A theory's prototype standing is its revision cost: external binding plus lost investment

Type: kb/types/note.md · Tags: learning-theory, constraining, self-improving-systems

Take a theory in the sense of Theory warrant should be tracked at the finest granularity evidence licenses: an account whose premises, mechanism, consequences, and scope can be inspected and revised as named parts, and that has at least one implication that could discriminate it from a rival. Such a theory has prototype standing while it is still cheap to revise or reject. That standing is set by the theory's expected revision cost: the lower the cost, the more standing. The cost has two components. External binding is what a revision propagates to: the consumers coupled to the current version. Intrinsic reconstruction cost is what a revision discards: the investment sunk into the current version. The cost is the total of the two in kind, assessed in advance for the scope a revision would touch. There is no formula and no weighting; "expected" means anticipated at assessment time, not probability-weighted. The claim is universal over theories in this sense: each such theory's standing is set by these two components, and anything else that appears to set it must reduce to one of them. The closing paragraph states what would refute it.

Prototype standing is a standing in the theory's engineering lifecycle — how cheaply it can still be changed — not a phase of the discovery lifecycle. Whether a theory is accepted is a recorded decision that its evidence meets a named criterion for an intended use. That decision adds no consumer and discards no investment, so by itself it neither raises nor lowers revision cost. An accepted theory can therefore keep prototype standing, and a conjecture can become entrenched or heavily invested before it earns acceptance. "Prototype" here is an engineering gloss for a build kept cheap to revise while its commitments are being tested. It is not the collection-prototype sense, which names clone-once creation-time text for a new contract, and it does not name an exemplar. The disclaimer is required because Load-bearing vocabulary collisions should be prevented or visibly scoped at write time forbids one unqualified word carrying two load-bearing senses across co-loadable artifacts.

External binding is the set of consumers coupled to a theory's current version, so that a change propagates to them. Procedures, validators, and executables are consumers of this kind; so, for instance, are a certification or a training regime built on the theory. The coupling need not be machine-readable: a procedure, an audit, or a contract can bind natural-language text, as a validator binds a schema. The mechanism is accumulation. Each coupled consumer adds a dependant a revision must migrate, so replacement grows expensive as consumers accumulate — the mechanism Current-task fit alone does not warrant costly structural entrenchment states for a knowledge base's structural layer (applying it to theories is a transfer). Form does not cap the component. A harness-loaded instruction is natural language whose consumption is guaranteed on each run, so an accepted change becomes operative at once, as the prompt-editing corner of Gödel machines are a proof-governed case of reflective self-modification shows (that note discusses prompt self-editing; reading it as a theory case is likewise a transfer).

Intrinsic reconstruction cost is the investment a revision discards: for instance a large proof development, an approved safety case, or a trained model. It does not depend on consumer count; a proof development with no consumer still loses its proofs when a premise changes. This is why internal proof or model dependencies and lost evidential investment count before any external adoption: they are the second component, not an exception to the first. Improvements outside the admitted formal language need a pre-formal stage somewhere already names sunk work beside downstream coupling as what makes rejection expensive, and denies that the medium makes it cheap. A faithful rationale lowers the component: a theory retained with a faithful rationale for its parts can be repaired part by part, while one without it must be deleted and re-derived, since Selective revision needs a faithful rationale, not just a legible one. The two components are paid to different parties: propagation to the consumers, discarding to whoever holds the theory. So one can be zero while the other is large, as with an unbound proof development or a one-sentence natural-language theory that many procedures rely on. A maximum would hide one bill, which is why the cost is their total. With no consumers, standing is set by reconstruction cost alone, and an artifact of either form with neither consumers nor investment is cheap to discard.

