Pith Number

pith:UKAKTBP6

pith:2016:UKAKTBP6KFYUW6DZWC7OIJ57OA

not attested not anchored not stored refs pending

On the Vinogradov mean value

Jean Bourgain

arxiv:1601.08173 v1 · 2016-01-29 · 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{UKAKTBP6KFYUW6DZWC7OIJ57OA}

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	2026-05-18T01:21:40.177944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a280a985fe51714b7879b0bee427bf702068de5dc318381fd436c21120543cea

Aliases

arxiv: 1601.08173 · arxiv_version: 1601.08173v1 · doi: 10.48550/arxiv.1601.08173 · pith_short_12: UKAKTBP6KFYU · pith_short_16: UKAKTBP6KFYUW6DZ · pith_short_8: UKAKTBP6

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/UKAKTBP6KFYUW6DZWC7OIJ57OA \
  | 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: a280a985fe51714b7879b0bee427bf702068de5dc318381fd436c21120543cea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94b8b81371c036515b78d5bfda1066f6b964e6548e9134a10eb8e3a5886655ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-29T16:09:55Z",
    "title_canon_sha256": "c28ab0b9e3a3a459bab3baa93a79148343fe5c9e4cad777cbe76b0a860627464"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.08173",
    "kind": "arxiv",
    "version": 1
  }
}