Pith Number

pith:3VGM76GV

pith:2025:3VGM76GVSSLYATM2ETFMY7U4ZB

not attested not anchored not stored refs pending

Weighted $K$-$k$-Schur functions and their application to the $K$-$k$-Schur alternating conjecture

Xing Gao, Yaozhou Fan

arxiv:2507.23222 v1 · 2025-07-31 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VGM76GVSSLYATM2ETFMY7U4ZB}

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	2026-07-05T11:46:07.819253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd4ccff8d59497804d9a24cacc7e9cc84908eb34dc0b3d3a1a9b192195f8bf21

Aliases

arxiv: 2507.23222 · arxiv_version: 2507.23222v1 · doi: 10.48550/arxiv.2507.23222 · pith_short_12: 3VGM76GVSSLY · pith_short_16: 3VGM76GVSSLYATM2 · pith_short_8: 3VGM76GV

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/3VGM76GVSSLYATM2ETFMY7U4ZB \
  | 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: dd4ccff8d59497804d9a24cacc7e9cc84908eb34dc0b3d3a1a9b192195f8bf21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6dd09ed5c0583804be270a3e11d634d3613a90a8ea4afade2dc0c5d589bb2bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-31T03:31:25Z",
    "title_canon_sha256": "4e8eec2373f93b4bd56708df8df24503061fc928accbbb2f353702cf6eee85d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.23222",
    "kind": "arxiv",
    "version": 1
  }
}