Representational form, taken here as natural-language versus symbolic, determines neither component. A natural-language theory bound through a procedure, an audit, or a contract is expensive to revise. A low-authority formal sketch stays disposable. Codification is a change of form and consumer kind, from natural language into a symbolic artifact with assigned consequences, and the definition says nothing about deployment or acceptance. Codification makes formal consumption available; standing changes when a validator or executable is actually coupled, and the added consumer, not the form, is the cause. Form gets mistaken for standing when availability is read as coupling. Form does determine which checks are available, as Theory warrant should be tracked at the finest granularity evidence licenses states, and what each use costs in interpretation: a natural-language premise is revisable without a build step but is reinterpreted at each use. Form does not determine what a revision costs; the bound theory and the disposable sketch above show each component set by something other than form. At most, form correlates weakly with the second component — symbolic artifacts may tend to carry construction investment that natural-language statements do not — a tendency that prevalence evidence of form failing to predict discarded investment at equal binding would refute.

Since binding is a cost component, binding a consumer to a theory before the theory is accepted for that consumer's scope spends standing that evidence has not yet licensed. Acceptance for the bound scope licenses binding. Current fit does not, and current form does not. Executable success does not either, because Exact implementation does not validate a requirement against its objective: a passing executable shows the artifact matches its requirement, and adoption supplies authority rather than prudence. So binding is the act to withhold before acceptance for the bound scope, whatever form the theory has. Binding before acceptance may still be chosen for coordination value or forced by an enduring constraint. It is then knowingly spent standing, weighed as the current-task-fit note weighs entrenchment, which leaves the threshold open.

Standing is assessed per part, at the grain consumers bind to. Warrant is already tracked per part, and binding and investment attach to parts as well, so their total is per part too. Parts differ in standing where either component differs. In partial codification the parts share their discarded investment unless the codified part carried its own construction, such as a proof development, so the difference in standing sits in binding except where it did. A premise that becomes a checked operative invariant loses standing while the rest of the theory keeps it.

A symbolic artifact can exist unbound, so an unbound, lightly invested formal model has prototype standing. Only where the cost of construction, proof generation, or checking was the bottleneck does cheaper formalization let formal models enter the prototype loop as experiments. Competing formal models of one theory then preserve alternatives by exposing different consequences before anything is bound, and a theory may move between forms, or be revised wholly in symbolic form, while both components stay low. Formalization cost is a bundle whose parts fall independently — translation into a model, construction, proof generation, checking, and evidence of world fit, per Improvements outside the admitted formal language need a pre-formal stage somewhere — so cheaper checking leaves translation and world-fit costs where they were, and leaves the need for cheap rejection in place. It also leaves what a proof warrants where it was: entailment inside the model, not correspondence to the world, as Causal and proof obligations are two formal routes to assessing explanatory-reach shows.

Two theories of the same form and the same epistemic status should differ in prototype standing when their binding or reconstruction cost differs. Two theories of different form should not differ when both components are equal. A pair equal in both assessed components whose revisions, when attempted, differ materially in what they propagate to or discard refutes the claim. So does one theory whose revision cost is materially set by something that reduces to neither component. The pre-formal stage note names authority and rollback cost beside coupling and sunk work; on this note's reading, rollback cost is propagation to consumers and authority is consumers obliged to follow, so both reduce to binding. If either resists that reduction, it is the counterexample. No paired case has been observed, so the comparison stands as a prediction.

Scope

  • Rejection retracts the claim and ends its standing. Revision and suspension preserve a surviving claim's standing only while both components stay low. Procedures and state records are superseded rather than refuted, so they fall outside the theory sense used here.
  • Cheap is relative to the named consumers a revision would reach and the investment it would discard.
  • The "determines neither" bound covers natural-language versus symbolic form and no other.
  • Distributed-parametric form is outside that bound. There a revision is a retraining rather than a per-item edit, so the reconstruction component is set largely by the form.

Open Questions

  • Which observable costs measure external binding and reconstruction cost, so that the paired comparison above can be run rather than stated?
  • Does a bounded operative trial, run to produce the acceptance evidence, count as binding before acceptance or as acceptance for a trial-sized scope? The warrant rule above does not settle it.
  • How should a system inventory prose authorities whose binding is real but not machine-readable?
  • When consumers bind to partially codified theories at different grains, which grain should a review or acceptance decision target?

Relevant Notes: