Pith Number

pith:CIUMHXGK

pith:2003:CIUMHXGKWH3N5IHHVNISS7HIGL

not attested not anchored not stored refs pending

Singular spherical maximal operators on a class of two step nilpotent Lie groups

Andreas Seeger, Detlef Mueller

arxiv:math/0307042 v1 · 2003-07-03 · 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{CIUMHXGKWH3N5IHHVNISS7HIGL}

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	2026-07-04T17:23:15.207763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1228c3dccab1f6dea0e7ab51297ce832ccbf8a19d777df1ae631977671d326fa

Aliases

arxiv: math/0307042 · arxiv_version: math/0307042v1 · doi: 10.48550/arxiv.math/0307042 · pith_short_12: CIUMHXGKWH3N · pith_short_16: CIUMHXGKWH3N5IHH · pith_short_8: CIUMHXGK

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/CIUMHXGKWH3N5IHHVNISS7HIGL \
  | 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: 1228c3dccab1f6dea0e7ab51297ce832ccbf8a19d777df1ae631977671d326fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b0fd278c6a6cd86e4ccf49e0fd40ff517c7be2362292b0e5ae63c4309dc2f49",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2003-07-03T08:54:58Z",
    "title_canon_sha256": "042542d25e46188678aca8d50fabc3c10e3a1c6fa32d6cf82dd77271ed0eba4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307042",
    "kind": "arxiv",
    "version": 1
  }
}