Pith Number

pith:PQKS7ANC

pith:2011:PQKS7ANC4SFPXGP6XBFHPNSLBW

not attested not anchored not stored refs pending

Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps

James Lepowsky, Lin Zhang, Yi-Zhi Huang

arxiv:1110.1929 v2 · 2011-10-10 · 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{PQKS7ANC4SFPXGP6XBFHPNSLBW}

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	2026-05-18T03:55:56.074151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c152f81a2e48afb99feb84a77b64b0dbfaa737c81fcb2f519c8e81d81594b6b

Aliases

arxiv: 1110.1929 · arxiv_version: 1110.1929v2 · doi: 10.48550/arxiv.1110.1929 · pith_short_12: PQKS7ANC4SFP · pith_short_16: PQKS7ANC4SFPXGP6 · pith_short_8: PQKS7ANC

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/PQKS7ANC4SFPXGP6XBFHPNSLBW \
  | 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: 7c152f81a2e48afb99feb84a77b64b0dbfaa737c81fcb2f519c8e81d81594b6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c700d2c6ee2614dd3f47937d73ea2184e2b4a0ab4cfe833c9985f2bfb019c570",
    "cross_cats_sorted": [
      "hep-th",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-10-10T05:26:34Z",
    "title_canon_sha256": "66ef02d749143aa57d1e0c16089077b932a926665ed3bc610b2d8264af813296"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1929",
    "kind": "arxiv",
    "version": 2
  }
}