Pith Number

pith:DQEQMP6L

pith:2016:DQEQMP6L7FBXI5QMBUBQW27M7K

not attested not anchored not stored refs pending

On Convergence of Oscillatory Ergodic Hilbert Transforms

Ben Krause, M\'at\'e Wierdl, Michael Lacey

arxiv:1610.04968 v3 · 2016-10-17 · 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{DQEQMP6L7FBXI5QMBUBQW27M7K}

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	2026-05-18T00:44:45.868954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c09063fcbf94374760c0d030b6becfaa131e962b5994a249b427c56ccf5459e

Aliases

arxiv: 1610.04968 · arxiv_version: 1610.04968v3 · doi: 10.48550/arxiv.1610.04968 · pith_short_12: DQEQMP6L7FBX · pith_short_16: DQEQMP6L7FBXI5QM · pith_short_8: DQEQMP6L

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/DQEQMP6L7FBXI5QMBUBQW27M7K \
  | 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: 1c09063fcbf94374760c0d030b6becfaa131e962b5994a249b427c56ccf5459e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88f63641df09c603b03f3fe470ad1d6ef91f3e7f5a4233b608dee791a1e766bd",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-10-17T04:19:34Z",
    "title_canon_sha256": "a4de1b5182fb6cac7175103989505d234ddc915fc5689d2f96289e6f5e3912cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04968",
    "kind": "arxiv",
    "version": 3
  }
}