Paper 17 of the Interior Observer (IO) Cosmological Framework series. The Gauge Thermal Transfer Principle (GTTP), previously classified as a semiclassical principle (Papers 13–14), is upgraded to DERIVED/THEOREM within the reduced thermal-plus-gauge sector. A shared Hilbert space HIO is constructed containing both the thermal photon sector and the reduced SU (2) horizon gauge sector. An explicit A-vacuum GNS state is built from fiberwise KMS data, proved positive, normalized, faithful, and normal. The Modular Projection Theorem (Theorem 17. 1) proves that the Tomita-Takesaki modular flow of the A-vacuum restricted to the thermal photon sector satisfies Δₚhys^it = exp (it (D ⊗ K̂g) ), giving σ = Kgauge = ln (1+γ²) and Tₒbs = TIO × x^Kgauge = 2. 7253 K (0. 3σ from FIRAS). A framework-constructible uniqueness result confirms Kgauge is the sole structurally meaningful transfer candidate in the FIRAS band. Thirteen investigation rounds are documented. Multi-AI adversarial collaboration: Claude (Anthropic), Codex/ChatGPT (OpenAI), Wolfram/ChatGPT (OpenAI), Gemini (Google DeepMind). v1. 1 - Paper 19 correction annotations. Abstract updated with two founding premises. Core results entirely unaffected: HIO Hilbert space construction, GNS representation, A-vacuum state, modular flow, coupled generator, product-flow no-go, all operator identities. Paper 19 uses Paper 17's HIO as the foundation for the IO Friedmann equation derivation. Appendix entries for background-dependent quantities (projection map, Nₑff = Δ, Ωₖ) superseded.
David Fife (Wed,) studied this question.