Pith Number

pith:AS2QUSZZ

pith:2011:AS2QUSZZ4OT4NPAHVDV7MQUMBD

not attested not anchored not stored refs pending

On the Convergence of Lacunary Walsh-Fourier Series

Michael T. Lacey, Yen Do

arxiv:1101.2461 v2 · 2011-01-12 · 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{AS2QUSZZ4OT4NPAHVDV7MQUMBD}

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	2026-05-18T02:58:01.267145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04b50a4b39e3a7c6bc07a8ebf6428c08ff29613f95dbaebd6d0fa211fb45a1ec

Aliases

arxiv: 1101.2461 · arxiv_version: 1101.2461v2 · doi: 10.48550/arxiv.1101.2461 · pith_short_12: AS2QUSZZ4OT4 · pith_short_16: AS2QUSZZ4OT4NPAH · pith_short_8: AS2QUSZZ

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/AS2QUSZZ4OT4NPAHVDV7MQUMBD \
  | 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: 04b50a4b39e3a7c6bc07a8ebf6428c08ff29613f95dbaebd6d0fa211fb45a1ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c0eef71a5245724770eab51881f7a0bdfdb44e3e4ba440b2caf19018eeae075",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-01-12T22:44:06Z",
    "title_canon_sha256": "1cdd2fb355c46d1b837db014b58df972248f57d3733ff942db9bd3beb37b8aad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2461",
    "kind": "arxiv",
    "version": 2
  }
}