Pith Number

pith:VJBZCGJW

pith:2014:VJBZCGJWG3VJEO45DG7NGOW72T

not attested not anchored not stored refs pending

A Littlewood-Richardson Rule for Dual Stable Grothendieck Polynomials

Pavel Galashin

arxiv:1501.00051 v2 · 2014-12-31 · 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{VJBZCGJWG3VJEO45DG7NGOW72T}

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	2026-05-18T00:40:41.930523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa4391193636ea923b9d19bed33adfd4d7340c200c6c55c9eb13e6cd476b1ebf

Aliases

arxiv: 1501.00051 · arxiv_version: 1501.00051v2 · doi: 10.48550/arxiv.1501.00051 · pith_short_12: VJBZCGJWG3VJ · pith_short_16: VJBZCGJWG3VJEO45 · pith_short_8: VJBZCGJW

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/VJBZCGJWG3VJEO45DG7NGOW72T \
  | 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: aa4391193636ea923b9d19bed33adfd4d7340c200c6c55c9eb13e6cd476b1ebf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a51ecd71126a172ffb418fd237174ab20292b608c69bd3027a829a11580243c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-31T00:22:29Z",
    "title_canon_sha256": "ef9388096a489fec66b983872f183125db1e5bd01ae38f52f329fa8280ce0eee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.00051",
    "kind": "arxiv",
    "version": 2
  }
}