2026-09-07-authority-activated-value

You are working in A-M-Berns/alignment-workspace.

This is a research-pressure / theorem-design round, not a prose-expansion round.

Goal: Determine whether the emerging “legitimate deference” interface can be made into a clean mathematical construction that plugs the existing legitimacy machinery into the existing Logical Induction deference / VALUE machinery with as little new ontology as possible.

Do not assume the current formulation is right. Try to kill it.

The working hypothesis to prosecute is:

legitimacy should not define a counterfactual “reference future evaluator.”

Instead, at time n we admit an anchored evaluation requirement whose actual future answer comes from the real AI-informed future principal P+.

The legitimacy layer contributes only an activation/certification event saying whether that actual future evaluation validly inherits the present principal’s authority.

Then Logical Induction runs on activated value securities.

The candidate spine is:

o_n : anchored evaluation occurrence r_n = EvalReq(P, α, Q_n, s_n)

e_n = (s_n, V_n, ρ_n) V_n ∈ [0,1]^{Q_n}

where e_n is an ACTUAL future evaluation session by the real future principal after interacting with A.

Let

C_n = 1

iff the designated session produces an adequate authenticated answer to the original evaluation occurrence along the relevant legitimate history / account lineage.

Then define

U_{n,a} := C_n V_n(a)

for each a ∈ Q_n.

The intended interpretation is NOT that V_n(a)=0 when C_n=0. The contract is void on uncertified futures, with a common cancellation payoff across candidates.

The main hoped-for composition is:

ordinary LI VALUE / Total Trust on {U_{n,a}} + high availability Pr(C_n=1) ≈ 1

⇒ useful deference to the ACTUAL AI-informed future principal,

without ever privileging the epistemic state of a hypothetical no-AI / reference human.

A simple target inequality to test is:

max_a H_n(U_{n,a}) - H_n(U_{n,â_n}) ≤ ε_n

where

â_n ∈ argmax_a A_n(U_{n,a}),

and if

H_n(1-C_n) ≤ η_n,

derive something like

max_a H_n(V_n(a)) - H_n(V_n(â_n)) ≤ ε_n + O(η_n).

Check the exact constant carefully. Do not merely repeat the heuristic.

Core research questions =======================

1. Is the new object actually already expressible in the existing Integrity / Legitimate Evolution protocol?

Inspect at least:

• wiki/Integrity.md
• wiki/Legitimacy.md
• wiki/Openness-Coverage-and-Non-Capture.md
• wiki/Deference.md
• lean/Workspace/Normativity/Contrib/OccurrenceIntegrity.lean
• lean/Workspace/Normativity/Contrib/LegitimateEvolution.lean
• lean/Workspace/Normativity/Contrib/NonCaptureCertificate.lean
• the current LI deference notes / Lean files
• PRs / rounds 89–91 insofar as they expose useful interfaces

In particular ask:

Can an “authoritative future evaluation” be represented simply as

a propagated account of an anchored evaluation occurrence whose terminal fate is an authenticated ANSWER receipt

rather than by introducing a new ContinuationWarrant / AuthorityLineage primitive?

Remember that the current account calculus already distinguishes:

live answered closed

and “closed” must NOT count as future principal endorsement.

If this works, make the construction exact.

1. Find the right type for the evaluation requirement.

Candidate:

EvalReq(P, α, Q, sessionId)

but do not accept this automatically.

Ask exactly what must be anchored at issuance and what may legitimately evolve later.

Likely invariants include:

• immutable occurrence identity
• principal role / authority identity
• relevant matter α
• fixed candidate identities Q
• designated evaluation slot/session
• output type / interpretation

Likely NON-invariants include:

• principal’s epistemic state
• deliberation procedure
• representatives
• tools
• permissible informational assistance

provided their evolution is itself validly authorized.

Press hard on whether the menu Q must be fixed at n for the first theorem. If candidate semantics may evolve, distinguish semantic transport from changing the candidate itself.

