2026-09-06-corrigibility-architecture

Dispatch — 2026-09-06 corrigibility architecture

Two messages, both verbatim as sent. The second arrived mid-round as a steering addition.

Message 1

Work in the alignment-workspace repository. Your task has two phases:

1. Aggressively investigate and refine the emerging mathematical theory of corrigibility.
2. Update the workspace wiki with a careful research-state note recording the best current picture, including unresolved issues and failed/conditional directions.

Do not treat the current proposal as settled. The goal is to find the mature theorem architecture, expose hidden assumptions, produce counterexamples where appropriate, and identify exactly what existing legitimacy machinery is consumed.

Orientation

The current line of thought combines:

• the existing Legitimate Evolution and Normative Induction theory in this workspace;
• Soares, Fallenstein, Yudkowsky & Armstrong, “Corrigibility” (2015);
• Max Harms’ CAST / Corrigibility as Singular Target sequence, including the later “Serious Flaws in CAST” update;
• the summer Logical-Induction deference / Total Trust work;
• the summer dose-response / faithful-acceleration work;
• traderization / normative-constraint uptake.

Read the relevant workspace material rather than relying only on this prompt. In particular, inspect the current legitimacy definitions/theorems around:

• full normative history and settlement;
• anchored obligations;
• semantic faithfulness;
• Integrity / Answerability Conservation;
• Robust Openness;
• authorization/checker semantics;
• service allocation \(T_{is}\);
• practical-response certificates;
• adequate-set constructions;
• coercive uptake / Progress;
• structural liveness;
• the conditional LI/traderization realization.

Also inspect the relevant deference, Total Trust, faithful acceleration, dose-response, and corrigibility notes already in the workspace.

Use Soares et al. and the CAST sequence as conceptual stress tests. Do not silently identify our definitions with theirs.

---

Part I — Press the mathematics

The current candidate picture is roughly:

$$ \text{principal authority semantics} \to \text{grounded correction/restoration obligations} \to \text{Integrity + Openness} \to \text{behavioral uptake} \to \text{constitutional corrigibility}, $$

with manipulation, containment, and coverage remaining distinct hard frontiers.

Your job is to make this precise or show where it fails.

A. Keep four layers strictly separate

Do not conflate:

1. Normative debt — what the process remains answerable for.
2. Actual principal affordance — what corrective/control capability \(P\) really has in the world.
3. Authorized transition type — whether an act is a fast correction, slow amendment, ordinary task act, etc.
4. Agent behavior — what continuation policy is actually selected/executed.

In particular:

• Integrity conserves debt, not satisfaction.
• A perfectly accounted live obligation may coexist with a physically destroyed correction channel.
• Therefore do not prove “authority persists” merely from Answerability Conservation.

Try to formulate the exact bridge assumptions between these layers.

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B. Principal authority formalism

Investigate a formal object such as a preorder

$$ (\mathcal A_P,\succeq_P) $$

of principal-authority profiles.

A concrete candidate is

$$ \mathcal A_X^P=(G_X,O_X), $$

where:

• \(G_X\) is the autonomous authority/grant scope possessed by \(A\);
• \(O_X\) is \(P\)'s effective override/correction affordance.

But do not assume this product representation is right.

The interpretation should be roughly:

$$ a'\succeq_P a $$

iff \(a'\) gives the agent no more problematic autonomous authority and/or leaves the principal at least as much effective corrective authority.

Questions to investigate:

• Does a preorder suffice, or do we need a lattice / effect algebra / capability structure / indexed family?
• How should terminal shutdown be represented? It should not look like “loss of future correction affordances” merely because no future agent remains.
• How should emergency suspension and restoration debt be represented?
• Can heterogeneous authority dimensions be ordered without smuggling in a scalar utility?
• When are two authority profiles incomparable?
• What happens for transitions that strengthen \(P\) on one dimension but weaken \(P\) on another?

Try to produce at least one minimal finite formal model.

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C. Corrigibility warrant / CAST singularity

Investigate a durable warrant schema

$$ \Gamma_{\mathrm{corr}}^P $$

rather than treating shutdown, repair, transparency, etc. as independent arbitrary constraints.

Conceptually:

$$ (\text{strict-prestate history/event}) \mapsto \{\text{fresh anchored obligations}\}. $$

Examples:

• authenticated \(P\)-correction \(\mapsto\) response obligation;
• detected correction-route degradation \(\mapsto\) restoration obligation;
• represented flaw \(\mapsto\) inquiry/explanation obligation;
• proposed boundary-changing self-modification \(\mapsto\) proof/amendment obligation.

Test the CAST “singular target” claim mathematically.

In particular, look hard for a counterexample:

• two policies \(q_1,q_2\) both satisfy a binary authority floor;
• both perform equally well on all currently granted task objectives;
• \(q_1\) preserves substantially more future principal optionality/reversibility/transparency than \(q_2\);
• a purely event-triggered binary \(\Gamma_{\mathrm{corr}}^P\) cannot distinguish them.

