Pith Number

pith:HCVLW647

pith:2018:HCVLW647J2TS7DUHU66DCWNJAT

not attested not anchored not stored refs pending

GCD sums and sum-product estimates

Aled Walker, Thomas F. Bloom

arxiv:1806.07849 v1 · 2018-06-20 · 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{HCVLW647J2TS7DUHU66DCWNJAT}

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.

Cited by

1 paper in Pith

Decoupling theorems for the Duffin-Schaeffer problem

Receipt and verification

First computed	2026-05-18T00:12:46.445207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38aabb7b9f4ea72f8e87a7bc3159a904f4c814bde9d7f0b9c7144edc90e2b6df

Aliases

arxiv: 1806.07849 · arxiv_version: 1806.07849v1 · doi: 10.48550/arxiv.1806.07849 · pith_short_12: HCVLW647J2TS · pith_short_16: HCVLW647J2TS7DUH · pith_short_8: HCVLW647

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/HCVLW647J2TS7DUHU66DCWNJAT \
  | 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: 38aabb7b9f4ea72f8e87a7bc3159a904f4c814bde9d7f0b9c7144edc90e2b6df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dab9bab69906b0a79f57e3e8409576567b27f03007d2734e6af82eed0d863922",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-06-20T17:20:00Z",
    "title_canon_sha256": "59db609be131c6fde377640d36eaccf42ef1dd1dc4da5398903602db27d48ede"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.07849",
    "kind": "arxiv",
    "version": 1
  }
}