Pith Number

pith:Y3XX7MPF

pith:2010:Y3XX7MPFL2DBCEPT3642RDCK3J

not attested not anchored not stored refs pending

Singularities with G_m-action and the log minimal model program for $\bar{M}_g$

David Ishii Smyth, Jarod Alper, Maksym Fedorchuk

arxiv:1010.3751 v2 · 2010-10-18 · 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{Y3XX7MPFL2DBCEPT3642RDCK3J}

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	2026-05-18T04:20:38.407597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc

Aliases

arxiv: 1010.3751 · arxiv_version: 1010.3751v2 · doi: 10.48550/arxiv.1010.3751 · pith_short_12: Y3XX7MPFL2DB · pith_short_16: Y3XX7MPFL2DBCEPT · pith_short_8: Y3XX7MPF

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/Y3XX7MPFL2DBCEPT3642RDCK3J \
  | 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: c6ef7fb1e55e861111f3dfb9a88c4ada4b6535228d3f208f40480e52493aeabc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0786eb96dfc811fdaed46dd8c2604bbe81f366a9fda8160a51a4299abbeb744",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-10-18T22:11:32Z",
    "title_canon_sha256": "2d074115b8b85022a7a2826c324885009a804e2d4c33b6394470734fbbb72509"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3751",
    "kind": "arxiv",
    "version": 2
  }
}