Pith Number

pith:Q65B4ROO

pith:2015:Q65B4ROO3FUF55IWLHW2HW2OAU

not attested not anchored not stored refs pending

On probabilistic aspects of Chebyshev polynomials

Pawe{\l} J. Szab{\l}owski

arxiv:1508.04450 v3 · 2015-08-18 · 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{Q65B4ROO3FUF55IWLHW2HW2OAU}

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	2026-05-18T00:08:46.633477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87ba1e45ced9685ef51659eda3db4e051457bfeb374bbf118618a6d053eb2af0

Aliases

arxiv: 1508.04450 · arxiv_version: 1508.04450v3 · doi: 10.48550/arxiv.1508.04450 · pith_short_12: Q65B4ROO3FUF · pith_short_16: Q65B4ROO3FUF55IW · pith_short_8: Q65B4ROO

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/Q65B4ROO3FUF55IWLHW2HW2OAU \
  | 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: 87ba1e45ced9685ef51659eda3db4e051457bfeb374bbf118618a6d053eb2af0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07a8d73b22513c8e10318e1455b5e8aafc97a5ffc8f0deb99ca387be0ab082a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-18T20:27:26Z",
    "title_canon_sha256": "a5b7a0b186f5fcb90d89e2c8ddfccd9d13037c8755c5d068ba54160bca37a145"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.04450",
    "kind": "arxiv",
    "version": 3
  }
}