Pith Number

pith:CRADCXBK

pith:2013:CRADCXBKTG6PHGDQHAOO7N2YO2

not attested not anchored not stored refs pending

Average size of 2-Selmer groups of elliptic curves over function fields

B.C. Ngo, B.V. Le Hung, Q.P. Ho

arxiv:1310.7963 v3 · 2013-10-29 · math.NT · 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{CRADCXBKTG6PHGDQHAOO7N2YO2}

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.

Cited by

1 paper in Pith

Geometry-of-numbers methods over global fields II: Coregular representations

Receipt and verification

First computed	2026-07-05T03:13:46.158146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1440315c2a99bcf39870381cefb75876a01baf8e6b8ddafe4acdec78a3dca8df

Aliases

arxiv: 1310.7963 · arxiv_version: 1310.7963v3 · doi: 10.48550/arxiv.1310.7963 · pith_short_12: CRADCXBKTG6P · pith_short_16: CRADCXBKTG6PHGDQ · pith_short_8: CRADCXBK

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/CRADCXBKTG6PHGDQHAOO7N2YO2 \
  | 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: 1440315c2a99bcf39870381cefb75876a01baf8e6b8ddafe4acdec78a3dca8df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c1ed183045431199c75c03d726067e47da606c61f3df3907a598c3a388f7cb8",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-10-29T20:51:03Z",
    "title_canon_sha256": "352ea606d46405491a3d4367549185b12f4d4379e056d21a451ec54ba3e4ef77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7963",
    "kind": "arxiv",
    "version": 3
  }
}