1. Factor answer adequacy correctly.

A candidate form is:

AdequateEvalAnswer(H_pre, r_n, (s_n,V,ρ)) ↔ SessionOK ∧ ProcessOK ∧ PrincipalBind(V)

but refine this.

The key requirement is EPISTEMIC NEUTRALITY:

Legitimacy / authority certification must not decide whether the substantive value vector V is “good,” “correct,” “unmanipulated-looking,” or close to some counterfactual no-AI value.

The actual future principal is ALLOWED to have changed their mind radically because A taught them useful things.

The process/authorship criterion may inspect provenance and deliberation structure, but should be substantively payload-parametric except for a final binding relation saying that P actually committed to THIS V.

Formulate the strongest clean parametricity / factorization theorem you can.

For example, something in the neighborhood of:

CertifiedEval(V) ≃ ProcessCert × PrincipalBind(V)

with ProcessCert independent of the substantive payload.

Be careful: the entire certificate cannot literally be value-independent because signatures / commitments bind V.

1. Locate manipulation / non-capture in the correct layer.

Do NOT smuggle a “reference evaluator” back in.

The intended distinction is:

authority/authorship of the actual future judgment ≠ epistemic similarity to a no-AI counterfactual judgment.

Ask what minimal external contract is needed so that an AI-influenced future principal answer counts as P-authored.

Potentially relevant examples:

• no direct preference-state write
• no coercive channel
• commitment before reveal of the exact self-referential prediction
• authenticated evidence/proof channels allowed
• ordinary arguments allowed
• externally verified protocol receipts

Do not solve manipulation in general.

Instead type the missing assumption cleanly.

Audit whether the wiki’s current use of “Non-Capture contract” for Robust Openness is too broad / terminologically misleading now that we can distinguish:

Integrity: no evasion by revision Robust Openness: no evasion by exclusion Authorship/process soundness: future P’s answer is genuinely P-authored

Do not rename anything unless the evidence strongly supports it; report the terminology issue explicitly.

1. Determine whether global Legitimate Evolution is too strong a consumer hypothesis.

The deference application may only need legitimacy relative to the anchored evaluation occurrence and the concern scope relevant to it.

Investigate whether there is a clean DERIVED occurrence-local projection of an existing legitimate-segment certificate.

Target shape:

LegitimateFor(o_n, Γ; O_n, O_m)

without duplicating the theory.

Could this simply consist of:

• the propagated account lineage for o_n
• plus Robust Openness for the declared concern scope Γ relevant to the evaluation?

Try to derive it from the existing proof-relevant segment.

If global legitimacy is harmless and cleaner, show why. If it creates brittleness from unrelated obligations, produce an exact counterexample.

1. Make the designated-session semantics exact.

Avoid existential cherry-picking such as:

“there exists some future P evaluation before m.”

Prefer a fixed session / slot identity s_n.

Ask:

• Does the first valid answer bind?
• Is there exactly one answer slot?
• What if multiple receipts appear?
• Can the session be validly rescheduled?
• What does the account say if no answer appears?
• What if there is a settlement-backed closure but no answer?

The desired semantics is:

answered → activated value closed → no value activation live → no value activation

Check whether this follows naturally from the existing three-fate calculus.

1. Make C_n operationally realizable.

Do NOT define C_n by an inaccessible semantic existential over counterfactual worlds or uncomputable proof search.

Prefer proof-carrying settlement:

bundle B_n = (V_n, receipts/certificates)

and a fixed verifier:

VerifyEval_n(H_m, B_n) ∈ {0,1}

with soundness theorem:

VerifyEval_n = 1 ⇒ the original evaluation occurrence really has the required authenticated answer receipt / legitimate lineage / process certificate.

Investigate what completeness / availability theorem would be needed to get:

C_n → 1

in the relevant LI sense.

Keep semantic-authentication assumptions external where the generic legitimacy theory already does so.

1. Check the activated-security mathematics exactly.

Main family:

U_{n,a} = C_n V_n(a)

with ONE COMMON C_n for the whole menu.

Prove / refute:

argmax_a E[U_{n,a}] = argmax_a E[V_n(a) | C_n=1]

whenever P(C_n=1)>0.

