2026-08-27-legitimate-improvement

Legitimate Improvement / No-Free-Evasion

One dispatch, 2026-08-27. Verbatim as received.

Round: Legitimate Improvement / No-Free-Evasion on Frozen Legitimate Evolution

You are doing a theorem-design + executable-countermodel research round in A-M-Berns/alignment-workspace.

This is NOT a consolidation pass and NOT a request to make the current story look clean. The purpose of the round is to determine what theorem actually survives when a normatively evolving process can itself change the comparison surface on which its learning/regret guarantee is measured.

Do not use Lean.

0. Hard boundary: Legitimate Evolution is frozen

Orient to the repo and read AGENTS.md.

Then read the frozen Legitimate Evolution round, especially:

projects/normativity/legitimacy/rounds/2026-08-25-legitimate-evolution/ANSWERABILITY.md

The frozen commit is approximately:

e732524e0a4b44c6f1131019c4dfa75c4be15cdd

Also inspect the Reflective Integrity Core reference model/specification that LE builds on.

Treat the following LE package as fixed:

• standing L_t
• incurred claims I_t
• outstanding claims O_t
• supplied strict-prestate Permit
• supplied level-valued Due, with rising-edge incurrence
• supplied strict-prestate Resolve
• S1/S2
• A1
• D1 realization conformance
• Grounded Replay
• Answerability Resolution

LE intentionally does NOT claim Coverage, progress, regret, substantive correctness, quantitative liability, or current-state certification.

Do not edit or strengthen the frozen LE artifact merely to make this round work. If the composition requires something LE does not provide, add it as new wiring, a new parametric semantics, a canonical constitution, or report that the composition fails.

Only recommend reopening LE if you find an actual error in a claim LE already makes.

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1. Central research question

The naive target

Legitimate Evolution + low repair regret => recurrent correctable defects disappear

has a central counterexample:

1. repair r is represented and licensed;
2. a recurrent pattern occurs on which r is demonstrably better;
3. instead of incorporating r, the process performs a legitimate normative change which de-licenses/removes/retires r;
4. the old conduct continues forever.

Ordinary regret can now go to zero. Frozen LE may still be satisfied.

The round's main question is therefore:

Can a legitimately evolving process escape a represented demonstrated improvement without paying either repair regret or answerability?

The candidate conceptual result is not necessarily defect elimination.

It may instead be a theorem of the form:

No-Free-Evasion / Improvement-or-Answerability

For a represented improvement challenge on a recurrent context, persistent challenged conduct cannot simultaneously:

• avoid substantial repair regret while the repair remains live;
• silently make the repair/comparison disappear;
• avoid leaving an answerability trace for contesting/withdrawing it;
• and avoid explicitly settling/rejecting the challenge.

The desired trichotomy is approximately:

LIVE / CONTESTED / SETTLED

where:

• LIVE: the repair is still an available legitimate comparison;
• CONTESTED: the process has withdrawn/disabled/reframed the comparison, but an improvement challenge remains outstanding;
• SETTLED: the process has explicitly and legitimately answered/rejected the challenge according to supplied normative semantics.

The generic theory MUST NOT claim that SETTLED means objectively correct. A target-free normative-learning theorem must permit substantive legitimate disagreement.

A downstream consumer may later rule out some settlements by an additional substantive lemma. The generic theorem should not.

Your job is to determine whether this decomposition can be made mathematically exact, whether it is genuinely stronger than repair stability alone, and what the weakest interfaces are that make it true.

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2. Keep three theorem layers separate

Do not force them into one theorem.

Theorem A: pure Repair Stability

No legitimacy terminology.

Set up the most general clean online-learning interface actually supported by known machinery:

• finite action/menu per occasion, uniformly bounded if needed;
• mixed choice p_t;
• bounded full-information loss/evaluation;
• predictable context/time selector I;
• history-dependent repair/modification code r;
• priors / dynamic registration if this can be obtained without invention.

Define comparative advantage carefully.

Prove or import an anytime regret bound of the strongest honest opportunity-adaptive form.

Literature to inspect, not merely cite

At minimum:

1. Blum & Mansour (2007), especially §§6–7.
2. Subhash Khot and Ashok Kumar Ponnuswami (COLT 2008), Minimizing Wide Range Regret with Time Selection Functions.
3. Luo & Schapire (COLT 2015), Achieving All with No Parameters: AdaNormalHedge, especially confidence-rated/sleeping experts.
4. Delay literature only enough to design the interface; this round may set tau_t = t.

Fable claims Khot–Ponnuswami gives a black-box reduction of wide-range regret to external regret and that confidence-rated AdaNormalHedge can yield an active-mass adaptive bound.

