Pith Number

pith:4M36VLTF

pith:2000:4M36VLTFJ2ZXY73BKWOFCFBL4J

not attested not anchored not stored refs pending

Operational Galois adjunctions

Bob Coecke, David Moore

arxiv:quant-ph/0008021 v1 · 2000-08-03 · quant-ph · math-ph · 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{4M36VLTFJ2ZXY73BKWOFCFBL4J}

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	2026-07-04T14:45:30.741791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e337eaae654eb37c7f61559c51142be27f5c90c76148605dbc914c6bd296ae86

Aliases

arxiv: quant-ph/0008021 · arxiv_version: quant-ph/0008021v1 · doi: 10.48550/arxiv.quant-ph/0008021 · pith_short_12: 4M36VLTFJ2ZX · pith_short_16: 4M36VLTFJ2ZXY73B · pith_short_8: 4M36VLTF

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/4M36VLTFJ2ZXY73BKWOFCFBL4J \
  | 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: e337eaae654eb37c7f61559c51142be27f5c90c76148605dbc914c6bd296ae86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "239df728e10055d878dc4ab4ef245be1465cdb0a203a1720d2de46ede28b5114",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2000-08-03T17:05:40Z",
    "title_canon_sha256": "e3436bec1b6fbef2b78b6b69a6ce4593dee5ef07db1565e0c15eb6ee06366da5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0008021",
    "kind": "arxiv",
    "version": 1
  }
}