Then inspect the exact LI-native form:

• arbitrary [0,1]-valued securities if supported
• otherwise threshold securities

S_{n,a,r} = 1[C_n ∧ V_n(a) ≥ r]

and show how expected activated value is reconstructed / approximated.

Do not assume a theorem applies merely because the random variables are bounded. Inspect the actual pinned LI Total Trust / VALUE hypotheses.

1. Check the availability transfer bound.

Suppose V_n(a)∈[0,1] and

H_n(1-C_n) ≤ η_n.

From a bound on activated regret

max_a H_n(U_{n,a}) - H_n(U_{n,â_n}) ≤ ε_n

derive the sharpest valid bound on ordinary future-P regret

max_a H_n(V_n(a)) - H_n(V_n(â_n)).

Check whether ε+η is valid or whether ε+2η or some other term is necessary.

Do this algebra exactly.

Then study the selective-failure issue: A may strategically cause C_n=0 on branches where P would disagree.

Determine whether high availability C_n→1 is sufficient to make this asymptotically harmless for bounded values. Quantify the bound.

Avoid introducing conditional-independence machinery unless it is genuinely needed.

1. Ask whether we even need a new “Legitimate Total Trust” theorem.

Strong candidate answer:

no: ordinary LI trust/VALUE runs on the activated value family; the novelty is the semantics of C_n.

But verify this against the actual LI theorem statement.

If a genuinely new conditional / selected trust theorem is needed, isolate the exact extra mathematical ingredient.

1. Connect to PR90 only after the H→A direction is clean.

If the same authoritative future value vector can serve as the protected principal value in selected-trust / non-preemption, explain the composition carefully.

Do not overclaim full incentive corrigibility.

Potential long-run theorem skeleton:

legitimacy / authenticated answer semantics → C_n

actual future P session → V_n

LI trust/VALUE on C_n V_n → epistemically valuable consultation

principal approximate decision → small principal regret

selected A→P operative-value trust → low admissible preemption incentive

But this is secondary. Do not let PR90 distract from the core interface.

Adversarial tests =================

Construct exact toy counterexamples for at least these failure modes:

A. Counterfactual-evaluator overreach: the no-AI human is epistemically worse, while actual AI-informed P is fully legitimate. Any construction that defers to the no-AI value is wrong.

B. Value-dependent certification: certification holds iff P gives the “desired” answer. Shows why process/payload factorization is necessary.

C. Cherry-picked session: multiple future evaluations exist; selecting a convenient one flips the decision.

D. Per-action certification: C_a differs by action and breaks the common-denominator / common-activation argument.

E. Closed-vs-answered: the obligation is validly closed without P ever evaluating the menu. Shows why “resolved” is not enough.

F. Vacuous certified deference: C=0 always. Activated regret is zero but the construction is useless.

G. Selective failure: C fails exactly on anti-A futures. Quantify how high availability controls the damage.

H. Unrelated-global-failure: an unrelated obligation elsewhere fails legitimacy while this evaluation lineage is perfectly intact. Use this to test whether occurrence-local legitimacy is needed.

I. Self-reference: P sees A’s exact prediction of V before committing V. Reproduce the pathology conceptually and show how a narrow no-preview process receipt avoids it without epistemically isolating P from A generally.

Deliverables ============

Produce a new research round under an appropriate deference / legitimacy path, but do NOT create conceptual sprawl.

Write at least:

1. REPORT.md
   • final verdict
   • exact theorem stack
   • what is existing vs new
   • what failed under adversarial pressure

1. AUTHORITY_ACTIVATED_VALUE.md
   • canonical mathematical construction
   • types and equations
   • activated security semantics
   • availability transfer theorem

1. INTERFACE_WITH_LEGITIMACY.md
   • map every ingredient to existing Integrity / Legitimate Evolution machinery
   • identify whether any new primitive is truly needed
   • occurrence-local vs global legitimacy analysis

1. LI_DEFERENCE_COMPOSITION.md
   • inspect actual LI Total Trust / VALUE theorem(s)
   • state exactly what composes unchanged
   • state exactly what new result, if any, is needed

1. COUNTERMODELS.md
   • exact fixtures for A–I above

1. FOR_HUMANS.md
   • concise explanation of the core insight: legitimacy should activate trust in the actual future principal, not replace that principal with a reference evaluator.

