Pith Number

pith:2HT5F4NP

pith:2014:2HT5F4NP6TIDY2WNP442YBHDF5

not attested not anchored not stored refs pending

Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves

Igor E. Shparlinski, Min Sha

arxiv:1404.0182 v3 · 2014-04-01 · 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{2HT5F4NP6TIDY2WNP442YBHDF5}

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	2026-05-18T01:33:57.091554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1e7d2f1aff4d03c6acd7f39ac04e32f5cb20d95887133e03152c6a87ca5aad3

Aliases

arxiv: 1404.0182 · arxiv_version: 1404.0182v3 · doi: 10.48550/arxiv.1404.0182 · pith_short_12: 2HT5F4NP6TID · pith_short_16: 2HT5F4NP6TIDY2WN · pith_short_8: 2HT5F4NP

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/2HT5F4NP6TIDY2WNP442YBHDF5 \
  | 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: d1e7d2f1aff4d03c6acd7f39ac04e32f5cb20d95887133e03152c6a87ca5aad3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c93fd1c0ef3ce6a645d24765d30b9e27a533a531144b16106488f58d41bb3504",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-04-01T09:57:04Z",
    "title_canon_sha256": "ed5b1fbda4a3ea3dd63a3662f5b41d161c8d80ae6b98c6ab1ad6c6115e8d541a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.0182",
    "kind": "arxiv",
    "version": 3
  }
}