trace-nonrecoverability

and · drafted

Statement

No function of the observable trace is a legitimacy predicate: two valid finite systems share a trace and have influence defects 0 and one half, and the defects consistent with a trace form exactly the interval from 0 to the trace's maximal defect.

Source

projects/deference/note-dump-2026-08-11/notes/legitimacy-theory-v1.md, section 2.3 ("Why legitimacy cannot be a trace condition"), whose provenance principle says every safety-relevant boundary is a fact about "where a value came from"; projects/deference/faf-cleanroom-2026-10-02/packages/legit-finite-defect/legit-finite-defect-report.md, the declarations no_recovery and IdentifiedSet.defect_consistent_iff (the exact identified set).

Notes

A formal result in the landed shape, finite version. The LI-register version is the question trace-nonrecoverability-li. Its validity as an implication is evidence for the picture of the local-rules crux under which no sound local rule set exists (records cannot certify provenance).

Bridge card

Connected to no informal claim yet: held by legitimacy.

Declaration IdentifiedSet.defect_consistent_iff (record trace-nonrecoverability.record)

Bridge (formalizer-stated; trace-nonrecoverability.bridge, drafted):

The package's defect, the prior-weighted gap between the advised report and the reference on a weight, is the note's influence defect on the report layer, and the identified set is the set of defects of systems sharing the observable trace.

Hypotheses, read:

trace-finite-report-layer : The systems are finite report-layer systems: a finite set of worlds with a prior, a report function and a reference, so that the trace is a finite object.

Completeness (trace-nonrecoverability.complete): No premise beyond the kernel-checked declarations, their bridge and the finite report-layer setting is needed for the two-system witness and the identified-set interval to hold.

Author and human events

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

No human event has touched this node.

Edges

Above

held by legitimacy

Children

part: trace-nonrecoverability.record leaf/record
part: trace-nonrecoverability.bridge leaf/bridge
part: trace-finite-report-layer leaf/assumption
part: trace-nonrecoverability.complete leaf/completeness

Ranking (the lens, not the structure)

{
 "status": "open",
 "diagnosis": null,
 "flags": [
  "AI number",
  "held by legitimacy"
 ],
 "V": {
  "V_prior": null,
  "display": "2",
  "headline": 2,
  "ref": 2,
  "valid": 2,
  "weaker": "both"
 },
 "belief": null,
 "draft": "ai"
}

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