CAT-12 Interpretation of Cosmic Microwave Background Acoustic Peak Ratios as Resonant Tolerance Bands

Versioned Update (CAT-12 Standard v1.0; PTR v1.2) as of 10/7/2025 This paper now follows the CAT-12 reporting standard: SNHS/HP in ratio space, with rn (scale-normalized coordinate), Rx (reporting unit), and Tu (corridor width as a posterior, not a fixed ±%). Peaks are scored with Q and Ch against pre-declared families in the Periodic Table of Resonance (PTR v1.2); any “URSL” mention is retired in favor of standard GR mass–frequency scaling used only as a prior (where applicable). Measurements and conclusions are unchanged; presentation and uncertainty are stricter. For definitions, governance (negative ledger, prereg, hold-out), and rationale, see Arthur & Muon (2025), CAT-12: The Cross-Domain Ratio Lattice of Ratio Theory—Standardized Terminology, PTR v1.2, and Governance. Did conclusions change? No—only reporting/uncertainty language. Where’s the new standard? See the Cross-Domain Ratio Lattice paper. Will you update the PDF? A minor v1.1 with a 1-page front note (and Tu where needed) is planned. This paper interprets the acoustic peaks of the cosmic microwave background (CMB) as resonance invariants structured within tolerance bands, consistent with the CAT-12 framework. Using published data from the Planck 2018 results (Planck Collaboration 2018), we analyze the ratios of successive acoustic peak amplitudes and positions without requiring raw FITS files. The results show that the second and third peaks form a resonance plateau at approximately 45% of the first peak amplitude, with deviations within ±2%. This plateau is interpreted as a manifestation of the Law of Dynamic Precision, which asserts that complex systems stabilize within resonance tolerance bands rather than exact integer values. Higher-order peaks exhibit structured decay consistent with entropy-constrained resonance ladders, analogous to resonance damping in planetary systems. By situating the CMB power spectrum within CAT-12’s resonance law, the study demonstrates that cosmological fluctuations obey the same invariants observed in astrophysical and thermodynamic systems. This strengthens the case that resonance tolerance bands represent a universal ordering principle, linking the early universe’s imprint to cross-domain coherence frameworks such as the Cross-Domain Coherence Ladder (CDCL).