Pith Number

pith:XRQ6FHSU

pith:2011:XRQ6FHSUJFGXLECAMT457CJPPS

not attested not anchored not stored refs pending

K-theoretic analogues of factorial Schur P- and Q-functions

Hiroshi Naruse, Takeshi Ikeda

arxiv:1112.5223 v3 · 2011-12-22 · math.CO · math.AG · math.KT · 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{XRQ6FHSUJFGXLECAMT457CJPPS}

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.

Cited by

1 paper in Pith

Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations

Receipt and verification

First computed	2026-05-18T03:25:04.356817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc61e29e54494d75904064f9df892f7cbba9debf9a90d58e16572eadd9a256ab

Aliases

arxiv: 1112.5223 · arxiv_version: 1112.5223v3 · doi: 10.48550/arxiv.1112.5223 · pith_short_12: XRQ6FHSUJFGX · pith_short_16: XRQ6FHSUJFGXLECA · pith_short_8: XRQ6FHSU

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/XRQ6FHSUJFGXLECAMT457CJPPS \
  | 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: bc61e29e54494d75904064f9df892f7cbba9debf9a90d58e16572eadd9a256ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e3dbf7fafac39477012a7d1c722a3d830021f4c1bb3eed50efe8778b01add78",
    "cross_cats_sorted": [
      "math.AG",
      "math.KT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-22T02:39:15Z",
    "title_canon_sha256": "ef074cf4a825b163b68f4efc8a3a74a894fe300437d2fc7a6fc6d3b23f2fff97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5223",
    "kind": "arxiv",
    "version": 3
  }
}