Binomial-Kernel Supercongruences and Laurent Constant-Term Identities

We organize six integer sequences—A220119, A376460, A376461, A376463, A376464, and A376465—around the binomial kernel OEIS A108625. For A376460, A376461, A376463, A376464, and A376465 we present all-height cubic supercongruence arguments for the applicable unshifted and shifted towers, and an exact counterexample to the shifted analogue for A376465. We also treat the Laurent constant-term identities associated with A376460 and A376461. The A220119 sequence joins the same kernel framework through an exact finite-sum bridge; its proposed five-variable constant-term identity is established by a specialization of the classical terminating Whipple transformation. We distinguish these sequence-specific derivations from the pre-existing OEIS definitions and proposals, generalized Jacobsthal congruences, Euler–Pfaff–Whipple identities, the known A220119 recurrence, Delaygue's valuation theorem and a separately attributed divisibility result. Finite calculations in the accompanying materials are used only to check exact formulas and do not replace proofs of universal statements. Licensing note: The manuscript is licensed under CC BY 4.0. The OEIS b-file snapshots included in the supplementary archive retain their original CC BY-SA 4.0 license and attribution. The independently authored verification code is made available under CC BY 4.0.