Pith Number

pith:3ZSFIXVU

pith:2009:3ZSFIXVUCS2VGSJIOOXLOQQFA5

not attested not anchored not stored refs pending

Torelli theorem for stable curves

Filippo Viviani, Lucia Caporaso

arxiv:0904.4039 v4 · 2009-04-26 · 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{3ZSFIXVUCS2VGSJIOOXLOQQFA5}

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	2026-05-18T04:16:42.494779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de64545eb414b553492873aeb74205076680bfaa0fb1d0d22d1f1dad2805f087

Aliases

arxiv: 0904.4039 · arxiv_version: 0904.4039v4 · doi: 10.48550/arxiv.0904.4039 · pith_short_12: 3ZSFIXVUCS2V · pith_short_16: 3ZSFIXVUCS2VGSJI · pith_short_8: 3ZSFIXVU

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/3ZSFIXVUCS2VGSJIOOXLOQQFA5 \
  | 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: de64545eb414b553492873aeb74205076680bfaa0fb1d0d22d1f1dad2805f087

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6b85881e4ca54db8dd288eac94a795aa5d6df954a371cbe9e11e67db0a9a290",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-04-26T17:00:15Z",
    "title_canon_sha256": "498f68bbf57c9b5ecebec1c6004a73e8d0f82da72f99aa877036de5507238e6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.4039",
    "kind": "arxiv",
    "version": 4
  }
}