Pith Number

pith:PY2YDUJC

pith:2025:PY2YDUJCOHXIIWA2UFFVVGA45C

not attested not anchored not stored refs pending

Pointwise ergodic theorem along primes of the form $x^2 + ny^2$

Jan Fornal

arxiv:2508.15466 v1 · 2025-08-21 · math.DS · 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{PY2YDUJCOHXIIWA2UFFVVGA45C}

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	2026-07-05T11:57:12.745561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e3581d12271ee84581aa14b5a981ce8ba10f2dc346f12165e99a3cc041cc726

Aliases

arxiv: 2508.15466 · arxiv_version: 2508.15466v1 · doi: 10.48550/arxiv.2508.15466 · pith_short_12: PY2YDUJCOHXI · pith_short_16: PY2YDUJCOHXIIWA2 · pith_short_8: PY2YDUJC

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/PY2YDUJCOHXIIWA2UFFVVGA45C \
  | 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: 7e3581d12271ee84581aa14b5a981ce8ba10f2dc346f12165e99a3cc041cc726

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89d054bb0573d2f96cb612f5c880f0e9cedfa7a16a542c70ece3740cda923465",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-08-21T11:40:07Z",
    "title_canon_sha256": "ea0c18189ba4e02b25489f1a462672e883258391c80111b090533489a4b5f862"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.15466",
    "kind": "arxiv",
    "version": 1
  }
}