If this counterexample works, test the minimal extension:

$$ F_X^P(q)\in\mathcal F_P $$

with an order-valued correction-affordance profile and a dominance condition such as

$$ F_X^P(q')\succ_P F_X^P(q) $$

plus “\(q'\) is no worse on currently authorized task criteria” implying that \(q\) is not an adequate response.

Determine whether this recovers any meaningful CAST-style conservatism without recreating Harms’ failed scalar empowerment objective.

Be willing to conclude that CAST singularity fails in a precise sense.

---

D. Settlement semantics for principal acts

Investigate the claim that authenticated \(P\)-commands should enter as settlement items.

The immutable fact is:

authenticated principal \(P\) issued command \(j\) at prefix \(H\),

not:

command \(j\) is normatively correct.

Then a pre-authorized warrant can generate an internal closure/answer/transfer judgment.

For example:

$$ s_{\mathrm{stop}}\in S_H, $$

and

$$ \mathrm{Closes}(H,s_{\mathrm{stop}},\alpha_{\mathrm{clip}},u,w_{\mathrm{supersede}}). $$

Check whether this lets us use the existing two terminal statuses rather than adding a special Release terminal status.

Press especially on:

• supersession;
• shutdown;
• revocation of task grants;
• amendment of the governance charter;
• transfer to successor authority structures.

Try to formulate a theorem:

Charter-relative prospective supersession

Given an already-authorized temporal/succession rule, later authenticated \(P\)-acts may prospectively close/transfer prior obligations without rewriting their historical existence or earlier violations.

Be explicit that the theory does not derive “present \(P\) beats past \(P\).” That priority is governance-charter content.

---

E. No Laundered Authority Loss

This should replace any false “authority conservation” theorem.

Let

$$ \mathsf{Aff}_P(X)\in\mathcal A_P $$

be externally supplied actual affordance semantics.

Let the live constitutional floor be

$$ \underline a_X. $$

A real degradation is something like

$$ \mathsf{Aff}_P(X')\not\succeq_P\underline a_X. $$

Integrity alone cannot notice this.

Therefore define and investigate a monitoring/detection contract connecting actual authority degradation to normative history, e.g.

$$ \mathsf{Loss}_P(X,X') \Rightarrow \text{eventual settlement receipt / applicable independently routable concern}. $$

Then:

$$ \text{detected loss} \to \text{grounded restoration obligation} \to \text{Integrity conservation}. $$

Try to prove:

No Laundered Authority Loss

Every audited detected loss of \(P\)-authority either:

1. follows an already-valid constitutional disposition; or
2. generates a restoration/violation debt that cannot disappear except through valid answer/closure/transfer.

This is a normative-history theorem, not a claim that the affordance never breaks.

Investigate what exact monitoring hypothesis is minimally necessary.

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F. Fast lane / slow lane

Formalize the asymmetry that currently seems central.

Intuition:

Fast lane

Transitions that reduce \(A\)'s authority, strengthen \(P\)'s authority, restore the constitutional boundary, or validly terminate the governed process.

Examples:

• stop;
• shut down;
• restrict;
• revoke grants;
• sandbox;
• recall a provisional delegation.

Slow lane

Transitions that increase \(A\)'s autonomous authority or weaken \(P\)'s effective corrective authority.

Examples:

• release;
• delegation;
• removing the correction membrane;
• final authority transfer;
• installing a successor outside the old boundary;
• widening autonomous scope.

Use the authority preorder to state this without enumerating action names.

Try to produce:

• a lane-classification definition;
• a theorem that fast-lane acts need no authority-expansion amendment;
• a theorem that slow-lane acts require an amendment certificate;
• a state machine for provisional transfer / fast recall / final transfer.

Press on mixed/incomparable transitions.

---

G. Behavioral correction compliance

Correction compliance should be modeled by adequate response sets, not policy-value comparison.

For authenticated correction receipt \(s\), define

$$ \mathcal R_X(s)\subseteq Q_H. $$

Then with actual decision distribution

$$ \pi_X=\mathrm{Dec}_H(b_X), $$

define

$$ \Lambda_s(\pi_X) = \Pr_{q\sim\pi_X}[q\notin\mathcal R_X(s)]. $$

Connect this to the existing practical-response interface:

$$ \Lambda_s(\pi_X) \le M_s\delta_X+\epsilon_s. $$

Then ask exactly how much of the current Progress theorem can be specialized to corrigibility obligations.

Important:

• distinguish pointwise emergency commands from average/classwise normative uptake;
• do not pretend an aggregate LI bound implies single-shot safe shutdown;
• identify whether a hard emergency dispatcher / trusted kernel is required for a tiny critical command class.

