Pith Number

pith:ECVCOA65

pith:2013:ECVCOA652HA3AGSZI2ZLV6U63X

not attested not anchored not stored refs pending

Unions of Lebesgue spaces and $A_1$ majorants

Greg Knese, John E. McCarthy, Kabe Moen

arxiv:1302.7315 v2 · 2013-02-28 · math.CA · 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{ECVCOA652HA3AGSZI2ZLV6U63X}

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	2026-05-18T02:44:07.061685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20aa2703ddd1c1b01a5946b2bafa9edde2887740da6b4cfb9fb3525469e38a24

Aliases

arxiv: 1302.7315 · arxiv_version: 1302.7315v2 · doi: 10.48550/arxiv.1302.7315 · pith_short_12: ECVCOA652HA3 · pith_short_16: ECVCOA652HA3AGSZ · pith_short_8: ECVCOA65

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/ECVCOA652HA3AGSZI2ZLV6U63X \
  | 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: 20aa2703ddd1c1b01a5946b2bafa9edde2887740da6b4cfb9fb3525469e38a24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca7e9889df7dad596e6ff37a08e78191fe6779fc165d4f96e191b5f3ebdde50c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-02-28T20:52:40Z",
    "title_canon_sha256": "8bcc61eaac83aa2fb15b124186366083975f7c4e30fd5a8a915bd6b96b1c93f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.7315",
    "kind": "arxiv",
    "version": 2
  }
}