Pith Number

pith:DSVQPIO3

pith:2011:DSVQPIO37ADDFWKMO5AO2QIGGL

not attested not anchored not stored refs pending

Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve

Mohammad Sadek

arxiv:1102.2980 v3 · 2011-02-15 · 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{DSVQPIO37ADDFWKMO5AO2QIGGL}

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	2026-05-18T04:27:37.628347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cab07a1dbf80632d94c7740ed410632c6d60645c1d6f274354dc0ddad1b4b81

Aliases

arxiv: 1102.2980 · arxiv_version: 1102.2980v3 · doi: 10.48550/arxiv.1102.2980 · pith_short_12: DSVQPIO37ADD · pith_short_16: DSVQPIO37ADDFWKM · pith_short_8: DSVQPIO3

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/DSVQPIO37ADDFWKMO5AO2QIGGL \
  | 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: 1cab07a1dbf80632d94c7740ed410632c6d60645c1d6f274354dc0ddad1b4b81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff8b8cc75c3a51ccb50f4a88077eb41db34ecef1bbd030b8327cdff54c082508",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-15T07:08:10Z",
    "title_canon_sha256": "bc4e9a837bfae79964d141d06a285d599c497d01086035ba3cd7bdbfeb7a678a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2980",
    "kind": "arxiv",
    "version": 3
  }
}