Pith Number

pith:WGUMLSL2

pith:2013:WGUMLSL2FPLL25AY4HNYGSJUMB

not attested not anchored not stored refs pending

The Fourier transform of multiradial functions

Frederic Bernicot (LMJL), Loukas Grafakos (MU Mathematics), Yandan Zhang

arxiv:1307.8408 v1 · 2013-07-31 · 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{WGUMLSL2FPLL25AY4HNYGSJUMB}

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	2026-05-18T03:17:01.242519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1a8c5c97a2bd6bd7418e1db834934604fb7c53aed42150d8137a3e1d2c2c7ba

Aliases

arxiv: 1307.8408 · arxiv_version: 1307.8408v1 · doi: 10.48550/arxiv.1307.8408 · pith_short_12: WGUMLSL2FPLL · pith_short_16: WGUMLSL2FPLL25AY · pith_short_8: WGUMLSL2

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/WGUMLSL2FPLL25AY4HNYGSJUMB \
  | 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: b1a8c5c97a2bd6bd7418e1db834934604fb7c53aed42150d8137a3e1d2c2c7ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dde7d791850cd2340af62ea4577bdb467f03ff831e5228d6eaf230ff3729ae1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-07-31T18:06:10Z",
    "title_canon_sha256": "834b4adf8b4c5335f63e513470b0266995d206305106cbdd4033f48ad8fad4ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.8408",
    "kind": "arxiv",
    "version": 1
  }
}