Pith Number

pith:N4B7XRLU

pith:2026:N4B7XRLULP7S6FCT5JN3O27WG6

not attested not anchored not stored refs pending

Rank recursion for $q$-Whittaker and Macdonald operators

Hieu Trung Vu, Philippe Di Francesco

arxiv:2606.12796 v1 · 2026-06-11 · math.RT · math-ph · math.CO · 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{N4B7XRLULP7S6FCT5JN3O27WG6}

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	2026-06-12T01:08:51.496161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f03fbc5745bff2f1453ea5bb76bf637b33b5d3c805dcc896f46d4cb3e9c7e4f

Aliases

arxiv: 2606.12796 · arxiv_version: 2606.12796v1 · doi: 10.48550/arxiv.2606.12796 · pith_short_12: N4B7XRLULP7S · pith_short_16: N4B7XRLULP7S6FCT · pith_short_8: N4B7XRLU

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/N4B7XRLULP7S6FCT5JN3O27WG6 \
  | 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: 6f03fbc5745bff2f1453ea5bb76bf637b33b5d3c805dcc896f46d4cb3e9c7e4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a7eb5e5de1b8998bd71bd68ddfea4c56ecf3eac92fb4c39e0d0e4155d288497",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-06-11T01:46:01Z",
    "title_canon_sha256": "ee6d19316b47993014a90f37402aed9294a546b26517e3762a4600ff352ac857"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12796",
    "kind": "arxiv",
    "version": 1
  }
}