Normative Record and Inquiry

Normative Record and Inquiry

Normative learning needs a left side. Before a learner can answer a demand, something must determine why the demand arose, how evidence enters the practice, what authorizes a normative response, and what keeps an unanswered question from vanishing. The working architecture is afoundational: it permits one primitive induction into a normative practice and then requires every later exercise of normative authority to remain genealogically answerable to that practice.

one-time initialization
  afoundational seed S₀ ──pre-licensed induction──▶ normative record R₀

recurrent learning loop
  (N_{≤n}, Lₙ) ──inquiry──▶ world ──receipts──▶ Lₙ₊₁
      └────────────────reasoned uptake────────────▶ N_{≤n+1}

normative realization
  N_{≤n} ──authorization──▶ Oₙ ──credal interpretation──▶ Cₙ
     ──price realization──▶ Kₙ ──traderization──▶ Eₙ

The left side develops the practice and its questions. The right side gives some current demands operative form. An enforcement mechanism cannot legitimate its input, and an impeccable record does not compile itself into a credal constraint.

Status: open / unregistered research. A finite prosecution supports a repaired interface and counterexamples. No new claim is registered or Lean-checked. “Proved” below means a conditional paper derivation in that round, not Established workspace state.

Scope. This page describes the process architecture of the record-and-inquiry subline: seeds, transcripts, due tokens, the reason state, coverage as three questions, and the hand-off to a compiler. The conceptual account of what the whole history must satisfy is on Integrity, Diachronic Answerability and the settlement interface; the compiler this page hands off to is specified by the Normative Inductor. Where the two differ in vocabulary — N_{≤n} here is the full normative history H, and Lₙ the transcript the settlement view is read from — those pages govern.

An afoundational start

The seed S₀ is a small induction into a practice: enough initial authority to begin making and assessing normative moves. It is pre-licensed because there is no earlier state inside the model from which its license could come. This is the model's one explicit expenditure of primitive normativity.

The seed is not a set of eternal truths. Its contents can be criticized, reinterpreted, revised, or retired through the practice it begins. The intended invariant is not that S₀ entails every later norm. It is:

every later exercise of normative authority has an accountable ancestry
through earlier authority-bearing acts, ending at an occurrence in S₀.

Later empirical experience may supply nearly all the grounds for a current judgment. Seed ancestry says why the judgment belongs to this continuing practice; it does not say the seed substantively entails or justifies it.

S₀ is an initialization interface, not an explanation of normative bootstrapping. A future theory might instead factor the start as I₀ --Uptake--> R₀, where I₀ is an ordinary empirical, social, or practical induction history and Uptake spends only a minimal primitive participation license. The present architecture does not determine whether this factorization works or what normative structure the uptake operation must contain.

The fixed checker sits at an important boundary. Ideally it enforces only the grammar of pre-state authority, version binding, scope, and accountable disposition. Any substantive norm hardcoded into that checker is another primitive normative expenditure, even if it is not drawn as a root.

A thin world and two records

The interactive world supplies actions, utterances, measurements, testimony, query responses, and consequences. It does not label them “really due” or “truly authoritative.” Those labels would install an external normative oracle inside the positive model.

Lₙ is the permanent empirical and logical transcript. It records what was received or done and when. An interpretation of an observation—what it indicates, whether it defeats a warrant, what it calls for—is a revisable judgment in N_{≤n}.

N_{≤n} is the append-only history of normative acts: commitments, rules, undertaken reasons, due tokens, accounts, and reviews. The current standing state is a derived view:

Vₙ = View(N_{≤n}, Lₙ).

The closest analogy is a self-amending court with an immutable transcript.

• S₀ is its initial charter and induction, not a declaration of moral truth.
• L is the court reporter's permanent interaction transcript.
• R contains changing rules, cases, commitments, reasons, and accounts.
• May rules state what normative acts the court is empowered to make.
• Must rules state what cases or tasks it incurs when triggers occur.
• A due token records that a case was incurred while a rule stood.
• Amendment changes future operation; an incurred case needs a recorded account.
• Service leaves evidence under the specification governing the case.

