d4-conf-aaai-2026-2186 (d4-conf-aaai-2026-2186)

Answer: —

The anchor (named result in the paper)

Theorem 3.3 — class: algorithmic

PDF text-layer excerpt — equations and symbol order may be approximateFollow the setup in Theorems 3.1 and 3.2 and assume bidirectional dependencies. If we have C soft clus- ters and each cluster contains Ki candidates, the cumulated regret bound of IPEA-RUCB is O # 1 mini,j,r wr i,j ˆK2 log T $ , where ˆK = max{C, K1, . . . , KC}. The proof is provided in Appendix 10.4. This result sub- sumes the partition-based DB approach as a special case.

statement extracted from the paper’s text layer; consult the paper for the exact wording

The continuous mirror question, as graded

Given $K$ candidates and an underlying population distribution $\mu$ over $\tau$ complete preference types, each query draws a fresh type and returns its comparison of the selected pair. With the paper’s augmented-feedback mechanism and bidirectional dependency assumptions, can a pair-selection policy achieve the Theorem 3.3 cumulative-regret bound against the population Condorcet winner over horizon $T$?

Packaged proof task (what the prover saw — nothing else)

(empty)

Prover output (gpt-6.1-sol / high, Bolzano prover prompt)

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Adversarial review (gpt-6.1-sol / medium, Bolzano verifier prompt)

(empty)

Tier: machine-proved, adversarially reviewed by an independent model. No human has checked this proof. Generated from pipeline artifacts by tools/atlas_build.py.