Pith Number

pith:VDNYJ2OT

pith:2015:VDNYJ2OT23TYPKZSMZNZNJCBIW

not attested not anchored not stored refs pending

The Bogoliubov free energy functional I. Existence of minimizers and phase diagram

Jan Philip Solovej, Marcin Napi\'orkowski, Robin Reuvers

arxiv:1511.05935 v3 · 2015-11-18 · 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{VDNYJ2OT23TYPKZSMZNZNJCBIW}

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	2026-05-18T00:22:53.116847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8db84e9d3d6e787ab32665b96a44145b4b625dc9c23825ddb46822ba82008b4

Aliases

arxiv: 1511.05935 · arxiv_version: 1511.05935v3 · doi: 10.48550/arxiv.1511.05935 · pith_short_12: VDNYJ2OT23TY · pith_short_16: VDNYJ2OT23TYPKZS · pith_short_8: VDNYJ2OT

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/VDNYJ2OT23TYPKZSMZNZNJCBIW \
  | 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: a8db84e9d3d6e787ab32665b96a44145b4b625dc9c23825ddb46822ba82008b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0255339ddb49eb39c2454d8c40bbd6035d969e1afa2f7d9ec626a90f21b10165",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-11-18T20:29:26Z",
    "title_canon_sha256": "91fbaa6356b8f1541b4a700713733069afa848dea77ac23f64e31b689553bb25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05935",
    "kind": "arxiv",
    "version": 3
  }
}