Pith Number

pith:KKUY3R3Y

pith:2018:KKUY3R3Y42WU2ON4ZM2XEED6WW

not attested not anchored not stored refs pending

A positive-definite inner product for vector-valued Macdonald polynomials

Charles F. Dunkl

arxiv:1808.05251 v1 · 2018-08-15 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KKUY3R3Y42WU2ON4ZM2XEED6WW}

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	2026-05-17T23:55:03.371536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52a98dc778e6ad4d39bccb3572107eb5950596cc254b72cf9da175bc41c48643

Aliases

arxiv: 1808.05251 · arxiv_version: 1808.05251v1 · doi: 10.48550/arxiv.1808.05251 · pith_short_12: KKUY3R3Y42WU · pith_short_16: KKUY3R3Y42WU2ON4 · pith_short_8: KKUY3R3Y

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/KKUY3R3Y42WU2ON4ZM2XEED6WW \
  | 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: 52a98dc778e6ad4d39bccb3572107eb5950596cc254b72cf9da175bc41c48643

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25b19d0ae2c90a80793bc084713d3c0d09faf2313060a182a13b3c6596b018c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2018-08-15T18:55:50Z",
    "title_canon_sha256": "5eb18cd3659b1b7f1912651401370b1ccde12fe7e7820a7379e839ca148a0109"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05251",
    "kind": "arxiv",
    "version": 1
  }
}