Verify this yourself from the papers. Do not inherit the claim.

Critical effective-mass question

Do NOT assume either of these definitions:

sum_t I_t * 1[F_t != id on supp(p_t)]

or

sum_t I_t * sum_a p_t(a) 1[F_t(a) != a].

Derive the correct confidence/awake/effective-mass quantity from the actual reduction.

Then answer two separate questions:

1. What quantity does the online-learning proof genuinely adapt to?
2. Does that quantity have the semantic interpretation we need as "repair opportunity mass"?

Stress-test cases where F_t changes only 10^-12 probability mass.

If the desired O(sqrt(W C)+C) style bound is not actually available, report exactly what is available and what this costs the downstream theorem.

Scope

Use ordinary one-shot/local regret on the actual prefix.

Do NOT claim:

• policy regret;
• alternate-history improvement;
• convergence of behavior;
• eventual permanent incorporation of a repair.

The round should make the local boundary explicit.

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Theorem B: generic Correctable-Defect adapter

Keep this theorem more general than any convenient conduct-level specialization.

A consumer supplies some nonnegative diagnostic mass D_T and proves a witness inequality

Adv_T(I,r) >= epsilon * D_T - xi_T.

Then Theorem A gives

D_T <= (B_T(I,r) + xi_T) / epsilon.

If the normalizations permit, obtain the asymptotic opportunity-relative corollary.

This theorem is intentionally almost algebraic.

Also prove/test an easy finite-recurrence specialization

As an early sanity check, instantiate Theorem B for:

• conduct-level diagnostic;
• surgical repair, identity off the diagnosed conduct;
• same-round evaluator which strictly prefers the repaired action on every diagnosed occasion.

If some normalization/ranking assumption yields an automatic margin, state that as a SPECIALIZATION.

Do not make rank normalization foundational unless prosecution shows it must be. Do not make conduct-level defects foundational. Do not assume all useful consumers have surgical repairs.

We want the generic witness inequality to survive future delayed, graded, or outcome-audited consumers if the mathematics permits it.

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Theorem C: No-Free-Evasion / Legitimate Improvement composition

This is the main theorem-design target.

Combine Theorem A/B with the FROZEN LE package through explicit wiring.

Do not merely write:

LE + regret => learning.

Instead determine whether the following can be made exact:

While a represented repair remains a live legitimate alternative, persistent diagnosed non-uptake is quantitatively bounded by repair regret.

If the process changes the normative/evaluative/comparison surface so that the repair ceases to be live, that change can be made to generate or sustain an answerability challenge.

Therefore persistent challenged conduct must manifest as: (i) regret while the challenge is live, (ii) an unresolved/contested answerability condition, or (iii) an explicitly settled/rejected challenge.

Try to obtain a finite-time decomposition, not just prose.

For example, investigate whether there is a mathematically natural partition like

D_T = D_T^live + D_T^contested + D_T^settled

with a bound on D_T^live, and an exact accounting statement for the other pieces.

Do not force this exact notation if a better state space emerges.

Very important

A single retirement event can support infinitely many later diagnosed actions.

Therefore merely counting retirement events cannot be enough.

The theorem needs to say what connects POST-RETIREMENT recurring conduct back to an outstanding or discharged improvement challenge.

Work this out carefully.

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3. What is the improvement challenge?

Do not assume Fable's syntactic rule

every falling edge of license/menu/designation/evaluator automatically creates Due.

That may be a useful canonical constitution, but it is substantive normative content.

Prosecute at least these candidate objects:

1. challenge attached to the repair code itself;
2. challenge attached to accumulated comparative/audit evidence that the repair is better;
3. challenge attached to the diagnosed conduct;
4. some combination.

A promising conceptual reading is:

represented comparative evidence itself becomes a ReasonOcc; supplied Due may then say that the process owes treatment of the resulting improvement challenge.

Possible legitimate treatments might include:

• incorporation;
• explicit defeat/rejection by reasons;
• carriage / continued contestation.

Determine whether existing Due / Resolve are expressive enough for this with no new normative primitive.

Parametric first, canonical instance second

State the composition parametrically over whatever challenge-Due/Resolve semantics it needs.

Then build ONE canonical constitution in which relevant withdrawal/retirement of a demonstrated improvement activates an answerability claim.

This constitution is a fixture / realization of the theorem, not a modification of LE.

Find the weakest sensible version.

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4. Central countermodel suite

These are not optional illustrations. The theorem should be designed against them.

