Pith Number

pith:XSOS3OTD

pith:2012:XSOS3OTDZTUHUUAHM5QZ4YURVI

not attested not anchored not stored refs pending

A Ces\`aro Average of Hardy-Littlewood numbers

Alessandro Languasco, Alessandro Zaccagnini

arxiv:1206.0255 v1 · 2012-06-01 · 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{XSOS3OTDZTUHUUAHM5QZ4YURVI}

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	2026-05-18T00:12:46.330977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc9d2dba63cce87a500767619e6291aa1a7da286da6b171e05fab7a4499c3039

Aliases

arxiv: 1206.0255 · arxiv_version: 1206.0255v1 · doi: 10.48550/arxiv.1206.0255 · pith_short_12: XSOS3OTDZTUH · pith_short_16: XSOS3OTDZTUHUUAH · pith_short_8: XSOS3OTD

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/XSOS3OTDZTUHUUAHM5QZ4YURVI \
  | 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: bc9d2dba63cce87a500767619e6291aa1a7da286da6b171e05fab7a4499c3039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd858d46e92668437002b1fcea214b3999096709b7cc52a166e3dda2ca91e33c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-06-01T17:18:30Z",
    "title_canon_sha256": "0439ec95beb042a3e0efae390497fe38a608e09dae2ea66c113d4bb1441a1162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0255",
    "kind": "arxiv",
    "version": 1
  }
}