Pith Number

pith:LF7C33K2

pith:2011:LF7C33K2Y6QCZVUIR7REDD6L4Z

not attested not anchored not stored refs pending

The Dual Potential, the involution kernel and Transport in Ergodic Optimization

Artur O. Lopes, Elismar R. Oliveira, Philippe Thieullen

arxiv:1111.0281 v3 · 2011-11-01 · math.DS · cond-mat.stat-mech · math-ph · math.MP · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LF7C33K2Y6QCZVUIR7REDD6L4Z}

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	2026-05-18T02:38:46.450657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

597e2ded5ac7a02cd6888fe2418fcbe66315098bad26e86d0d6b1b6f783dbee3

Aliases

arxiv: 1111.0281 · arxiv_version: 1111.0281v3 · doi: 10.48550/arxiv.1111.0281 · pith_short_12: LF7C33K2Y6QC · pith_short_16: LF7C33K2Y6QCZVUI · pith_short_8: LF7C33K2

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/LF7C33K2Y6QCZVUIR7REDD6L4Z \
  | 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: 597e2ded5ac7a02cd6888fe2418fcbe66315098bad26e86d0d6b1b6f783dbee3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "218ef861c146e1d0ef387d74165fdbc2d8591a97ed13921ecdce256d04a71f88",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP",
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-11-01T19:40:29Z",
    "title_canon_sha256": "12fb898a45dfde64f01b06471537ef004ee3e4347b57d2c70c7b94966ff97c0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0281",
    "kind": "arxiv",
    "version": 3
  }
}