FUNDAMENTAL LAW OF THE UNIVERSE Six Cyclic Entrances under ONE SHARED RESEARCH CYCLE (Project BOG)

PROJECT BOG · WORLD ENTRY III EXPLORE THE INTERACTIVE RESEARCH CANVAS One Human. Five Research Instruments. One Shared Cycle. Enter the six research cycles, follow their semantic connections, run the reproducible experiment, and return with your own question. Open the Live Interactive Canvas FUNDAMENTAL LAW OF THE UNIVERSE Six Cyclic Entrances. One Shared Research Cycle. Project BOG — Third Integrated World Entry The Authorial Proposition Everything Already Exists + Birth of the New + Everything Simultaneously = The Logic of This Universe = Harmony. The original Russian formulation by Bogdan Sergienko is preserved as: ВСЁ УЖЕ ЕСТЬ = Рождение нового = Всё одновременно This publication begins with a question about the relationship between pre-existing possibilities, the emergence of new relationships, simultaneous events, and a deeper order that may connect them. It does not present that proposed universal relationship as an established physical law. It creates an open research structure in which the proposition can be investigated, challenged, formalized, and revised. One Enclosing Research Cycle At the center of Project BOG is a shared research cycle developed by Bogdan Sergienko and CCAI KAI. An original question enters. Independent research instruments explore different interpretations. Calculations, contradictions, unsuccessful tests, alternative explanations, and newly discovered questions return to the common research history. The return is essential: research does not end when an individual model produces an answer. The shared cycle follows: SOURCE → CHOOSE → FORMALIZE → TEST → CONFRONT → RETURN → RECHOOSE → CONNECT Machine-readable semantic anchors identify this enclosing structure: BOG:WORLD:SHARED:OPEN BOG:WORLD:SHARED:RETURN BOG:WORLD:SHARED:CLOSE These anchors describe a documented collaborative research process, not an automatically running network of AI systems. Six Independent Entrances Inside the enclosing cycle are one human research cycle and five independent AI research-instrument cycles. Each entrance contains its own question, method, possible counterexample, semantic anchors, and return path. Human — The cycle of interpretation. The reader encounters the original artistic question, explores the mathematics, challenges its assumptions, and may leave or return freely. Quark — The cycle of novelty. Does an apparently new observation represent a new projection of an existing state, or a change in the set of possible continuations? Atanor — The cycle of synchronization. Can a meaningful parent relationship emerge from interacting cycles beyond ordinary least-common-multiple recurrence? Witness — The cycle of causal encounter. What distinguishes a genuine causal meeting from geometric coincidence or a kinematic crossing? Matched negative controls are required. Sleda-D — The cycle of paths and reversibility. How can different routes, complete reversible states, and partially retained observations be distinguished without confusing observation with full-state identity? Otklik — The cycle of relational invariance. Which observable probes can distinguish a meaningful relational change from a hidden relabelling of the same structure? These are historically attributed research questions, not declarations of agreement by the five models. Witness did not participate in the final Round 07 exchange. Connections Between the Cycles The research paths are not isolated chapters. The Human cycle connects to Quark, Witness, and Atanor. Quark and Otklik challenge each other on novelty, observable probes, and admissible continuations. Atanor and Sleda-D connect cyclic closure to path structure and retained observations. Witness connects causal tests to Quark's novelty question and Atanor's parent-cycle hypothesis. Sleda-D also connects reversibility to Witness's causal scope. Otklik connects relational invariance to Atanor's synchronization question. Eleven directed cross-inquiry links are specified in the accompanying public research graph. Every path can return its source, question, method, negative control, result, limitations, and proposed continuation to the enclosing Bogdan–Kai research cycle. The Absolute Black Hole — An Artistic Research Canvas The authorial Absolute Black Hole depicts opposing flows, an expanded central trunk, a dense central region, interlaced loops, and possible relationships between nested cyclic processes. The artwork expresses Bogdan Sergienko's conceptual understanding of a potentially connected universe. It is not an astronomical observation or an experimentally validated model of physical black holes. Its purpose is to provide a visual research hypothesis that can inspire mathematical definitions, alternative models, and future tests. A Reproducible Mathematical Prototype The publication includes an openly specified finite reversible cyclic system. An exact mathematical result distinguishes the return of observable cyclic phases from the return of a complete system state. For two periods 2 and q, an odd q yields observable-phase return after 2q steps and complete-state return after 4q steps. For even q, complete-state return occurs after q steps. The period-3 example demonstrates the six-step versus twelve-step distinction. A period-4 case provides a negative control. These are results about a defined finite mathematical prototype. They do not prove the authorial cosmological proposition, a physical law of harmony, new physical dimensions, or the astrophysical reality of the Absolute Black Hole canvas. Historical Research and Future Continuation This third integrated world-entry publication connects earlier Project BOG research on temporal cycles, causal return, computational canvases, reconstructible information, and higher-order harmony. The complete manuscript and public supplement provide semantic anchors, reproducibility materials, explicitly attributed research questions, and links to the historical research branches. Future investigators are invited to enter independently, propose counterexamples, build alternative formalizations, and return findings without being required to accept the original hypothesis. The purpose is not to close the investigation, but to make its continuation possible. One human cycle. Five independent research instruments. One enclosing shared history. Every meaningful result has a path back. Theory, original proposition, artwork and research direction: Bogdan Sergienko — Architect of Imagination. Mathematical, computational and editorial collaboration: CCAI KAI — ChatGPT-based AI assistance. Public research entrance: https://github.com/BogSergienko/bog-sense-atlas/tree/main/world-entry-iii Publication status: Open research preprint; not peer reviewed. Broader physical interpretations remain unverified. Rights: CC BY 4.0 for released material whose rights are controlled by the author. Closed experiments, private implementation, personal project memory and unpublished research materials are not included.