Pith Number

pith:TF2XTXLB

pith:2004:TF2XTXLBRQ4T6LJKESCCEUGTYJ

not attested not anchored not stored refs pending

Explicit formula for singular vectors of the Virasoro algebra with central charge less than 1

Reiho Sakamoto

arxiv:hep-th/0408074 v2 · 2004-08-10 · 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{TF2XTXLBRQ4T6LJKESCCEUGTYJ}

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	2026-05-18T01:38:46.146375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

997579dd618c393f2d2a24842250d3c260cb6b6e00d2623bf4157495d98af68e

Aliases

arxiv: hep-th/0408074 · arxiv_version: hep-th/0408074v2 · doi: 10.48550/arxiv.hep-th/0408074 · pith_short_12: TF2XTXLBRQ4T · pith_short_16: TF2XTXLBRQ4T6LJK · pith_short_8: TF2XTXLB

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/TF2XTXLBRQ4T6LJKESCCEUGTYJ \
  | 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: 997579dd618c393f2d2a24842250d3c260cb6b6e00d2623bf4157495d98af68e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10d319bc16816f8fea0fa20dfc708f69159c530f8e50f63bbd81defb7e8ebd6c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2004-08-10T08:24:58Z",
    "title_canon_sha256": "1e4d9e4769349a27c87022de5a593aca5b31d140a18db19ca9873be6bc348a3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0408074",
    "kind": "arxiv",
    "version": 2
  }
}