Pith Number

pith:BT3PQ5R6

pith:2011:BT3PQ5R6533G4MHSVPPZJI2QZN

not attested not anchored not stored refs pending

Ergodic Transport Theory, periodic maximizing probabilities and the twist condition

A. O. Lopes, E. R. Oliveira, G. Contreras

arxiv:1103.0816 v4 · 2011-03-04 · math.DS · cond-mat.stat-mech · 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{BT3PQ5R6533G4MHSVPPZJI2QZN}

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	2026-05-18T03:26:00.414818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cf6f8763eeef66e30f2abdf94a350cb419306537bdacc87b3c27c98bb4dbf3b

Aliases

arxiv: 1103.0816 · arxiv_version: 1103.0816v4 · doi: 10.48550/arxiv.1103.0816 · pith_short_12: BT3PQ5R6533G · pith_short_16: BT3PQ5R6533G4MHS · pith_short_8: BT3PQ5R6

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/BT3PQ5R6533G4MHSVPPZJI2QZN \
  | 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: 0cf6f8763eeef66e30f2abdf94a350cb419306537bdacc87b3c27c98bb4dbf3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e24a276ef1584f9512648faeb151369e16dafccb971017a35303cae3f6dc1072",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-04T03:19:02Z",
    "title_canon_sha256": "63e36b168742ddc48d917fc090d04677089a7c262985bafea0eba7a6ecbb44a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0816",
    "kind": "arxiv",
    "version": 4
  }
}