dd-is-conditional-independence

and · drafted

Statement

Decision-determination is the conditional independence of the environment from decisions given the policy latent, FAF's ordered-Markov clause, and not perfect condensation of the policy latent: a decision-determined structure exists whose policy latent is not a function of the environment.

Source

projects/deference/faf-cleanroom-2026-10-02/DIGEST.md, §2 item 26: "Decision-determination is conditional independence, not perfect condensation — decisionDetermined_iff_condMutualInfo_eq_zero … orderedMarkov_polLatent_iff_dd (DD is FAF's ordered-Markov clause), Three.dd_not_perfectlyCondenses (N+: a decision-determined structure whose policy latent is not a function of the environment)".

Notes

Bounds the udt representation chain: what the chain calls decision-determination is a conditional independence, so Stage 5 cannot get perfect condensation of the policy for free.

Bridge card

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

Declaration decisionDetermined_iff_condMutualInfo_eq_zero (record dd-is-conditional-independence.record)

Bridge (formalizer-stated; dd-is-conditional-independence.bridge, drafted):

The declaration's equivalence is the corpus's decision-determination stated over PFR's conditional mutual information, and Three.dd_not_perfectlyCondenses is the separating instance.

Hypotheses, read:

Completeness (dd-is-conditional-independence.complete): No premise beyond the corpus's definition of decision-determination is needed for the characterization.

Author and human events

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

No human event has touched this node.

Edges

Above

part of stage5-li-representation-theorem
root (shared-claim) of stage5-li-representation-theorem

Children

part: dd-is-conditional-independence.record leaf/record
part: dd-is-conditional-independence.bridge leaf/bridge
part: dd-is-conditional-independence.complete leaf/completeness

Ranking (the lens, not the structure)

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