The proof-relevant narrow waist

Many normative objects can share one identity-bearing account form:

Commitment
  Hold(judgment)
  Do(task)

Interpretations, rule activation, warrant applicability, standing, and authorization can be Hold contents. Consideration, investigation, review, response, and substantive performance can be Do contents. Once an inquiry is docketed as Do(investigate …), the existing answerability machinery supplies stable identity, split and merge, delegation, suspension, explicit release, basis-loss review, successor obligations, and typed terminal dispositions.

This is only a partial unification under the tested representation. There, a due token is the historical receipt that a standing rule fired. A coverage debt records that the token has not yet become an identity-bearing commitment or received an explicit terminal account. Equal content does not identify occurrences. Two identical investigations may share evidence or one physical action, but both old identities require their own adequacy and account edges.

The finite implementation therefore uses an event family larger than Root/Undertake/Account:

Observe(receipt, time)                         in L

Seed(commitment, induction receipt)            in R
Undertake(act, grounds, license, account, certificate)
Accrue(due token, rule version, receipt, service specification)
Account(inputs, disposition, successors, certificate)
BasisLost(historical use, epoch, review occurrence)

That operational distinction is not a representation-theoretic minimality result. The current three constructors do not expose all information used by the checker, but the round does not prove that accrual, review, or due tokens cannot be compiled faithfully into a differently typed smaller calculus.

The reason state beneath the record

This page's R is the record: the append-only history of normative acts. A research round now prosecutes a separate object beneath it — the practice's current reason structure, provisionally the reason state. Its candidate form: particular reason applications are identity-bearing hyperedges whose sources cite both revisable claims and transcript receipts; schema membership and staged applicability are themselves ordinary contents (Inst(e,σ), App(σ,c@n)), so undercutting a reason is an ordinary reason against its applicability, and reorganizing schemas is reason-guided revision rather than external clustering. The substrate stores no belief statuses and runs no update rule: it answers which reasons are enabled under a candidate stance and what depends on what, while adjudication — what to retain, adopt, suspend, or investigate when live reasons conflict — belongs to the normative learner. Two demands survived prosecution: contents need a constitutive contradiction floor, and applicability must be staged, with persistence across stages earned by defeasible schemas rather than granted by the substrate.

The reason state is 𝓡_n and the normative record is N_{≤n}; the two are different objects and the ledger settled the split so that one letter cannot name both. Evidence: the reason-representation round.

A successor round derives the boundary above the substrate: a normative transition carries a certificate citing its grounds — particular reason occurrences — its license — a prior, scoped authority act — and its lineage — the commitments it answers — as separate sorts, all checked strictly against the pre-state. Three principles carry the discipline: strict pre-state citation, constitutive immutability, and answerability continuation. Under them, a transition cannot mint its own reasons or authority, its claimed historical basis cannot be rewritten, and losing a relied-on basis is detected at the frozen citation even when a substitute reason stands — refusals that fall out of the principles rather than from dedicated anti-laundering rules. What a valid certificate establishes is that the act was licensed within the current accountable practice, not that the practice is apt. The reason-state interface is a living note under a freeze: prosecution by subtraction and by addition and a consumer-completeness pass found no missing representational kind, so a new primitive now requires a concrete inexpressibility counterexample, and the remaining open work is semantics, authorization, and policy above the substrate.

The human-facing picture of the frozen architecture is three books. The notebook is the reason ledger: it remembers particular reasons — who cited what, resting on which receipts and which revisable interpretations — and never forgets one because it was later defeated. The current view is the stance: the finite set of contents presently endorsed, including quantitative constraints, whose endorsement is membership rather than weight. The diary is the normative record: what was actually undertaken, relied on, licensed, and accounted for. A reason state is a reason ledger, not a reasoner: having a reason for a conclusion is not endorsing it; receipts are persistent while interpretations are defeasible; a schema-mediated reason explicitly depends on its staged applicability judgment, which is why undercutting is ordinary reasoning rather than a special attack mechanism; and staging separates I was wrong that it applied then from it applied then and things changed. The object language is reflectively expressive enough for the learner to reason about the applicability and organization of its own reasons, without making the historical structure itself stance-relative. Inquiry acts on the left by supplying receipts and new reasons; frontier compilation acts on the right by selecting record-accounted contents for operative realization — an arbitrary stance may be queried, but only a diary-bound stance is a candidate for force. And the three books do not substitute for one another: a reason can support an endorsement, but only the diary can establish that the endorsement actually occurred. Evidence: the transition-certificates round, its frozen interface, and its consumer contracts for inquiry and the frontier.