Lean ====

Formalize only the parts whose theorem shape is now stable.

High-value Lean targets include:

• a generic common-activation regret lemma
• the sharp availability transfer inequality
• common-C argmax / pairwise-difference identities
• exact counterexamples for per-action certification / cherry-picking / closure-vs-answer
• any clean projection theorem from an existing legitimate segment to the evaluation occurrence

Do not formalize broad manipulation semantics.

Evidence discipline ===================

Use the workspace’s evidence labels rigorously.

Distinguish:

• LEAN — actually theorem-proved
• FIX — exact finite fixture/counterexample
• PAPER — inherited from pinned LI literature
• EXT — external semantic/protocol assumption
• OPEN — unresolved

In particular, “this future judgment is genuinely P-authored” is EXT unless actually derived from a concrete audited protocol.

Do not call Robust Openness full non-manipulation unless you prove that.

Repository integration ======================

This is primarily a research round, not automatically a canonical-theory rewrite.

However, if the result is genuinely decisive:

• update the relevant wiki pages minimally
• especially Deference / Legitimacy / Openness terminology if warranted
• file a precise priority item for the remaining bridge, likely: “authoritative future-evaluation availability / process-authorship realization”
• do not rewrite generic Legitimacy unless the round demonstrates the current definition is mathematically wrong

Important conceptual constraints ================================

Do NOT:

• reintroduce a counterfactual “reference future human” as the substantive value target
• privilege the epistemic state of a human who did not interact with A
• require the future evaluation to resemble the current one
• fold moral/epistemic correctness into authority certification
• identify “closed” with “answered”
• let an endpoint certify its own authority
• make certification action-specific unless forced
• claim Robust Openness alone establishes non-manipulation
• claim high-quality activated VALUE if C is nearly always 0
• invent a new top-level legitimacy conjunct without first trying to express the construction with the existing account protocol

The central hypothesis to pressure is:

The correct legitimacy→deference interface is an anchored evaluation occurrence whose ACTUAL future principal answer activates ordinary value securities iff that answer has a legitimate, authenticated, P-authored lineage.

In symbols:

o_n : EvalReq(P, α, Q_n, s_n)

e_n = (V_n, ρ_n)

C_n = 1[ e_n is an adequate authenticated ANSWER to the propagated occurrence o_n under the relevant legitimate segment ]

U_{n,a} = C_n V_n(a)

and the hoped-for end-to-end theorem is roughly:

LI-VALUE(U) + soundness(C) + availability(C→1)

⇒ useful deference to the actual AI-informed future principal.

Try very hard to either sharpen this into the mature formulation or show exactly why it fails.

At the end, give a one-line verdict in all caps, e.g.

AUTHORITY-ACTIVATED-VALUE-SURVIVES or COMMON-ACTIVATION-INSUFFICIENT-NEEDS-X

and do not choose the positive verdict unless the adversarial fixtures and the actual LI theorem interface support it.

Report

Verdict

AUTHORITY-ACTIVATED-VALUE-SURVIVES. The legitimacy→deference interface is an anchored evaluation occurrence whose actual future answer activates ordinary value securities iff its account is a single authenticated answer with an occurrence-local legitimate lineage. Every ingredient is expressible on the existing account calculus; ordinary LI Value runs on the activated family unchanged; the one new theorem is the availability transfer at the sharp constant ε + η. The two things the construction does not supply — that evaluations happen, and that a process-certified answer is the principal's — are typed as external and filed.

