Pith Number

pith:WVKIULN6

pith:1994:WVKIULN6L5HMPKNRO2ZPFXLSKL

not attested not anchored not stored refs pending

Liouville Theory: Ward Identities for Generating Functional and Modular Geometry

Leon Takhtajan

arxiv:hep-th/9403013 v1 · 1994-03-02 · 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{WVKIULN6L5HMPKNRO2ZPFXLSKL}

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	2026-05-18T01:38:42.025801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5548a2dbe5f4ec7a9b176b2f2dd7252c9537e7eeb51d66c90606f5daf40a4b0

Aliases

arxiv: hep-th/9403013 · arxiv_version: hep-th/9403013v1 · doi: 10.48550/arxiv.hep-th/9403013 · pith_short_12: WVKIULN6L5HM · pith_short_16: WVKIULN6L5HMPKNR · pith_short_8: WVKIULN6

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/WVKIULN6L5HMPKNRO2ZPFXLSKL \
  | 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: b5548a2dbe5f4ec7a9b176b2f2dd7252c9537e7eeb51d66c90606f5daf40a4b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "741c130e49148938627e30f2efa0b72d89d440b4eed8c20aeacb37cbe45cfeac",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1994-03-02T20:14:56Z",
    "title_canon_sha256": "bd8a4577b375e7ae874d90321e5f4f2d27ef5aa974657f0ea91d7c48f1d75933"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9403013",
    "kind": "arxiv",
    "version": 1
  }
}