Pith Number

pith:5PCZZM45

pith:2012:5PCZZM452YH2FYWZS5JSXADYNV

not attested not anchored not stored refs pending

A generic Hopf algebra for quantum statistical mechanics

Allan I. Solomon, Andrzej Horzela, Gerard E. H. Duchamp, Karol A. Penson, Pawel Blasiak

arxiv:1203.1446 v1 · 2012-03-07 · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PCZZM452YH2FYWZS5JSXADYNV}

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	2026-05-18T01:58:13.773840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebc59cb39dd60fa2e2d997532b80786d4ccb25eeef30661f30d704c29f20db30

Aliases

arxiv: 1203.1446 · arxiv_version: 1203.1446v1 · doi: 10.48550/arxiv.1203.1446 · pith_short_12: 5PCZZM452YH2 · pith_short_16: 5PCZZM452YH2FYWZ · pith_short_8: 5PCZZM45

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/5PCZZM452YH2FYWZS5JSXADYNV \
  | 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: ebc59cb39dd60fa2e2d997532b80786d4ccb25eeef30661f30d704c29f20db30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6372775369b7fcf3747b036d892b46abd5224159f2767d30849e5be40ee7fe82",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-03-07T11:54:40Z",
    "title_canon_sha256": "0a854d9e489bf7310b66f87282716e981d4e5908db0abaac67d671ffff5ef604"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1446",
    "kind": "arxiv",
    "version": 1
  }
}