Pith Number

pith:2RKTW7M3

pith:2013:2RKTW7M3AXKG3U2MHEUQMPBRUP

not attested not anchored not stored refs pending

On positive proportion of rank zero twists of elliptic curves over Q

Maosheng Xiong

arxiv:1311.5105 v1 · 2013-11-20 · 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{2RKTW7M3AXKG3U2MHEUQMPBRUP}

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	2026-05-17T23:53:35.211601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4553b7d9b05d46dd34c3929063c31a3e7e3ace7f5b1904890ccf816eae59e9e

Aliases

arxiv: 1311.5105 · arxiv_version: 1311.5105v1 · doi: 10.48550/arxiv.1311.5105 · pith_short_12: 2RKTW7M3AXKG · pith_short_16: 2RKTW7M3AXKG3U2M · pith_short_8: 2RKTW7M3

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/2RKTW7M3AXKG3U2MHEUQMPBRUP \
  | 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: d4553b7d9b05d46dd34c3929063c31a3e7e3ace7f5b1904890ccf816eae59e9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03e8b193b0e4e9343adcfae437004ee633f8d4d9e41d0dde4434e0080c214e23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-20T15:41:13Z",
    "title_canon_sha256": "1c04a56f678b3caf46f257b4de7e856c927d7a3cca4cc00fa15e13c5d481e223"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5105",
    "kind": "arxiv",
    "version": 1
  }
}