Pith Number

pith:WCHRH2HP

pith:2011:WCHRH2HPQM3PNUUJ7YL63G7SIS

not attested not anchored not stored refs pending

Vinogradov's mean value theorem via efficient congruencing

Trevor D. Wooley

arxiv:1101.0574 v1 · 2011-01-03 · 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{WCHRH2HPQM3PNUUJ7YL63G7SIS}

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	2026-05-18T03:49:01.229822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b08f13e8ef8336f6d289fe17ed9bf244afbd3ec78d94ae881d299bd9de42a3fa

Aliases

arxiv: 1101.0574 · arxiv_version: 1101.0574v1 · doi: 10.48550/arxiv.1101.0574 · pith_short_12: WCHRH2HPQM3P · pith_short_16: WCHRH2HPQM3PNUUJ · pith_short_8: WCHRH2HP

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/WCHRH2HPQM3PNUUJ7YL63G7SIS \
  | 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: b08f13e8ef8336f6d289fe17ed9bf244afbd3ec78d94ae881d299bd9de42a3fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c3f6c62755b8838a590d3b367191c1bf458b666c17b7dcfdfffa3dc974232ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-03T18:28:26Z",
    "title_canon_sha256": "13ee88dbd03aecfa63e76c85a9677aa74e6ff105660d4bc8b819a8439ca6019b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0574",
    "kind": "arxiv",
    "version": 1
  }
}