Pith Number

pith:QKXY6D2W

pith:2011:QKXY6D2W5WDFA35KLFIZMWMG4R

not attested not anchored not stored refs pending

Four families of orthogonal polynomials of C2 and symmetric and antisymmetric generalizations of sine and cosine functions

Jiri Patera, Lenka Motlochova

arxiv:1101.3597 v1 · 2011-01-19 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QKXY6D2W5WDFA35KLFIZMWMG4R}

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	2026-05-18T02:22:51.521820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82af8f0f56ed86506faa5951965986e47c5ed20dd3f7d171aefc4a25ce39342f

Aliases

arxiv: 1101.3597 · arxiv_version: 1101.3597v1 · doi: 10.48550/arxiv.1101.3597 · pith_short_12: QKXY6D2W5WDF · pith_short_16: QKXY6D2W5WDFA35K · pith_short_8: QKXY6D2W

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/QKXY6D2W5WDFA35KLFIZMWMG4R \
  | 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: 82af8f0f56ed86506faa5951965986e47c5ed20dd3f7d171aefc4a25ce39342f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b0eaa608b115c5eaffd88a55c4e54b0a8da18392fb9bc1c240c0f859f80e3cf",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-01-19T01:08:32Z",
    "title_canon_sha256": "15e47e9ae6cbb5f643801a02a2e743358acb1ccf7c4cf2096e685810d827c10c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3597",
    "kind": "arxiv",
    "version": 1
  }
}