Pith Number

pith:56O6RAQM

pith:2004:56O6RAQMFIBLUT2TUV2E2IHUVP

not attested not anchored not stored refs pending

Some useful combinatorial formulae for bosonic operators

2), (2) The Open University, 3), (3) Polish Academy of Sciences, (4) LIFAR, A. Horzela (3), A.I. Solomon (1, France, France), G.E.H. Duchamp (4)((1) LPTMC, K.A. Penson (1), Krakow, Milton Keynes, P. Blasiak (1, Poland, UK, University of Paris VI, University of Rouen

arxiv:quant-ph/0405103 v2 · 2004-05-18 · 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{56O6RAQMFIBLUT2TUV2E2IHUVP}

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	2026-05-18T01:37:58.574929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef9de8820c2a02ba4f53a5744d20f4abe1508ea4851cafd3f0a807a800226575

Aliases

arxiv: quant-ph/0405103 · arxiv_version: quant-ph/0405103v2 · doi: 10.48550/arxiv.quant-ph/0405103 · pith_short_12: 56O6RAQMFIBL · pith_short_16: 56O6RAQMFIBLUT2T · pith_short_8: 56O6RAQM

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/56O6RAQMFIBLUT2TUV2E2IHUVP \
  | 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: ef9de8820c2a02ba4f53a5744d20f4abe1508ea4851cafd3f0a807a800226575

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f711f3d59b9e35a3a2c54e3e26fd2163250bfb5f83c84f4a85093ac3b41f390d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2004-05-18T15:54:55Z",
    "title_canon_sha256": "d4ddc9c880412f104fdb5a6ba33fd2961a3019f92824f43bd337585a2a16968f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0405103",
    "kind": "arxiv",
    "version": 2
  }
}