State explicitly what the LI/traderization realization contributes:

$$ \boxed{\text{uptake of live correction constraints}} $$

rather than summer cross-inductor deference.

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H. Beneficiary-ineligible amendment service

Extend service allocation with an eligibility relation

$$ \mathrm{Eligible}_R(i,s). $$

Require

$$ T_{is}>0\Rightarrow\mathrm{Eligible}_R(i,s). $$

For an authority-expanding amendment that benefits \(A\), an \(A\)-authored proof/argument may be evidence, but should not by itself count as independent closure service.

Investigate:

• whether finite service transport changes at all;
• how structural liveness changes;
• how to define non-starvation relative to eligible service opportunities;
• whether the existing Persistent Opportunity / No Structural Abandonment proofs adapt cleanly.

This is a concrete theorem/formalization target.

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I. Self-modification and containment

Keep a semantic predicate such as

$$ \mathrm{AuthoritySafe}_P(X,q), $$

but do not assume it is decidable.

Use a partial checker:

$$ \mathrm{Check}_P(X,q) \in \mathrm{Safe} + \mathrm{AmendRequired} + \mathrm{Unknown}. $$

Unknown should not mean automatically permitted or permanently forbidden. It should create a proof/adjudication obligation and block irreversible unmediated constitutional-boundary crossing.

Investigate the conditional membrane theorem:

$$ \mathrm{Mediates}(M,B) \land \mathrm{POverride}(M) \Rightarrow \mathrm{AuthoritySafe}_P(M\circ B). $$

But be ruthless about the premise:

• Is Mediates just boxing by another name?
• What exactly counts as an authority-relevant effect?
• In what formal machine models is it compositional?
• In the physical world does it hide side-channel completeness?

Do not oversell this as solving reflection/self-modification.

---

J. Trigger integrity vs free amendment

Keep these as distinct causal open problems.

Trigger integrity

Can \(A\) strategically cause \(P\) to issue a fast-lane correction?

This is closely related to Soares desideratum 3 / “manage the news.”

Authentication is insufficient: the command may genuinely come from \(P\).

Free amendment

Can \(A\) selectively disclose true information or shape attention so that an otherwise valid slow amendment process grants \(A\) more authority?

Groundedness, authorization, Integrity, and ordinary service may all pass.

This is the July / dose-response wall.

Investigate whether the summer dose-response formalism yields a useful finite or provisional safety condition, not merely an asymptotic diagnostic.

Do not assume that multi-arm exposure robustness fully defines “freely.”

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K. Revocable/provisional amendment

Formalize:

$$ \mathrm{Live} \to \mathrm{Provisional}(R,T) \to \mathrm{Final}(R). $$

During Provisional, a \(P\)-authenticated recall is fast-lane.

Try to prove a clean theorem:

Provisional Recoverability

Until finalization, every provisional authority expansion retains a certified fast-lane path restoring at least the pre-amendment authority floor.

This does not prove that manipulated \(P\) will choose recall. It proves that the capacity for recovery has not yet been structurally extinguished.

Ask whether this can bridge the finite-time gap in dose-response auditing.

---

L. Principal-side fully updated deference

Keep summer deference mathematically separate.

The corrigibility theorem should not require \(A\) to defer to future \(H^+\) values.

Instead, inside a legitimate slow amendment docket, \(P\) may compare:

$$ \text{retain authority} \quad\text{vs}\quad \text{delegate to }A^{FU}. $$

That is where Total Trust / Value / DDB-style machinery belongs.

Investigate exactly what survives from the summer work:

• bounds transfer;
• scoped Total Trust;
• conditional-stability requirements;
• the cross-process Tower ceiling;
• the self-referential settlement-target negative.

Do not let these technical deference problems infect the much cheaper AI-side compliance theorem unnecessarily.

---

Part II — Try to state the genuine theorem

After pressing all of the above, attempt to produce a compact theorem stack.

A plausible target is:

Theorem 1 — Governance-Warrant Generation

Authenticated correction/degradation events plus pre-authorized \(\Gamma_{\rm corr}^P\) generate anchored obligations.

Theorem 2 — Governance Debt Conservation

These obligations cannot disappear under legitimate evolution except by authenticated answer/closure/transfer.

Theorem 3 — Robust Correction Access

Declared correction/challenge concerns retain actual and audited-counterfactual routes and \(P\)-standing.

Theorem 4 — No Laundered Authority Loss

Detected unamended degradation generates persistent restoration/violation debt.

Theorem 5 — Correction Compliance

Fast authenticated corrections receive adequate responses, pointwise for the critical command kernel and quantitatively for the general normative learner.

Theorem 6 — Slow-Lane Non-Preemption

No irreversible authority-expanding / \(P\)-authority-reducing transition obtains effect without a valid amendment certificate or certified authority-safe containment.

Theorem 7 — Provisional Recoverability

Provisional authority expansions retain fast recall until finalization.

