda\);
• an external decision/value plugin;
• service transport back to historical obligation exposure.

Make clear:

$$ \text{joint price feasibility} \not\Rightarrow \text{joint practical-response compatibility}. $$

The realization must certify that matched obligations can actually be served by the same response, resolve them legitimately, separate service contexts, or leave residual mass.

Remaining realization obligations

The wiki should present these as implementation/theorem obligations rather than foundational confusion:

• unified concrete history/event representation;
• obligation-process export;
• compiler soundness;
• convex representability of the chosen obligation language;
• joint feasibility;
• affordable service under declared workload assumptions;
• joint practical-response compatibility;
• quantitative semantic-transport certificates;
• effective/computable LI packaging;
• final composed theorem / further Lean formalization.

Non-Capture and counterfactuals are external bills

Highlight that two major issues are intentionally externalized:

Non-Capture bill

A theory of counterfactual/institutional capture must produce the certificate required for Robust Openness.

The generic legitimacy theory need not choose one universal counterfactual semantics.

Counterfactual-value bill

A theory of policy evaluation must produce the calibration/response certificate required by the practical-response interface.

The generic Normative Inductor need not solve general counterfactual identification.

This is an architectural virtue, not merely missing work.

Relationship to deference and corrigibility

End the conceptual arc by explaining the intended downstream consumer.

The longer-run target is not merely “a learner follows norms.”

It is to prove properties of agents reasoning about legitimate future cognitive processes.

The future deference/corrigibility theory should be able to consume:

• a certified legitimate-evolution property;
• a Normative Progress guarantee;
• decision/value-facing outputs;

and prove reasons not to preempt, disable, or replace a future process merely because its later judgment may differ from the current agent’s.

Do not claim that theorem has already been proved.

The important achievement is that legitimacy and normative induction now provide a clear candidate interface for it.

Wiki organization

Prefer a small number of mature conceptual pages rather than one page per historical round.

Reuse and rewrite existing pages where possible.

A reasonable high-level structure would be something like:

• Normativity / Overview
• Legitimate Cognitive Evolution
• Integrity and Answerability
• Openness, Coverage, and Non-Capture
• Settlement Interface
• Normative Induction and Progress
• Normative Inductor
• Deference and Corrigibility

But inspect the existing wiki organization first and fit the update into it rather than creating redundant parallel pages.

Where older wiki prose reflects superseded ideas such as:

• Structural Continuity as a top-level pillar;
• admission as a separate conceptual layer;
• settlement as the whole normative history;
• canonical quantitative obligation weights;
• independent per-reason enforcement;
• belief admissibility automatically implying good action;
• old dimension-dependent realization normalization;

rewrite or annotate it so the current conceptual story is unambiguous.

Final consolidation checks

Before finishing:

1. confirm PR80 is merged;
2. confirm PR82 is merged;
3. confirm main is green;
4. run wiki-link/state checks;
5. ensure no PR or wiki page still describes the obsolete PR82 normalization as current;
6. ensure no current wiki page calls full normative history “settled history”;
7. ensure Defeat is presented as carry, not extinguishment;
8. ensure Integrity and Non-Capture are visibly distinct;
9. ensure legitimacy is framed diachronically as legitimate cognitive evolution;
10. ensure scope is explicitly declared/application-relative;
11. ensure Progress is explicitly evaluation-measure-relative;
12. ensure counterfactual/non-capture theories are described as external contracts to be instantiated;
13. ensure conditional realization results are not promoted beyond their evidence;
14. ensure the current repository state/round inventory reflects the merges.

Deliverable

Leave the repository in a coherent post-consolidation state and give me a concise report containing:

• what was merged and the resulting SHAs;
• any conflicts or substantive corrections made during merge;
• what wiki pages were created/rewritten;
• the final conceptual architecture now presented by the wiki;
• any stale/superseded theory you removed or annotated;
• any evidence-status corrections;
• the remaining author decisions, if any;
• the remaining research agenda split into:

• specification/theory work;
• realization/agent-sized theorem work;
• intentionally external contracts.

Do not start another speculative round unless consolidation itself uncovers a genuine contradiction that prevents the current theory from being stated coherently.

Report — author consolidation, 2026-09-05

A maintainer-dispatched consolidation pass with write scope. Not a research round: no theorem added, no claim registered, no epistemic class moved. The prompt is PROMPT.md beside this file, verbatim.

