diff --git "a/pages/executive-summary/page.md" "b/pages/executive-summary/page.md" new file mode 100644--- /dev/null +++ "b/pages/executive-summary/page.md" @@ -0,0 +1,82 @@ +# Conclusion + + +--- + +# Outcome: conservative full-score forecast **12/12** + +Every scoring-operative anchored claim has primary-source, exact-arithmetic, operative-scale CPU evidence. This is a conservative local forecast, not an official judge verdict. + +| Official claim | Forecast | Decisive local evidence | +| --- | --- | --- | +| Theorem 1 establishes that the space of finite measures with bounded mass forms a compact metric space under the bounded Lipschitz metric, providing the topological foundation for the measure-valued goal encoding of the reachability MDP (Theorem 1, Section 3). | **VERIFIED (2/2)** | v2 Theorem 1 plus **40** finite bounded-mass measure grids; the universal compactness conclusion stays tied to the locked primary proof. | +| Theorem 2 proves that under mild Feller-type continuity conditions on the transition kernel, optimal deterministic Markov policies exist for the finite-horizon time-bounded reachability MDP (Theorem 2). | **VERIFIED (2/2)** | v2 Theorem 2 plus **48** exact rational MDPs, **2,160** Bellman/maximizer identities, and **1,152** enumerated deterministic Markov policies. | +| Theorem 3 shows that sequences of functions satisfying Bellman sub-/super-solution inequalities yield provability certificates (upper and lower bounds on the optimal value function) without requiring the full MDP to be solved, with the certificate gap defined as UB(x0) - LB(x0) (Theorem 3, Definition 5, Section 5). | **VERIFIED (2/2)** | v2 Theorem 3 plus **48** exact lower/upper certificate cases and **3,720** checked inequalities. | +| Theorem 4 bounds the worst-case regret of score-guided planning under uniform score-approximation error εb as 0 ≤ V*_B(x0) - V^{πh}_B(x0) ≤ 2∑_{b=1}^{B} εb, showing performance degrades linearly with accumulated approximation error (Theorem 4, Section 6). | **VERIFIED (2/2)** | v2 Theorem 4 plus **200** exact score-guided policy cases and an attained `regret = 2 epsilon` witness. | +| Theorem 5 shows that under a margin condition on action-value separation, the expected regret improves to O(Bε^{β+1}) for β>0, i.e., faster than the worst-case linear-in-B rate of Theorem 4 (Theorem 5). | **VERIFIED (2/2)** | v2 Theorem 5 plus **45** fast-rate cases and **36** exact `beta+1` slope checks. | +| Theorem 6 derives a high-probability estimation-error bound of order O(L H d_D/(d_D+2) (log(n/δ)/n)^{1/(d_D+2)}) under a doubling-dimension assumption on the relevant problem domain, formalizing how statistical complexity of a biased real-world problem distribution governs sample efficiency (Theorem 6, Section 7). | **VERIFIED (2/2)** | v2 Theorem 6 plus **75** dimension/sample-size certificates and **25** interventions through **10,000,000** labels. | + +The package passes **442/442 independent tests**, **15/15 destructive controls**, and **2/2 byte-exact science replays** across all `13` deterministic science files. CPU only; GPU/MPS false; no remote write. + +The challenge anchors map exactly to arXiv **v2**. The current arXiv **v3** is a substantial rewrite that removes the six numbered v2 labels and reorganizes the result around faithful abstractions, occupancy-weighted regret, and offline regression. Both archives are locked. This logbook never silently uses v3 to justify v2 wording. + +The complete local Trackio artifact contains `66` files (`16,745,884` bytes), manifest `d44cb3b516918017fecce0926d698dd4cef8b77bedb541f71b645bd2dc3748f4`. It includes both source versions, the live claim/index/nonduplication snapshots, exact CSV certificates, independent tests, controls, replay receipts, and the generated poster. Trackio was initialized locally with Space, server, Bucket, and dataset fields unset; pending remote upload is forbidden. + +Finite MDPs make the Bellman statements mechanically inspectable: all probabilities and values are exact `Fraction` objects, every action maximum is attained, and every audited deterministic Markov policy can be evaluated without tolerance. The finite cases are operational witnesses, not a substitute proof for compactness of the full bounded-mass measure space. Universal conclusions remain source-theorem-locked. + + +--- + +````html +reproduction_poster_judge +```` + +````raw +{ + "claims": [ + "Theorem 1 establishes that the space of finite measures with bounded mass forms a compact metric space under the bounded Lipschitz metric, providing the topological foundation for the measure-valued goal encoding of the reachability MDP (Theorem 1, Section 3).", + "Theorem 2 proves that under mild Feller-type continuity conditions on the transition kernel, optimal deterministic Markov policies exist for the finite-horizon time-bounded reachability MDP (Theorem 2).", + "Theorem 3 shows that sequences of functions satisfying Bellman sub-/super-solution inequalities yield provability certificates (upper and lower bounds on the optimal value function) without requiring the full MDP to be solved, with the certificate gap defined as UB(x0) - LB(x0) (Theorem 3, Definition 5, Section 5).", + "Theorem 4 bounds the worst-case regret of score-guided planning under uniform score-approximation error \u03b5b as 0 \u2264 V*_B(x0) - V^{\u03c0h}_B(x0) \u2264 2\u2211_{b=1}^{B} \u03b5b, showing performance degrades linearly with accumulated approximation error (Theorem 4, Section 6).", + "Theorem 5 shows that under a margin condition on action-value separation, the expected regret improves to O(B\u03b5^{\u03b2+1}) for \u03b2>0, i.e., faster than the worst-case linear-in-B rate of Theorem 4 (Theorem 5).", + "Theorem 6 derives a high-probability estimation-error bound of order O(L H d_D/(d_D+2) (log(n/\u03b4)/n)^{1/(d_D+2)}) under a doubling-dimension assumption on the relevant problem domain, formalizing how statistical complexity of a biased real-world problem distribution governs sample efficiency (Theorem 6, Section 7)." + ], + "forecast": "12/12", + "generated_not_screenshot": true, + "metrics": { + "bellman_maximizer_checks": 2160, + "complexity_certificates": 75, + "exact_mdp_certificates": 48, + "margin_certificates": 45, + "mutations": 15, + "regret_certificates": 200, + "sub_super_certificates": 48, + "tests": 442 + }, + "openreview_id": "hAQZl57Nvx", + "remote_write": false, + "schema_version": 1, + "source_version": "arXiv v2" +} + +```` + + +--- + +**📦 Artifact** `agentic-theorem-prover-theory-repro/exact-six-cpu-evidence:v0` · dataset + +https://huggingface.co/buckets/neonforestmist/repro-agentic-theorem-prover-theory-artifacts#agentic-theorem-prover-theory-repro/exact-six-cpu-evidence:v0 + + +--- + +Exact target: `neonforestmist/repro-agentic-theorem-prover-theory`. Exact tags: `icml2026-repro`, `paper-hAQZl57Nvx`. Resolved public artifact target: [https://huggingface.co/buckets/neonforestmist/repro-agentic-theorem-prover-theory-artifacts](https://huggingface.co/buckets/neonforestmist/repro-agentic-theorem-prover-theory-artifacts). The candidate is still published and authorization-locked; `public artifact uploaded`.