Pith Number

pith:I3UW3ELW

pith:2011:I3UW3ELWLXPGP2EB3J7X4KLTGD

not attested not anchored not stored refs pending

Virasoro action on Imaginary Verma modules and the operator form of the KZ-equation

Ben Cox, Renato Martins, Vyacheslav Futorny

arxiv:1112.5361 v1 · 2011-12-22 · math.RT · 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{I3UW3ELWLXPGP2EB3J7X4KLTGD}

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	2026-05-18T01:59:03.107920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b

Aliases

arxiv: 1112.5361 · arxiv_version: 1112.5361v1 · doi: 10.48550/arxiv.1112.5361 · pith_short_12: I3UW3ELWLXPG · pith_short_16: I3UW3ELWLXPGP2EB · pith_short_8: I3UW3ELW

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/I3UW3ELWLXPGP2EB3J7X4KLTGD \
  | 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: 46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b599656ef66b283bd510301a656935d624aa25232b8f06e8efd7224c7cbc33a9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-12-22T16:06:13Z",
    "title_canon_sha256": "a79ab06c12d9484ce4db96a5c6ba0b1e8249bb6fb366660f2aaf9cdd02e7bc9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5361",
    "kind": "arxiv",
    "version": 1
  }
}