Pith Number

pith:6BAVG4AX

pith:2010:6BAVG4AXMBUSWDNEPPYJOVE6MA

not attested not anchored not stored refs pending

Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

Kazuhiko Yamaki

arxiv:1007.1081 v5 · 2010-07-07 · 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{6BAVG4AXMBUSWDNEPPYJOVE6MA}

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	2026-05-18T03:36:46.895085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f04153701760692b0da47bf097549e6038a3ef100f66d91fb1054a1bc5d58d94

Aliases

arxiv: 1007.1081 · arxiv_version: 1007.1081v5 · doi: 10.48550/arxiv.1007.1081 · pith_short_12: 6BAVG4AXMBUS · pith_short_16: 6BAVG4AXMBUSWDNE · pith_short_8: 6BAVG4AX

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/6BAVG4AXMBUSWDNEPPYJOVE6MA \
  | 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: f04153701760692b0da47bf097549e6038a3ef100f66d91fb1054a1bc5d58d94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fa5df6a2952952c2bdb6ebe234b5fcbcb50d35b54af605a3792d5003a66f18d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-07-07T08:59:11Z",
    "title_canon_sha256": "cd7067c124be119e9494e4e230e179a4bfe92bc0bcf03058fa33f694554606ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1081",
    "kind": "arxiv",
    "version": 5
  }
}