Pith Number

pith:VRQHJIAY

pith:2009:VRQHJIAYTQCNHX57KMDMFAGDJ5

not attested not anchored not stored refs pending

Essential dimension of moduli of curves and other algebraic stacks

Angelo Vistoli, Najmuddin Fakhruddin, Patrick Brosnan, Zinovy Reichstein

arxiv:0907.0924 v2 · 2009-07-06 · math.AG · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRQHJIAYTQCNHX57KMDMFAGDJ5}

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	2026-05-18T00:50:24.207414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac6074a0189c04d3dfbf5306c280c34f75cead00539c5ff5eef442a5cc6b4801

Aliases

arxiv: 0907.0924 · arxiv_version: 0907.0924v2 · doi: 10.48550/arxiv.0907.0924 · pith_short_12: VRQHJIAYTQCN · pith_short_16: VRQHJIAYTQCNHX57 · pith_short_8: VRQHJIAY

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/VRQHJIAYTQCNHX57KMDMFAGDJ5 \
  | 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: ac6074a0189c04d3dfbf5306c280c34f75cead00539c5ff5eef442a5cc6b4801

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e07de2070d2311e8ee572c4ccfc024800696189d8481f1bf8d362b9349af1ca",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-07-06T07:04:03Z",
    "title_canon_sha256": "c6833f322da09e726dc7e24306d040549d177458a14b6ea3656706138097bdd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0924",
    "kind": "arxiv",
    "version": 2
  }
}