Pith Number

pith:TWSGI3RZ

pith:2011:TWSGI3RZJXRV56IYJSLTITZFXF

not attested not anchored not stored refs pending

Singularities of pluri-theta divisors in Char $p>0$

Christopher D. Hacon

arxiv:1112.2219 v1 · 2011-12-09 · 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{TWSGI3RZJXRV56IYJSLTITZFXF}

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	2026-05-18T04:06:35.131294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9da4646e394de35ef9184c97344f25b945fb43047bbe0822a1588f48b508c5f2

Aliases

arxiv: 1112.2219 · arxiv_version: 1112.2219v1 · doi: 10.48550/arxiv.1112.2219 · pith_short_12: TWSGI3RZJXRV · pith_short_16: TWSGI3RZJXRV56IY · pith_short_8: TWSGI3RZ

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/TWSGI3RZJXRV56IYJSLTITZFXF \
  | 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: 9da4646e394de35ef9184c97344f25b945fb43047bbe0822a1588f48b508c5f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a8b2cdcb6e2e7c7b42b0169247d3e57b33f382705a5a921e7a68d8277627683",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-12-09T21:29:10Z",
    "title_canon_sha256": "b6f6da5f12107ab290c63a82a9335358372081bb75a4337550e8b7151078cbd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2219",
    "kind": "arxiv",
    "version": 1
  }
}