Pith Number

pith:MCKRZXS6

pith:2010:MCKRZXS6RGMHTQTDIEDDEZDWZY

not attested not anchored not stored refs pending

Effective equidistribution and the Sato-Tate law for families of elliptic curves

M. Ram Murty, Steven J. Miller

arxiv:1004.2753 v2 · 2010-04-16 · 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{MCKRZXS6RGMHTQTDIEDDEZDWZY}

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	2026-05-18T04:41:05.019759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60951cde5e899879c2634106326476ce1648163e604756634f35e074c5132b29

Aliases

arxiv: 1004.2753 · arxiv_version: 1004.2753v2 · doi: 10.48550/arxiv.1004.2753 · pith_short_12: MCKRZXS6RGMH · pith_short_16: MCKRZXS6RGMHTQTD · pith_short_8: MCKRZXS6

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/MCKRZXS6RGMHTQTDIEDDEZDWZY \
  | 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: 60951cde5e899879c2634106326476ce1648163e604756634f35e074c5132b29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76eb466302a0b68660b49f9060e567a057ddbfa156e699a27542a41db2aba1cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-04-16T03:45:24Z",
    "title_canon_sha256": "cf5717667a414c39047ec3ca5fd9712aaa0080e5ec28d9ccf891a6dee5d34410"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2753",
    "kind": "arxiv",
    "version": 2
  }
}