Pith Number

pith:KDBLYHD7

pith:2015:KDBLYHD76GWJ6ISLM5VLZQKPZE

not attested not anchored not stored refs pending

The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves

Igor E. Shparlinski, Jos\'e Felipe Voloch, Min Sha, R\'egis de la Bret\`eche

arxiv:1509.03009 v4 · 2015-09-10 · 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{KDBLYHD76GWJ6ISLM5VLZQKPZE}

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	2026-05-18T00:21:51.651000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50c2bc1c7ff1ac9f224b676abcc14fc90e2b95c362fb2a4f487b47927caf789d

Aliases

arxiv: 1509.03009 · arxiv_version: 1509.03009v4 · doi: 10.48550/arxiv.1509.03009 · pith_short_12: KDBLYHD76GWJ · pith_short_16: KDBLYHD76GWJ6ISL · pith_short_8: KDBLYHD7

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/KDBLYHD76GWJ6ISLM5VLZQKPZE \
  | 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: 50c2bc1c7ff1ac9f224b676abcc14fc90e2b95c362fb2a4f487b47927caf789d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dd08efc29a904aa56f11caf28b5ce4e8f398080fd986e80ec392f6bb80df638",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-10T04:34:30Z",
    "title_canon_sha256": "e0a616bb83c441a7990071da61f63c81170d065403445cac83043d73e01d6ede"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03009",
    "kind": "arxiv",
    "version": 4
  }
}