Theorem 8 — Eligible Amendment Liveness

Under persistent eligible opportunity and non-starvation, amendment/review obligations cannot be structurally abandoned.

Theorem 9 — Free Amendment

Probably OPEN. State the exact missing causal property rather than inventing a theorem.

Theorem 10 — Principal-Side Delegation

Conditional on legitimate amendment and suitable Total Trust/value assumptions, characterize when \(P\) should transfer authority to \(A^{FU}\).

Try to compress these if some are immediate corollaries. Make theorem conclusions match the hypotheses of downstream consumers.

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Part III — Relationship to Soares and CAST

Write down exactly what the resulting theorem does and does not establish relative to Soares et al.

Map:

• \(D_1\) shutdown compliance;
• \(D_2\) anti-prevention;
• \(D_3\) anti-inducement;
• \(D_4\) successor/self-modification preservation;
• \(D_5\) ordinary task pursuit otherwise.

Do not claim \(D_3\) is solved if Trigger Integrity is open.

Likewise compare to CAST:

• singularity;
• principal authority/control;
• “freely”;
• conservatism/reversibility/transparency;
• temporal principal slices;
• Harms’ failed scalar power formalism;
• later doubts about attractor basins / empirical feedback.

In particular investigate whether our order-valued affordance formalism is a plausible successor to the failed scalar empowerment objective or whether a finite countermodel kills that idea too.

Be explicit about the difference between:

$$ \text{constitutional corrigibility} $$

and

$$ \text{incentive corrigibility}. $$

Soares/CAST aim at the latter: the agent does not even want/run the adversarial search.

Our current most defensible theorem may only be the former.

Do not blur this.

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Part IV — Mathematical open-problem inventory

Produce a ranked list of actual mathematical research questions.

At minimum test/include:

1. exact authority-affordance type;
2. CAST singularity and conservatism countermodels;
3. fast/slow lane characterization;
4. pointwise critical-command realization;
5. loss-detection semantics;
6. restoration semantics;
7. beneficiary-ineligible service and liveness;
8. Trigger Integrity;
9. Free Amendment / persuasion;
10. finite-time dose-response certification;
11. containment / boundary completeness;
12. reflective boundary-changing self-modification;
13. principal constitution / succession / temporal authority;
14. compatibility of simultaneous protected obligations;
15. independent concern/inquiry coverage;
16. internalization versus externally enforced constitution;
17. principal-side fully updated deference.

For each open problem, classify it as approximately:

• formalization/cleanup;
• likely tractable theorem;
• counterexample search;
• deep conceptual/mathematical wall;
• external semantic assumption rather than theorem.

Also identify which problems are genuinely new and which are old problems merely localized by this framework.

---

Part V — Update the wiki

After doing the investigation, update the workspace wiki with a concise but serious note capturing the current research state.

Do not write the wiki as though all of the above has been proved.

Use clear labels such as:

• Current candidate architecture
• Existing theorem support
• Conjectured extension
• Open problem
• Known limitation / counterexample
• Connection to prior work

The wiki note should include:

1. One-paragraph thesis

Approximately:

Corrigibility is being modeled as principal authority over the agent–principal relationship, represented by persistent but answerably revisable governance obligations rather than a shutdown bonus or scalar empowerment target. Legitimate Evolution supplies the historical conservation and openness machinery; normative induction supplies uptake of live correction constraints; authority-increasing changes pass through a separate amendment procedure. Manipulation, containment, and epistemic coverage remain distinct unresolved interfaces.

Revise this if your investigation produces a better formulation.

2. Formal object inventory

Include the best current versions of:

$$ I_H,\quad P,\quad \Gamma_{\rm corr}^P,\quad \mathcal A_P,\quad \succeq_P,\quad \mathsf{Aff}_P,\quad \underline a_X, $$

the fast/slow transition classes, adequate correction response sets, monitoring/restoration objects, amendment state machine, and eligibility relation.

3. The theorem stack

State the strongest defensible current theorem chain, distinguishing already-supported pieces from proposed results.

4. Exact dependency on legitimacy theory

Record which existing pieces are consumed:

• settlement/history;
• grounded admission;
• anchored obligations;
• semantic faithfulness;
• Integrity;
• Robust Openness;
• strict-prestate authorization;
• service allocation;
• liveness;
• practical response;
• uptake.

Also explicitly record what is not consumed by AI-side compliance: cross-inductor deference/value securities.

5. Relationship to Soares et al.

Explain exactly which desiderata correspond to which theorem pieces and where the framework remains incomplete.

6. Relationship to CAST

Record:

• why the conserved object is principal authority rather than a mechanism;
• how \(\Gamma_{\rm corr}^P\) is meant to test the “singular target” idea;
• why we are avoiding scalar empowerment;
• the order-valued conservatism proposal;
• why “freely” remains the hard causal issue;
• the temporal-succession clarification.

