Pith Number

pith:64IXFQI5

pith:1998:64IXFQI5KRCV3V4YQ6WUV62EYK

not attested not anchored not stored refs pending

Higher-Dimensional Algebra IV: 2-Tangles

John C. Baez, Laurel Langford

arxiv:math/9811139 v3 · 1998-11-24 · math.QA · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64IXFQI5KRCV3V4YQ6WUV62EYK}

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.

Cited by

1 paper in Pith

Transposing cartesian and other structure in double categories

Receipt and verification

First computed	2026-07-04T14:48:25.222078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f71172c11d54455dd79887ad4afb44c29975ac2ae562da7da7aa24c3ad232985

Aliases

arxiv: math/9811139 · arxiv_version: math/9811139v3 · doi: 10.48550/arxiv.math/9811139 · pith_short_12: 64IXFQI5KRCV · pith_short_16: 64IXFQI5KRCV3V4Y · pith_short_8: 64IXFQI5

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/64IXFQI5KRCV3V4YQ6WUV62EYK \
  | 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: f71172c11d54455dd79887ad4afb44c29975ac2ae562da7da7aa24c3ad232985

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73e54b2439b0594d44c08f3c4b41ffb809f92834ee4e1918d0e0c6f981fee87f",
    "cross_cats_sorted": [
      "math.AT",
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "1998-11-24T05:03:07Z",
    "title_canon_sha256": "359559c5cec21228ee3d2bcd8e76cb4063efa65bd90ad6c232f670561e71ece8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9811139",
    "kind": "arxiv",
    "version": 3
  }
}