decision-problems-lean-done

and · drafted

Statement

On strongly fair finite trees every strict local maximum of the formal core's optimality notion is global (Theorems 1 and 2 of the formal core transposed to trees), kernel-checked; the remaining load-bearing propositions of sections 3 to 8 and the fairness and relocation repair are checked in the other dp packages, or refuted with their surviving neighbours stated.

Source

projects/deference/faf-cleanroom-2026-10-02/packages/dp-local-opt/dp-local-opt-report.md: stronglyFair_strictLocalMax_isOptimal, almostFair_strictLocalMax_not_isOptimal. The sixteen dp-* packages under projects/deference/faf-cleanroom-2026-10-02/packages/ (dp-core-tree, dp-calibration, dp-calib-limits, dp-fairness-reloc, dp-edt-udt-fair, dp-faithful-udt, dp-smoking-lesion, dp-two-lesions, dp-worlds-jb, dp-devices-catalog, dp-dutch-book, dp-firstperson-sc, dp-cartesian-frames, dp-referents-cdt, dp-causal-consist, dp-learner-nr, dp-troll-bridge); projects/deference/faf-cleanroom-2026-10-02/DIGEST.md, the decision areas.

Notes

The local-optimum theorem (stronglyFair_strictLocalMax_isOptimal) is the record; the parent names the packages that check the rest. Fourteen of seventeen decision packages passed; the probe witnesses of dp-calib-limits and dp-fairness-reloc await a lift (listed in the branch's notes).

Bridge card

A conjunct of the informal claim formal-core-v2-checked: The formal core's v2 propositions are machine-checked over finite-tree semantics, and calibration of the subjective states a procedure holds at its decision points is defended as a fairness condition on decision problems.

Declaration stronglyFair_strictLocalMax_isOptimal (record decision-problems-lean-done.record)

Bridge (formalizer-stated; decision-problems-lean-done.bridge, drafted):

The declaration's strongly fair trees and optimality notion are the formal core's Definitions as transposed to dp-core-tree's finite trees, so its conclusion is Theorems 1 and 2 of the draft in tree form, and the sibling packages' declarations stand to their sections the same way.

Hypotheses, read:

finite-tree-semantics-setting definitional: Decision problems are finite trees over decision points with the grade-(a) hypotheses dp-core-tree fixes.

Completeness (decision-problems-lean-done.complete): No hypothesis beyond the finite-tree semantics is needed for the local-optimum theorem and its siblings.

Author and human events

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

No human event has touched this node.

Edges

Above

part of formal-core-v2-checked

Children

part: decision-problems-lean-done.record leaf/record
part: decision-problems-lean-done.bridge leaf/bridge
part: finite-tree-semantics-setting leaf/hypothesis
part: decision-problems-lean-done.complete leaf/completeness

Ranking (the lens, not the structure)

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