Pith Number

pith:NCQUWY67

pith:2022:NCQUWY67FLD5DOWQCEMKE5OOLH

not attested not anchored not stored refs pending

The tangent function and power residues modulo primes

Zhi-Wei Sun

arxiv:2208.05928 v3 · 2022-08-11 · 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{NCQUWY67FLD5DOWQCEMKE5OOLH}

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	2026-07-05T06:44:18.726609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68a14b63df2ac7d1bad01118a275ce59ddf85a1eb87a63df7ed29eafbb91c8fa

Aliases

arxiv: 2208.05928 · arxiv_version: 2208.05928v3 · doi: 10.48550/arxiv.2208.05928 · pith_short_12: NCQUWY67FLD5 · pith_short_16: NCQUWY67FLD5DOWQ · pith_short_8: NCQUWY67

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/NCQUWY67FLD5DOWQCEMKE5OOLH \
  | 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: 68a14b63df2ac7d1bad01118a275ce59ddf85a1eb87a63df7ed29eafbb91c8fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3b9320ead275444acbd4a21cfb5cf5f275ed34bce76ed20af183b252044f087",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-08-11T17:04:33Z",
    "title_canon_sha256": "36487c42622cb288fe4f72452439fde92b254a008720b05d9662db3cb8691c1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.05928",
    "kind": "arxiv",
    "version": 3
  }
}