Pith Number

pith:MD4FUVIZ

pith:2007:MD4FUVIZILQMNHUYEIPVKNTSPL

not attested not anchored not stored refs pending

Standard vs. Reduced Genus-One Gromov-Witten Invariants

Aleksey Zinger

arxiv:0706.0715 v3 · 2007-06-05 · math.AG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MD4FUVIZILQMNHUYEIPVKNTSPL}

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	2026-05-18T01:22:31.233898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60f85a551942e0c69e98221f5536727ac755cb5405f47370007f0cd7fa6aa3db

Aliases

arxiv: 0706.0715 · arxiv_version: 0706.0715v3 · doi: 10.48550/arxiv.0706.0715 · pith_short_12: MD4FUVIZILQM · pith_short_16: MD4FUVIZILQMNHUY · pith_short_8: MD4FUVIZ

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/MD4FUVIZILQMNHUYEIPVKNTSPL \
  | 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: 60f85a551942e0c69e98221f5536727ac755cb5405f47370007f0cd7fa6aa3db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e0790a5c3ffc53e626f2decd134043fc366ca2e569d473af391a5d8a5879773",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-06-05T18:33:32Z",
    "title_canon_sha256": "5819ac384b4ed23b850061b8d7e125ac7739c772450e6d5ab65edfbdbbcd96a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.0715",
    "kind": "arxiv",
    "version": 3
  }
}