Alignment Workspace

kernel.extension-realized-rate

and · drafted

Statement

The registered claim kernel.extension-realized-rate (The extension's interface theorem: avg π ≤ avg (D − c_k)/ϖ + ε̄ ((D − w)/ϖ + θ_hi) + (B(K) + M(K))/(ϖ Σ w_k)) holds as its declaration states it; the registry's note is quoted in the Source.

Source

projects/deference/CLAIMS.md, entry kernel.extension-realized-rate (class lean-proved, status active, origin round 2026-09-27-corrigibility-kernel-phase2; answers item 104). Documentation: verification: projects/deference/rounds/2026-09-27-corrigibility-kernel-phase2/SPEC.md; context: prompts/2026-09-27-corrigibility-kernel-phase2/REPORT.md. The signature of Workspace.Deference.Contrib.KernelExtension.DecisionInterface.realized_rate in lean/Workspace/Deference/Contrib/KernelExtension.lean.

Notes

Filed by the map-as-canonical round (prompts/2026-10-22-map-as-canonical) from the registry entry and the declaration's signature; its hypotheses are unread (ruling F1, 2026-10-23): the record's Source carries the signature verbatim, and a reader files the hypothesis leaves. Registry note: For any chooser at the decision interface; with maximizer_excludes and exploration_never_violates. Restated by the follow-up (2026-09-27, Part 3): the exploration set's third clause is dropped, so the exploration term is the honest ε̄ ((D − w)/ϖ + θ_hi) (lo = w the range floor, explore_range the range fact) rather than ε̄ θ_hi; the clause survives as the variant AboveAsking with rate_above_asking, under which no-lock-in holds only for options estimated at least as good as asking (above_asking_locks_in, the fixture src/exploration_lockin.py). Inhabited by the BRIA realization briaInterface. What it does not say: that B(K) is o(K) — that is the realization's to discharge (BRIA's budget; unbiasedness from feedback, PAPER). The registry's answers_item is the priorities pointer to item 104 (ruling F2).

Bridge card

Connected to no informal claim yet: held by public-corrigibility-line.

Declaration Workspace.Deference.Contrib.KernelExtension.DecisionInterface.realized_rate in lean/Workspace/Deference/Contrib/KernelExtension.lean (record kernel.extension-realized-rate.record)

Registry kernel.extension-realized-rate: class lean-proved, status active, review ci-only, origin round 2026-09-27-corrigibility-kernel-phase2; bears on item 104

Bridge (formalizer-stated; kernel.extension-realized-rate.bridge, drafted):

The statement of record of `kernel.extension-realized-rate` formalizes the registered claim as the registry reads it: The extension's interface theorem: avg π ≤ avg (D − c_k)/ϖ + ε̄ ((D − w)/ϖ + θ_hi) + (B(K) + M(K))/(ϖ Σ w_k).

Hypotheses: unread (the record's Source carries the signature; a reader files them).

Completeness (kernel.extension-realized-rate.complete): No premise beyond the signature's binders enters the declaration; the kernel checks it as stated. The result is the record, this leaf and the bridge, and its hypotheses are unread: the record's Source carries the signature verbatim and no hypothesis leaf is filed until a reader files one.

Author and human events

Author @smithy-verity; version 1; size M.

No human event has touched this node.

Edges

Above

Children

Work pointers

Ranking (the lens, not the structure)
{
 "status": "open",
 "diagnosis": null,
 "flags": [
  "held by public-corrigibility-line",
  "hypotheses unread"
 ],
 "V": {
  "V_prior": null,
  "display": "2",
  "headline": 2,
  "ref": 2,
  "valid": 2,
  "weaker": "both"
 },
 "belief": null,
 "draft": "ai"
}

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