Pith Number

pith:A4UWLDDO

pith:2017:A4UWLDDOZVEOH2CJMXZJ6LAKY3

not attested not anchored not stored refs pending

Nested efficient congruencing and relatives of Vinogradov's mean value theorem

Trevor D. Wooley

arxiv:1708.01220 v2 · 2017-08-03 · 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{A4UWLDDOZVEOH2CJMXZJ6LAKY3}

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	2026-05-18T00:01:30.472010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0729658c6ecd48e3e84965f29f2c0ac6fecdca98655c39f802b235eabeec5422

Aliases

arxiv: 1708.01220 · arxiv_version: 1708.01220v2 · doi: 10.48550/arxiv.1708.01220 · pith_short_12: A4UWLDDOZVEO · pith_short_16: A4UWLDDOZVEOH2CJ · pith_short_8: A4UWLDDO

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/A4UWLDDOZVEOH2CJMXZJ6LAKY3 \
  | 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: 0729658c6ecd48e3e84965f29f2c0ac6fecdca98655c39f802b235eabeec5422

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26f9ac4532c6371b24bf839cee6e1cf3cf03956f43702a1cdb82b8ebfba30b4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-08-03T17:10:29Z",
    "title_canon_sha256": "deab4a2cad7a3646335f9be9327f29368bb636d555c56770f153f1951616ece7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01220",
    "kind": "arxiv",
    "version": 2
  }
}