Pith Number

pith:TTOYBYFB

pith:1996:TTOYBYFB5YFOGAHX2MPGPOLBY4

not attested not anchored not stored refs pending

Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b_+=1

Don Zagier, Lothar G\"ottsche

arxiv:alg-geom/9612020 v1 · 1996-12-26 · alg-geom · 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{TTOYBYFB5YFOGAHX2MPGPOLBY4}

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	2026-07-04T15:08:07.747958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cdd80e0a1ee0ae300f7d31e67b961c73999c13fb819927e92ab8d3cc546d3c2

Aliases

arxiv: alg-geom/9612020 · arxiv_version: alg-geom/9612020v1 · doi: 10.48550/arxiv.alg-geom/9612020 · pith_short_12: TTOYBYFB5YFO · pith_short_16: TTOYBYFB5YFOGAHX · pith_short_8: TTOYBYFB

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/TTOYBYFB5YFOGAHX2MPGPOLBY4 \
  | 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: 9cdd80e0a1ee0ae300f7d31e67b961c73999c13fb819927e92ab8d3cc546d3c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9665be90d4acce8275eeafea4e749488817d911fc53f62957228918cfcbce54d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "alg-geom",
    "submitted_at": "1996-12-26T15:48:32Z",
    "title_canon_sha256": "ae73c2319655fa9aa6431e3a51e7f164869811b3a032447e6dbf1a92d2351c82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "alg-geom/9612020",
    "kind": "arxiv",
    "version": 1
  }
}