Pith Number

pith:SHBAT7BJ

pith:2012:SHBAT7BJZ3XBZBCXMR4RDHFZ3X

not attested not anchored not stored refs pending

On some binomial coefficients related to the evaluation of tan(nx)

Shi-Mei Ma

arxiv:1205.0735 v4 · 2012-05-03 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SHBAT7BJZ3XBZBCXMR4RDHFZ3X}

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	2026-05-18T03:42:11.424160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91c209fc29ceee1c84576479119cb9dde8066aabddad959837149da51c1930b1

Aliases

arxiv: 1205.0735 · arxiv_version: 1205.0735v4 · doi: 10.48550/arxiv.1205.0735 · pith_short_12: SHBAT7BJZ3XB · pith_short_16: SHBAT7BJZ3XBZBCX · pith_short_8: SHBAT7BJ

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/SHBAT7BJZ3XBZBCXMR4RDHFZ3X \
  | 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: 91c209fc29ceee1c84576479119cb9dde8066aabddad959837149da51c1930b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99de8db1ea41e914c58799eed7d9a6911c8554d15c0beab324fd8f1b70af6176",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-03T15:19:50Z",
    "title_canon_sha256": "99ec41260e2484ea082216536876c45cd4c803c971f4d93c8b42056cd5a8a79c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0735",
    "kind": "arxiv",
    "version": 4
  }
}