Pith Number

pith:NWZFD7U5

pith:2016:NWZFD7U5MEZUMP5CQLR3A4TBRB

not attested not anchored not stored refs pending

The Virasoro vertex algebra and factorization algebras on Riemann surfaces

Brian R Williams

arxiv:1603.02349 v2 · 2016-03-08 · math.QA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWZFD7U5MEZUMP5CQLR3A4TBRB}

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	2026-05-18T00:35:25.152595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6db251fe9d6133463fa282e3b07261885973111546d7187e997cc963354bdb12

Aliases

arxiv: 1603.02349 · arxiv_version: 1603.02349v2 · doi: 10.48550/arxiv.1603.02349 · pith_short_12: NWZFD7U5MEZU · pith_short_16: NWZFD7U5MEZUMP5C · pith_short_8: NWZFD7U5

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/NWZFD7U5MEZUMP5CQLR3A4TBRB \
  | 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: 6db251fe9d6133463fa282e3b07261885973111546d7187e997cc963354bdb12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47f7408068c38cf0bde5fae8b782003088f1f1dc3c8b33a5ecf8338c3cf7a83c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2016-03-08T01:03:24Z",
    "title_canon_sha256": "b68ae207e9cabc48b5266ea169413c7b4bdb2a6002c2e0ebabf257c26b6e54b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.02349",
    "kind": "arxiv",
    "version": 2
  }
}