Pith Number

pith:2QKDML7V

pith:2016:2QKDML7VVWJEQT46HAVJZPKC2D

not attested not anchored not stored refs pending

Fast evaluation of real and complex exponential sums

Ines Melzer, Stefan Kunis

arxiv:1606.03255 v1 · 2016-06-10 · 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{2QKDML7VVWJEQT46HAVJZPKC2D}

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	2026-05-18T01:12:37.272589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d414362ff5ad92484f9e382a9cbd42d0d6122bdf82cbfb48d64cbe931b89cc1a

Aliases

arxiv: 1606.03255 · arxiv_version: 1606.03255v1 · doi: 10.48550/arxiv.1606.03255 · pith_short_12: 2QKDML7VVWJE · pith_short_16: 2QKDML7VVWJEQT46 · pith_short_8: 2QKDML7V

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/2QKDML7VVWJEQT46HAVJZPKC2D \
  | 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: d414362ff5ad92484f9e382a9cbd42d0d6122bdf82cbfb48d64cbe931b89cc1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e5dcfa7e68d9a5b0268323f4c0714cf754dfa85f88e24c7beb7a7f2711ac9d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-06-10T10:17:50Z",
    "title_canon_sha256": "94961a109e04910561d57e23415cdae447dd8bea3ce021ce2d8c3eb7c12eecda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03255",
    "kind": "arxiv",
    "version": 1
  }
}