Grounds, license, and account lineage

Relation	What it answers	Typical inputs
grounds	Why this content?	empirical receipts and earlier judgments
normative license	What entitled this kind of move?	standing authority in the pre-state
account lineage	Which old commitment is being answered?	input-scoped occurrence identities

Empirical receipts may ground a normative move. They do not create normative authority by themselves. A measurement can explain why a practice revises a rule; some already standing authority must license revision of that kind.

License edges point strictly backward. This blocks self-installing authority and same-transition mutual licensing. In a finite accepted record, the decreasing time index makes every maximal license path terminate at a seed. That “no new roots” derivation concerns continuity of authority, not normative truth.

Account edges preserve another history: which inherited commitments were performed, closed, suspended, split, merged, or transformed. Authorization is not automatically adequate disposition; the pinned lifecycle version and input-scoped evidence still matter.

May, Must, and event-time accrual

May and Must are rule modes, not a complete logic. A May rule licenses a typed normative act. A Must rule emits a typed due token when its finite trigger fires. Every rule is itself a versioned Hold commitment whose authority comes from the practice. This avoids defining coverage as closure under every semantic implication of an open-ended theory.

A due token records the generating rule version, triggering receipt, accrual time, required task, and service-specification version. Later repeal does not rewrite it.

“When the trigger occurs” needs explicit ordering:

append receipt → evaluate triggers under the fixed pre-state rule view
               → append due tokens and coverage debts
               → admit amendments → derive the next view

A receipt followed by repeal in one transaction therefore incurs the case; repeal governs later receipts. A revision effective before the receipt changes the rule view first. Delayed recognition normally accrues when the practice receives evidence. A rule may reason about an earlier world-time field, but that retroactive reach is itself substantive and versioned.

New evidence may show that the original interpretation was mistaken. The token then receives review, cancellation, migration, or another typed account. It does not disappear. Even an authorized retroactive amendment changes current treatment through accountable dispositions rather than erasing the transcript.

Coverage is three questions

Docket coverage asks whether every generated token becomes a commitment or remains represented by a visible coverage debt. Atomic debt creation makes this safety-like. A docketing deadline requires a processor bound; eventual docketing requires fairness and serviceability.

Service coverage asks whether live inquiry liabilities are eventually serviced or receive another authorized disposition. This is liveness. It cannot be unconditional for a bounded reasoner: if two tasks arrive per step and only one can be processed, backlog grows forever.

Service certification asks what justifies closure. Each liability pins a versioned specification σℓ. Partial progress may be represented by fℓ(history) ∈ [0,1], but even fℓ=1 does not silently close the liability. A terminal account needs a certificate against the pinned σℓ. Revising σℓ requires a licensed, lineage-linked migration.

Basis loss uses the existing review mechanism. A commitment validly undertaken under an old basis remains historical. Recognized undercutting emits a Review task concerning current consequences and descendants. A different proof can make review easy to close; it does not alter the originally undertaken basis.

Bounded scheduling is downstream

The normative record determines what inquiry is owed. A scheduler decides how a bounded reasoner allocates actions across the docket. A finite snapshot may include actions, pinned specifications, progress functions, delay or urgency, context costs, and certified progress.

Mathematical class	Exact fit	What is not inherited
Set Cover with Delay	Dynamic deterministic arrivals; an action serves all pending tokens in its fixed subset; action and accumulated-delay costs are preserved.	Finite terminal delay permits permanent nonservice. The model supplies no certification or normative adequacy.
Submodular ranking / MLSC	Fixed docket; one normalized monotone submodular progress function per liability; unit-cost ordering for ranking, or metric path for MLSC; sum of cover times is preserved.	Complementary investigations need not be submodular. Mutable dockets, stateful repetition, and nonmetric costs need another model.
Adaptive submodular coverage	Fixed item set and realization space, known prior, immutable objective, and adaptive monotonicity/submodularity. Coverage requires success for every realization consistent with observations.	It is a diminishing-returns tractability condition, not legitimacy. Conditional synergy and realization-changing actions fall outside it.
Interactive submodular set cover	Finite hypothesis class, known valid responses, adversarial response consistent with a fixed target, and pointwise-submodular objectives.	The class may be misspecified; the base model assumes noiseless consistency and fixed service semantics.

