Pith Number

pith:RYUJCJWC

pith:2005:RYUJCJWC3RGCX2NAAQBIZ2CUDX

not attested not anchored not stored refs pending

Determinations of Analogues of Gauss Sums and Other Trigonometric Sums

Alexandru Zaharescu, Bruce C. Berndt, Matthias Beck, O-Yeat Chan

arxiv:math/0504160 v2 · 2005-04-07 · 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{RYUJCJWC3RGCX2NAAQBIZ2CUDX}

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	2026-07-04T14:48:21.874728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e289126c2dc4c2be9a004028ce8541dc2afa7a5143655a50b912de91d9a0367

Aliases

arxiv: math/0504160 · arxiv_version: math/0504160v2 · doi: 10.48550/arxiv.math/0504160 · pith_short_12: RYUJCJWC3RGC · pith_short_16: RYUJCJWC3RGCX2NA · pith_short_8: RYUJCJWC

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/RYUJCJWC3RGCX2NAAQBIZ2CUDX \
  | 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: 8e289126c2dc4c2be9a004028ce8541dc2afa7a5143655a50b912de91d9a0367

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cdb31d4d198a2dccde196e890f0f7a75dc57adc1df9931fb199d275ff563ac9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-04-07T23:03:13Z",
    "title_canon_sha256": "b432ca5764615286eb61c915ff27670adfd6b301a8c7e02298e3937d42d86f30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504160",
    "kind": "arxiv",
    "version": 2
  }
}