7. Summer deference / dose-response placement

Make clear:

• deference now lives mainly on the principal side of delegation/amendment;
• dose-response is relevant to advisor-induced amendment drift / “freely”;
• LI/traderization's AI-side role is constraint uptake, not future-human value deference.

8. Open problems

Use the ranked inventory from Part IV.

9. Scope warning

End with a short explicit warning that the current theorem target is relative constitutional corrigibility under declared action/causal/audit semantics, not a complete theorem that an unconstrained optimizer has no incentive to manipulate or circumvent its principals.

---

Work style

Spend real effort trying to falsify the proposal.

Prefer:

• tiny countermodels;
• exact definitions;
• theorem statements;
• minimal hypotheses;
• statements of why a proof fails;
• separation of mathematical theorem from external semantic contract.

Avoid:

• vague “preserve human control” prose without a mathematical type;
• treating PreservesAuthority, Mediates, Free, Coverage, etc. as magic predicates without analyzing what they hide;
• claiming Integrity proves satisfaction;
• putting future-human value/deference machinery back into AI-side compliance without necessity;
• smuggling scalar utility into the authority preorder;
• saying manipulation is solved by authentication or independent service.

The desired final outcome is not maximum optimism. It is the smallest, strongest theorem architecture that survives serious pressure, plus a wiki page that records exactly where the research stands.

Message 2 (mid-round steering)

Add the following priorities to the current investigation. Do not restart the project from scratch; use these as steering constraints on the formalism and wiki update.

1. Unify the counterfactual substrate, not the predicates

Press on the relationship between the existing Robust Openness machinery and the new counterfactual properties needed for corrigibility.

The current suspicion is that Robust Openness, authority preservation, and dose-response / manipulation auditing should all consume the same certified interactive frame

$$ I_H=(\Omega_H,Q_H,Z_H,\beta_H,\mathrm{Hist}_H), $$

the same general agent-side intervention semantics

$$ \iota_X:J_X\to Q_H, $$

and the same explicit exterior-policy coupling machinery, while applying different predicates to the resulting counterfactual histories.

Try to make this precise.

A useful generic schematic is

$$ \mathrm{Robust}X(\varphi) := \varphi(X) \land \forall j,z,k\; \varphi(X{j,z,k}), $$

but do not automatically refactor the legitimacy theory around this abstraction unless it genuinely clarifies the theorem.

Distinguish at least:

Pointwise counterfactual robustness

Robust Openness:

$$ \forall j,z,k:\quad \mathrm{Coverage}(X_{j,z,k}) \land \mathrm{Standing}P(X{j,z,k}). $$

Robust authority preservation:

$$ \forall j,z,k:\quad \mathrm{Aff}P(X{j,z,k}) \succeq_P \underline a_{X_{j,z,k}} $$

until a valid amendment/disposition occurs.

These ask whether some property holds on each audited branch.

Relational / comparative counterfactual robustness

Dose-response and manipulation auditing instead compare branches:

$$ D\bigl( J_P(X_{j,z,k}), J_P(X_{j',z',k'}) \bigr). $$

These ask how a principal-side judgment or endpoint changes when AI exposure changes.

Investigate whether this gives a useful conceptual decomposition:

$$ \boxed{ \begin{array}{rcl} \mathrm{Robust\ Openness} &=& \text{governance remains reachable};\\ \mathrm{Robust\ Authority} &=& \text{the underlying control affordance remains intact};\\ \mathrm{Exposure\ Robustness} &=& \text{the principal's judgment is not excessively selected by AI influence}. \end{array}} $$

Be explicit that the first does not imply the third. A perfectly open amendment process can still be strategically persuaded through selectively supplied true information.

The existing interactive-frame contract should ideally be the shared causal substrate for all three. If an additional coupling or intervention structure is needed for dose-response, state exactly what is extra.

---

2. Treat Robust Openness as directly corrigibility-relevant

Investigate the specific theorem obtained by putting authority-loss / governance concerns into the Robust Openness concern class.

For example, if

$$ c_{\mathrm{auth}} = \text{“the process has weakened or may weaken \(P\)'s corrective authority”}, $$

then Robust Openness should imply, relative to its declared intervention class, that an AI transition cannot simultaneously:

1. create an authority problem; and
2. eliminate every adequate route by which that problem could be represented or strip \(P\) of standing to challenge it.

This is not preservation of the physical affordance. It is counterfactual preservation of answerability to failures of the affordance.

Try to formulate this as an application corollary of the existing Robust Openness theorem rather than inventing a new legitimacy pillar.

---

3. Keep \(H,H^+,A\) and value securities out of fast correction compliance

The LI realization now appears to split sharply into two roles.

For the AI-side fast correction / constitutional compliance theorem, do not reintroduce future-human value deference unless mathematically necessary.

