Pith Number

pith:6TI5YY47

pith:2016:6TI5YY47UMX3CO7A4EDRRRYDHT

not attested not anchored not stored refs pending

Series representations of the remainders in the expansion for certain trigonometric and hyperbolic functions with applications

C.-P. Chen, R.B. Paris

arxiv:1601.03180 v1 · 2016-01-13 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6TI5YY47UMX3CO7A4EDRRRYDHT}

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	2026-05-18T01:22:55.137134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4d1dc639fa32fb13be0e10718c7033ce9085061b70d56430c474e2c88b4d790

Aliases

arxiv: 1601.03180 · arxiv_version: 1601.03180v1 · doi: 10.48550/arxiv.1601.03180 · pith_short_12: 6TI5YY47UMX3 · pith_short_16: 6TI5YY47UMX3CO7A · pith_short_8: 6TI5YY47

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/6TI5YY47UMX3CO7A4EDRRRYDHT \
  | 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: f4d1dc639fa32fb13be0e10718c7033ce9085061b70d56430c474e2c88b4d790

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69f33e8963a233061e757086ccd8bfb319458d89419c5b9c01d6e3a72b5f64c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-01-13T09:31:17Z",
    "title_canon_sha256": "ca6830136df9129fa3909de45e4a42a090773c72a2cc21a7e1ecee9f0f94f6e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03180",
    "kind": "arxiv",
    "version": 1
  }
}