Pith Number

pith:K2B7TDUU

pith:2008:K2B7TDUUXOH5ZGGVLKTYBJ335M

not attested not anchored not stored refs pending

Bose Einstein condensation on inhomogeneous amenable graphs

Daniele Guido, Francesco Fidaleo, Tommaso Isola

arxiv:0812.0274 v2 · 2008-12-01 · math.OA · 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{K2B7TDUUXOH5ZGGVLKTYBJ335M}

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	2026-05-18T04:19:33.626164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5683f98e94bb8fdc98d55aa780a77beb17cd367bcc4cfa5e6e7dc485e200f52b

Aliases

arxiv: 0812.0274 · arxiv_version: 0812.0274v2 · doi: 10.48550/arxiv.0812.0274 · pith_short_12: K2B7TDUUXOH5 · pith_short_16: K2B7TDUUXOH5ZGGV · pith_short_8: K2B7TDUU

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/K2B7TDUUXOH5ZGGVLKTYBJ335M \
  | 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: 5683f98e94bb8fdc98d55aa780a77beb17cd367bcc4cfa5e6e7dc485e200f52b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1e2db79516d4658b36878a9ffe3d7b96630d375ab794f426025260173343dc0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-12-01T11:58:03Z",
    "title_canon_sha256": "e3126c624a8ae1b40265e557d108c7c8a07ae298fc46c66e70d924c45bb1c94e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.0274",
    "kind": "arxiv",
    "version": 2
  }
}