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The paper aims to reconstruct foundational concepts related to canonical words over a specific set while clarifying several structural theorems.

April 10, 2026Open Access

Prime Blocks and Recursive Additive Ancestry

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This version clarifies the injectivity and extension of prime blocks in canonical words, suggesting implications for structural theories.

The paper aims to reconstruct foundational concepts related to canonical words over a specific set while clarifying several structural theorems.
Developed canonical word E(n) over the set {1,2,3,5,7}
Established prime-block replay E(p+r) and prime-word recursion
Clarified normalization and suffix reduction processes
Reorganized the theory surrounding exact structural theorems
Introduced explicit leaf-sum conservation and derived injectivity of the canonical word map
Corrected the block-extension formalism at prime-block boundaries
Promoted the exact trichotomy Δℓ(n) ∈ {−1, 0, 1} as a key finding
Formulated a uniform recursive generation law for sign strata M₊, M₀, M₋

David Betzer (2026) studied this question.

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