Pith Number

pith:X3QDS3BT

pith:2003:X3QDS3BTY57MXOBBFICOHWHGOB

not attested not anchored not stored refs pending

Applications of Minor Summation Formula III, Plucker Relations, Lattice Paths and Pfaffian Identities

Masao Ishikawa, Masato Wakayama

arxiv:math/0312358 v3 · 2003-12-18 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3QDS3BTY57MXOBBFICOHWHGOB}

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

Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

Receipt and verification

First computed	2026-07-04T14:48:28.465640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bee0396c33c77ecbb8212a04e3d8e67078570b0ab812f29b4ded3474ad2d351e

Aliases

arxiv: math/0312358 · arxiv_version: math/0312358v3 · doi: 10.48550/arxiv.math/0312358 · pith_short_12: X3QDS3BTY57M · pith_short_16: X3QDS3BTY57MXOBB · pith_short_8: X3QDS3BT

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/X3QDS3BTY57MXOBBFICOHWHGOB \
  | 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: bee0396c33c77ecbb8212a04e3d8e67078570b0ab812f29b4ded3474ad2d351e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "708bff98ae2c67ad2919853ddf031d078056728aad3f9963513f5156ee357ee5",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-12-18T18:39:13Z",
    "title_canon_sha256": "a715e5fe9ceba2a0eaa77d65390a415eab20446ab0cb3f665a7badd010de8768"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312358",
    "kind": "arxiv",
    "version": 3
  }
}