Pith Number

pith:ACA4URLZ

pith:2005:ACA4URLZHIFEXRKH7W3DYKJ4ZN

not attested not anchored not stored refs pending

Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras

Aaron D. Lauda, Hendryk Pfeiffer

arxiv:math/0510664 v3 · 2005-10-31 · math.AT · hep-th · 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{ACA4URLZHIFEXRKH7W3DYKJ4ZN}

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

The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity

Receipt and verification

First computed	2026-07-04T15:09:44.665469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0081ca45793a0a4bc547fdb63c293ccb587becfc43404fa784cfe7c680b56ace

Aliases

arxiv: math/0510664 · arxiv_version: math/0510664v3 · doi: 10.48550/arxiv.math/0510664 · pith_short_12: ACA4URLZHIFE · pith_short_16: ACA4URLZHIFEXRKH · pith_short_8: ACA4URLZ

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/ACA4URLZHIFEXRKH7W3DYKJ4ZN \
  | 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: 0081ca45793a0a4bc547fdb63c293ccb587becfc43404fa784cfe7c680b56ace

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e59de8634bbc7e5a9bf556d1e4d01fb5cbee1118809ed5021b12fdf8507cd64",
    "cross_cats_sorted": [
      "hep-th",
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2005-10-31T18:16:37Z",
    "title_canon_sha256": "611be456880d5ba4e10197681029e0621006efff1cc64113ccc19f2b2cdc1c3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510664",
    "kind": "arxiv",
    "version": 3
  }
}