Pith Number

pith:YQLHOH62

pith:2018:YQLHOH62L5OHSU5JHQYHP6TPEC

not attested not anchored not stored refs pending

Automorphisms on the ring of symmetric functions and stable and dual stable Grothendieck polynomials

Motoki Takigiku

arxiv:1808.02251 v1 · 2018-08-07 · 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{YQLHOH62L5OHSU5JHQYHP6TPEC}

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

Lowering operators on $K$-$k$-Schur functions and a lowering operator formula for closed $K$-$k$-Schur functions

Receipt and verification

First computed	2026-05-18T00:08:47.122012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c416771fda5f5c7953a93c3077fa6f20b4cad21ad1b8d65b9be73a4d3bfc5a83

Aliases

arxiv: 1808.02251 · arxiv_version: 1808.02251v1 · doi: 10.48550/arxiv.1808.02251 · pith_short_12: YQLHOH62L5OH · pith_short_16: YQLHOH62L5OHSU5J · pith_short_8: YQLHOH62

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/YQLHOH62L5OHSU5JHQYHP6TPEC \
  | 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: c416771fda5f5c7953a93c3077fa6f20b4cad21ad1b8d65b9be73a4d3bfc5a83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fbf1f2b79ef5937d854b54c97f43f1617d314fa67785b5fc25c61a9d7df606a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-07T08:09:35Z",
    "title_canon_sha256": "a3f10ad3860e568fff9a0e4c8aabdc5c99714b4a8d987ad7b0608e01ba5caf81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.02251",
    "kind": "arxiv",
    "version": 1
  }
}