Pith Number

pith:VBGYEWK6

pith:2010:VBGYEWK6MECAJP6YLMPD5I5EJJ

not attested not anchored not stored refs pending

Relative and orbifold Gromov-Witten invariants

Charles Cadman, Dan Abramovich, Jonathan Wise

arxiv:1004.0981 v2 · 2010-04-06 · 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{VBGYEWK6MECAJP6YLMPD5I5EJJ}

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	2026-05-18T02:18:31.887194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a84d82595e610404bfd85b1e3ea3a44a7904efb5a16467f027a1aec07585e332

Aliases

arxiv: 1004.0981 · arxiv_version: 1004.0981v2 · doi: 10.48550/arxiv.1004.0981 · pith_short_12: VBGYEWK6MECA · pith_short_16: VBGYEWK6MECAJP6Y · pith_short_8: VBGYEWK6

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/VBGYEWK6MECAJP6YLMPD5I5EJJ \
  | 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: a84d82595e610404bfd85b1e3ea3a44a7904efb5a16467f027a1aec07585e332

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1872efbd6fcdafabb93560d02968b8013dab07b65e0d12fc500f73bb8ae5941a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-04-06T22:16:03Z",
    "title_canon_sha256": "8cb175f94a4060cecaa09b964a90c2012e247c15034d0ea6eab8755a7475ca2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0981",
    "kind": "arxiv",
    "version": 2
  }
}