Pith Number

pith:4D52P3NU

pith:2009:4D52P3NUH7JZADRNWSNC5EV7F2

not attested not anchored not stored refs pending

Ladder Operators and Endomorphisms in Combinatorial Physics

Allan I. Solomon (LPTMC), Andrzej Horzela (IFJ-PAN - Polish Academy of Sciences), G\'erard Henry Edmond Duchamp (LIPN), Karol A. Penson (LPTMC), Laurent Poinsot (LIPN), Pawel Blasiak (IFJ-PAN - Polish Academy of Sciences)

arxiv:0908.2332 v2 · 2009-08-17 · math.CO · cs.SC · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4D52P3NUH7JZADRNWSNC5EV7F2}

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	2026-05-18T04:37:20.849076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0fba7edb43fd3900e2db49a2e92bf2ea00259668ef74cb8c39a697c38c29844

Aliases

arxiv: 0908.2332 · arxiv_version: 0908.2332v2 · doi: 10.48550/arxiv.0908.2332 · pith_short_12: 4D52P3NUH7JZ · pith_short_16: 4D52P3NUH7JZADRN · pith_short_8: 4D52P3NU

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/4D52P3NUH7JZADRNWSNC5EV7F2 \
  | 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: e0fba7edb43fd3900e2db49a2e92bf2ea00259668ef74cb8c39a697c38c29844

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d81db0a6061eedb6f8b719ca7c0b7f1159fbe128356c24422b702bc3b22deb54",
    "cross_cats_sorted": [
      "cs.SC",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-08-17T11:40:06Z",
    "title_canon_sha256": "571891018a696c18b433e9a9ae9207b8739154aa90c50e9ee8d6955ab7ec5d18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.2332",
    "kind": "arxiv",
    "version": 2
  }
}