Pith Number

pith:4P7B3Y3N

pith:2011:4P7B3Y3N4LETOCWKRS3MEF7S76

not attested not anchored not stored refs pending

Multiple cover formula of generalized DT invariants II: Jacobian localizations

Yukinobu Toda

arxiv:1108.4993 v1 · 2011-08-25 · 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{4P7B3Y3N4LETOCWKRS3MEF7S76}

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	2026-05-18T04:14:45.649110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3fe1de36de2c9370aca8cb6c217f2ff922842a9be3fa4a3a2cf3bb266c021e2

Aliases

arxiv: 1108.4993 · arxiv_version: 1108.4993v1 · doi: 10.48550/arxiv.1108.4993 · pith_short_12: 4P7B3Y3N4LET · pith_short_16: 4P7B3Y3N4LETOCWK · pith_short_8: 4P7B3Y3N

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/4P7B3Y3N4LETOCWKRS3MEF7S76 \
  | 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: e3fe1de36de2c9370aca8cb6c217f2ff922842a9be3fa4a3a2cf3bb266c021e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "464655951ebddbe7a8290b1c4d7a981d0c9a55ccd2548493df2d3c18c2af19cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-08-25T02:15:17Z",
    "title_canon_sha256": "e6abede26999e0a32c4ecff671cf2773dcf25624bf77237962f96e49d33d94e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4993",
    "kind": "arxiv",
    "version": 1
  }
}