Pith Number

pith:X2UPU36R

pith:2010:X2UPU36RHJA7QMBJUB36SIRJE3

not attested not anchored not stored refs pending

Improved bounds for Stein's square functions

Andreas Seeger, Keith M. Rogers, Sanghyuk Lee

arxiv:1012.2159 v2 · 2010-12-10 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X2UPU36RHJA7QMBJUB36SIRJE3}

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	2026-05-18T02:58:01.403933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bea8fa6fd13a41f83029a077e9222926de05933c53855d20a5fefe5a1b1442c9

Aliases

arxiv: 1012.2159 · arxiv_version: 1012.2159v2 · doi: 10.48550/arxiv.1012.2159 · pith_short_12: X2UPU36RHJA7 · pith_short_16: X2UPU36RHJA7QMBJ · pith_short_8: X2UPU36R

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/X2UPU36RHJA7QMBJUB36SIRJE3 \
  | 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: bea8fa6fd13a41f83029a077e9222926de05933c53855d20a5fefe5a1b1442c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ec7e45ba18b6966b0c06ca4f4371406d13dbf8cd654d1790536e3db6137b737",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-12-10T02:28:34Z",
    "title_canon_sha256": "a263ae1b7b0384f91962889109675bf2a63072b03e4847ea4b66c2a73476521b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2159",
    "kind": "arxiv",
    "version": 2
  }
}