Pith Number

pith:G63BW7AH

pith:2016:G63BW7AHAYKZLBQ53N3CQ6UJBO

not attested not anchored not stored refs pending

A New $k$-th Derivative Estimate for Exponential Sums via Vinogradov's Mean Value

D.R. Heath-Brown

arxiv:1601.04493 v3 · 2016-01-18 · 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{G63BW7AHAYKZLBQ53N3CQ6UJBO}

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	2026-05-18T01:19:33.846258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37b61b7c07061595861ddb76287a890baaef13cbde10a6eafcc0b49336bb81bb

Aliases

arxiv: 1601.04493 · arxiv_version: 1601.04493v3 · doi: 10.48550/arxiv.1601.04493 · pith_short_12: G63BW7AHAYKZ · pith_short_16: G63BW7AHAYKZLBQ5 · pith_short_8: G63BW7AH

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/G63BW7AHAYKZLBQ53N3CQ6UJBO \
  | 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: 37b61b7c07061595861ddb76287a890baaef13cbde10a6eafcc0b49336bb81bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7e2fba8c838c034173850fc3b31ccd8687cec49a49fe101c53e0f487736de17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-18T12:54:28Z",
    "title_canon_sha256": "61d7f0d3e2fb333c4c52a39b31eea0d721b8d3d03c6390ae9bda94a6ac93aa72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04493",
    "kind": "arxiv",
    "version": 3
  }
}