Pith Number

pith:Y3H4WMVQ

pith:2012:Y3H4WMVQO6TYKP7GGN7TP4EU4Q

not attested not anchored not stored refs pending

A local $Tb$ theorem for square functions in domains with Ahlfors-David regular boundaries

Ana Grau de la Herran, Mihalis Mourgoglou

arxiv:1210.0181 v1 · 2012-09-30 · 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{Y3H4WMVQO6TYKP7GGN7TP4EU4Q}

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	2026-05-18T03:44:23.065075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6cfcb32b077a7853fe6337f37f094e4156bdec5c79f3130968f35ccc384dc5b

Aliases

arxiv: 1210.0181 · arxiv_version: 1210.0181v1 · doi: 10.48550/arxiv.1210.0181 · pith_short_12: Y3H4WMVQO6TY · pith_short_16: Y3H4WMVQO6TYKP7G · pith_short_8: Y3H4WMVQ

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/Y3H4WMVQO6TYKP7GGN7TP4EU4Q \
  | 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: c6cfcb32b077a7853fe6337f37f094e4156bdec5c79f3130968f35ccc384dc5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "706d29d16ed2702d9f68ad735a927314185a7520169d7396622b839ac65423eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-30T09:32:34Z",
    "title_canon_sha256": "e58338fc00086bbb9f52f2e2264aa0f1f382784b289074ab5bb99eb4490c3b12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0181",
    "kind": "arxiv",
    "version": 1
  }
}