The Set Cover with Delay bridge exposes a liveness trap. Divergent delay for one ignored task plus a global competitive ratio does not guarantee service when background optimum cost grows. A policy can pay background cost T, accrue focal delay T, and remain two-competitive against a comparator costing T+1. Eventual service follows with a stronger condition: the competitive inequality plus a comparator whose total cost stays uniformly bounded, or an equivalent marginal guarantee.

Golovin–Krause's self-certification motivates the proof-relevant boundary: actual target achievement is not enough for stopping if observations do not certify achievement across every still-consistent realization. This architecture borrows that distinction without adopting a Bayesian prior or adaptive submodularity as constitutive of legitimate inquiry.

Guillory–Bilmes is useful where worst-case compatible responses are preferable to a prior. It still describes a scheduler class, not the authority by which a service objective enters the record.

The corrigibility line now supplies a concrete downstream consumer for docketed inquiry. Relative to a committed principal program, the inquiry obligation at any time is the inquiry frontier: the declared reasons still undetermined by the evidence whose conditional adverse sensitivity above the docket is positive; an empty frontier forces the discovery residual to zero, and the least worst-case residual any inquiry policy achieves is the information-cell gap of the declared repertoire (Corrigibility §5; the non-capture round's DISCOVERY_THEOREM.md). Whether that frontier and the record's Do(investigate …) obligations are one object, and which repertoires are witness-complete so that inquiry makes geometric progress, is PRIORITIES.md item 93; the defeater-uptake and inquiry-interface questions (items 54, 64) are the record-side halves of the same interface.

External evaluation and counterfactual legitimacy

An external evaluator may state which demands deserved confrontation from a meta-theoretic perspective. It remains useful for counterexamples and measuring divergence. It is not the preferred positive model, where inherited Must rules generate the docket. The evaluator and internal practice can disagree.

Actual-run legitimacy and counterfactual legitimacy remain separate:

legitimacy ≈ process integrity on the actual run
           + counterfactual non-capture and corrective control

A process can follow every internal rule, docket every generated obligation, and maintain flawless accounts while another agent strategically shapes how the rules evolve. Genealogy makes that evolution inspectable; it does not show that it was unmanipulated. Non-capture remains a hyperproperty over coupled runs.

Hand-off to the normative compiler

The current view of N_{≤n} should tell an operative compiler which liabilities stand, which are applicable, which are authorized to exert a kind of force, and which have credal-bearing content. That is the input boundary to R → O.

The compiler remains open. Joint semantics must be formed before lossy credal or price projection, and safety semantics alone does not guarantee a nonempty closed convex credal set. Once a valid operative object and credal presentation exist, the current O → C → K → E machinery handles interpretation, price realization, and traderized force under its own feasibility and funding hypotheses. It does not validate the record.

Open questions

• Can the seed be factored into an ordinary induction history plus a minimal primitive uptake or participation license, and what normative structure must that uptake operation contain?
• Is there a semantics-preserving smaller event calculus for accrual, review, and due-token history, or an obstruction to one?
• Which checker clauses are grammar, and which spend substantive normativity?
• What finite trigger language avoids hidden logical omniscience?
• When should delayed evidence use current rules versus world-time rules?
• Which overload and fairness assumptions are appropriate for service coverage?
• How are service specifications compiled into evidence predicates?
• Which inquiry domains are submodular, and how should complementarity be scheduled?
• Can mutable objectives become auditable fixed scheduler instances with migration?
• Which current commitments compile through the open R → O interface?
• How should actual-run integrity compose with counterfactual non-capture?

Evidence and sources

• Afoundational inquiry round and status map
• Internal-answerability kernel
• Role-parametric answerability wrapper
• Set Cover with Delay
• Adaptive Submodularity
• Minimum Latency Submodular Cover
• Interactive Submodular Set Cover

The literature supplies scheduler definitions and guarantees only under the hypotheses described above. Authority, record, and certification are this program's proposed interfaces around those tools.