Pith Number

pith:YNJJPX2F

pith:2015:YNJJPX2F3YKFF7WZNV26Q7OBJ6

not attested not anchored not stored refs pending

Linnik's Theorem for Sato-Tate Laws on Elliptic Curves with Complex Multiplication

Ashvin Swaminathan, Evan Chen, Peter S. Park

arxiv:1506.09170 v3 · 2015-06-30 · 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{YNJJPX2F3YKFF7WZNV26Q7OBJ6}

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	2026-05-18T01:09:07.007751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c35297df45de1452fed96d75e87dc14fa1dd1b99e4c08b0d5e493efd2a4d6dd1

Aliases

arxiv: 1506.09170 · arxiv_version: 1506.09170v3 · doi: 10.48550/arxiv.1506.09170 · pith_short_12: YNJJPX2F3YKF · pith_short_16: YNJJPX2F3YKFF7WZ · pith_short_8: YNJJPX2F

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/YNJJPX2F3YKFF7WZNV26Q7OBJ6 \
  | 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: c35297df45de1452fed96d75e87dc14fa1dd1b99e4c08b0d5e493efd2a4d6dd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d57345cc8388a18de45a8c72612970e063998e76a19875f1ae63f14da995fbb6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-06-30T17:37:02Z",
    "title_canon_sha256": "1626f1be16ea2bbd4cff3fd6ab6daccf02ffbdde3e4ddd067ccc4eb98c4a4588"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.09170",
    "kind": "arxiv",
    "version": 3
  }
}