Pith Number

pith:TPAK572N

pith:2018:TPAK572NORGK66OV7LQ3PTNQHQ

not attested not anchored not stored refs pending

Riesz means of Fourier series and integrals: Strong summability at the critical index

Andreas Seeger, Jongchon Kim

arxiv:1807.07854 v2 · 2018-07-20 · 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{TPAK572NORGK66OV7LQ3PTNQHQ}

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	2026-05-17T23:43:51.042160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bc0aeff4d744caf79d5fae1b7cdb03c1a24aaa691a9821916f2228d035a317d

Aliases

arxiv: 1807.07854 · arxiv_version: 1807.07854v2 · doi: 10.48550/arxiv.1807.07854 · pith_short_12: TPAK572NORGK · pith_short_16: TPAK572NORGK66OV · pith_short_8: TPAK572N

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/TPAK572NORGK66OV7LQ3PTNQHQ \
  | 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: 9bc0aeff4d744caf79d5fae1b7cdb03c1a24aaa691a9821916f2228d035a317d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bfe8da8250d364e3d1df0e3daf6263043d4f45070046a2eefc4ecb036e45e36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-07-20T14:11:09Z",
    "title_canon_sha256": "e70f4daa387bc874d332f70bba397871c7f0bd845bf216938e1999d3a8d757c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.07854",
    "kind": "arxiv",
    "version": 2
  }
}