Pith Number

pith:2VQRQIUC

pith:2012:2VQRQIUCWJSVLCZGFYJGUD3M6B

not attested not anchored not stored refs pending

Elliptic Curves with Full 2-Torsion and Maximal Adelic Galois Representations

David Corwin, Sarah Trebat-Leder, Tony Feng, Zane Kun Li

arxiv:1207.5169 v2 · 2012-07-21 · 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{2VQRQIUCWJSVLCZGFYJGUD3M6B}

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	2026-05-18T03:34:35.427837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d561182282b265558b262e126a0f6cf05c02b6654009c72f1164610341e785f4

Aliases

arxiv: 1207.5169 · arxiv_version: 1207.5169v2 · doi: 10.48550/arxiv.1207.5169 · pith_short_12: 2VQRQIUCWJSV · pith_short_16: 2VQRQIUCWJSVLCZG · pith_short_8: 2VQRQIUC

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/2VQRQIUCWJSVLCZGFYJGUD3M6B \
  | 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: d561182282b265558b262e126a0f6cf05c02b6654009c72f1164610341e785f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d234be8532fc229d085209e5c47693bdf081ed294c2c555c807015174e94c5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-21T18:48:44Z",
    "title_canon_sha256": "39cfd23521570a7ae1aa10c4418739a68b29f3e57d58286311cb609b9f9a8aff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5169",
    "kind": "arxiv",
    "version": 2
  }
}