AWhat changed
For a strictly increasing positive-integer sequence whose counting function eventually exceeds N^theta for every theta<1, concatenating its base-b representations gives a b-normal real. This proves the prime-concatenation example and the sums-of-two-squares example using the stated counting estimates.
Scientific scope
For a strictly increasing positive-integer sequence whose counting function eventually exceeds N^theta for every theta<1, concatenating its base-b representations gives a b-normal real. This proves the prime-concatenation example and the sums-of-two-squares example using the stated counting estimates. Fixed-base normality of the corresponding constructed real, not absolute normality of the same decimal in every base or algorithmic randomness. The polynomial-value and simultaneous-base assertions at the end are conjectures, not proved here. Not absolute normality or algorithmic randomness. Finite leading digits do not alter normality. Besicovitch and Borel counting ingredients and Champernowne earlier construction keep credit; later polynomial and simultaneous-base paragraphs are explicitly conjectural in this source.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Fixed-base normality of the corresponding constructed real, not absolute normality of the same decimal in every base or algorithmic randomness. The polynomial-value and simultaneous-base assertions at the end are conjectures, not proved here. Not absolute normality or algorithmic randomness. Finite leading digits do not alter normality. Besicovitch and Borel counting ingredients and Champernowne earlier construction keep credit; later polynomial and simultaneous-base paragraphs are explicitly conjectural in this source.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.5. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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