Pith Number

pith:5HWQCE6M

pith:2010:5HWQCE6MITI66BVJ2R4XFI2TZW

not attested not anchored not stored refs pending

Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Form of Euler's Formula

Stephen J. Sangwine, Todd A. Ell

arxiv:1001.4379 v3 · 2010-01-25 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5HWQCE6MITI66BVJ2R4XFI2TZW}

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	2026-05-18T03:45:51.859411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9ed0113cc44d1ef06a9d47972a353cd999318229fbcf213f451a5349cd72b20

Aliases

arxiv: 1001.4379 · arxiv_version: 1001.4379v3 · doi: 10.48550/arxiv.1001.4379 · pith_short_12: 5HWQCE6MITI6 · pith_short_16: 5HWQCE6MITI66BVJ · pith_short_8: 5HWQCE6M

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/5HWQCE6MITI66BVJ2R4XFI2TZW \
  | 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: e9ed0113cc44d1ef06a9d47972a353cd999318229fbcf213f451a5349cd72b20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14a55c3f2f5dabd72e3be1ddda5580c922331e4954d2b27d2ffc0e1f0a797056",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-01-25T11:03:58Z",
    "title_canon_sha256": "aec8fea6f3b3e2c08d575a9fde2de90c1a37cafd110d1a767e43bfac7b9a9607"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.4379",
    "kind": "arxiv",
    "version": 3
  }
}