Pith Number

pith:TCJPXLAZ

pith:2009:TCJPXLAZ6V36ZK4Z7B2HXGLWDI

not attested not anchored not stored refs pending

Stable Degenerations of Surfaces Isogenous to a Product II

Wenfei Liu

arxiv:0911.5177 v3 · 2009-11-26 · 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{TCJPXLAZ6V36ZK4Z7B2HXGLWDI}

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	2026-05-18T03:46:17.167057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9892fbac19f577ecab99f8747b99761a1c4823f198c142a9d2839d64059d9733

Aliases

arxiv: 0911.5177 · arxiv_version: 0911.5177v3 · doi: 10.48550/arxiv.0911.5177 · pith_short_12: TCJPXLAZ6V36 · pith_short_16: TCJPXLAZ6V36ZK4Z · pith_short_8: TCJPXLAZ

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/TCJPXLAZ6V36ZK4Z7B2HXGLWDI \
  | 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: 9892fbac19f577ecab99f8747b99761a1c4823f198c142a9d2839d64059d9733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d3b7de5ae9e6dd8db214ca1e0f60bdc2832fe4eb013dfd9fcf59261693f982d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-11-26T23:50:17Z",
    "title_canon_sha256": "ae3057022ba5642923c65c50f8aba3a7b0854166f0a525e0ffbe9ba97f7ad87e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5177",
    "kind": "arxiv",
    "version": 3
  }
}