Pith Number

pith:DAXPQKNF

pith:2016:DAXPQKNFGAHP7O3ZJNZNHW7CVS

not attested not anchored not stored refs pending

Multiple-angle formulas of generalized trigonometric functions with two parameters

Shingo Takeuchi

arxiv:1603.06709 v1 · 2016-03-22 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DAXPQKNFGAHP7O3ZJNZNHW7CVS}

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	2026-05-17T23:51:44.690260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

182ef829a5300effbb794b72d3dbe2acbd8adf800a6f1bcfdae3e1179cc3bf93

Aliases

arxiv: 1603.06709 · arxiv_version: 1603.06709v1 · doi: 10.48550/arxiv.1603.06709 · pith_short_12: DAXPQKNFGAHP · pith_short_16: DAXPQKNFGAHP7O3Z · pith_short_8: DAXPQKNF

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/DAXPQKNFGAHP7O3ZJNZNHW7CVS \
  | 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: 182ef829a5300effbb794b72d3dbe2acbd8adf800a6f1bcfdae3e1179cc3bf93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18be5f71ff8c9ae7b03e256e9b06294e7ff6058211115d43ef8e79a291e1bb67",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-03-22T09:05:26Z",
    "title_canon_sha256": "ed6d6d6e3ffaa4ffa79307ec216f4a07958525105cf302fe3f76f8fdd644467a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06709",
    "kind": "arxiv",
    "version": 1
  }
}