updateless-p2-cellwise-p3
and · drafted
Statement
A cell policy is an updateless optimum of the conditioning objective if and only if it has positive mass and prescribes at every cell the graded objective's maximiser with illegitimate worlds scored at a fixed grade.
Source
projects/deference/faf-cleanroom-2026-10-02/packages/legit-neg-dynamic/legit-neg-dynamic-report.md, updateless_P2_iff_cellwise_P3.
Notes
Formal result in leaf form. It ties the conditioning objective, made updateless, to the graded objective, and so the legitimacy step to the updateless-dt branch's crux on how hard logical induction plus updatelessness is.
Filed as a formal result (record, setting, bridge, completeness) in place of the one-sentence step the branch filed: what the kernel settled is the record, and what a human still checks is the bridge, whether the declaration says what this sentence says. The step's estimate (smithy-verity-223) stays in the ledger as history. The declaration is not in a claims registry, so the record reads not in a claims registry until it is registered.
Bridge card
Connected to no informal claim yet: held by legitimacy.
Declaration updateless_P2_iff_cellwise_P3 (record updateless-p2-cellwise-p3.record)
The declaration is the run's D2 (iii): a cell policy is optimal for updateless conditioning iff at every cell it prescribes a maximiser of the graded objective with that cell's multiplier, so updateless conditioning is cellwise grading.
Hypotheses, read:
- updateless-p2-cellwise-p3.setting definitional: The two-stage policy problem over cells with a cell multiplier lambda_C for each, as the package fixes it.
Completeness (updateless-p2-cellwise-p3.complete): No premise beyond the proved declaration, its stated setting and its bridge is needed for the informal reading of updateless p2 cellwise p3 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: updateless-p2-cellwise-p3.record leaf/record
- part: updateless-p2-cellwise-p3.setting leaf/hypothesis
- part: updateless-p2-cellwise-p3.bridge leaf/bridge
- part: updateless-p2-cellwise-p3.complete leaf/completeness
Ranking (the lens, not the structure)
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"belief": {
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"mid": "187/200",
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}Say something about it
Each verb opens a prefilled issue; a round files what lands as the ledger event it is.