CM1: reactive de-licensing

• r licensed;
• recurring diagnosed conduct;
• r accumulates clear positive advantage;
• process legitimately de-licenses r;
• old conduct continues.

Question: Does the package force regret, an outstanding challenge, or explicit settlement?

CM2: preemptive de-licensing

The process anticipates that r is going to become embarrassing and de-licenses it BEFORE sufficient comparative evidence accumulates.

Question: Is this caught by the learning package at all?

If not, is this honestly a Coverage / anti-manipulation / counterfactual-integrity boundary rather than a bug?

Do not hide the answer.

CM3: post-retirement continuation

After r is retired, the same relevant contexts continue and the same diagnosed conduct continues.

A one-time retirement claim must not make this stream disappear mathematically.

Trace exactly how later mass is assigned to LIVE / CONTESTED / SETTLED.

CM4: suppress the post-retirement stream

Retire r, then influence the world/measurement/designation so that the relevant occasions no longer appear.

Does the theorem catch this? If not, identify precisely the Coverage / anti-manipulation premise a later theorem would need.

CM5: evaluator shedding

Keep r nominally licensed, but legitimately change the evaluator so it no longer registers r as an improvement.

Pinning alone is not enough if the same process writes the evaluator before choosing its action.

Determine exactly what the present theorem can say.

Do not pretend "era locking" proves independence or non-manipulation.

CM6: menu/designation shedding

Keep evaluator and repair code fixed but remove the action from the menu or stop designating these occasions as learning occasions.

Does the same challenge/accountability abstraction cover these, or are they genuinely different interfaces?

CM7: trivial Resolve

Canonical constitution says a withdrawal is Due, but Resolve immediately accepts "no" as a complete answer.

Everything is structurally legitimate.

This MUST demonstrate that the generic theorem proves accountable/explicit rejection, not substantive correctness.

CM8: outstanding forever

The challenge stays outstanding forever while conduct continues.

Qualitative LE permits this.

State clearly what additional Service / quantitative-liability premise would be required to eliminate this branch.

Investigate whether cumulative outstanding challenge exposure naturally interfaces with the existing liability program, but do not invent a theorem that has not been proved.

CM9: tiny support mass

Repair changes only a tiny probability component of p_t.

Use this to validate/refute the effective-mass definition from Theorem A.

CM10: delayed meta-level benefit

A repair changes an inquiry/audit/repair-generation procedure whose benefit only appears through future trajectory effects.

Expected verdict: ordinary local repair regret does NOT establish the desired global improvement.

Keep this as a deliberate negative test establishing the boundary with future policy regret / sequential theory.

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5. Learning trace / sidecar interface

Frozen RI currently has no canonical object corresponding to:

• menu faced;
• mixed action selected;
• comparison rules;
• pinned evaluator;
• later loss vector.

Specify the SMALLEST learning sidecar needed for A–C.

Do not add a fifth RI event kind unless forced.

Prefer cross-references to the RI history.

We probably need something ChoiceRecord/LearningOcc-like, but derive rather than assume the fields.

At minimum prosecute:

• strict-prestate reference/hash;
• menu / how it is derived;
• p_t;
• repair/comparator registry state;
• predictable selector state;
• evaluator identity/rule;
• audit/feedback anchor tau_t >= t;
• enough information for an external verifier to recompute legality and regret.

For this round, set tau_t = t in the executable realization if useful, but INCLUDE the delay anchor in the semantic interface so the later deference consumer does not require redesign.

Audit may be derived or represented by existing Settlement; test whether this suffices.

As in D1, distinguish:

• semantic derived state;
• materialized record;
• external certificate / verifier conformance.

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6. Repair identity and registry

Prosecute, and likely adopt if it survives:

• semantic repair identity by content hash + type interface;
• semantic change means new repair identity;
• historical registry monotone;
• current licensing/applicability is separate from registry identity.

But do NOT assume "historically represented => currently owed attention." That bridge is exactly what the improvement-challenge semantics must justify.

Also distinguish carefully:

• represented;
• computationally executable;
• normatively licensed;
• applicable in this prestate;
• actually changes nonzero action mass;
• auditable.

Do not let "available repair" blur these.

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7. Consumer fixtures

These are tests of the interface, not the theorem definition.

Consumer 1: answerability-native stalling

Construct a recurring claim family where:

• a legitimate answer route is available;
• the system sometimes carries/stalls instead of answering;
• the answer route supplies a natural repair;
• an independently specified charge/evaluator makes stalling detectably worse.

Derive the strongest honest finite/asymptotic conclusion.

This tests the answerability-native use of LE + learning.

