Pith Number

pith:ZNZ4UEPK

pith:2003:ZNZ4UEPK6XXK5MTEVH3OR2BI4U

not attested not anchored not stored refs pending

Equilibrium states for the Bose gas

A. Verbeure, L. Vandevenne, V. A. Zagrebnov

arxiv:math-ph/0307031 v3 · 2003-07-15 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZNZ4UEPK6XXK5MTEVH3OR2BI4U}

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	2026-05-18T01:38:33.739238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb73ca11eaf5eeaeb264a9f6e8e828e51b57990c230b8d7773be7ce40159c069

Aliases

arxiv: math-ph/0307031 · arxiv_version: math-ph/0307031v3 · doi: 10.48550/arxiv.math-ph/0307031 · pith_short_12: ZNZ4UEPK6XXK · pith_short_16: ZNZ4UEPK6XXK5MTE · pith_short_8: ZNZ4UEPK

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/ZNZ4UEPK6XXK5MTEVH3OR2BI4U \
  | 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: cb73ca11eaf5eeaeb264a9f6e8e828e51b57990c230b8d7773be7ce40159c069

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d9411170239223b75f4b61aa5eb4c4c06a6d11d668ce396c81cc8ba9bf5467a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2003-07-15T12:17:43Z",
    "title_canon_sha256": "4b9c7a189242a06a9e960d157b2eb19f48ec28b24b239a8391c96fdd5b2cabe3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0307031",
    "kind": "arxiv",
    "version": 3
  }
}