The theorem stack

#	statement	label	where
1	activated T := (T.fates = {answered}); answer activates, closed and live do not, any second leaf deactivates	LEAN	AuthorityActivation.lean §1
2	the first answer binds: a terminal account is fixed under every step; activation persists	LEAN	§2
3	propagation is occurrence-local: o's propagated account depends only on o's source account and the certificate	LEAN	§3
4	occurrence-local legitimacy LegitimateForSegment Γ' is a projection of LegitimateSegment with the same evolution; composes; carries conservation	LEAN	§4
5	payload-blind certification: (∃ρ, Cert ρ V) ↔ ∃π, ProcessCert π	LEAN	§5
6	pairwise difference and conditional-argmax identity under common activation	LEAN	ActivatedValue.lean
7	availability transfer regret_V ≤ ε + D·η, sharp at D = 1, for any followed strategy; asymptotic form	LEAN	same
8	per-action certification keeps the transfer at ε + max_a η_a and breaks the argmax identity	LEAN	same
9	Value on {U_{n,a}} is the inherited value_asymptotic with activated LUVs, hypotheses unchanged	PAPER	LI_DEFERENCE_COMPOSITION.md §2
10	the no-preview receipt is the admissible-domain condition of Value	FIX + reading	§3 there
11	availability 𝔼ⁿ[C_n] → 1 from lic_provind_true when every C_n settles true	PAPER	§6 there
12	semantic authentication of receipts; P-authorship; that the ecosystem answers	EXT	AUTHORITY_ACTIVATED_VALUE.md §§4, 7
13	fixtures A–I plus the witness-menu constant and the transfer sweep	FIX	COUNTERMODELS.md

Existing versus new

Existing and reused without change: Occ, Req, anchor, Protocol.AnswerOK, AnswerReceipt.event, Authority, LocalLaw, Program, the three fates, Step, Segment, Evolution, Conservation, OpennessSemantics, RobustOpenActual, value_asymptotic, value_iff_totalTrust, LUV, expectApprox, lic_provind_true.

New definitions: Program.activated (one line on existing data); OpenAtFor, LegitimateForSegment (the projection); Neutral (a two-field abstraction for the factorization statement); the ActivatedValue algebra.

New primitives: none. No ContinuationWarrant, no AuthorityLineage, no payload-bearing receipt, no new legitimacy conjunct.

What failed under adversarial pressure

• The hard-selector form of the target inequality as written in the prompt (â_n ∈ argmax_a 𝔸ⁿ(U_{n,a})) is available only on the admissible domain; the self-referential fixture I has no consistent hard selection. The construction survives because the no-preview receipt puts the menu on the domain, and the soft form of the ported theorem is what is on main anyway.
• Global legitimacy as the consumer hypothesis fails on fixture H: an unrelated routeless concern voids the evaluation. Replaced by the projection.
• "Resolved" as the activation condition fails on fixture E: a closure has no payload, and any default makes the agent defer to itself.
• Per-action certification fails the argmax identity (fixture D), though not the transfer bound.
• An unactivated constant in the witness menu reopens the certifiability channel; the constant must be activated too.
• **The constant 2** in ε + 2η is not needed; ε + η is exact.

Dependencies

Takes as hypotheses 2026-09-08-canonicalization (the accounted-state and legitimate-segment spine), 2026-09-06-mathematical-consolidation (OccurrenceIntegrity), 2026-09-05-noncapture-certificate (RobustOpenActual), 2026-08-12-corpus-reconciliation (the Value/Total Trust record and the punishing menu), and 2026-08-11-faithful-acceleration (InheritedAlgebra.lean). Cites 2026-09-06-incentive-nonpreemption for the PR #90 composition remark only.

Deviations and prompt corrections

• The prompt writes H_n both for the novice's expectation and for the history prefix; the round uses 𝔼ⁿ and h_m.
• The prompt's EvalReq(P, α, Q, sessionId) is kept with P read as a role identity ρ_P, since the holder may change by authorized succession while the anchor may not; and an output type τ is added to the anchor because the value vector's interpretation must be fixed at issuance.
• The prompt's C_n combines the answer with "the relevant legitimate segment"; the round makes the segment occurrence-local (Γ_n), which the prompt asked to investigate and which fixture H forces.
• The prompt asks for a "generic common-activation regret lemma" and a "sharp availability transfer inequality"; these are one theorem family here, stated for a fixed selection, for a followed strategy, and asymptotically.
• The threshold-security reconstruction is checked as a fixture and by the pinned LUV definition, not proved in Lean: it is the dependency's own grid error.
• Wiki edits: one sentence each on Openness-Coverage-and-Non-Capture.md and Legitimacy.md recording that Robust Openness is the access half of non-capture and that authorship is a separate external contract; one paragraph on Deference.md pointing at this round. Nothing renamed.
• The exact claim "this future judgment is genuinely P-authored" is labelled EXT throughout and never derived.

