Pith Number

pith:TGOEXYZ4

pith:2011:TGOEXYZ4M7USPOQIRCRJY6KXUM

not attested not anchored not stored refs pending

Hori-Vafa mirror periods, Picard-Fuchs equations, and Berglund-H\"{u}bsch-Krawitz duality

Charles F. Doran, Richard S. Garavuso

arxiv:1109.1686 v2 · 2011-09-08 · hep-th · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TGOEXYZ4M7USPOQIRCRJY6KXUM}

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	2026-05-18T02:00:37.976065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

999c4be33c67e927ba0888a29c7957a30d37fa397d88c03f1a5a064d5211f8e8

Aliases

arxiv: 1109.1686 · arxiv_version: 1109.1686v2 · doi: 10.48550/arxiv.1109.1686 · pith_short_12: TGOEXYZ4M7US · pith_short_16: TGOEXYZ4M7USPOQI · pith_short_8: TGOEXYZ4

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/TGOEXYZ4M7USPOQIRCRJY6KXUM \
  | 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: 999c4be33c67e927ba0888a29c7957a30d37fa397d88c03f1a5a064d5211f8e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45daecad220e05aa6431c15d2e33224aca56ec616ce2e382f4d6a507688e1e2f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2011-09-08T10:48:51Z",
    "title_canon_sha256": "00e2c1b7c1536a2147cfd43ff8a902aa097454a3b0027f5fdcd49e95f3954a71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1686",
    "kind": "arxiv",
    "version": 2
  }
}