The Interior Observer Cosmological Framework: Paper 13 - The Gauge Thermal Transfer Principle — Closing the 230σ TCMB Gap with Zero New Parameters

The Interior Observer (IO) framework predicts TIO = 2. 6635 K for the CMB temperature. The observed value TCMB = 2. 7255 ± 0. 0006 K (COBE/FIRAS) represents a 230σ tension — the framework's most significant open problem. This paper resolves the gap by introducing the Gauge Thermal Transfer Principle (GTTP), the third physical principle of the IO framework alongside the Conformal Modular Principle (Paper 10) and the Baryon Dictionary Principle (Paper 12). The GTTP states that conformal thermal observables acquire a boundary-to-bulk transfer law d (ln ω) /dλ = Kgauge in conformal radial coordinate λ = ln (r/RU), where Kgauge = ln (1+γ²) is derived from the tangential Ashtekar-Barbero Laplacian at the horizon (Paper 10 §10. 1). The resulting correction Tₒbs = TIO × xKgauge = 2. 7253 K reduces the gap from 230σ to 0. 3σ with zero new parameters. The principle is established through a five-piece Temperature Transfer Theorem: KMS-rigidity forcing uniform frequency rescaling, Cauchy segment-additivity forcing linearity in conformal distance, the Paper 10 conformal no-go excluding Kgeom, a source selector identifying Kgauge as the unique surviving IO scalar with normalization traced to Paper 10's own Gaussian determinant arithmetic, and a temperature transfer ladder selecting n = 1 at 51. 7σ over the nearest competitor. Eight independent mechanisms are killed. A generating potential V (α) = −2 ln (cos α) — the Fubini-Study Kähler potential on CP¹ — unifies all gauge-sector observables across Papers 9–13: exp (V) gives the Paper 9 spectral norm, V'' gives the Paper 10 S² mass term, V' gives the Paper 12 baryon fraction, and V gives the Paper 13 temperature correction. The GTTP independently predicts γBI = 0. 23789 from FIRAS, in 0. 16% agreement with the canonical LQG value — the first determination of the Barbero-Immirzi parameter from a cosmological observable. v1. 0 (March 2026): Initial publication. Gauge Thermal Transfer Principle (GTTP) proposed as third physical principle. Tₒbs = TIO × xKgauge = 2. 7253 K (103σ → 0. 3σ). Five-piece Temperature Transfer Theorem. Eight mechanisms excluded. V (α) = −2 ln (cos α) generating potential unifying Papers 9–13. γBI = 0. 23789 predicted from FIRAS (0. 16% from canonical LQG value). Eighteen-round adversarial multi-AI review. Wolfram final verdict: publication-quality. v1. 2 (March 2026): Wolfram editorial review incorporated. Claim calibration: GTTP consistently presented as "proposed" third principle, not established. σ convention standardized to 103σ (FIRAS precision) ; ~230σ legacy convention explained. Evidential tier classification box added to §3. 3. Search protocol specified (§3. 1). "Exhaustive" downgraded to "systematic bounded. " Tone normalized for journal submission (killed → excluded, c-number wall → semiclassical separation). Abstract tightened ~30%. AI-process narrative reduced in main text. Section 3. 4 clarifier distinguishing theorem-level vs principle-level pieces. Single new identification arrow (Kgauge → σ) made explicit in §3. 3 and conclusion. v1. 3 Corrected the lithium issue identified in Paper 12.