Pith Number

pith:D6RPTMJ3

pith:2024:D6RPTMJ3BBEFQ3XFJZF5SYKCHJ

not attested not anchored not stored refs pending

Refined canonical stable Grothendieck polynomials and their duals, Part 2

Byung-Hak Hwang, Jang Soo Kim, Jihyeug Jang, Minho Song, U-Keun Song

arxiv:2404.02483 v2 · 2024-04-03 · 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{D6RPTMJ3BBEFQ3XFJZF5SYKCHJ}

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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

Orthogonality of spin $q$-Whittaker polynomials

Receipt and verification

First computed	2026-07-05T10:52:11.398019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fa2f9b13b0848586ee54e4bd961423a53dccd688a7199a39542befd1e27e1c0

Aliases

arxiv: 2404.02483 · arxiv_version: 2404.02483v2 · doi: 10.48550/arxiv.2404.02483 · pith_short_12: D6RPTMJ3BBEF · pith_short_16: D6RPTMJ3BBEFQ3XF · pith_short_8: D6RPTMJ3

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/D6RPTMJ3BBEFQ3XFJZF5SYKCHJ \
  | 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: 1fa2f9b13b0848586ee54e4bd961423a53dccd688a7199a39542befd1e27e1c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "113ca0fbadf1e4addef1d1ee7e52ca364842fdbdb91a9d4032d4b0427be6e5c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-04-03T05:43:06Z",
    "title_canon_sha256": "fe515998737c886747b34d350b3e2ce3ffcfafae5da1b5c5d1adc63640df8679"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.02483",
    "kind": "arxiv",
    "version": 2
  }
}