Pith Number

pith:PPZKPBBF

pith:2010:PPZKPBBFXU5SO2UWMAZOZTWNGQ

not attested not anchored not stored refs pending

Partial monoids: associativity and confluence

Christophe Tollu (LIPN), G\'erard Duchamp (LIPN), Laurent Poinsot (LIPN)

arxiv:1002.2166 v1 · 2010-02-10 · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPZKPBBFXU5SO2UWMAZOZTWNGQ}

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	2026-05-18T04:40:09.407589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bf2a78425bd3b276a966032eccecd34031e33196b1f8bd85480b0fe50b44048

Aliases

arxiv: 1002.2166 · arxiv_version: 1002.2166v1 · doi: 10.48550/arxiv.1002.2166 · pith_short_12: PPZKPBBFXU5S · pith_short_16: PPZKPBBFXU5SO2UW · pith_short_8: PPZKPBBF

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/PPZKPBBFXU5SO2UWMAZOZTWNGQ \
  | 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: 7bf2a78425bd3b276a966032eccecd34031e33196b1f8bd85480b0fe50b44048

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86a823331310d6ef790bb297651075f2f0ad3be93cdca9500dcaadb5f9f3428e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2010-02-10T18:30:38Z",
    "title_canon_sha256": "48dd96de622a86f09dabbfe81b5f1595e7c559121f198aa1e0e5edf773768f79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2166",
    "kind": "arxiv",
    "version": 1
  }
}