Pith Number

pith:MSUVELT6

pith:2014:MSUVELT6G45DLMEOIZJ7JKKNPI

not attested not anchored not stored refs pending

Computing the Mazur and Swinnerton-Dyer critical subgroup of elliptic curves

Hao Chen

arxiv:1412.2827 v2 · 2014-12-09 · 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{MSUVELT6G45DLMEOIZJ7JKKNPI}

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	2026-05-18T02:29:10.247103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64a9522e7e373a35b08e4653f4a94d7a174b8f1a334ef3f7d9aead00939a1849

Aliases

arxiv: 1412.2827 · arxiv_version: 1412.2827v2 · doi: 10.48550/arxiv.1412.2827 · pith_short_12: MSUVELT6G45D · pith_short_16: MSUVELT6G45DLMEO · pith_short_8: MSUVELT6

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/MSUVELT6G45DLMEOIZJ7JKKNPI \
  | 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: 64a9522e7e373a35b08e4653f4a94d7a174b8f1a334ef3f7d9aead00939a1849

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c9ec58b1ba8898c74374b41d249090e17603204ea31d1ca77751347ec0bd963",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-12-09T01:41:09Z",
    "title_canon_sha256": "3fc3b75ba8987ccf9df7917705615bf8b85ac081b166822357ef8cb4810844c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2827",
    "kind": "arxiv",
    "version": 2
  }
}