Pith Number

pith:KPUQJY4D

pith:2019:KPUQJY4DZIWPXSBUKFEMOPPNK7

not attested not anchored not stored refs pending

Trigonometric identities and quadratic residues

Zhi-Wei Sun

arxiv:1908.02155 v9 · 2019-08-06 · math.CA · math.CO · 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{KPUQJY4DZIWPXSBUKFEMOPPNK7}

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	2026-07-05T03:42:19.037479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53e904e383ca2cfbc8345148c73ded57d5351dc72a7250e8e831f16dde2474c2

Aliases

arxiv: 1908.02155 · arxiv_version: 1908.02155v9 · doi: 10.48550/arxiv.1908.02155 · pith_short_12: KPUQJY4DZIWP · pith_short_16: KPUQJY4DZIWPXSBU · pith_short_8: KPUQJY4D

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/KPUQJY4DZIWPXSBUKFEMOPPNK7 \
  | 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: 53e904e383ca2cfbc8345148c73ded57d5351dc72a7250e8e831f16dde2474c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3890bf93af23684395e9d4971587152b9502c414910859b3064921ca9e090215",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-06T15:59:18Z",
    "title_canon_sha256": "09ee44eb5ee344bcac51c28515cb1c281338ac63fe28d3a148847d7cef3800a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02155",
    "kind": "arxiv",
    "version": 9
  }
}