Pith Number

pith:D7JV4A4O

pith:2026:D7JV4A4OUK3KZ4Z7F45NM5L2EP

not attested not anchored not stored refs pending

The $2j-k$ and $j-2k$ Bi-orthogonal Polynomials on the Unit Circle: Further Properties and Riemann-Hilbert Characterizations

Nicholas S. Witte, Roozbeh Gharakhloo

arxiv:2607.00231 v1 · 2026-06-30 · 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{D7JV4A4OUK3KZ4Z7F45NM5L2EP}

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	2026-07-02T00:18:40.289127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fd35e038ea2b6acf33f2f3ad6757a23d71a2b7a32fd19fd7bfb174daa3c6320

Aliases

arxiv: 2607.00231 · arxiv_version: 2607.00231v1 · doi: 10.48550/arxiv.2607.00231 · pith_short_12: D7JV4A4OUK3K · pith_short_16: D7JV4A4OUK3KZ4Z7 · pith_short_8: D7JV4A4O

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/D7JV4A4OUK3KZ4Z7F45NM5L2EP \
  | 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: 1fd35e038ea2b6acf33f2f3ad6757a23d71a2b7a32fd19fd7bfb174daa3c6320

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d55948bdcf0829a6cb21ac2cfee34b60e838428dbd827db0ae6c559b03b2fe8c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-06-30T22:18:42Z",
    "title_canon_sha256": "8d2ec8cc2fdeb5f4b3e0006d9cc4c9a0930b7366749bf7f7434403de0254aac5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00231",
    "kind": "arxiv",
    "version": 1
  }
}