Pith Number

pith:W4P2W2WW

pith:2010:W4P2W2WW4O4X62QXTTZHNNSM6I

not attested not anchored not stored refs pending

Exponential rarefaction of real curves with many components

Damien Gayet (ICJ), Jean-Yves Welschinger (ICJ)

arxiv:1005.3228 v1 · 2010-05-18 · 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{W4P2W2WW4O4X62QXTTZHNNSM6I}

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	2026-05-18T04:04:31.303028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b71fab6ad6e3b97f6a179cf276b64cf2273b0c28fd5a91e87ad119a2d099e000

Aliases

arxiv: 1005.3228 · arxiv_version: 1005.3228v1 · doi: 10.48550/arxiv.1005.3228 · pith_short_12: W4P2W2WW4O4X · pith_short_16: W4P2W2WW4O4X62QX · pith_short_8: W4P2W2WW

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/W4P2W2WW4O4X62QXTTZHNNSM6I \
  | 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: b71fab6ad6e3b97f6a179cf276b64cf2273b0c28fd5a91e87ad119a2d099e000

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4d4da5d754f0f9c3051864768555cb04da76ae1886989b595fd8e54b87274b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-05-18T15:22:59Z",
    "title_canon_sha256": "7baacd72c5ec92cf2d1bc529d7800d8dd8f05da4e8e55695556c139bbb293d85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3228",
    "kind": "arxiv",
    "version": 1
  }
}