Pith Number

pith:5GJF22S7

pith:2010:5GJF22S74IK3CTTJZCVLNFP3FM

not attested not anchored not stored refs pending

Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms

James Lepowsky, Lin Zhang, Yi-Zhi Huang

arxiv:1012.4202 v3 · 2010-12-19 · math.QA · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5GJF22S74IK3CTTJZCVLNFP3FM}

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	2026-05-18T03:55:56.223805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9925d6a5fe215b14e69c8aab695fb2b3530f2590229e2dbdc1565e09bd61288

Aliases

arxiv: 1012.4202 · arxiv_version: 1012.4202v3 · doi: 10.48550/arxiv.1012.4202 · pith_short_12: 5GJF22S74IK3 · pith_short_16: 5GJF22S74IK3CTTJ · pith_short_8: 5GJF22S7

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/5GJF22S74IK3CTTJZCVLNFP3FM \
  | 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: e9925d6a5fe215b14e69c8aab695fb2b3530f2590229e2dbdc1565e09bd61288

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a34d9d4b97f57d9af8c702844bfa614ee73d3cea68f049e1783f97a144e76798",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-12-19T19:25:01Z",
    "title_canon_sha256": "ca6d91913da8bb8b4f1a1a5b100ee452ea6402c0bf8eaee48c6bf477c53e4b1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4202",
    "kind": "arxiv",
    "version": 3
  }
}