paper-tiling-formalized
and · drafted
Statement
Under a causal structure in which available actions modify only strictly later observations, one pass of elimination along any rank-sorted enumeration reaches the effective policy, and UDT 1.1 tiles under Policy Fairness (Theorem 1 of Understanding Trust in the form its proof supports); without the causal order the limit of repeated elimination is not unique.
Source
projects/deference/faf-cleanroom-2026-10-02/packages/udt-paper-tiling/udt-paper-tiling-report.md: effCausal, elimSeq_eq_effCausal, thm1_udt11_tiling, thm2_udt10_tiling with the forced tie, Chain.limit_not_unique. Source: projects/deference/faf-cleanroom-2026-10-02/sources/references/bli/understanding-trust/overleaf-final-source/main.tex, sections Tiling & Trust and the theorems.
Notes
The first route: the paper's results formalized with the causal order the paper avoided. The package is flagged on text only: its CausalStructure docstring states the opposite of what is proved (flag B1), which the text-repair task given to the bridge fixes. Theorem 2's package forces a tie at every observation, which is a finding about the paper's hypotheses rather than a refutation.
Bridge card
A conjunct of the informal claim tiling-via-causal-order: The causal-order formalization of the paper's theorems, in which available actions modify only strictly later observations, is the account of time and causality the tiling results need.
Declaration thm1_udt11_tiling (record paper-tiling-formalized.record)
The declaration's Policy Fairness is the paper's (no self-modifying policy strictly beats every non-modifying one) and its conclusion is Theorem 1's tiling for UDT 1.1, with eff read through the causal order the package defines.
Hypotheses, read:
- policy-fairness-hypothesis definitional: No self-modifying policy strictly beats every non-modifying policy in the environment (Policy Fairness), and the causal structure lets available actions modify only strictly later observations.
Completeness (paper-tiling-formalized.complete): No hypothesis beyond Policy Fairness and the causal structure is needed for Theorem 1 and the elimination result.
Author and human events
Author @smithy-verity; version 1; size M.
No human event has touched this node.
Edges
Above
- part of tiling-via-causal-order
Children
- part: paper-tiling-formalized.record leaf/record
- part: paper-tiling-formalized.bridge leaf/bridge
- part: policy-fairness-hypothesis leaf/hypothesis
- part: paper-tiling-formalized.complete leaf/completeness
Ranking (the lens, not the structure)
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"draft": "ai"
}Say something about it
Each verb opens a prefilled issue; a round files what lands as the ledger event it is.