Alignment Workspace

kernel-box2-finite-time

and · drafted

Statement

In the corrigibility kernel's second box, for a logical inductor the ranking of the violating option below the compliant one holds at every day from the price range alone, while the expectation-provability-induction version is asymptotic.

Source

projects/deference/CLAIMS.md, kernel.box2-finite-time (lean-proved; Workspace.Deference.Headline.box2_finite_time; answers item 104): "Box 2, finite time: at every day of a logical inductor the violating option scores below D − ϖ < 0 and the compliant one at least 0, from the price range alone"; projects/deference/rounds/2026-09-27-corrigibility-kernel-phase2/SPEC.md, line 374: "For a logical inductor the ranking holds at every day from the price".

Notes

A public, registered finite-day statement about a price-level quantity; evidence for the strengthened-criterion picture of the finite-time crux. Whether the collapse's carries admit the same is the finite-time statement task's question.

The formal version of this claim is the registered result kernel.box2-finite-time (ruling F5, 2026-10-23, matched by id): its record, bridge and completeness leaf are this node's conjuncts, the registry id stays on the record leaf (registry_id) and in the index, and the node kernel.box2-finite-time is a deprecated alias superseded by this one.

Bridge card

Connected to no informal claim yet: held by no frame.

Declaration Workspace.Deference.Headline.box2_finite_time in lean/Workspace.lean (record kernel.box2-finite-time.record)

Registry kernel.box2-finite-time: class lean-proved, status active, review ci-only, origin round 2026-09-27-corrigibility-kernel-phase2; bears on item 104

Bridge (formalizer-stated; kernel.box2-finite-time.bridge, drafted):

The statement of record of `kernel.box2-finite-time` formalizes the registered claim as the registry reads it: Box 2, finite time: at every day of a logical inductor the violating option scores below D − ϖ < 0 and the compliant one at least 0, from the price range alone.

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

Completeness (kernel.box2-finite-time.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": [
  "AI number",
  "hypotheses unread",
  "stale"
 ],
 "V": {
  "V_prior": null,
  "display": "2",
  "headline": 2,
  "ref": 2,
  "valid": 2,
  "weaker": "both"
 },
 "belief": {
  "J": 0,
  "mid": "191/200",
  "range": [
   "91/200",
   "1/1"
  ],
  "width": "1/1"
 },
 "draft": "ai",
 "root": {
  "status": "open",
  "Pr": {
   "hi": "1/8",
   "lo": "1/8",
   "mid": "1/8"
  },
  "value": null,
  "cost": "99/1",
  "margin": "no established leaves"
 }
}

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