Pith Number

pith:TXOX5JDV

pith:2011:TXOX5JDVATE4XKHW43R5QYLCN2

not attested not anchored not stored refs pending

The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus

Ronny Bergmann

arxiv:1107.5415 v2 · 2011-07-27 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TXOX5JDVATE4XKHW43R5QYLCN2}

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	2026-05-18T03:20:57.161080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ddd7ea47504c9cba8f6e6e3d861626ebe4440f23e2b5d2d4c791237dc7aef7f

Aliases

arxiv: 1107.5415 · arxiv_version: 1107.5415v2 · doi: 10.48550/arxiv.1107.5415 · pith_short_12: TXOX5JDVATE4 · pith_short_16: TXOX5JDVATE4XKHW · pith_short_8: TXOX5JDV

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/TXOX5JDVATE4XKHW43R5QYLCN2 \
  | 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: 9ddd7ea47504c9cba8f6e6e3d861626ebe4440f23e2b5d2d4c791237dc7aef7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0d7f59bc90b737b69f627f77b52511b13d872bba4a8a3843877fcd0f0d7d898",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-07-27T08:51:51Z",
    "title_canon_sha256": "95852994e4250e55600175382e729711fc2ef8e5381d98c37897145b94e26b47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5415",
    "kind": "arxiv",
    "version": 2
  }
}