Pith Number

pith:SMBOP2IA

pith:2005:SMBOP2IAJYRJHZB32OIA2FAOJ6

not attested not anchored not stored refs pending

On maximal functions for Mikhlin-Hoermander multipliers

Andreas Seeger, Loukas Grafakos, Petr Honzik

arxiv:math/0501114 v1 · 2005-01-08 · 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{SMBOP2IAJYRJHZB32OIA2FAOJ6}

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	2026-07-04T17:23:15.300151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9302e7e9004e2293e43bd3900d140e4fb01cde56f6b6fd3ca7e2e5c13450e49a

Aliases

arxiv: math/0501114 · arxiv_version: math/0501114v1 · doi: 10.48550/arxiv.math/0501114 · pith_short_12: SMBOP2IAJYRJ · pith_short_16: SMBOP2IAJYRJHZB3 · pith_short_8: SMBOP2IA

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/SMBOP2IAJYRJHZB32OIA2FAOJ6 \
  | 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: 9302e7e9004e2293e43bd3900d140e4fb01cde56f6b6fd3ca7e2e5c13450e49a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ce1150b408d4f7d7a4cf1a88eb10cd3432c3f049f7cc3c69f170078e71c47c0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2005-01-08T16:26:35Z",
    "title_canon_sha256": "df1e5d8fcb4ed4460b4c39159d7b25ac6230ba357044d0d64983cea3dcb95781"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501114",
    "kind": "arxiv",
    "version": 1
  }
}