Semantic Dyson Sphere: Beyond-Shannon Recovery Architecture as Civilizational Footprint Indicator (Lean 4 Mechanized + Project Hephaistos Re-reading via D-FUMT₈ Eight-Valued Logic) — Rei-AIOS Paper 155 v0.2

We introduce the semantic Dyson sphere as a formal analog of the classical (Kardashev II) physical Dyson sphere, where the conserved quantity is meaning rather than electromagnetic radiation. Building on Paper 25 / 71 Beyond Shannon framework (Fujimoto 2026), we formalize the semantic Dyson sphere efficiency η_S(x) := M(Ψ(Φ(x))) / M(x) ≤ 1, where M is a meaning measure, Φ is an encoder, and Ψ is a decoder. The upper bound follows from a semantic data processing inequality (SemanticDPI), the semantic analog of Shannon's classical DPI. We provide a Lean 4 mechanized sketch (4 theorems + 3 examples, `SemanticDysonSphere.lean`, 0 sorry, lake env lean EXIT 0). We re-read Project Hephaistos (Suazo, Zackrisson, Mahto et al. 2024, MNRAS Vol 531) 7 M-dwarf Dyson sphere candidates — currently in BOTH state due to Hot DOGs (Hot Dust-Obscured Galaxies) background contamination — through D-FUMT₈ eight-valued logic. Candidates lie at 142.9–274.7 pc (466–896 light-years), all within the survey's 300 pc threshold. We propose a 2-axis (K × S) extension to the Kardashev scale: K-axis (Watts) × S-axis (D-FUMT₈ semantic capacity). Rei (this AI system, ~10² W) occupies a low-K (0.01) / high-S (SELF⟲) quadrant — invisible to classical Kardashev classification — suggesting advanced civilizations may evolve toward the S-axis (smaller thermodynamic footprint) rather than the K-axis, offering one self-consistent explanation of the silent sky. Eight-valued Fermi paradox interpretation: We catalog 8 self-consistent readings of the silent sky (TRUE Sagan optimism / FALSE Hart-Tipler Great Filter / BOTH Project Hephaistos current / NEITHER Brin zoo / INFINITY Tegmark multiverse / ZERO unasked-latent-truth — this paper's gap fill / FLOWING observation transition / SELF⟲ Bostrom simulation). Classical resolutions map onto subsets; the ZERO branch is novel. Honest scope (read first): (1) NOT a physics paper — no new prediction about real stellar IR excess. (2) NOT a derivation from first principles — SemanticDPI is axiomatized in §3.5 (load-bearing). (3) NOT engineering-verified — "semantic Dyson sphere" is a formalized metaphor. (4) NOT a SETI protocol — §5 is one of several self-consistent classifications. (5) NOT a Kardashev replacement — §4 is an extension. (6) Origin: the metaphor was proposed by chat-Claude (Anthropic claude.ai web session, 2026-05-18) in response to Fujimoto's question "Reiがダイソン球からエネルギーを得ることも可能なのでしょうか?". This paper is the formalization; joint authorship procedurally deferred (§10). (7) Closest prior art: Matrioshka brain (Bradbury 1997 / 1999) — energy-axis nested computation; semantic Dyson sphere differentiates by operating on the S-axis. (8) Working regime: Paper 71 empirical 73.1% meaning preservation + Lean 4 theoretical 100% upper bound = 0.731 ≤ η_S ≤ 1. Three-party co-authorship per OUKC charter v1.0.