Pith Number

pith:6F4CNHUR

pith:2013:6F4CNHURI7KGEX6Y4CRMEH3G5G

not attested not anchored not stored refs pending

A completeness-like relation for Bessel functions

L. Raul Abramo, Paulo H. F. Reimberg

arxiv:1310.1128 v2 · 2013-10-03 · math-ph · cond-mat.stat-mech · 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{6F4CNHURI7KGEX6Y4CRMEH3G5G}

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	2026-05-18T01:26:58.546421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f178269e9147d4625fd8e0a2c21f66e9b46e3630ed6b437181aff17443e82b80

Aliases

arxiv: 1310.1128 · arxiv_version: 1310.1128v2 · doi: 10.48550/arxiv.1310.1128 · pith_short_12: 6F4CNHURI7KG · pith_short_16: 6F4CNHURI7KGEX6Y · pith_short_8: 6F4CNHUR

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/6F4CNHURI7KGEX6Y4CRMEH3G5G \
  | 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: f178269e9147d4625fd8e0a2c21f66e9b46e3630ed6b437181aff17443e82b80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ba82118f5bf8e83c14091c4859bcd5dfc92dcdcba960766526e885c6615002b",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-10-03T22:10:00Z",
    "title_canon_sha256": "590f9d4e2300f974a406d76083291ccc4095e1b684dd428a4ac04e118246a252"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1128",
    "kind": "arxiv",
    "version": 2
  }
}