Pith Number

pith:6FPHRMGU

pith:2018:6FPHRMGUO5IMWUMVDKPNMD5BP6

not attested not anchored not stored refs pending

Counter-examples to the Dunford-Schwartz pointwise ergodic theorem on $L^1+L^\infty$

D\'avid Kunszenti-Kov\'acs

arxiv:1803.11040 v1 · 2018-03-29 · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6FPHRMGUO5IMWUMVDKPNMD5BP6}

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	2026-05-18T00:19:49.432764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f15e78b0d47750cb51951a9ed60fa17f92b8330e124de9682ae2783c0d27a934

Aliases

arxiv: 1803.11040 · arxiv_version: 1803.11040v1 · doi: 10.48550/arxiv.1803.11040 · pith_short_12: 6FPHRMGUO5IM · pith_short_16: 6FPHRMGUO5IMWUMV · pith_short_8: 6FPHRMGU

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/6FPHRMGUO5IMWUMVDKPNMD5BP6 \
  | 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: f15e78b0d47750cb51951a9ed60fa17f92b8330e124de9682ae2783c0d27a934

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a479e8f50eb59b98ba14e55d49441f790c4459531adc28797075541ed4cc9df",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-03-29T13:05:36Z",
    "title_canon_sha256": "4212eeb55bcbf03cb5b0356615d820968c7408ff539f9b5a38ec8061237177f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.11040",
    "kind": "arxiv",
    "version": 1
  }
}