Pith Number

pith:5XBMZ3ET

pith:2013:5XBMZ3ETFM2XH7EYYYEJYJ3I4E

not attested not anchored not stored refs pending

Maximal potentials, maximal singular integrals, and the spherical maximal function

Piotr Hajlasz, Zhuomin Liu

arxiv:1306.6358 v1 · 2013-06-26 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5XBMZ3ETFM2XH7EYYYEJYJ3I4E}

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	2026-05-18T03:19:45.004311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edc2ccec932b3573fc98c6089c2768e135025c1d540316967fe53f1487ae0f9a

Aliases

arxiv: 1306.6358 · arxiv_version: 1306.6358v1 · doi: 10.48550/arxiv.1306.6358 · pith_short_12: 5XBMZ3ETFM2X · pith_short_16: 5XBMZ3ETFM2XH7EY · pith_short_8: 5XBMZ3ET

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/5XBMZ3ETFM2XH7EYYYEJYJ3I4E \
  | 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: edc2ccec932b3573fc98c6089c2768e135025c1d540316967fe53f1487ae0f9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11cf01887c77dc4738de24b9247a9bd34dd9b9f8a0a0a04a5d509c17c408e474",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-06-26T20:42:37Z",
    "title_canon_sha256": "8d97085f0258d145e122a4710478c1d6ad4762eb2f0d43f7afb2bed53ddbe2bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6358",
    "kind": "arxiv",
    "version": 1
  }
}