Pith Number

pith:FPS4OT6K

pith:2006:FPS4OT6KHBX3F6KWGZYQVG2YHX

not attested not anchored not stored refs pending

The Mathematics of the Bose Gas and its Condensation

Elliott H. Lieb, Jakob Yngvason, Jan Philip Solovej, Robert Seiringer

arxiv:cond-mat/0610117 v1 · 2006-10-04 · cond-mat.stat-mech · 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{FPS4OT6KHBX3F6KWGZYQVG2YHX}

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.

Cited by

1 paper in Pith

The Huang--Yang formula for a two-dimensional Fermi gas: upper bound

Receipt and verification

First computed	2026-07-04T14:56:57.774018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2be5c74fca386fb2f95636710a9b583dc5414db2c6d22405b3903043aa3aac56

Aliases

arxiv: cond-mat/0610117 · arxiv_version: cond-mat/0610117v1 · doi: 10.48550/arxiv.cond-mat/0610117 · pith_short_12: FPS4OT6KHBX3 · pith_short_16: FPS4OT6KHBX3F6KW · pith_short_8: FPS4OT6K

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/FPS4OT6KHBX3F6KWGZYQVG2YHX \
  | 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: 2be5c74fca386fb2f95636710a9b583dc5414db2c6d22405b3903043aa3aac56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be2e5f5831c7c17925b6ec82d8c7ec02490d120341d241287bb80d4a50da1a1e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2006-10-04T14:52:45Z",
    "title_canon_sha256": "91b2c5690c8d80219669559061ff48940b38e989b79f642a1c49cc1071365454"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cond-mat/0610117",
    "kind": "arxiv",
    "version": 1
  }
}