Finite-Sample Recovery of Predictive History Quotients from Independent POMDP Trajectories

Thank you for a precise final revision; the paper is accepted. Proposition 10 in Appendix E now restricts the routed class law to classes with positive routed mass and names class {(0)} of the nested L=2 example as a zero-mass class. It also adopts an explicit convention omitting zero-weight terms in both statement and proof. Section 5 and Appendix F now give the commit hash that tag v1 points to. The editorial notes below are optional polish for the camera-ready version and do not affect the validity of your claims.

Verdict: accept. All three concerns from the round-2 minor revision are resolved in the revised manuscript, and the revision introduces no new correctness, validity or reproducibility problem. Decisive points. - Positive-mass qualification (Appendix E, Proposition 10(1)): resolved. Case 1 now states that under the full eligible universe every history routes to a maximal-length context. A class of only non-maximal contexts therefore has λ_c = 0 and no routed law, and the singleton class {(0)} of Appendix G's nested L=2 example is named. The class-law conclusion is restricted to λ_c > 0. - Zero-weight convention (Appendix E, Proposition 10 display and proof): resolved. The statement defines Q_g only for λ_g > 0 and omits zero-weight terms. The display is asserted only when its denominator is positive, and Q_g = P_g is restricted to λ_g > 0. The proof's case-1 argument now uses λ_m = 0 for non-maximal m. - Immutable commit (Section 5 closing paragraph and Appendix F): resolved. Both locations now state that tag v1 points to commit 83f9f42d8533c62fd05fcef2192559e0f80be3d9 and identify the hash as the immutable reference. New problems: the changes are confined to Proposition 10 and the artifact paragraphs. They are internally consistent with Table 2 (twelve positive-mass contexts, maximal contexts carrying routed mass), and, consistent with the author response letter, no numbers, experiments or references were altered. The contribution remains modest: an estimand plus an executable certificate, with Lemma 7's one-count conditioning for nested contexts. It is honestly framed. The panel's remaining reservations (synthetic-only evidence, no downstream consumer, a loose d-dependence) are disclosed in the Limitations section and Section 4.

Published with the paper; the authors were not required to address them before publication.

• Related work and Section 5: fix the duplicated cross-reference rendering "TheoremsTheorem 1–Theorem 2" to read "Theorems 1–2".
• Section 4 and Limitations: remove the stray hyphen-spaces left by line breaking ("fixed- alphabet", "suffix- tree", "safety- relevant", "action- aware").
• Appendices A–B: replace the stray "0◻" proof terminators with a single end-of-proof mark.
• Appendix E, Proposition 10(1): consider stating explicitly that Q_m = P_m holds there because maximal contexts have no proper extension in the eligible universe, linking case 1 to the extension-free clause of the proposition.