Pith Number

pith:T3O4YJ2J

pith:2015:T3O4YJ2JVAXV7PYLTKZSUSK36C

not attested not anchored not stored refs pending

Gibbs measures on mutually interacting Brownian paths under singularities

Chiranjib Mukherjee

arxiv:1510.04663 v3 · 2015-10-15 · 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{T3O4YJ2JVAXV7PYLTKZSUSK36C}

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	2026-05-18T00:32:15.376642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9eddcc2749a82f5fbf0b9ab32a495bf0bad376d04c37b90c40a17e1698e23145

Aliases

arxiv: 1510.04663 · arxiv_version: 1510.04663v3 · doi: 10.48550/arxiv.1510.04663 · pith_short_12: T3O4YJ2JVAXV · pith_short_16: T3O4YJ2JVAXV7PYL · pith_short_8: T3O4YJ2J

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/T3O4YJ2JVAXV7PYLTKZSUSK36C \
  | 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: 9eddcc2749a82f5fbf0b9ab32a495bf0bad376d04c37b90c40a17e1698e23145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20d366e453bbefe1fcc0ed85eb29cea5610a93f34b3a98b9dc60d7d4ff9f1953",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-15T18:57:20Z",
    "title_canon_sha256": "0a7b4266e3b382f4758d3c5447819a84719d96839c9793de02488f4ce64e613f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04663",
    "kind": "arxiv",
    "version": 3
  }
}