Pith Number

pith:JNOUPSHB

pith:2011:JNOUPSHBZXLZKG4VVNOVK7A3IB

not attested not anchored not stored refs pending

An easy method for finding the integral of the formula $\int (x^{n+p} - 2 x^n\cos\zeta + x^{n-p})/(x^{2n} - 2 x^n\cos\theta + 1) dx/x$ when the upper limit of integration is $x=1$ or $x=\infty$

Jacques G\'elinas, Leonhard Euler

arxiv:1111.5571 v2 · 2011-11-23 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JNOUPSHBZXLZKG4VVNOVK7A3IB}

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	2026-05-18T04:03:08.853703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b5d47c8e1cdd7951b95ab5d557c1b4071f7fdce9ab92749ee13eb892cf561f9

Aliases

arxiv: 1111.5571 · arxiv_version: 1111.5571v2 · doi: 10.48550/arxiv.1111.5571 · pith_short_12: JNOUPSHBZXLZ · pith_short_16: JNOUPSHBZXLZKG4V · pith_short_8: JNOUPSHB

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/JNOUPSHBZXLZKG4VVNOVK7A3IB \
  | 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: 4b5d47c8e1cdd7951b95ab5d557c1b4071f7fdce9ab92749ee13eb892cf561f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8e7eaad42268b0017bfe39bae18d49b76ed8fc08600b7d0a16b820280b30eaa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2011-11-23T17:45:52Z",
    "title_canon_sha256": "355e71a460e157baaa6ae2c6131b59f45b4a3e54605b7dafa375c12fc03d74da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5571",
    "kind": "arxiv",
    "version": 2
  }
}