the-program

Architecture

The program studies two ways a reasoner can remain responsive while changing. Normativity concerns learning from reasons inside a practice. Deference concerns trusting another process without surrendering correction. Legitimacy names the trajectory conditions both need.

        Normativity
 reasons → responses → learning
             |
         Legitimacy
  standing, records, write access
             |
          Deference
 trust → delegation → corrigibility

The current mathematical center is a conditional response-learning result. A normative layer says when a burden is due and which responses are licensed. A separate performance layer assigns bounded loss. A loss-blind compiler turns the normative inputs into surgical response maps, and an online-learning engine learns against those maps.

Due + Licensed + Performance
             ↓
       lawful compiler
             ↓
   surgical response maps
             ↓
     learning dynamics

This separation prevents two shortcuts. A response is not licensed merely because it lowers loss, and a licensed response need not improve loss. Coverage is also separate: a theorem about responding on due occasions cannot make those occasions occur.

Above the static interface sits a dynamic-competence layer for temporally extended behaviour, and it is a separate object from legitimacy:

   Legitimate Evolution / normative state
             ↓
   traderized Logical Induction — bounded belief, normative enforcement
             ↓
   constitutional execution interface — the gate, the admissible envelope
             ↓
   continuation BRIA — accountable selection among executable continuations
             ↓
   temporally extended behaviour

Logical Induction predicts and enforces; Continuation BRIA allocates realized experiments among causal continuations of the system's next block, scoring accountable claims on realized outcomes only. The two keep separate wealth accounts and separate theorems; a prediction that becomes an accountable claim is the bridge between them, and that bridge is an interface rather than a theorem. BRIA is not part of legitimacy: the constitution supplies the wrapper and the class of legitimate continuations, nothing about their value.

The results each layer rests on, stated at theorem level with their strength labels, are collected on the Theorem Spine.

Current mathematical shape

Let S be public pre-action states, D public burdens, and A a finite response space. The three primitive interfaces are:

Due      : S → D → Prop
Licensed : S → D → A → Prop
Loss     : S → A → [0, L]

Due and Licensed feed the compiler. Loss feeds the learning engine, not the compiler. For a targeted bad response b and licensed alternative r, a positive margin Loss(S,b) - Loss(S,r) ≥ δ_g > 0 is an additional performance hypothesis. Coverage measures how often the relevant Due occasions appear relative to the learning scale.

Current status — Open / unregistered. The abstract theorem and dynamics witness are current research results with exact round verdicts, but PR #31 registered no workspace claim. Due has no satisfactory substantive instantiation; Licensed has interface discipline but not substantive soundness; performance is successful only for the fixtures; coverage remains a hypothesis.

Hypothesis ledger

The following table is the machine-significant projection of normativity.learning.current. It mirrors the repository ledger rather than serving as an independent source of interface state.

ID	notation	kind	producers	consumers	write access	excluded from loss	presentation requirements	registered status	soundness claim IDs
due	Due : S → D → Prop	primitive-normative-interface	substrate.relational-answerability; interface.normative	compiler.surgical; interface.coverage	public-pre-action-record	—	—	null	—
licensed	Licensed : S → D → A → Prop	primitive-normative-interface	interface.normative	compiler.surgical	public-pre-action-record; normative-practice	—	—	null	—
performance-loss	Loss : S → A → [0, L]	primitive-performance-interface	interface.normative	engine.blum-mansour; theorem.response-learning; witness.learning-dynamics	learner-acknowledgments; ecology-challenges; scorekeeper-practice	standing; grants	—	null	—
response-space	A	finite-theorem-interface	interface.normative	compiler.surgical; engine.blum-mansour; theorem.response-learning	specification	—	—	null	—
due-selector-compilation	Due → selector	compiler-interface	interface.normative; compiler.surgical	engine.blum-mansour	public-pre-action-record; normative-compiler	—	decidable; record-computable; prospective	null	—
compiled-surgical-repairs	CertifiedSurgicalRepair	compiler-output	compiler.surgical	engine.blum-mansour; theorem.response-learning	normative-compiler	—	—	null	—
blum-mansour-engine	Blum–Mansour engine	learning-engine	engine.blum-mansour	theorem.response-learning; witness.learning-dynamics	learner-policy	—	—	null	—
positive-margin	δ_g > 0	joint-performance-hypothesis	interface.normative	theorem.response-learning	joint-licensed-response-and-performance	—	—	null	—
coverage	coverage(Due)	quantitative-property-of-due	interface.coverage	theorem.response-learning	ecology-trajectory	—	—	null	—
compiler-loss-blindness	compiler ⟂ Loss	compiler-discipline	audit.compiler-soundness; compiler.surgical	theorem.response-learning	compiler-input-boundary	—	—	null	—

Write access and legitimacy

The learner writes its own acknowledgments and policy. It does not get to decide whether a burden is due, and the compiler does not read current loss advantage. In the relational fixture, challenges, exposures, and the scorekeeper's practice come from other parts of the ecology. Standing and grants may gate what is due, but they are excluded from theorem-facing loss because a learner-controlled grant created a laundering route.

Answerability is owing an answer; auditability is the record knowing what became of every debt; efficacy is the answer-demand actually reaching you. Response learning uses the first two. Corrigibility uses the first and the third. Legitimacy is where their write and trajectory conditions meet: an internal half — an Integrity evolution of the accounted obligation state whose verdicts factor through its reasons — and an external half — the trajectory robustly open at every one of its states and every channel of influence transparent to its declared reference — with Diachronic Answerability derived from the record half and normative induction as the quantitative consequence.

What the theorem does—and does not—cover

The current accounting compares surgical responses against losses on the actual trajectory. With a positive margin, low modification regret bounds bad-response mass on due occasions. A separate coverage hypothesis turns that bound into a vanishing conditional rate. It does not establish that the counterfactual world in which the repair was always applied would have improved.

Nor does the abstract theorem solve normative content. It exposes typed sockets for Due, Licensed, and performance. Supplying those sockets soundly is the next substantive problem.

Evidence and verification

• [Crown-jewel final report — NORMATIVE-RESPONSE-LEARNING-THEOREM-SETTLED; BM-FEEDBACK-DYNAMICS-WITNESSED](https://github.com/A-M-Berns/alignment-workspace/blob/76b65e5cc327ca2f334e829a76548514813ab4b0/prompts/2026-08-13-crown-jewel-learning-theorem-final/REPORT.md) <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem-final/">[round]</a>
• Three-interface boundary <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Compiler soundness and loss-blindness <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Coverage interface <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Machine-readable interface ledger
• Legitimacy loss-dependency audit <a class="ref round" href="/rounds/2026-08-13-relational-scorekeeping-bridge/">[round]</a>