Pith Number

pith:TACQIIRS

pith:2025:TACQIIRSOMJ7JIEHJOKQPDLCFE

not attested not anchored not stored refs pending

Cauchy identities for Grothendieck polynomials and a dual RSK correspondence through pipe dreams

Hugh Dennin

arxiv:2506.21052 v1 · 2025-06-26 · 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{TACQIIRSOMJ7JIEHJOKQPDLCFE}

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	2026-07-05T11:27:38.801228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98050422327313f4a0874b95078d6229023469b81bab036b39696df5fcebaf0f

Aliases

arxiv: 2506.21052 · arxiv_version: 2506.21052v1 · doi: 10.48550/arxiv.2506.21052 · pith_short_12: TACQIIRSOMJ7 · pith_short_16: TACQIIRSOMJ7JIEH · pith_short_8: TACQIIRS

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/TACQIIRSOMJ7JIEHJOKQPDLCFE \
  | 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: 98050422327313f4a0874b95078d6229023469b81bab036b39696df5fcebaf0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2c8fe1762d41551f5d3669377b34588a33fe2a383b5dcef69da2bf8204b1f8d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-26T06:58:47Z",
    "title_canon_sha256": "094bbadbf07f376aee081a8db908257b0bd300bcc0eb84aa52d8bd9043a422ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.21052",
    "kind": "arxiv",
    "version": 1
  }
}