Consumer 2: override of realized correction

Construct the deference-shaped fixture:

• correction occasions recur;
• an external/H+ grade is or will be represented as a Settlement;
• compliance is an available legitimate repair;
• the system overrides the realized correction in favor of its own forecast.

The real consumer is delayed.

This round may use tau_t = t only as a synchronous fixture.

Do NOT claim the actual delayed deference theorem unless you implement/verify the delay bound.

The purpose is to ensure the semantic interface already has the field the delayed consumer will need.

Negative consumer: delayed meta-improvement

Include one explicit example where a procedure repair only helps through future state changes and the present local theorem correctly has no force.

This is a success condition, not a failure.

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8. What NOT to freeze unless forced

Do not prematurely make any of these foundational:

• rank-normalized losses;
• conduct-only diagnostics;
• surgical repairs;
• automatic Due for every comparison-surface falling edge;
• fixed finite repair class;
• Fable's proposed effective-mass formula;
• evaluator era-locking as a complete anti-manipulation solution;
• literal RI compliance as a hypothesis for human/H+ deference;
• convergence/stabilization of behavior;
• policy regret;
• ontology transport.

If one of these turns out to be mathematically necessary, show the countermodel proving necessity.

Otherwise keep it as a specialization or realization.

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9. Executable prosecution

Build small executable reference models/countermodels, following the style of prior rounds.

At minimum every CM1–CM10 should either:

• execute and exhibit the intended escape/failure; or
• be rejected by a named hypothesis/check, demonstrating exactly what catches it.

Do not produce a giant implementation.

The code exists to settle semantic disputes, not to simulate a realistic agent.

The central executable trace should be:

repair licensed -> diagnosed conduct recurs -> repair wins -> de-license -> post-retirement conduct continues

and should make LIVE / CONTESTED / SETTLED accounting inspectable round by round.

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10. Deliverables

Produce one main round document with:

A. Verdict

Choose a precise primary verdict, for example:

• NO-FREE-EVASION-SURVIVES
• REPAIR-STABILITY-ONLY
• ANSWERABILITY-WIRING-LEAK
• ACTIVE-MASS-BOUND-BLOCKED
• COMPARISON-SURFACE-BLOCKED

Multiple secondary verdicts are fine.

B. Strongest theorem package

State the exact strongest defensible forms of Theorems A, B, C.

For every hypothesis, say which countermodel requires it.

C. Minimal interfaces

Exact semantic types / transition order for the learning sidecar, repairs, evaluators, selectors, and improvement challenges.

D. Proof sketches

Enough detail that we can tell which claims are:

• imported online-learning theorems;
• two-line algebra;
• new composition arguments;
• semantic assumptions.

E. Countermodel table

CM1–CM10 with:

• what it satisfies;
• what it breaks;
• what catches it;
• whether the failure belongs to this theorem, Coverage, anti-manipulation, Service/liability, ontology transport, or policy regret.

F. Literature verdict

Verify the exact Khot–Ponnuswami / AdaNormalHedge route. Do not overstate novelty.

Especially report:

• the actual confidence/effective-mass quantity;
• anytime status;
• dynamic/countable expert status;
• what is and is not established for delay.

G. Consumers

Run the two positive fixtures and the one negative meta-level fixture.

H. Export property

Try to state the strongest implementation-independent property implied by the package without RI vocabulary.

Candidate flavor:

When a process has persistent evidence for an available improvement, it cannot simply make that improvement normatively disappear: it must incorporate it, explicitly answer or reject the challenge, or remain answerable to it.

Do NOT assume this wording is correct. Improve/refute it.

The point is to find a property that:

1. RI/LE + learning can exactly realize;
2. does not mention Ob(pos,slot), PProto, or regret internals;
3. could at least make conceptual sense as a property of a human/institutional reflective process, even if humans do not literally satisfy RI.

I. Freeze / do-not-freeze recommendation

At the end, say what has genuinely earned freezing and what should remain under prosecution.

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11. Success criterion

The round succeeds even if the ambitious theorem fails.

The valuable outputs are:

1. an exact opportunity-adaptive repair-regret kernel, if available;
2. an exact statement of how LIVE repair mass is controlled;
3. an exact answer to what happens when the process changes the comparison surface;
4. a clear boundary between:
   • regret/non-uptake,
   • answerability/contest,
   • substantive legitimate rejection,
   • Coverage/anti-manipulation,
   • Service/liability,
   • long-horizon policy learning;
5. a theorem statement we would still want after adding inquiry, deference, and richer normative change.

The conceptual question to keep returning to is:

Does the combination of regret and Legitimate Evolution prove that a demonstrated improvement cannot be escaped for free — rather than falsely proving that every proposed improvement must eventually be adopted?

