Pith Number

pith:HLKFWWVV

pith:2010:HLKFWWVVGJZKHKQPF4NS6G352Q

not attested not anchored not stored refs pending

Vertical versus conical square functions

Jos\'e Maria Martell, Pascal Auscher (LM-Orsay), Steve Hofmann

arxiv:1012.4184 v1 · 2010-12-19 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HLKFWWVVGJZKHKQPF4NS6G352Q}

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	2026-05-18T02:52:04.471852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da

Aliases

arxiv: 1012.4184 · arxiv_version: 1012.4184v1 · doi: 10.48550/arxiv.1012.4184 · pith_short_12: HLKFWWVVGJZK · pith_short_16: HLKFWWVVGJZKHKQP · pith_short_8: HLKFWWVV

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/HLKFWWVVGJZKHKQPF4NS6G352Q \
  | 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: 3ad45b5ab53272a3aa0f2f1b2f1b7dd40e4f62a01031cc83f8ff381acd0539da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a437ebcc168e6e1a30effed9ee2a276a0124dc2aa35e1bf3d022b402452da994",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-12-19T16:46:27Z",
    "title_canon_sha256": "19c07afb69c5acf1c57bb5a7ce1e0b99e22a070a19d65096802ae0ad7484cdff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4184",
    "kind": "arxiv",
    "version": 1
  }
}