Pith Number

pith:E6IPWPNA

pith:2005:E6IPWPNAY55WTTF5SFHY6HD2C7

not attested not anchored not stored refs pending

Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem

((1) IVIC, 2), (2) UCV, (3) LPTMC, 4), (4) Polish Academy of Sciences, Caracas, France, K A Penson (3), Krakow, M A Mendez (1, P Blasiak (3, Poland), University of Paris VI, Venezuela

arxiv:quant-ph/0505180 v1 · 2005-05-24 · quant-ph · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E6IPWPNAY55WTTF5SFHY6HD2C7}

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	2026-05-18T04:32:20.561851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2790fb3da0c77b69ccbd914f8f1c7a17d71a5a518ad1d9136683d74d5045252a

Aliases

arxiv: quant-ph/0505180 · arxiv_version: quant-ph/0505180v1 · doi: 10.48550/arxiv.quant-ph/0505180 · pith_short_12: E6IPWPNAY55W · pith_short_16: E6IPWPNAY55WTTF5 · pith_short_8: E6IPWPNA

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/E6IPWPNAY55WTTF5SFHY6HD2C7 \
  | 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: 2790fb3da0c77b69ccbd914f8f1c7a17d71a5a518ad1d9136683d74d5045252a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e548165fe8876f0e7419177069911b19562539e4d62302faeae79b2e2af0829d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2005-05-24T10:18:08Z",
    "title_canon_sha256": "9add9eb119a58cd06132ade299fbde73fe77b968593c481b0f0842b835ebb075"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0505180",
    "kind": "arxiv",
    "version": 1
  }
}