Pith Number

pith:F55QDURB

pith:2015:F55QDURBM4PX6GVZHUEQCRS6VU

not attested not anchored not stored refs pending

Hardy-Stein identities and square functions for semigroups

Krzysztof Bogdan, Rodrigo Ba\~nuelos, Tomasz Luks

arxiv:1506.09007 v1 · 2015-06-30 · math.FA · math.AP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F55QDURBM4PX6GVZHUEQCRS6VU}

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	2026-05-18T01:37:33.878719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f7b01d221671f7f1ab93d0901465ead304863649c0bd577064a952a3797c67f

Aliases

arxiv: 1506.09007 · arxiv_version: 1506.09007v1 · doi: 10.48550/arxiv.1506.09007 · pith_short_12: F55QDURBM4PX · pith_short_16: F55QDURBM4PX6GVZ · pith_short_8: F55QDURB

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/F55QDURBM4PX6GVZHUEQCRS6VU \
  | 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: 2f7b01d221671f7f1ab93d0901465ead304863649c0bd577064a952a3797c67f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eba89a224638dc809eb6fc2479c30aaed4a48e07e233f8831fa8b363ef27ae92",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-06-30T09:41:17Z",
    "title_canon_sha256": "69615d4ec01e5dde3ebfedb1a7ee356fdff6a4ed9236d49ee7b4b8f9e0d879d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.09007",
    "kind": "arxiv",
    "version": 1
  }
}