Pith Number

pith:OEFAL42Y

pith:2009:OEFAL42Y2YJIRU5V6BQE5VER6R

not attested not anchored not stored refs pending

The $q$-tangent and $q$-secant numbers via continued fractions

Heesung Shin, Jiang Zeng

arxiv:0911.4658 v3 · 2009-11-24 · 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{OEFAL42Y2YJIRU5V6BQE5VER6R}

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	2026-07-05T04:06:38.584864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

710a05f358d61288d3b5f0604ed491f44dd3d90c9dcd8645300a49de398dbb1f

Aliases

arxiv: 0911.4658 · arxiv_version: 0911.4658v3 · doi: 10.48550/arxiv.0911.4658 · pith_short_12: OEFAL42Y2YJI · pith_short_16: OEFAL42Y2YJIRU5V · pith_short_8: OEFAL42Y

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/OEFAL42Y2YJIRU5V6BQE5VER6R \
  | 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: 710a05f358d61288d3b5f0604ed491f44dd3d90c9dcd8645300a49de398dbb1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b3da58472e7308dd6b5102841f1a6422f06cd710df0e3c73f36f2b438809ae3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-11-24T20:10:27Z",
    "title_canon_sha256": "a22d36272378e084eb2c05662d7f11374318d930b566d485b34b34bf72244369"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4658",
    "kind": "arxiv",
    "version": 3
  }
}