Pith Number

pith:DG7FD23G

pith:2015:DG7FD23G7C7JMC2FV2BV4NOVQY

not attested not anchored not stored refs pending

Restricted weak-type endpoint estimates for discrete k-spherical maximal functions

Kevin Hughes

arxiv:1509.04482 v1 · 2015-09-15 · math.CA · 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{DG7FD23G7C7JMC2FV2BV4NOVQY}

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	2026-05-18T01:32:58.793457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19be51eb66f8be960b45ae835e35d58639488b157b90c6edbb57a19c348cd153

Aliases

arxiv: 1509.04482 · arxiv_version: 1509.04482v1 · doi: 10.48550/arxiv.1509.04482 · pith_short_12: DG7FD23G7C7J · pith_short_16: DG7FD23G7C7JMC2F · pith_short_8: DG7FD23G

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/DG7FD23G7C7JMC2FV2BV4NOVQY \
  | 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: 19be51eb66f8be960b45ae835e35d58639488b157b90c6edbb57a19c348cd153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e7ed6f1fb9c12b18f361da8b9aaf5e551fb5cdb134ca0c50814c37d64d16f31",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-15T10:28:23Z",
    "title_canon_sha256": "a76b92506c62d8b9ebc1162ca874cb10de40091136eb55ecb50efe1c122e3647"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04482",
    "kind": "arxiv",
    "version": 1
  }
}