Pith Number

pith:AVV3K7ZI

pith:2015:AVV3K7ZIMY42SVMW2WWUMGCC3X

not attested not anchored not stored refs pending

The Multifractal Nature of Boltzmann Processes

Liping Xu

arxiv:1504.06725 v1 · 2015-04-25 · 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{AVV3K7ZIMY42SVMW2WWUMGCC3X}

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	2026-05-18T02:17:44.531222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

056bb57f286639a95596d5ad461842ddf21843f0239736a812b5bd4dd6e29212

Aliases

arxiv: 1504.06725 · arxiv_version: 1504.06725v1 · doi: 10.48550/arxiv.1504.06725 · pith_short_12: AVV3K7ZIMY42 · pith_short_16: AVV3K7ZIMY42SVMW · pith_short_8: AVV3K7ZI

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/AVV3K7ZIMY42SVMW2WWUMGCC3X \
  | 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: 056bb57f286639a95596d5ad461842ddf21843f0239736a812b5bd4dd6e29212

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a166ca0d916a449b7ef05a859052bd762f9732013dfd90277c54769aa22f99c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-04-25T13:35:36Z",
    "title_canon_sha256": "90780bb9f77e8e68a06702ed9d608a4acc48e42dc0d31afe0346fbfe9b0b7194"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06725",
    "kind": "arxiv",
    "version": 1
  }
}