Pith Number

pith:ZJH63FIA

pith:2019:ZJH63FIA2RZMNHI25H4HU56GVS

not attested not anchored not stored refs pending

Averages Along the Primes: Improving and Sparse Bounds

Ben Krause, Fan Yang, Michael Lacey, Rui Han

arxiv:1909.02883 v2 · 2019-09-06 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZJH63FIA2RZMNHI25H4HU56GVS}

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

Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages

Receipt and verification

First computed	2026-07-05T01:11:41.525765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca4fed9500d472c69d1ae9f87a77c6ac85ec646684e31370e6adfeba2af75a54

Aliases

arxiv: 1909.02883 · arxiv_version: 1909.02883v2 · doi: 10.48550/arxiv.1909.02883 · pith_short_12: ZJH63FIA2RZM · pith_short_16: ZJH63FIA2RZMNHI2 · pith_short_8: ZJH63FIA

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/ZJH63FIA2RZMNHI25H4HU56GVS \
  | 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: ca4fed9500d472c69d1ae9f87a77c6ac85ec646684e31370e6adfeba2af75a54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49c1588184c5b3ddca56b2c08c912483f2eeefc67a49b85f1723485bcbacc885",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-09-06T16:44:27Z",
    "title_canon_sha256": "5787d32cc1664a41a094a0263f44b25967f1274211bcb040cd339e96ecbfbecb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.02883",
    "kind": "arxiv",
    "version": 2
  }
}