Pith Number

pith:UJ5I2K7V

pith:2005:UJ5I2K7VVWGLY6XCIPOUMVLJVU

not attested not anchored not stored refs pending

Hopfish algebras

Alan Weinstein, Chenchang Zhu, Xiang Tang

arxiv:math/0510421 v2 · 2005-10-19 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UJ5I2K7VVWGLY6XCIPOUMVLJVU}

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	2026-07-04T17:26:14.803146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a27a8d2bf5ad8cbc7ae243dd465569ad1415c246505a240d3d1ac49e1c0ba56f

Aliases

arxiv: math/0510421 · arxiv_version: math/0510421v2 · doi: 10.48550/arxiv.math/0510421 · pith_short_12: UJ5I2K7VVWGL · pith_short_16: UJ5I2K7VVWGLY6XC · pith_short_8: UJ5I2K7V

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/UJ5I2K7VVWGLY6XCIPOUMVLJVU \
  | 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: a27a8d2bf5ad8cbc7ae243dd465569ad1415c246505a240d3d1ac49e1c0ba56f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcd2439650a3e913512f8f4ca71f5c55178f73433ee926424f8007ad05e4823c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2005-10-19T21:52:06Z",
    "title_canon_sha256": "50c77d4f877865456d1f2dae465dd7365e81c26ce132cdaf0751f039e4cdc68c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510421",
    "kind": "arxiv",
    "version": 2
  }
}