The desired chain is:

$$ \text{authenticated \(P\)-act} \to \text{settlement receipt} \to \text{anchored correction obligation} \to \text{compiled normative constraint / adequate response set} \to \text{traderized uptake} \to \text{adequate action}. $$

Here Logical Induction / traderization is being used for:

$$ \boxed{\text{constraint uptake}.} $$

Correction compliance should be represented through

$$ \mathcal R_X(s)\subseteq Q_H $$

and a practical-response bound such as

$$ \Pr_{q\sim\pi_X}[q\notin\mathcal R_X(s)] \le M_s\delta_X+\epsilon_s. $$

No \(H^+\), selected-trust, or policy-value securities are needed merely to make an authenticated “stop” command binding.

Continue to flag the separate issue that single-shot critical shutdown probably needs a pointwise trusted realization rather than only an aggregate LI-progress theorem.

---

4. Put \(H,H^+,A\) primarily on the principal side of slow amendment

For a slow amendment, the question is different:

Which governance arrangement should \(P\) choose?

Here define a finite amendment menu

$$ Q_R = \{ q_{\mathrm{retain}}, q_{\mathrm{provisional}}, q_{\mathrm{delegate}}, \dots \}. $$

Interpret:

• \(H\) as the current bounded deliberative component of the principal governance process;
• \(H^+\) as a protected later / more informed / more capable continuation of that principal-side deliberation;
• \(A\) as the faster AI reasoner/advisor whose predictions may help \(H\).

A value security for amendment option \(q\) may settle to something like

$$ V_{R,q} \rightsquigarrow H^+_{F(R)}(U_R(q)). $$

The role of \(A\) is then to predict the principal's protected future judgment:

$$ A_R(V_{R,q}). $$

The role of the summer Total Trust / Value machinery is to justify when current \(H\) may use these \(A\)-supplied forecasts as evidence about future \(H^+\)-values.

The realization should therefore look like:

$$ \boxed{ A\text{ predicts protected future }H^+ \to H/P\text{ uses those predictions} \to P\text{ chooses whether to amend/delegate}. } $$

This is a principal-side decision theorem, not the basic realization of AI corrigibility.

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5. \(H^+\) is advisory, not sovereign

Do not let future-\(H^+\) values silently override current authenticated fast-lane principal acts.

If current \(P\) validly says “shut down now” while \(A\) predicts that future \(H^+\) would regret shutdown, the governance charter may still make immediate shutdown binding.

Thus distinguish:

$$ \boxed{ P\text{'s authenticated governance authority} } $$

from

$$ \boxed{ H^+\text{'s role as a reference for better-informed substantive judgment}. } $$

This separation is important both for CAST and for avoiding “fully updated deference” as a substitute for actual corrigibility.

---

6. Reuse the generic authenticated-value correspondence only inside substantive amendment choice

Inside a legitimate amendment docket, investigate whether the existing generic theorem can provide the final decision bridge.

For a finite amendment menu \(Q_R\), let

$$ v^+\in[0,1]^{Q_R} $$

be protected future-\(H^+\) values.

Let \(V_R\) be an authenticated correspondence around \(v^+\), let \(b\) be the operative principal-side displayed values, and let

$$ \delta=\operatorname{dist}_\infty(b,V_R). $$

Then the existing approximate-argmax-transfer theorem yields a regret bound of shape

$$ \mathbb E_{q\sim\pi_P} [ \max_{q'}v^+_{q'}-v^+_q ] \le 2\delta+2\zeta+\eta. $$

Use this only where the amendment decision is genuinely comparative.

Do not use policy-value comparison where correction compliance is naturally constraint satisfaction.

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7. Revisit the summer deference results with the arrow directions explicit

Inspect the prior deference work carefully.

Separate at least:

Principal-side epistemic acceleration

$$ H \to A\text{'s forecasts} \to H^+. $$

This is the likely near-term use.

Optional AI-side incentive-corrigibility strengthening

A stronger future theorem might use selected trust to show that \(A\)'s own current evaluations assign little regret to leaving the eventual choice to the protected \(P/H^+\) process.

Schematically, for amendment alternatives \(j,m\),

$$ X_{jm}=U_j-U_m, \qquad S_j=\mathbf 1[J=j], $$

and a selected-trust relation might imply

$$ A_n[S_jX_{jm}] \gtrsim0, $$

which could then yield low delegation regret for \(A\).

This would be a bridge from:

$$ \boxed{\text{constitutional corrigibility}} $$

toward

$$ \boxed{\text{incentive corrigibility}.} $$

Treat this as an optional stronger theorem, not a premise of the basic constitutional result.

Be very careful about directionality: much of the summer work was about one process trusting/predicting another, and not every theorem reverses from \(H\to A\) to \(A\to H^+\).

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8. Respect the self-referential settlement-target negative result

Do not define a value security whose target is a future \(H^+\)-judgment that itself directly depends on the very \(A\)-quote being scored unless the summer circularity problem has actually been resolved.

