Pith Number

pith:B53DDJJR

pith:2026:B53DDJJRHUKZ7DWHY3JQINPCTB

not attested not anchored not stored refs pending

Metric Non-Collapse in Learned World Models for Control: Approximation Theory, Finite-Sample Geometric Guarantees, and Deterministic Planning Transfer

Alain Bensoussan, Minh-Binh Tran, Minh-Nhat Phung

arxiv:2608.07265 v1 · 2026-08-07 · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B53DDJJRHUKZ7DWHY3JQINPCTB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-08-10T01:14:48.002499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f7631a5313d159f8ec7c6d30435e298490f5c24899c077ea6c3a803b7c011dd

Aliases

arxiv: 2608.07265 · arxiv_version: 2608.07265v1 · doi: 10.48550/arxiv.2608.07265 · pith_short_12: B53DDJJRHUKZ · pith_short_16: B53DDJJRHUKZ7DWH · pith_short_8: B53DDJJR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/B53DDJJRHUKZ7DWHY3JQINPCTB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0f7631a5313d159f8ec7c6d30435e298490f5c24899c077ea6c3a803b7c011dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11b782e401539356cb551a8ad9cb3bdc0a36c23cbb1a109cb1233f5742d4a13b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-07T14:25:33Z",
    "title_canon_sha256": "b12c2539c3fb66cd2833d16be363246eeeef6becdf5c200e0eaaa55e0f1cc48c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07265",
    "kind": "arxiv",
    "version": 1
  }
}