Pith Number

pith:TA5WPQ33

pith:2010:TA5WPQ33XIEHAG5TDRVDANKYNX

not attested not anchored not stored refs pending

Orthogonality Relations for Multivariate Krawtchouk Polynomials

Hiroshi Mizukawa

arxiv:1009.1203 v5 · 2010-09-07 · math.CO · 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{TA5WPQ33XIEHAG5TDRVDANKYNX}

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	2026-05-18T04:28:09.631941Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

983b67c37bba08701bb31c6a3035586de766a11964ee05ae376679e39b6e9689

Aliases

arxiv: 1009.1203 · arxiv_version: 1009.1203v5 · doi: 10.48550/arxiv.1009.1203 · pith_short_12: TA5WPQ33XIEH · pith_short_16: TA5WPQ33XIEHAG5T · pith_short_8: TA5WPQ33

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/TA5WPQ33XIEHAG5TDRVDANKYNX \
  | 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: 983b67c37bba08701bb31c6a3035586de766a11964ee05ae376679e39b6e9689

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcce5516c0d18ee4a792719e4d488d93d2703f1bba9c64512d228050c198a729",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-07T06:39:35Z",
    "title_canon_sha256": "ba5f3057fc6906c3ecddf06d505ac3d5587036b10947b6047b6285f7ab86378c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1203",
    "kind": "arxiv",
    "version": 5
  }
}