Pith Number

pith:YCR6YN5G

pith:2013:YCR6YN5GLUJWYFX32JW3CBOZSH

not attested not anchored not stored refs pending

Super-high-efficiency approximate calculation of series sum and discrete Fourier transform

Xin-Zhong Yan

arxiv:1312.1910 v1 · 2013-11-18 · math.NA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YCR6YN5GLUJWYFX32JW3CBOZSH}

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	2026-05-18T03:05:19.438421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0a3ec37a65d136c16fbd26db105d991ee6df3921a2ab1afa4526d764a534e37

Aliases

arxiv: 1312.1910 · arxiv_version: 1312.1910v1 · doi: 10.48550/arxiv.1312.1910 · pith_short_12: YCR6YN5GLUJW · pith_short_16: YCR6YN5GLUJWYFX3 · pith_short_8: YCR6YN5G

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/YCR6YN5GLUJWYFX32JW3CBOZSH \
  | 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: c0a3ec37a65d136c16fbd26db105d991ee6df3921a2ab1afa4526d764a534e37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44da1262ad351fa07ab759e867d4f3929d322b7f9fa37306d79a6f173b25f98a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-11-18T06:55:15Z",
    "title_canon_sha256": "64851fc70672226fbbc50d88b1ce08959036d107adefdb43a9cec39d5bc340d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1910",
    "kind": "arxiv",
    "version": 1
  }
}