Pith Number

pith:OY5N7UL2

pith:2016:OY5N7UL2SPPFYKI7Z6NBCTP5WI

not attested not anchored not stored refs pending

A bijective proof of the Cauchy identity for Grothendieck polynomials

Yasuhide Numata

arxiv:1604.00104 v1 · 2016-04-01 · math.CO · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OY5N7UL2SPPFYKI7Z6NBCTP5WI}

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	2026-05-18T01:17:54.550369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

763adfd17a93de5c291fcf9a114dfdb22ae1465e1e168024fbb1af35b6f203b8

Aliases

arxiv: 1604.00104 · arxiv_version: 1604.00104v1 · doi: 10.48550/arxiv.1604.00104 · pith_short_12: OY5N7UL2SPPF · pith_short_16: OY5N7UL2SPPFYKI7 · pith_short_8: OY5N7UL2

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/OY5N7UL2SPPFYKI7Z6NBCTP5WI \
  | 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: 763adfd17a93de5c291fcf9a114dfdb22ae1465e1e168024fbb1af35b6f203b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf3f13c19482b4565c6a161fdba81e72b80fb44668b2aec60219e9661ef92a87",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-01T02:16:48Z",
    "title_canon_sha256": "f61bdea82a19dab00848e65d57d8654830d566c5caa3881c2887cd48d2b887b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.00104",
    "kind": "arxiv",
    "version": 1
  }
}