Pith Number

pith:B3LOQRRT

pith:2015:B3LOQRRTRNVHHCVAXV6FTKKOBW

not attested not anchored not stored refs pending

Equivalence of zero entropy and the Liouville property for stationary random graphs

Matias Carrasco Piaggio, Pablo Lessa

arxiv:1510.04244 v1 · 2015-10-14 · 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{B3LOQRRTRNVHHCVAXV6FTKKOBW}

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	2026-05-18T01:30:08.800831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ed6e846338b6a738aa0bd7c59a94e0dac6ce5594850ac1c387588f7584eea72

Aliases

arxiv: 1510.04244 · arxiv_version: 1510.04244v1 · doi: 10.48550/arxiv.1510.04244 · pith_short_12: B3LOQRRTRNVH · pith_short_16: B3LOQRRTRNVHHCVA · pith_short_8: B3LOQRRT

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/B3LOQRRTRNVHHCVAXV6FTKKOBW \
  | 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: 0ed6e846338b6a738aa0bd7c59a94e0dac6ce5594850ac1c387588f7584eea72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e29cf1eb0450f2065ab0938287f42c538dc34bd040c9168650c8ea90dce01de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-14T19:25:06Z",
    "title_canon_sha256": "1f77acbd1f64938efee682df90428ec7de206a32fcb782d99ca16cf73150b070"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04244",
    "kind": "arxiv",
    "version": 1
  }
}