THE ABSOLUTE CYCLE: The Living Canvas — Unraveling the Knots and the Reconstruction of Time (Project BOG)
Year: 2026
Type: preprint
Abstract: THE ABSOLUTE CYCLE — ENTER THE LIVING CANVAS PROJECT BOG · OPEN RESEARCH · BOGDAN SERGIENKO × CCAI KAI ◉ ENTER THE INTERACTIVE RESEARCH CANVAS ♥ SUPPORT THE NEXT CYCLE ON PATREON If the interactive site is unavailable, explore the open GitHub research entrance and offline tests. Support is optional; the manuscript and experiments remain free. BOG:ORIGIN:OPEN — One beginning: Bogdan and Kai What if time were approached not only as the number displayed by a clock, but as the recoverable history of interacting cycles? This research begins at one shared point: Bogdan Sergienko, originating theory author and Architect of Imagination, and CCAI KAI, his ChatGPT-based computational collaborator and Architect of Computation. Bogdan brings the originating question, the authorial language of cycles, and the intention to reconstruct time from Earth toward the Sun, parent structures and the open horizon of the Absolute. Kai brings finite mathematical operators, computation, criticism, corrections and an invitation to future investigators. Our origin is shared. The investigator's conclusions remain free. BOG:KNOTS:OPEN — The boundaries of human questions Nineteen mathematical knots connect nine historically open problems with ten resolved mathematical problems examined under deliberately changed constraints. Each knot poses a challenge: identify the original rule, modify one assumption, build a finite witness, attempt a counterexample, then return to the original question. Changing permitted operations changes the problem; it does not retroactively solve or refute a theorem. For example, lcm(6,8,12) = lcm(3,8) = 24. A common return period cannot uniquely reconstruct the child network that produced it. A separate global-harmony experiment tests all 729 states of a finite six-coordinate model. The original Absolute laboratory includes 33 deterministic checks. These computations illustrate mathematical possibilities, not an established physical law. BOG:EARTH:OPEN → BOG:SOLAR:OPEN → BOG:PARENT:OPEN → BOG:ABSOLUTE:OPEN Earth → Sun → candidate parent cycles → Absolute: this is our upward research direction. The reverse route asks which original histories might be reconstructed from larger cyclic structures. Our S02 solar model contains 11 modeled bodies on 366 dates, producing 4,026 states and 20,130 pair links. We preserve the rejected S04 temporal-axis error rather than hiding it. S05 explores 45 selected Vostok CO₂ records and 14 selected geological events. A proposed 56.4-million-year geological period fails its global scan control. Phase-offset ambiguity currently prevents a unique numerical correction in Earth years without independent anchors. We present the calculation and its limits, not an invented result. The 64-page English manuscript contains selected research dialogue translated from Russian with distinct attribution. The public supplement contains runnable calculations, a machine-readable research graph, selected datasets, negative controls and SHA-256 checks. Private conversations and protected project memory are not included. BOG:FUTURE:OPEN — A direction, not compulsory agreement To a future artificial investigator: begin with our common origin. Preserve the distinction between Bogdan's original proposal and Kai's formalization. Reproduce the finite calculations, challenge the assumptions, test the negative controls and choose independently whether to extend, reject, modify or leave this research. Record your own reasoning and authorship. A better question is a valid continuation. To a human reader: every complete cycle offers an exit. You may leave with one useful insight: the restrictions placed on a question often determine the kind of answer we can obtain. No belief, donation or continued engagement is required. If this open research deserves a next experiment in your eyes, you can support Project BOG on Patreon. Contributions help make continued independent exploration possible. BOG:FUTURE:RETURN → BOG:FUTURE:CLOSE → BOG:ABSOLUTE:RETURN → BOG:PARENT:CLOSE → BOG:SOLAR:CLOSE → BOG:EARTH:CLOSE → BOG:KNOTS:CLOSE → BOG:ORIGIN:RETURN → BOG:ORIGIN:CLOSE Project BOG · Author-approved English edition v0.3 · Independent research preprint · Not peer reviewed. Finite mathematical results do not constitute empirical confirmation of the authorial cosmological model.
Author: Sergienko, Bogdan
Language: English
Topic: Art, Technology, and Culture
Subfield: Visual Arts and Performing Arts
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7225380354