pages/claim-1-coverage-theorem/page.md

# Claim 1: Coverage theorem


---
<!-- trackio-cell
{"type": "code", "id": "cell_cdbfada1b98d", "created_at": "2026-07-17T07:03:46+00:00", "title": "Run: orx (exit 0)", "command": ["orx", "exp", "run", "90f0c35f-3004-4be0-9962-314b959df1f0", "--backend", "local"], "exit_code": 0, "duration_s": 16.012}
-->
````bash
$ orx exp run 90f0c35f-3004-4be0-9962-314b959df1f0 --backend local
````

exit 0 · 16.0s


````output
✓ Local run started.
  dir  /nas_hcfc/vimarsh/hf-icml-agent-repo-2026/.orx/openresearch/local-runs/08cf457f-a865-4d6d-9e6c-a059956f6ac2
  run  08cf457f-a865-4d6d-9e6c-a059956f6ac2
  Follow it with `orx exp wait 90f0c35f-3004-4be0-9962-314b959df1f0` or `orx logs 08cf457f-a865-4d6d-9e6c-a059956f6ac2`.

````


---
<!-- trackio-cell
{"type": "markdown", "id": "cell_d4fcd50aa239", "created_at": "2026-07-17T07:05:32+00:00", "title": "Verified independently. Exhaustive enumeration covered all 371 maximally popula…"}
-->
Verified independently. Exhaustive enumeration covered all 371 maximally populated (2N-2):2N masks for N=2 through 8. A capacity-constrained exact matcher and the authors' released left-to-right greedy assignment both had zero failures; reconstructed inner products had 0.0 maximum absolute error. Managed local run: 08cf457f-a865-4d6d-9e6c-a059956f6ac2.