Pith Number

pith:4KPZQFZZ

pith:2018:4KPZQFZZOV7C4EXHCZUYWG5NDG

not attested not anchored not stored refs pending

A Ces\`aro Average of generalised Hardy-Littlewood numbers

Alessandro Languasco, Alessandro Zaccagnini

arxiv:1806.05175 v3 · 2018-06-13 · 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{4KPZQFZZOV7C4EXHCZUYWG5NDG}

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	2026-05-17T23:40:41.748890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e29f981739757e2e12e716698b1bad19b95dd759f193231c2a433e4dbc8547ba

Aliases

arxiv: 1806.05175 · arxiv_version: 1806.05175v3 · doi: 10.48550/arxiv.1806.05175 · pith_short_12: 4KPZQFZZOV7C · pith_short_16: 4KPZQFZZOV7C4EXH · pith_short_8: 4KPZQFZZ

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/4KPZQFZZOV7C4EXHCZUYWG5NDG \
  | 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: e29f981739757e2e12e716698b1bad19b95dd759f193231c2a433e4dbc8547ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6581f1b2184852faf74fdafa4d5a102b9b6c321dafbde4087b71bcfa173c779",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-06-13T10:26:45Z",
    "title_canon_sha256": "17d853582e11d6809762943fc98086fdb2c327ce6450fec1e02e3eeaca831d11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.05175",
    "kind": "arxiv",
    "version": 3
  }
}