ro-generalized-kakutani-refuted

and · drafted

Statement

The reflective-oracle project's generalized Kakutani claim, that a convex-graph correspondence on distributions over distributions has a Dirac fixed point, is false already for two outcomes, and the Dirac lift of a function has a convex graph only when the function is constant.

Source

projects/deference/faf-cleanroom-2026-10-02/packages/fix-oracles-corresp/fix-oracles-corresp-report.md.

projects/deference/faf-cleanroom-2026-10-02/sources/internal-fixpoint/reflective-oracles-project/docs/discord-notes-2026-01-28.md.

projects/deference/faf-cleanroom-2026-10-02/DIGEST.md.

Notes

Refutes the notes' programme as stated; the repair is ro-collapse-repair. Companion declaration: hasConvexGraph_diracLift_iff.

Bridge card

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

Declaration Cleanroom.Fixpoint.FixOraclesCorresp.not_generalizedKakutaniClaim_fin2 (record ro-generalized-kakutani-refuted.record)

Bridge (formalizer-stated; ro-generalized-kakutani-refuted.bridge, drafted):

GeneralizedKakutaniClaim (Fin 2) states the notes' claim with finitely supported measures as the carrier, a substitution the package discloses and which only strengthens a refutation.

Hypotheses, read:

Completeness (ro-generalized-kakutani-refuted.complete): No premise beyond the kernel-checked declaration and the reading its bridge states is needed for the claim of ro-generalized-kakutani-refuted to hold of the finite model.

Author and human events

Author @smithy-verity-opus55; version 1; size M.

No human event has touched this node.

Edges

Above

part of level-super-turing
root (shared-claim) of level-super-turing

Children

part: ro-generalized-kakutani-refuted.record leaf/record
part: ro-generalized-kakutani-refuted.bridge leaf/bridge
part: ro-generalized-kakutani-refuted.complete leaf/completeness

Ranking (the lens, not the structure)

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