Pith Number

pith:A4NGXIRZ

pith:2012:A4NGXIRZHK3ZIMFNU2RJBS4MT2

not attested not anchored not stored refs pending

Multi-frequency Calderon-Zygmund analysis and connexion to Bochner-Riesz multipliers

Frederic Bernicot (LMJL)

arxiv:1211.5218 v2 · 2012-11-22 · 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{A4NGXIRZHK3ZIMFNU2RJBS4MT2}

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	2026-05-18T03:26:42.685704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

071a6ba2393ab79430ada6a290cb8c9e863be94abadc696b429f8091a3614002

Aliases

arxiv: 1211.5218 · arxiv_version: 1211.5218v2 · doi: 10.48550/arxiv.1211.5218 · pith_short_12: A4NGXIRZHK3Z · pith_short_16: A4NGXIRZHK3ZIMFN · pith_short_8: A4NGXIRZ

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/A4NGXIRZHK3ZIMFNU2RJBS4MT2 \
  | 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: 071a6ba2393ab79430ada6a290cb8c9e863be94abadc696b429f8091a3614002

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d763eae5fdfede0c05a029f6796e6aa594808a252b89b330cd87a03184988fc0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-22T07:12:45Z",
    "title_canon_sha256": "7e109268c5abc4ddf3997ca2a52059e39f9cccb502dfd6828e56f63662cff1af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5218",
    "kind": "arxiv",
    "version": 2
  }
}