R-layer Mode Theory (RLMT) XXVI-C: Observational Unification across Deep, Informational, and Global Layers
Description
R-layer Mode Theory (RLMT) Volume XXVI‑C develops the observational sector of the R‑layer hierarchy, establishing a unified phenomenological dictionary that connects microscopic, informational, and cosmological data within a single layered geometric framework. Building on the analytical and geometric foundations of Volumes XXVI‑A and XXVI‑B, this volume maps deep-layer, informational-layer, global-layer, and compact-global phenomena to curvature functionals and hierarchical propagation structures.
As stated in the introduction:
“We construct an explicit correspondence between these layers and a broad set of recent observations… The result is a unified phenomenological dictionary that links microscopic, mesoscopic, and cosmological data within a single layered geometric picture.”
The volume organizes observations into three sectors:
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Deep-layer sector: neutrinoless double beta decay candidates, Lieb–Robinson bounds, Population III supernova remnants
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Informational-layer sector: 21 cm cosmology, early Lyman‑α emitters at z ≈ 13, dark-star candidates
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Global-layer sector: overmassive SMBHs in compact galaxies, G1–G2–G2t clouds near Sgr A*, voids and filaments, background gravitational waves, satellite-galaxy overabundance
A key refinement is the introduction of the compact-global sublayer Ω28, representing dense galactic nuclei and ultra‑compact stellar systems hosting overmassive SMBHs. The associated curvature functional KG,28 isolates nuclear contributions within the global layer.
Major contributions of this volume include:
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hierarchical light‑cone structure for deep, informational, and global propagation
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curvature functionals KD,KI,KG,KG,28 and their observational interpretations
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scaling relations such as filament spacing df∝(KI+KG)−1/2 and satellite spacing Δrsat∝(KI(2))−1/4
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full observational–theoretical correspondence tables (Appendix B)
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phenomenological predictions linking layered curvature to measurable astrophysical signatures
Volume XXVI‑C completes the observational unification of the R‑layer hierarchy and provides a framework for testing the theory with current and upcoming surveys.
Notes (English)
This Version 2 update adds the AI‑usage declaration and applies minor corrections. All equations, figures, and scientific results remain unchanged.
Notes (English)
This volume has not been updated to Appendix X‑II, but its contents should be interpreted according to the rules defined in Appendix X‑II. All discrete mode specifications in early RLMT volumes (AUP/MUP integer counts) are to be reinterpreted under the Rules for Conversion as continuous mode‑density integrals within the Meta–Tension–Field (MTFE) framework. Furthermore, all small‑mode structures (Small AUP/MUP) have been fully removed, and any discrete mode expressions appearing in this volume should be read as expectation values of continuous mode densities.
The physical conclusions of this volume remain unchanged. All results are preserved as coarse‑grained effective limits of the continuous MTFE theory.
For reference, Appendix X‑II is available at the following DOI: https://doi.org/10.5281/zenodo.21366422
Files
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Additional details
Software
- Repository URL
- https://tohi308.github.io/R-layer-Mode-Theory/