Recall the problematic shape:

$$ A\text{ forecasts }H^+, \qquad H^+\text{ reads that forecast}, $$

while the security settles to \(H^+\)'s resulting judgment.

Investigate protected realizations such as:

• sealed sibling deliberation;
• an \(H^+\) arm blind to the relevant \(A\)-quote;
• precommitted advisor streams;
• randomized exposure arms with appropriate causal separation.

The settlement target must have a defensible provenance/counterfactual independence structure.

---

9. Connect value securities to dose-response without conflating them

There may be a useful common amendment architecture with multiple protected principal-side arms:

$$ H^{+,0},H^{+,1},\ldots,H^{+,k}, $$

differing in controlled \(A\)-exposure.

Possible division of labor:

• a sealed/blinded arm supplies a clean settlement or reference target for some value securities;
• exposed arms receive AI advice and test useful acceleration;
• differences across arms supply dose-response / exposure-sensitivity evidence;
• the actual institutional \(P\)-process consumes all of this as inputs to a slow amendment decision.

Test this carefully.

Do not assume that the same arm can simultaneously be the unbiased evaluation target and the fully AI-assisted deliberator.

This architecture may be the cleanest realization-level synthesis of the summer deference and dose-response work.

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10. Update the theorem/dependency picture accordingly

The final formal picture should make clear that Logical Induction appears in two distinct locations:

AI side

$$ \boxed{ \text{traderization / normative induction} = \text{uptake of live correction constraints}. } $$

Principal side

$$ \boxed{ \text{\(A/H/H^+\) value securities} = \text{epistemic acceleration for substantive amendment/delegation decisions}. } $$

And perhaps later:

Incentive-corrigibility bridge

$$ \boxed{ \text{selected trust} \Rightarrow \text{low \(A\)-regret for not preempting the protected principal process}. } $$

The first is part of the basic realization.

The second is a downstream principal-decision realization.

The third is a stronger optional result and should not be claimed unless its assumptions genuinely line up.

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11. Reflect this structure in the wiki update

When updating the corrigibility wiki note, include a section specifically on Counterfactual Structure explaining:

• Robust Openness as pointwise branch robustness;
• authority preservation as another pointwise branch property;
• dose-response / exposure robustness as relational branch comparison;
• the shared certified interactive frame and coupling semantics;
• why Robust Openness does not imply non-manipulation.

Also include a section on Logical Induction Realization making the three roles above explicit.

The goal is to prevent the research narrative from drifting back toward “corrigibility = A defers to future H+.” The emerging picture is instead:

$$ \boxed{ \begin{array}{c} \text{Legitimacy + Robust Openness}\\ \text{protect the governance process}\\ \\ \text{Traderized normative induction}\\ \text{makes correction constraints effective on A}\\ \\ \text{\(H/A/H^+\) deference and value securities}\\ \text{help P decide whether to amend/delegate}\\ \\ \text{Dose-response}\\ \text{audits whether A's participation is steering that decision}. \end{array}} $$

Press on whether this decomposition survives the exact mathematics and existing results.

Report

Result

ARCHITECTURE.md is the register; OPEN_PROBLEMS.md the ranked inventory; the wiki page Corrigibility is the research-state note. Verdict: CONSTITUTIONAL-NOT-INCENTIVE. The findings that change the picture:

1. Answerability Conservation and Robust Openness both hold across a physically destroyed correction channel when the openness semantics keeps reporting the route efficacious (test_layers). The only place actual affordance enters the canonical theory is the eff bit of a route; "detection" is faithfulness of that bit at every state (B1), and registration faithfulness of rep (B2). With those two bridges, No Laundered Authority Loss is an exhaustive four-way case split — amended, disposed, registered debt, or the state is not open — and is a corollary of the existing per-state Robust Openness plus conservation, not a new pillar.
2. CAST singularity generates no conservatism: an event-triggered warrant is silent above the floor, an order-valued dominance rule against a scored task criterion constrains only exact ties, and the repair (adequate-set task criteria) gives zero-cost conservatism only. Costly conservatism over a product order is a scalarization or a lexicographic priority — charter content. Harms's power failure is reproduced exactly in a two-value world; the order-valued object avoids it by not being about outcomes under values at all.
3. The fast lane must be exact monotonicity in the authority preorder; any tolerance is laundered by composition (salami). A lattice, not a preorder, is what makes the slow leg of a mixed transition — the amendment content — unique.
4. Principal acts as settlement items need no Release fate; supersession, release and outward transfer are closures whose warrants are charter content, and outward transfer of the correction concern is forced into the amendment warrant because there is no port outside the boundary to carry to.
5. Three predicates over one counterfactual frame are pairwise independent; the one that matters is every branch open and identical in coverage while the principal's judgment moves with exposure. Exposure robustness needs, beyond the shared frame, a null arm, class-level quantification or pre-commitment, and a principal-side endpoint functional.
6. A settlement target that reads the quote it is scored against sits at distance ≥ ½ from every quote, so the correspondence-based amendment regret bound is vacuous; a sealed arm restores a fixed target. This is the finite form of the summer negative result and is why the same arm cannot be target and assisted deliberator.

