# Conclusion
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This cell was recorded before reportable collection. It fixed the synthesis and verdict rules without asserting an outcome; the audited result cells added later on this page apply those rules.
The preregistered conclusion contract required:
- a claim-by-claim table linking each verdict to concrete Job URLs, commands, configs, canonical tables, and raw artifacts;
- explicit separation of v1 challenge wording from arXiv v4 targets;
- a split treatment of Pendulum and the blocked physical Aero 2 subclaim;
- an outcome-first 3–5 sentence Executive summary;
- a `## Scope & cost` table with Scope, Hardware, Compute time, Cost, and Outcome rows for this reproduction versus full replication;
- a downloadable reproduction bundle and Hugging Face Collection link;
- a Posterly-generated reproduction poster only after strict gates pass.
Verdict language follows the challenge rules: `verified` or `falsified` requires concrete non-toy evidence at the declared scale; `toy` denotes an explicitly reduced or proxy run; `inconclusive` denotes missing, blocked, or insufficient evidence. Self-assigned labels never substitute for executed evidence. The Executive summary and poster were reserved for addition and pinning only after results and artifacts had been audited.
---
## Complete scheduler chronology
| Attempt | Scope | HF Job | Scheduler status | Evidence disposition | Scheduling | Running | Total | Estimated cost |
| --- | --- | --- | --- | --- | ---: | ---: | ---: | ---: |
| v2 | Claims 1–3 | [6a57cd8cb1669a49bf075b3f](https://huggingface.co/jobs/JacobLinCool/6a57cd8cb1669a49bf075b3f) | ERROR | rejected; a TensorBoard writer hit a mounted-Bucket `FileNotFoundError` | 129 s | 543 s | 672 s | $0.0905 |
| v2 | Claim 4 | [6a57cd9ab1669a49bf075b43](https://huggingface.co/jobs/JacobLinCool/6a57cd9ab1669a49bf075b43) | CANCELED | canceled after the v2 writer failure; no result accepted | — | — | — | — |
| v2 | Claim 5 | [6a57cda7b1669a49bf075b47](https://huggingface.co/jobs/JacobLinCool/6a57cda7b1669a49bf075b47) | CANCELED | canceled after the v2 writer failure; no result accepted | — | — | — | — |
| v3 | Claims 1–3 | [6a57d127b1669a49bf075baf](https://huggingface.co/jobs/JacobLinCool/6a57d127b1669a49bf075baf) | COMPLETED | rejected; mounted-Bucket append loss left 2,200 of 2,400 declared episodes | 9 s | 564 s | 573 s | $0.0940 |
| v3 | Claim 4 | [6a57d133b1669a49bf075bb1](https://huggingface.co/jobs/JacobLinCool/6a57d133b1669a49bf075bb1) | CANCELED | canceled after the v3 integrity failure; no result accepted | — | — | — | — |
| v3 | Claim 5 | [6a57d14485d9643ce16d53b6](https://huggingface.co/jobs/JacobLinCool/6a57d14485d9643ce16d53b6) | CANCELED | canceled after the v3 integrity failure; no result accepted | — | — | — | — |
| v4 | Claims 1–3 | [6a57d4e3b1669a49bf075be3](https://huggingface.co/jobs/JacobLinCool/6a57d4e3b1669a49bf075be3) | COMPLETED | accepted; closed batch byte-validated | 8 s | 551 s | 560 s | $0.0918 |
| v4 | Claim 4 | [6a57d4f185d9643ce16d53d7](https://huggingface.co/jobs/JacobLinCool/6a57d4f185d9643ce16d53d7) | COMPLETED | accepted; 85/85 public files byte-validated | 8 s | 17,957 s | 17,965 s | $2.9928 |
| v4 | Claim 5 | [6a57d52785d9643ce16d53df](https://huggingface.co/jobs/JacobLinCool/6a57d52785d9643ce16d53df) | COMPLETED | accepted; 65/65 public files byte-validated | 8 s | 30,245 s | 30,253 s | $5.0408 |
Accepted evidence consumed `48,753` scheduler-running seconds (`13.5425` job-hours) and an estimated `$8.1255`. Across all nine submitted Jobs, including rejected v2/v3 compute, recorded billable runtime was `49,860` seconds (`13.85` job-hours) and estimated cost was `$8.3100`. Costs use the recorded `t4-medium` price of `$0.0100/min` and exclude scheduling time; canceled Jobs with no reported running duration are shown as em dashes. The three accepted Jobs overlapped in wall time, completing from the first accepted batch start to the last accepted batch finish in about 8.4 hours.
