Pith Number

pith:6SQZAYG4

pith:1999:6SQZAYG4BAKW2EUWJE6OOLTZMX

not attested not anchored not stored refs pending

A Fredholm determinant formula for Toeplitz determinants

Alexei Borodin, Andrei Okounkov

arxiv:math/9907165 v1 · 1999-07-25 · math.CA · 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{6SQZAYG4BAKW2EUWJE6OOLTZMX}

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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

A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors

Receipt and verification

First computed	2026-07-04T14:41:15.091745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4a19060dc08156d1296493ce72e7965e031ae1990f7c05ac0bbbfb80db481eb

Aliases

arxiv: math/9907165 · arxiv_version: math/9907165v1 · doi: 10.48550/arxiv.math/9907165 · pith_short_12: 6SQZAYG4BAKW · pith_short_16: 6SQZAYG4BAKW2EUW · pith_short_8: 6SQZAYG4

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/6SQZAYG4BAKW2EUWJE6OOLTZMX \
  | 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: f4a19060dc08156d1296493ce72e7965e031ae1990f7c05ac0bbbfb80db481eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adcff7fd8d0b7cc5dd7e3666bba271ed0c54c06af750295f84b8b6ddae459492",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "1999-07-25T05:15:50Z",
    "title_canon_sha256": "2c7d750b23f38972f10cb6224c9a8dc65c7f8fd2912884e5ec9208bab3f6269d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907165",
    "kind": "arxiv",
    "version": 1
  }
}