Pith Number

pith:B4HIZX72

pith:2015:B4HIZX72O6U7S5WGQT6TZW7C6T

not attested not anchored not stored refs pending

Bose-Einstein condensation in a hyperbolic model for the Kompaneets equation

Gautam Iyer, Joshua Ballew, Robert L. Pego

arxiv:1512.06950 v2 · 2015-12-22 · 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{B4HIZX72O6U7S5WGQT6TZW7C6T}

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	2026-05-18T01:04:57.676080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417

Aliases

arxiv: 1512.06950 · arxiv_version: 1512.06950v2 · doi: 10.48550/arxiv.1512.06950 · pith_short_12: B4HIZX72O6U7 · pith_short_16: B4HIZX72O6U7S5WG · pith_short_8: B4HIZX72

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/B4HIZX72O6U7S5WGQT6TZW7C6T \
  | 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: 0f0e8cdffa77a9f976c684fd3cdbe2f4da8372df23f8d679cdf397608b285417

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1dc9d44b70b610406875720516beca9141d38d4539f5534d31bf9f4346fdf6e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-22T03:48:51Z",
    "title_canon_sha256": "2bd2e43db02630517102bf0119dbc9d46bf9ab95028b53739cfeda6a36d54b42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06950",
    "kind": "arxiv",
    "version": 2
  }
}