Pith Number

pith:KCH5N5XW

pith:2026:KCH5N5XW4V2WUZYHLVPKMGWFLY

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Bispectrality and the ad conditions

F. Alberto Grunbaum

Adapted ad-conditions provide a route to new examples in exceptional orthogonal polynomials and non-commutative bispectral problems.

arxiv:2603.00939 v2 · 2026-03-01 · math-ph · math.MP

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\pithnumber{KCH5N5XW4V2WUZYHLVPKMGWFLY}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

Properly adapted versions of these conditions, see [44], can play an important role in areas including, for instance, the study of exceptional orthogonal polynomials. This is also true in the non-commutative case.

C2weakest assumption

That finding explicit solutions of these ad-conditions will provide an additional route to new examples, based on their prior role in the bispectral problem.

C3one line summary

Adapted ad-conditions from bispectrality offer a route to new examples of exceptional orthogonal polynomials in commutative and non-commutative cases.

References

52 extracted · 52 resolved · 0 Pith anchors

[1] Adler, M., Moser, J.,On a class of polynomials connected with the Korteweg-deVries equationComm. Math. Phys.611, (1978) 1–30 1978

[2] Airault, H. , McKean, H. P., Moser, J.,Rational and elliptic solutions of the Korteweg-deVries equation and a related many body problemCommun. Pure and Applied Math3097 (1977) 95–178 1977

[3] Letters A 222(1996) pp 59-66 1996

[4] Bakalov, B., Horozov, E., Yakimov, M.,Bispectral algebras of commuting differentail operatorsComm. Math. Physics190,2, 1997 pp 331-373 1997

[5] Bargman, V.On the connection between Phase Shifts and Scattering Potential, Rev, Modern Physics,211, July 1949 pp 488–493 1949

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:15.902603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

508fd6f6f6e5756a67075d5ea61ac55e1c67c491a15630561cac67567614368e

Aliases

arxiv: 2603.00939 · arxiv_version: 2603.00939v2 · doi: 10.48550/arxiv.2603.00939 · pith_short_12: KCH5N5XW4V2W · pith_short_16: KCH5N5XW4V2WUZYH · pith_short_8: KCH5N5XW

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/KCH5N5XW4V2WUZYHLVPKMGWFLY \
  | 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: 508fd6f6f6e5756a67075d5ea61ac55e1c67c491a15630561cac67567614368e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81d0b1e3f996193e5902e84280ac6238c87d8c9b91535bb028c4ed5130b99c7c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-03-01T06:17:41Z",
    "title_canon_sha256": "5b804b2a15d50fe7feb2daa052e0df7cd570fee9ea64341bc01c96445e57b5df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.00939",
    "kind": "arxiv",
    "version": 2
  }
}