What does this research mean for the field?

Prime generation can be formalized as an interaction between additive order and multiplicative closure, yielding topological and homological structures that quantify nested connectivity and branching information. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To formalize prime generation as an interaction between additive order and multiplicative closure, mapping its algebraic, topological, and logical boundary properties.

August 23, 2026Open Access

Additive Carries, Multiplicative Closure, and Prime Dependency Topology: Nested Generation, Homological Filtrations, and Logical Boundaries

View Full Paper

Ask AI

Bookmark

Authors

KWKianming(Jianming) Wang

Discussion

Member takes

Implication

Theoretical analysis reveals the topological and algebraic structure of prime generation through additive carries and multiplicative closures, highlighting logical and structural complexity...

Key Points

To formalize prime generation as an interaction between additive order and multiplicative closure, mapping its algebraic, topological, and logical boundary properties.
Constructed typed expression languages, Pratt dependency trees, and iterated least-gap completions alongside Euclid product-plus-one recursion models.
Applied Alexandrov order complexes, Dowker duality, persistent homology, and spectral sequences to characterize topological prime dependencies.
Iterated prime-power carry closures contain every prime with unbounded depth, whereas uniform bounds on expression depth or additive-node count omit infinitely many primes.
Unfolded history trees yield compact ultrametric boundaries with persistent state-graph barcodes defined by rank merge excess.
Prime-dependency relations define contractible global Alexandrov order complexes featuring non-trivial local homology and Dowker-dual simultaneous-coupling nerves.

Cite This Study

Kianming(Jianming) Wang (2026) studied this question.

synapsesocial.com/papers/6a8aae0f7677a34114446bb6 https://doi.org/10.5281/zenodo.22026157

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis reveals the topological and algebraic structure of prime generation through additive carries and multiplicative closures, highlighting logical and structural complexity...

Additive Carries, Multiplicative Closure, and Prime Dependency Topology: Nested Generation, Homological Filtrations, and Logical Boundaries

Discussion

Member takes

Implication

Key Points

Cite This Study

Additive Carries, Multiplicative Closure, and Prime Dependency Topology: Nested Generation, Homological Filtrations, and Logical Boundaries

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider