Pith Number

pith:XTF2SO62

pith:2012:XTF2SO623QFMC3UTUEPHNAW6PM

not attested not anchored not stored refs pending

Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots

Cumrun Vafa, Mina Aganagic

arxiv:1204.4709 v4 · 2012-04-20 · hep-th · math.AG · math.KT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XTF2SO623QFMC3UTUEPHNAW6PM}

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

2 papers in Pith

Shading A-polynomials via huge representations of $U_q(\mathfrak{su}_N)$

Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas

Receipt and verification

First computed	2026-05-18T03:50:48.322918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bccba93bdadc0ac16e93a11e7682de7b33fc9ada3dddd74117438b1fb1d3e3ff

Aliases

arxiv: 1204.4709 · arxiv_version: 1204.4709v4 · doi: 10.48550/arxiv.1204.4709 · pith_short_12: XTF2SO623QFM · pith_short_16: XTF2SO623QFMC3UT · pith_short_8: XTF2SO62

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/XTF2SO623QFMC3UTUEPHNAW6PM \
  | 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: bccba93bdadc0ac16e93a11e7682de7b33fc9ada3dddd74117438b1fb1d3e3ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "146b030038f2d7d0e5083481ee90ea1381ea15f25c290d30cf4dc83b92d85cf1",
    "cross_cats_sorted": [
      "math.AG",
      "math.KT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2012-04-20T19:25:35Z",
    "title_canon_sha256": "f04ec1bb8559cce4af492824171826cef479491432c923563d0ce93daad7c813"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4709",
    "kind": "arxiv",
    "version": 4
  }
}