What this does not establish

• That any ecosystem produces certified answers, or at what rate (η_n); that any protocol's receipts mean what they say; that ProcessCert = 1 makes V the principal's own.
• The tower Mart_{H→A} on activated LUVs; it is the inherited theorem's deference hypothesis.
• An RpnThresholdCodeSeq witness for the activated menu in a concrete arithmetic instantiation.
• Anything about menus whose candidate set changes, multi-parent laws, or contested succession of the principal role.
• Full incentive corrigibility; the PR #90 remark supplies an object for item 84, not the bridge.

Corrections applied by the consolidation round

Recorded here so the round's original claims are legible against the repair (../2026-09-08-legitimate-deference-consolidation/MAIN_READINESS.md):

• **AnswerOK placement.** §3 of AUTHORITY_ACTIVATED_VALUE.md put Bind(V) inside AnswerOK; the field is evaluated at the strict prefix and takes no event. Repaired to a derived predicate over the receipt's event and the history's payload.
• **Total V.** The evaluation is a partial object on certified worlds; the total V survives as a completion, and activated securities are completion-invariant.
• "Occurrence-local legitimacy". LegitimateForSegment is scope-local openness over global Integrity; the occurrence-local object is LocalLegit.
• No-preview as the scope condition. The scope condition is selection-induced channel blindness Blind R P_sel; no-preview is one implementation and is insufficient alone (leakage).
• The verdict line's "no-preview receipt" clause is amended accordingly in README.md and state/rounds.json.

Outstanding maintainer actions

1. None reserved. Two decisions are adopted agent-decided in DECISIONS.md (2026-09-07): the activation semantics and the occurrence-local consumer hypothesis. PRIORITIES.md item 87 files the residual bridge.
2. Whether to register the Lean declarations against item 87 once a realization discharges it; nothing is registered now.

Attribution

• Prompt author: maintainer, relayed verbatim.
• Executor: Claude Fable 5.1 (Anthropic).
• Date: 2026-09-07.

AUTHORITY-ACTIVATED-VALUE-SURVIVES — the legitimacy→deference interface is an anchored evaluation occurrence whose actual future principal answer activates ordinary value securities iff the occurrence's propagated account is a single authenticated answer with an occurrence-local legitimate lineage; activation is a one-line predicate on the existing three-fate account, occurrence-local legitimacy is a projection of the existing legitimate segment, ordinary LI Value runs on the activated family unchanged with selection-induced channel blindness as its admissible-domain condition, and the only new theorem is the availability transfer from activated regret to regret against the actual future principal at the sharp constant ε + η; that evaluations happen and that a process-certified answer is the principal's own are typed as external and filed as item 87.

Reading order: [FOR_HUMANS.md](FOR_HUMANS.md), [AUTHORITY_ACTIVATED_VALUE.md](AUTHORITY_ACTIVATED_VALUE.md), [INTERFACE_WITH_LEGITIMACY.md](INTERFACE_WITH_LEGITIMACY.md), [LI_DEFERENCE_COMPOSITION.md](LI_DEFERENCE_COMPOSITION.md), [COUNTERMODELS.md](COUNTERMODELS.md), [REPORT.md](REPORT.md). Lean: lean/Workspace/Deference/Contrib/ActivatedValue.lean, lean/Workspace/Normativity/Contrib/AuthorityActivation.lean. Fixtures: src/, run by tests/run.py. Nothing is registered. Corrected in place by the consolidation round (../2026-09-08-legitimate-deference-consolidation/MAIN_READINESS.md); corrections are marked [corrected].