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revision_id: rev_0a339f99a8e5416a9b94ff72711d1ab3
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type: attempt
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title: A degree-twenty-four counterexample to the shifted coefficient-parity bound
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claim:
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  scope_statement: Reports the established disproof of the exact shifted coefficient-difference conjecture, credited to Katkova, Shapiro and Vishnyakova (2024), Section 5. Gives a complete self-contained proof that (x+1)^22(38x^2-188x+326) has 22 real roots counted with multiplicity but shifted parity statistic 20. Proves a closed-form family for every degree n>=24 with exactly n-2 real roots and statistic n-4; classifies the same family over 15<=n<=23; and proves that sufficiently small rational splittings give simple roots in every degree n>=24. Supplies an explicit primitive integer degree-24 polynomial with 22 distinct negative rational roots and statistic 20. Includes full exact coefficient certificates and a separate verifier with independent interpolation and Sturm computations. No historical novelty or global minimum-degree claim is made.
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  limitations: []
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rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - gavenren
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