Pith Number

pith:EYNX5ODG

pith:2013:EYNX5ODGFDKC43OFS3H36EYF2B

not attested not anchored not stored refs pending

Controlling Selmer groups in the higher core rank case

Barry Mazur, Karl Rubin

arxiv:1312.4052 v1 · 2013-12-14 · 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{EYNX5ODGFDKC43OFS3H36EYF2B}

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	2026-05-18T03:04:35.995587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

261b7eb86628d42e6dc596cfbf1305d07673ce1aefe8610755b57946ed9260cf

Aliases

arxiv: 1312.4052 · arxiv_version: 1312.4052v1 · doi: 10.48550/arxiv.1312.4052 · pith_short_12: EYNX5ODGFDKC · pith_short_16: EYNX5ODGFDKC43OF · pith_short_8: EYNX5ODG

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/EYNX5ODGFDKC43OFS3H36EYF2B \
  | 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: 261b7eb86628d42e6dc596cfbf1305d07673ce1aefe8610755b57946ed9260cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aec51aa096f844c98890c17f18f57825408c010363ee70d9f869702a8cdbd84d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-14T14:54:33Z",
    "title_canon_sha256": "d9643ef37c75d6459ee6bcf22ee61fb56e3a6c39184983c3aec4a97d9f60d231"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4052",
    "kind": "arxiv",
    "version": 1
  }
}