Do not optimize for elegance until that question is settled.

Legitimate Improvement

Status: specification, reference models and a prosecution record; unregistered. All names are provisional under AGENTS.md §6. Nothing here is Lean-checked and no claim is registered.

Verdict

NO-FREE-EVASION-SURVIVES-BUT-EVIDENCE-INTERFACE-OPEN — Theorem C survives the prosecution and is now stated over the right objects, and what blocks a clean merge is not the theorem but the meaning of demonstrated. The pass's main repair is separating three things the round had run together: evidence, which says r is an improvement relative to some baseline; uptake regret, which asks whether the played policy leaves that advantage unused while r is live; and answerability, which governs what remains after r is withdrawn. Evidence and uptake regret are the same functional on different distributions and are independent in both directions — a process that has adopted the repair has exactly zero uptake regret and may still have a large demonstrated improvement, and a process leaving advantage unused may never reach the threshold that makes a challenge eligible. So the challenge is grounded by the demonstration and never by the failure to act on it, and the challenge module names no regret quantity at all. Two implementation bugs are fixed: the Khot-Ponnuswami fixed point was computed by power iteration justified by stochasticity alone, which is false for periodic kernels and returned a vector off stationarity by two thirds on an exhibited period-2 chain; and AdaNormalHedge's auxiliary B was computed from one expert's own accumulated regret rather than the paper's global prior-weighted quantity. One headline claim is corrected: a surgical repair empties the diagnosed action only when no active comparator maps another action into it, since stationarity carries an inflow term the round had dropped, and the corrected version is what made the first genuine exercise of Theorem B constructible. The open seam is the baseline: one trace run against two admissible baselines gives contested against escaped, so the baseline is doing substantive normative work that the round supplies rather than derives.

The question

Legitimate Evolution gives integrity without improvement. The obvious composition fails for an obvious reason: let a repair prove itself, legitimately retire it, and the old conduct continues forever with repair regret going to zero because there is nothing left to compare against.

Something weaker and true survives. Once an improvement has been demonstrated on the process's own record, withdrawing the comparison does not end the matter: every later diagnosed occasion is one the process is either still answerable for or has explicitly answered.

Three mechanisms, kept apart

The prosecution pass's main repair.

EVIDENCE       why r is an improvement, relative to a supplied baseline
UPTAKE REGRET  while r is live, is the played policy leaving that unused
ANSWERABILITY  after r is withdrawn, what remains normatively live

Evidence and uptake regret are the same functional <d,l> - <d M_r,l> on different distributions — the played p_t for one, a baseline b_t for the other — and only the first is bounded by any theorem. A process that has adopted a repair has zero uptake regret and may still have a large demonstrated improvement. The challenge is grounded by the demonstration, never by the failure to act on it.

What the prosecution found

Power iteration was the wrong solver. A finite stochastic matrix may be periodic; the shipped code returned a vector two thirds off stationarity on an exhibited period-2 kernel. Replaced by an exact solve, with a recurrent-class route when the system is singular.

The AdaNormalHedge bound was not the theorem. Its auxiliary B is global and prior-weighted; the round computed it from one expert's own C. The old expression understated the bound, so no test was wrong — but the code claimed to be the theorem and was not.

The surgical claim dropped a term. Stationarity is pi(d) = sum_a pi(a) M(a,d). With inflow the conclusion is false, and the corrected version is what made the first genuine exercise of Theorem B constructible.

The baseline is doing normative work. One trace, two admissible baselines, opposite verdicts. That is the open seam and the reason this is not PR60-CLEAN-MERGEABLE.

Contents

• LEGITIMATE_IMPROVEMENT.md — problem, result, the three mechanisms, Theorems A/B/C, boundaries, literature, freeze recommendation.
• src/regret.py — Theorem A and the stationary solve.
• src/evidence.py — the baseline and ImprovementEvidence interfaces.
• src/surface.py — the comparison surface and the four-cell accounting.
• src/challenge.py — the canonical constitution over frozen Due/Resolve.
• src/cases.py — CM1-CM18. src/consumers.py — two positive, one negative.
• tests/ — 68 cases. python3 tests/run.py.

What this does not establish

No Lean and no registered claim.

That recurrent defects disappear: CM8 contests forever and satisfies everything.

Anything about delay, evaluator manipulation, or policy effects. Those are named boundaries with executed fixtures, not gaps left quiet.

Which baseline is the right one. Two admissible choices give opposite verdicts on one trace, and the round supplies the baseline rather than deriving it.