Pith Number

pith:VM4HFJ7T

pith:2007:VM4HFJ7TMK4X5AO2AF4KGA4XE7

not attested not anchored not stored refs pending

From Boltzmann-Gibbs ensemble to generalized ensembles

Thomas Oikonomou

arxiv:0712.2310 v3 · 2007-12-14 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VM4HFJ7TMK4X5AO2AF4KGA4XE7}

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	2026-05-18T04:14:38.395643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab3872a7f362b97e81da0178a3039727ee8c8e37975eba086c8dfefaf650d0e8

Aliases

arxiv: 0712.2310 · arxiv_version: 0712.2310v3 · doi: 10.48550/arxiv.0712.2310 · pith_short_12: VM4HFJ7TMK4X · pith_short_16: VM4HFJ7TMK4X5AO2 · pith_short_8: VM4HFJ7T

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/VM4HFJ7TMK4X5AO2AF4KGA4XE7 \
  | 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: ab3872a7f362b97e81da0178a3039727ee8c8e37975eba086c8dfefaf650d0e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da26d8aefa5470a4f1a093f263b964c2a0b2dc18b46ffff690e8707bd22dc630",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2007-12-14T09:18:24Z",
    "title_canon_sha256": "57f95976a3cd81ed78a17683b2c8282deac4fdab9e1ba52a671cb9a44f9c2d5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.2310",
    "kind": "arxiv",
    "version": 3
  }
}