Pith Number

pith:22KHCALY

pith:2015:22KHCALYN6CQ7WZGHQG357OAJ7

not attested not anchored not stored refs pending

L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates

Bartosz Trojan, Elias M. Stein, Mariusz Mirek

arxiv:1512.07523 v1 · 2015-12-23 · math.CA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{22KHCALYN6CQ7WZGHQG357OAJ7}

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	2026-05-18T01:23:49.465446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6947101786f850fdb263c0dbefdc04fd13809f7c6b42c4053d9c64b32712fc7

Aliases

arxiv: 1512.07523 · arxiv_version: 1512.07523v1 · doi: 10.48550/arxiv.1512.07523 · pith_short_12: 22KHCALYN6CQ · pith_short_16: 22KHCALYN6CQ7WZG · pith_short_8: 22KHCALY

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/22KHCALYN6CQ7WZGHQG357OAJ7 \
  | 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: d6947101786f850fdb263c0dbefdc04fd13809f7c6b42c4053d9c64b32712fc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a56b52c4c4bcfff74bcc358074f3bb870188c027dd0b801f94b8d1f621b8e9e8",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-23T15:47:06Z",
    "title_canon_sha256": "a76d1548c3e3034c08ffeba2114cd8210618ed7d5fd2e3bc41487c15ea272ae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07523",
    "kind": "arxiv",
    "version": 1
  }
}