Pith Number

pith:VZ3S32WC

pith:2004:VZ3S32WCVLW5444S54DJDT5ZGS

not attested not anchored not stored refs pending

Khovanov-Rozansky Homology and Topological Strings

Albert Schwarz, Cumrun Vafa, Sergei Gukov

arxiv:hep-th/0412243 v3 · 2004-12-20 · hep-th · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZ3S32WCVLW5444S54DJDT5ZGS}

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.

Cited by

1 paper in Pith

Reductions in Khovanov-Rozansky operator formalism

Receipt and verification

First computed	2026-07-04T16:49:08.336934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae772deac2aaedde7392ef0691cfb934be21215e36ad6010f77541c10b29d9e2

Aliases

arxiv: hep-th/0412243 · arxiv_version: hep-th/0412243v3 · doi: 10.48550/arxiv.hep-th/0412243 · pith_short_12: VZ3S32WCVLW5 · pith_short_16: VZ3S32WCVLW5444S · pith_short_8: VZ3S32WC

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/VZ3S32WCVLW5444S54DJDT5ZGS \
  | 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: ae772deac2aaedde7392ef0691cfb934be21215e36ad6010f77541c10b29d9e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7479a0b1461b656b673379cc8a465bf014b998e14e5f810663f7c68fc80dcaf",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2004-12-20T21:29:58Z",
    "title_canon_sha256": "264248c341f42096f1c8cade1a50c46e71b587558deb0849b29d8f751bad8bb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0412243",
    "kind": "arxiv",
    "version": 3
  }
}