Pith Number

pith:FJW2ZXBT

pith:2013:FJW2ZXBTSQ5MOHF3R5765HUWO4

not attested not anchored not stored refs pending

The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1

Arul Shankar, Manjul Bhargava

arxiv:1312.7859 v1 · 2013-12-30 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FJW2ZXBTSQ5MOHF3R5765HUWO4}

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

3 papers in Pith

A Heuristic approach to the Iwasawa theory of elliptic curves

Non-vanishing of Artin $L$-functions associated with $D_4$-quartic function fields ordered by conductor

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

Receipt and verification

First computed	2026-05-18T03:03:33.587704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a6dacdc33943ac71cbb8f7fee9e96771c3f33b009d25daf7ee320a9b73615c7

Aliases

arxiv: 1312.7859 · arxiv_version: 1312.7859v1 · doi: 10.48550/arxiv.1312.7859 · pith_short_12: FJW2ZXBTSQ5M · pith_short_16: FJW2ZXBTSQ5MOHF3 · pith_short_8: FJW2ZXBT

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/FJW2ZXBTSQ5MOHF3R5765HUWO4 \
  | 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: 2a6dacdc33943ac71cbb8f7fee9e96771c3f33b009d25daf7ee320a9b73615c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cd0d3847d4137e25d473635cfffaedb301f36ffaa26ffa0d8f2d9daf38e86e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-30T20:43:23Z",
    "title_canon_sha256": "ce32f8ddaa985efcc90adb571d39710f0445a649d6c92be9c36e536f8cace665"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7859",
    "kind": "arxiv",
    "version": 1
  }
}