Pith Number

pith:GXMGGDWA

pith:2003:GXMGGDWAFCY77WOJ7X2N3ZLAGS

not attested not anchored not stored refs pending

Appendix to "Welschinger invariant and enumeration of real rational curves"

Eugenii Shustin, Ilia Itenberg, Viatcheslav Kharlamov

arxiv:math/0312142 v2 · 2003-12-07 · math.AG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GXMGGDWAFCY77WOJ7X2N3ZLAGS}

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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.

Cited by

1 paper in Pith

BPS polynomials and Welschinger invariants

Receipt and verification

First computed	2026-07-04T14:38:04.100869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35d8630ec028b1ffd9c9fdf4dde56034b6748e771202744761fccec28537ac80

Aliases

arxiv: math/0312142 · arxiv_version: math/0312142v2 · doi: 10.48550/arxiv.math/0312142 · pith_short_12: GXMGGDWAFCY7 · pith_short_16: GXMGGDWAFCY77WOJ · pith_short_8: GXMGGDWA

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/GXMGGDWAFCY77WOJ7X2N3ZLAGS \
  | 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: 35d8630ec028b1ffd9c9fdf4dde56034b6748e771202744761fccec28537ac80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2ce32b27f14eacffc42e03cd109b6706bae629a80c2418c761e2e564b9a6c7a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2003-12-07T13:31:18Z",
    "title_canon_sha256": "99982bfe058e765c9c6f36f42ee233d7110335d06e342b0a6926fbb9eb0bdfe6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312142",
    "kind": "arxiv",
    "version": 2
  }
}