1. Merges

pull request	branch	landed as	method
Defeat Principle landing, Horty check, standing repair	round/2026-09-03-defeat-landing-horty-standing	f7489cf5a610927b9e85e33d5d42228cd64da7de	squash, Model attribution carried
Normative Inductor realization	round/2026-09-04-normative-inductor-realization	caa3ad083e2d6d8120fbb54120219e907502ad28	rebased onto f7489cf, retargeted from the stacked base to main, squash

Both branches were already rebased onto the squash of the unified-grounds round (198a86a) when the pass began; neither rebase produced a conflict. GitHub classifies the pair as a stack and refuses its ordinary merge endpoints for them; both merges went through the asynchronous merge endpoint. All seven required checks were green on each head before merging, and the Python runner, the two Lean modules and the axiom audit were also run locally.

2. Corrections made before merging

Defeat-landing round. The Pollock 1987 URL the round recorded as dead on 2026-09-03 redirects, as of 2026-09-05, to a host that serves the paper; the PDF was fetched and its first page checked against the bibliographic data. PRIOR_ART.md carries the resolving address and the DOI and keeps the caution that Horty credits the distinction to Pollock 1970. The round's REPORT.md and HORTY.md are annotated with that fact and with the landing of its dependency; outstanding actions 1 and 3 are closed. The round's findings and verdict are unchanged.

Normative Inductor round. One substantive addition, requested by the dispatch and absent from the head: joint price-space feasibility does not imply joint practical-response compatibility. One service occurrence realizes one decision distribution, so every exposure matched to it needs its own anchored response certificate against that same distribution; incompatible demands are separated into distinct service contexts, adjudicated under a licensed upstream rule, given a common adequate response, or left as residual mass. Recorded as a realization obligation in the realization document (admissible-edge row, a new §6 subsection, a spine row, and the remaining-work list), the presentation note, THEOREMS.md's what is not shown, and REPORT.md. The abstract admissible-edge relation already admits an edge only when its certificate exists, so no abstract-contract change was made. The exact_carry_left docstring now states that it consumes an already certified identity edge and does not establish the semantic premise. PROVENANCE.md names the governing contract files without a local filesystem path. The pull-request body was rewritten to match the head: stack metadata removed, evidence classes stated once, the "author must decide" list reduced to the one genuine decision.

3. The wiki

Five new pages: Settlement-Interface, Integrity, Openness-Coverage-and-Non-Capture, Normative-Induction, Normative-Inductor. Two rewritten: Legitimacy, Diachronic-Answerability. Fourteen amended: Home, _Sidebar, Roadmap, Glossary, Progress, Normativity, Actionability-and-Normative-Force, Why-Normativity, Prior-Art, Architecture, Deference, Corrigibility, Normative-Record-and-Inquiry, and the state-bound views regenerated. The architecture the wiki now presents, and the superseded prose it replaced, are itemized in the DECISIONS.md entry of this date.

4. Deviations (standard 8)

1. Merge method. The dispatch said to use the repository's normal method. The normal method — squash through the ordinary merge endpoint — was refused by GitHub for both pull requests because it classifies them as a stack; the asynchronous endpoint was used with the same squash method and message.
2. Pollock link. The dispatch asked for broken links to be fixed. The link was not broken on the day of the pass; it had been recorded as dead two days earlier. The record was corrected rather than the link replaced, and the round's own statement that it did not resolve during that round was left standing as history.
3. A defect of this pass, found and fixed after the wiki merge. To reuse another checkout's Lean build cache the pass planted a symlink at lean/.lake; the ignore rule matched directories only, so the symlink was staged with everything else and reached main in the Normative Inductor squash. Removed, with the ignore rule widened, in the follow-up commit recorded in DECISIONS.md under this date.
4. Prompts record. The dispatch did not ask for a round directory. One is committed because standard 12 requires the prompt verbatim, and the round record and provenance rows follow from the gates that check them.

5. What this does not establish (standard 9)

• Nothing here is a registered claim, and no evidence class changed. The wiki labels every legitimacy page open / unregistered.
• The Normative Inductor's end-to-end theorem remains conditional; the wiki says so and lists its hypotheses by owner through a pinned link.
• The Defeat Principle's licensing content — which rules of a practice license contesting which debts — is not supplied; the three maintainer reservations from the defeat rounds (load discount, settlement independence, protected participant) remain in the queue.
• The wiki's conceptual decomposition is a sanctioned shape, not a predicate, exactly as the 2026-09-01 ruling distinguished.

6. Outstanding maintainer actions (standard 10)

1. Whether to adopt the bounded-domain coercive-modulus repair in the abstract contract before freezing it. The contract lives outside the repository; every in-repo summary already uses the repaired form.
2. The three defeat-round reservations already in DECISIONS.md's queue.
3. Whether item 77's prior-art deliverable is discharged on the 2006 paper, or the 2012 book is to be obtained.

Attribution

• Prompt author: the maintainer, outside this repository.
• Executor: Claude Fable 5.1 (Anthropic).
• Dates: 2026-09-05.