Pith Number

pith:VYK52C2J

pith:2014:VYK52C2JT2ANBPJI655EUBMIJR

not attested not anchored not stored refs pending

Backward Clusters, Hierarchy and Wild Sums for a Hard Sphere System in a Low-Density Regime

K. Aoki, M. Pulvirenti, S. Simonella, T. Tsuji

arxiv:1408.6571 v1 · 2014-08-27 · math-ph · math.AP · 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{VYK52C2JT2ANBPJI655EUBMIJR}

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	2026-05-18T00:56:46.942767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae15dd0b499e80d0bd28f77a4a05884c6056432d9ee39e03ccadf0e778cb2f3e

Aliases

arxiv: 1408.6571 · arxiv_version: 1408.6571v1 · doi: 10.48550/arxiv.1408.6571 · pith_short_12: VYK52C2JT2AN · pith_short_16: VYK52C2JT2ANBPJI · pith_short_8: VYK52C2J

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/VYK52C2JT2ANBPJI655EUBMIJR \
  | 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: ae15dd0b499e80d0bd28f77a4a05884c6056432d9ee39e03ccadf0e778cb2f3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6e8d059feb7838551803c2c6061e22283651723495b92331e5fceec19409838",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-08-27T21:27:44Z",
    "title_canon_sha256": "771f0ba74d58158df6a419eaa49c1672142a84e7f40ef8440be380dd025f45aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.6571",
    "kind": "arxiv",
    "version": 1
  }
}