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Numerical polynomial envelopes

Abstract

Numerical polynomial envelopes.

PolynomialBound is only a numerical upper-envelope relation. Sums, products, fixed powers and compositions preserve that relation. These statements do not assign runtime to arbitrary functions; they bound algorithms whose counted executions are separately proved.

Theorem 1.1 (PolynomialBound.comp).

Lean statement: D5/S0/Computability/BinaryMachine/PolynomialBound.comp

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/PolynomialBound.comp (✓ std3). ∎

Citation. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

This declaration and its proof are attributed immutable source supply. The mathematical namespace and proof body are preserved. Full license, source correspondence and the finite retirement contract are recorded in docs/reports/licenses/RBarishBinaryMachine.md. This port supplies no new classification or independent mathematical escape content.

References