Pith Number

pith:XXT4CN5F

pith:1999:XXT4CN5FJD23VNPFJXOJGQJB4M

not attested not anchored not stored refs pending

Generalization of the Lie-Trotter Product Formula for q-Exponential Operators

A.K. Rajagopal (Naval Research Laboratory, Brazil), Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, USA), Washington DC

arxiv:cond-mat/9903106 v1 · 1999-03-05 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XXT4CN5FJD23VNPFJXOJGQJB4M}

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	2026-07-04T16:12:21.244038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bde7c137a548f5bab5e54ddc934121e32178b58870c232324608b2a38ce7e270

Aliases

arxiv: cond-mat/9903106 · arxiv_version: cond-mat/9903106v1 · doi: 10.48550/arxiv.cond-mat/9903106 · pith_short_12: XXT4CN5FJD23 · pith_short_16: XXT4CN5FJD23VNPF · pith_short_8: XXT4CN5F

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/XXT4CN5FJD23VNPFJXOJGQJB4M \
  | 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: bde7c137a548f5bab5e54ddc934121e32178b58870c232324608b2a38ce7e270

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "891c21484db503ce32f45b3103fba5babe816a78223c7071f0659f11ba8ec423",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "1999-03-05T20:59:23Z",
    "title_canon_sha256": "f912e2986cea9daa02339a0cd6fd4f61a81b648c63e9c446750d94f6eb3afae3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cond-mat/9903106",
    "kind": "arxiv",
    "version": 1
  }
}