AWhat changed
Introduces a three-recursive-square multiplication mechanism alongside separately attributed grouped machine-size/time tradeoffs.
Scientific scope
Introduces a three-recursive-square multiplication mechanism alongside separately attributed grouped machine-size/time tradeoffs. Exact target is the 1962 two-page note’s binary-automaton constructions/proof schemes, not arbitrary unit-cost arithmetic or every modern big-integer library. Theorem 1 is explicitly Ofman’s grouped size/time construction; Theorem 2 is explicitly Karatsuba’s recursive squaring construction. Three smaller squares plus additions/shifts give the subquadratic-size mechanism; the carry footnote addresses the extra sum digit. N(machine size) and T(time) are different resources. Corrupted formula exponents prevent reliable transcription of every joint bound or timing exponent here; neither elementary separate lower bounds nor the constructions prove optimality or attain both best orders together. Original 294 distinguishes feedback-free representations from automata with reusable components, so no unconditional circuit tradeoff equivalence is inferred. Earlier Ofman addition/model definitions are cited but unread. Both Russian pages prose read; no independent full automaton reconstruction, clean-formula visual check or program/benchmark replay. The 1963 English translation is the same work, not another achievement.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Anatolii A. Karatsuba · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Yu. Ofman · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- A. Karatsuba and Yu. Ofman, Умножение многозначных чисел на автоматах, Doklady 145(2),293–294 (1962)
- Steklov author bibliography:1962 Russian article and 1963 English translation
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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