Pith Number

pith:42W2WBZM

pith:2008:42W2WBZMSMQQSHWATU4J5ZH2R6

not attested not anchored not stored refs pending

Finite Trigonometric Character Sums Via Discrete Fourier Analysis

Mary Halloran, Matthias Beck

arxiv:0804.0645 v2 · 2008-04-04 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42W2WBZMSMQQSHWATU4J5ZH2R6}

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	2026-05-18T03:07:53.087633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6adab072c9321091ec09d389ee4fa8f8c1899c12ca46ddd999fb3981aeb4dbf

Aliases

arxiv: 0804.0645 · arxiv_version: 0804.0645v2 · doi: 10.48550/arxiv.0804.0645 · pith_short_12: 42W2WBZMSMQQ · pith_short_16: 42W2WBZMSMQQSHWA · pith_short_8: 42W2WBZM

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/42W2WBZMSMQQSHWATU4J5ZH2R6 \
  | 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: e6adab072c9321091ec09d389ee4fa8f8c1899c12ca46ddd999fb3981aeb4dbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b02fb43baf59950bb61fd3fb6592c70f3ef789b52743e6a176023dd12a84ad1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-04-04T02:43:03Z",
    "title_canon_sha256": "094c98c4dad6aa96d7911a1be92567677ab0e205af92bd7c92a368c9d28eebea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.0645",
    "kind": "arxiv",
    "version": 2
  }
}