Pith Number

pith:VNCKVUXQ

pith:2011:VNCKVUXQPL5KPH6KRXFTYRKCRY

not attested not anchored not stored refs pending

On the Newton polygons of abelian varieties of Mumford's type

Kang Zuo, Mao Sheng

arxiv:1106.3505 v1 · 2011-06-17 · 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{VNCKVUXQPL5KPH6KRXFTYRKCRY}

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	2026-05-18T04:19:52.612986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab44aad2f07afaa79fca8dcb3c45428e251fc1cc2d5009f735c71b3088d8180c

Aliases

arxiv: 1106.3505 · arxiv_version: 1106.3505v1 · doi: 10.48550/arxiv.1106.3505 · pith_short_12: VNCKVUXQPL5K · pith_short_16: VNCKVUXQPL5KPH6K · pith_short_8: VNCKVUXQ

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/VNCKVUXQPL5KPH6KRXFTYRKCRY \
  | 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: ab44aad2f07afaa79fca8dcb3c45428e251fc1cc2d5009f735c71b3088d8180c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4066ce6a2a4c9bf6870762cb4aa424d375eee39596211e7607dd92a689260cab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-06-17T14:58:50Z",
    "title_canon_sha256": "e42be29dadd87e542e60beadbd8cd2f284e12333c97b338401e9a236063645f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3505",
    "kind": "arxiv",
    "version": 1
  }
}