Pith Number

pith:DZ5WVQJO

pith:2011:DZ5WVQJOX67PGAMMBTPF36UWYM

not attested not anchored not stored refs pending

Simple proof of Gallagher's singular series sum estimate

Kevin Ford

arxiv:1108.3861 v2 · 2011-08-18 · 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{DZ5WVQJOX67PGAMMBTPF36UWYM}

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	2026-05-18T00:55:52.443211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e7b6ac12ebfbef3018c0cde5dfa96c30237376ef4bac795dffd3510a1a01a8f

Aliases

arxiv: 1108.3861 · arxiv_version: 1108.3861v2 · doi: 10.48550/arxiv.1108.3861 · pith_short_12: DZ5WVQJOX67P · pith_short_16: DZ5WVQJOX67PGAMM · pith_short_8: DZ5WVQJO

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/DZ5WVQJOX67PGAMMBTPF36UWYM \
  | 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: 1e7b6ac12ebfbef3018c0cde5dfa96c30237376ef4bac795dffd3510a1a01a8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed991158e8812ddb466df4c49ea4d702be7e859c2564df34b1bc5d1abf45551f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-18T21:39:52Z",
    "title_canon_sha256": "f6b5a68cb2de7674b0b0f0aa7489ddee9eef843dfad138c20bff77d3f3c8675d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3861",
    "kind": "arxiv",
    "version": 2
  }
}