Pith Number

pith:O47UFQH3

pith:2015:O47UFQH3CGQ5W3XM4HUKSGVSOR

not attested not anchored not stored refs pending

Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation

C. David Levermore, Hailiang Liu, Robert L. Pego

arxiv:1512.06780 v2 · 2015-12-21 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O47UFQH3CGQ5W3XM4HUKSGVSOR}

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	2026-05-18T01:23:53.632412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

773f42c0fb11a1db6eece1e8a91ab27457f67ac5ef1a60f102cdce2038a8e9b2

Aliases

arxiv: 1512.06780 · arxiv_version: 1512.06780v2 · doi: 10.48550/arxiv.1512.06780 · pith_short_12: O47UFQH3CGQ5 · pith_short_16: O47UFQH3CGQ5W3XM · pith_short_8: O47UFQH3

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/O47UFQH3CGQ5W3XM4HUKSGVSOR \
  | 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: 773f42c0fb11a1db6eece1e8a91ab27457f67ac5ef1a60f102cdce2038a8e9b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1972524a7ce5209dc613959c995ab6f7db8a269f6092f6421ede8b220f740bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-21T19:40:32Z",
    "title_canon_sha256": "722ecdc4b320a7d5424477f32f9090d46afa2014b1e30cc8d8bd1820232ec384"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06780",
    "kind": "arxiv",
    "version": 2
  }
}