Pith Number

pith:XCZZYGBZ

pith:2010:XCZZYGBZOBGH2AJNTKF4FJ5G7P

not attested not anchored not stored refs pending

Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions

James Lepowsky, Lin Zhang, Yi-Zhi Huang

arxiv:1012.4198 v2 · 2010-12-19 · math.QA · hep-th · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCZZYGBZOBGH2AJNTKF4FJ5G7P}

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	2026-05-18T03:55:56.243556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8b39c1839704c7d012d9a8bc2a7a6fbdf77abcb7a90be928752db6a9f59e121

Aliases

arxiv: 1012.4198 · arxiv_version: 1012.4198v2 · doi: 10.48550/arxiv.1012.4198 · pith_short_12: XCZZYGBZOBGH · pith_short_16: XCZZYGBZOBGH2AJN · pith_short_8: XCZZYGBZ

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/XCZZYGBZOBGH2AJNTKF4FJ5G7P \
  | 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: b8b39c1839704c7d012d9a8bc2a7a6fbdf77abcb7a90be928752db6a9f59e121

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d3bf6fabcebb3bb08613b036d8663eade3bc8c7622603d87b93b8321b7b4fb2",
    "cross_cats_sorted": [
      "hep-th",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-12-19T19:19:25Z",
    "title_canon_sha256": "f05430d5411cfc0be0c27cc6ab8a46ccb5caa92e894bb13d30ac279ce7409cc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4198",
    "kind": "arxiv",
    "version": 2
  }
}