The machine-readable [Jobs inventory](https://huggingface.co/buckets/JacobLinCool/chebyshev-job-artifacts) preserves each inspected scheduler argv separately from a public, SHA-256-verified rerun recipe. A scheduler `COMPLETED` status alone was never sufficient for evidence acceptance.
---
Claims 2 and current-v4 Claim 3 performance reproduce, but Claim 4 does not. Claim 1 supports the continuous unconstrained velocity-proportional mechanism while leaving historical priority and bounded discrete-Gym optimality unresolved; Claim 3's 16-coefficient performance reproduces but its MLP parameter arithmetic is incorrect. In Claim 4, best-of-20 CH-3-PPO reaches only `84.5836` and fresh-seeded CH-3-REINFORCE `96.0097`, with narrow start-state failures erasing the reported gains. On Pendulum, released ARS (`-218.3231`) and the `+67.8248` Chebyshev ordering margin reproduce, while fresh CH-6 (`-150.4982`) misses the strict point-estimate tolerance and physical Aero 2 remains inconclusive. Three accepted byte-validated `t4-medium` Jobs used 48,753 scheduler-running seconds, stayed within a 30 GB flavor, and cost approximately `$8.1255`.
## Scope & cost
| Item | This reproduction | Full replication |
| --- | --- | --- |
| Scope | Five challenge claims: theorem-scope and priority audits, complete Mountain Car panels, complete Pendulum 30-seed/82,500-episode panel, reset sensitivity, and an explicit Aero 2 hardware exclusion | Every paper result and ablation plus calibrated physical Quanser Aero 2 sim-to-real trials |
| Hardware | Three accepted `t4-medium` Jobs, each with 8 vCPU, 30 GB RAM, and one 16 GB T4; maximum manifest parent-process RSS `852.48 MB` | Matching training systems plus physical Aero 2, sensors, actuators, calibration, and real-time HIL interface |
| Compute time | `48,753` scheduler-running seconds (`13.5425` job-hours); about `8.4` hours overlapping wall time | Not estimated |
| Cost | `$8.1255` accepted evidence; `$8.3100` across all nine attempts | Not estimated |
| Outcome | Claim 2 reproduced; Claim 3 performance reproduced with corrected arithmetic; Claim 1 materially narrower; Claim 4 not reproduced; Pendulum partially reproduced; Aero 2 inconclusive | Not attempted |
---
**📦 Artifact** `icml2026-chebyshev-reproduction/reproduction-bundle:v0` · dataset
https://huggingface.co/buckets/JacobLinCool/repro-chebyshev-policies-mountain-car-artifacts#icml2026-chebyshev-reproduction/reproduction-bundle:v0
---
The immutable release v1 contains the rerun scripts, frozen configs and lockfile, validation tests, canonical tables, claim analysis, four interactive reports, poster, nine-attempt HF Jobs inventory, raw-batch manifests, newly trained JSON checkpoints, and complete integrity metadata. It contains 174 files (76,360,550 artifact bytes); `MANIFEST.sha256` covers all 173 payload files and has SHA-256 `61bb48124dd152d22187467fce124360c0dfabb90811278323d028c59bec17d1`.
- [Download the release integrity manifest](https://huggingface.co/buckets/JacobLinCool/chebyshev-job-artifacts/resolve/release/v1/MANIFEST.sha256)
- [Browse the public raw-evidence Bucket](https://huggingface.co/buckets/JacobLinCool/chebyshev-job-artifacts)
- [Open the public reproduction Collection](https://huggingface.co/collections/JacobLinCool/icml-2026-reproduction-chebyshev-policies-6a57e3b6f9a6a2862ed7a8d1)
The Trackio artifact cell above versions the same release as `icml2026-chebyshev-reproduction/reproduction-bundle:v0`. Large append-only raw records remain in the evidence Bucket and are anchored by exact byte counts and hashes rather than duplicated inside the curated bundle.
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