Pith Number

pith:P7BQAYRP

pith:2012:P7BQAYRPB5C3UP3GIKCI43CV5O

not attested not anchored not stored refs pending

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

Boris Dubrovin, Si-Qi Liu, Youjin Zhang

arxiv:1205.5990 v2 · 2012-05-27 · math-ph · math.AG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P7BQAYRPB5C3UP3GIKCI43CV5O}

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	2026-05-18T01:57:16.761161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117

Aliases

arxiv: 1205.5990 · arxiv_version: 1205.5990v2 · doi: 10.48550/arxiv.1205.5990 · pith_short_12: P7BQAYRPB5C3 · pith_short_16: P7BQAYRPB5C3UP3G · pith_short_8: P7BQAYRP

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/P7BQAYRPB5C3UP3GIKCI43CV5O \
  | 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: 7fc300622f0f45ba3f6642848e6c55eba1d65472025c2f599296749593b23117

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a0481d6bb94cfa55ce4472acc28bfe6753bb0eae239c0aafd0ec115cc1d0311",
    "cross_cats_sorted": [
      "math.AG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-05-27T17:52:14Z",
    "title_canon_sha256": "9ec0a4c08f3d5b825fa4e6ae3c935d16470506af22b235ba10f100406fc9d05d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5990",
    "kind": "arxiv",
    "version": 2
  }
}