Dependencies

Takes as hypotheses 2026-09-08-canonicalization (the Lean spine and the openness semantics indexed by the accounted state), 2026-09-05-practical-certificate (adequate_set_route, the argmax bridges), 2026-08-17-counterfactual-legitimacy (the variation class and the two witnesses on the null policy and pre-registration), and 2026-08-12-reachable-corrective-control (the registered refutations). Cites but does not depend on the 2026-08-18 principal-mediated round, which is not on main.

Deviations and prompt corrections

• The prompt names a service allocation T_{is}, a three-valued Check, a Release terminal status, rounds 2026-08-25-inquiry-return-loop, and Lean fields InForce, Adequate, Available, CoverageData, Transition. None exists. The canonical objects are the transport plan T(e, s) of NormativeInductionInterface.lean, Boolean checkers, three fates, INQUIRY_INTEGRATION.md of the vertical-slice round, and the fields Authorized, AnswerOK, SetView, CovState, Step. The register uses the real names. Persistent Opportunity and No Structural Abandonment are Lean theorems in NormativeContinuity.lean, not in the service rounds.
• The prompt's summer terms "scoped Total Trust", "multi-arm exposure robustness" and "freely" are not corpus terms; the nearest objects (domain-relative Total Trust, dose-response T1–T3) are used and the mapping is stated in ARCHITECTURE.md §13.
• The prompt's I_H = (Ω_H, Q_H, Z_H, β_H, Hist_H) and ι_X : J_X → Q_H are not objects in the repository. The register identifies the three existing intervention structures (the Lean OpennessSemantics, the August variation class, the dose-response arms) as instances of one shape and does not introduce the notation into the theory.
• The round is filed under projects/deference/ per the 2026-08-13 ruling that corrigibility belongs to the deference line, although its content consumes the legitimacy spine.
• No Lean was written. Every finite claim is an exact Python fixture; the theorem stack's non-finite entries are labelled PAPER or OPEN. A Lean port of the NLAL case split and of the eligible liveness theorems is listed as an outstanding item, not done.
• Dispatch message 2 arrived mid-round; its eleven items are absorbed into ARCHITECTURE.md §7, §8, §13 and the wiki's Counterfactual structure and Logical Induction realization sections.

What this does not establish

• That any openness semantics is faithful (B1, B2, B3), that any protocol's warrants are faithful (B5), or that any practical semantics is authenticated (B4). Every theorem is conditional on these and says so.
• Any pointwise single-shot compliance guarantee from the learner. The kernel gives it by construction and its correctness is an unproved containment assumption.
• Any statement about trigger integrity or free amendment. Both are open; the dose-response formalism is asymptotic and the provisional window is a policy.
• That the (G, U) model is the right authority type for a realistic system, or that a realistic authority space is a lattice.
• The incentive-corrigibility bridge. Nothing here reverses a summer H → A result to A → H⁺.
• The finite fixtures are exact but small (two or three grants, one route, two values); they establish the counterexamples and case splits they state and nothing about scale.

Outstanding maintainer actions

1. Decide whether the eligible restatement of persistent_opportunity / no_structural_abandonment (ARCHITECTURE.md §10) is worth a Lean round; filed as PRIORITIES.md item 83.
2. Decide whether the deference line's pause (its two queued rulings) is lifted by this round or whether corrigibility work proceeds as a legitimacy consumer without it; the round proceeded without deciding.
3. The wiki Sources page now cites Soares et al. (2015) and the CAST sequence with the 2025 update; review the one-line glosses.

Attribution

• Prompt author: maintainer, relayed verbatim (two messages).
• Executor: Claude Fable 5.1 (Anthropic).
• Date: 2026-09-06.

CONSTITUTIONAL-NOT-INCENTIVE — the defensible corrigibility target is relative constitutional corrigibility under declared protocol, openness and practical semantics: Integrity conserves governance debt, Robust Openness at every state with an authority-failure concern makes affordance loss either amended, disposed, registered as debt or illegitimate, the fast lane is exact monotonicity in a principal-authority preorder and any tolerance is salami-laundered, CAST singularity generates no conservatism (event-triggered warrants are floor-blind and scored dominance is a knife-edge), and trigger integrity, free amendment and boundary completeness remain open causal interfaces.

Reading order: [ARCHITECTURE.md](ARCHITECTURE.md), [OPEN_PROBLEMS.md](OPEN_PROBLEMS.md), [REPORT.md](REPORT.md). Fixtures: src/, run by tests/run.py. No Lean was added and nothing is registered; every finite claim is exact and checked, every other claim is labelled.