From Structural Signal to Observable Prediction: Bridge Assumptions B1-B3 in Hierarchical Compression
From Structural Signal to Observable Prediction: Bridge Assumptions B1-B3 in Hierarchical Compression
This paper formalizes the bridge assumptions B1–B3 that connect the proved Hierarchical Compression (HC) entropy identity to domain-specific observables, conducts a 45-row cross-domain audit of the existing corpus, and identifies bridge incompleteness as the dominant failure mode. Two empirical channels are validated: gravitational-wave ringdown (surface gravity κM confirmed as B2 bridge coordinate across 382 NR simulations) and transformer inference (NHIM admissibility confirmed with normal-bundle contraction ρN=0.730). Together these bracket the degenerate and non-degenerate cases of the generalized convergence theorem. Terminology. The foundational publications developed the framework under the name Harmonic Coherence, reflecting its origin in physics domains where phase-locked resonance and coherent-structure formation are the operative bridge mechanisms. As the framework extended to number theory, complexity theory, and algebraic geometry—domains with no physical harmonic content—the name became a source of friction. This paper uses Hierarchical Compression (HC) for the domain-independent Layer 1 framework and reserves Harmonic Coherence (always spelled out, never abbreviated) for the Layer 2 physics-domain bridge instantiation. The abbreviation HC refers exclusively to the framework.
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cross-domain audit, 引力波铃宕, B3 entropy attribution, Условие C, 跨域审计, افتراضات الجسر, 双対多様体分解, quasinormal modes, hierarchical compression, bridge assumptions, Междисциплинарный аудит, 障害分類, normally hyperbolic invariant manifold, المتشعب الثابت طبيعيًا الزائدي, 失效分类, Condition C, contraction mapping, surface gravity, Kerr coordinates, 条件 C, Динамика трансформеров, التدقيق عبر المجالات, Kerr ringdown, Нормально гиперболическое инвариантное многообразие, Harmonic Coherence, corpus audit, spectral radius, dual-manifold decomposition, 正規双曲的不変多様体, transformers, harmonic coherence, تصنيف الأعطال, ديناميكا المحوّلات, failure taxonomy, gravitational waves, 对偶流形分解, transformer dynamics, transformer, observable prediction, رنين الموجات الثقالية, Hodge conjecture, 分层压缩\, falsifiability, gravitational-wave ringdown, 橋渡し仮定, entropy minimization, تحليل المتشعب المزدوج, الشرط C, 桥接假设, 法向双曲不变流形, トランスフォーマー力学, B2 structure preservation, NHIM, 分野横断的監査, Разложение на двойственные многообразия, Таксономия отказов, Hierarchical Compression, 重力波リングダウン, 階層的圧縮, \Гравитационно-волновой звон, layered framework, entropy reduction, B1 admissibility, Иерархическое сжатие, الضغط الهرمي, Мостовые предположения, regularity conditions
cross-domain audit, 引力波铃宕, B3 entropy attribution, Условие C, 跨域审计, افتراضات الجسر, 双対多様体分解, quasinormal modes, hierarchical compression, bridge assumptions, Междисциплинарный аудит, 障害分類, normally hyperbolic invariant manifold, المتشعب الثابت طبيعيًا الزائدي, 失效分类, Condition C, contraction mapping, surface gravity, Kerr coordinates, 条件 C, Динамика трансформеров, التدقيق عبر المجالات, Kerr ringdown, Нормально гиперболическое инвариантное многообразие, Harmonic Coherence, corpus audit, spectral radius, dual-manifold decomposition, 正規双曲的不変多様体, transformers, harmonic coherence, تصنيف الأعطال, ديناميكا المحوّلات, failure taxonomy, gravitational waves, 对偶流形分解, transformer dynamics, transformer, observable prediction, رنين الموجات الثقالية, Hodge conjecture, 分层压缩\, falsifiability, gravitational-wave ringdown, 橋渡し仮定, entropy minimization, تحليل المتشعب المزدوج, الشرط C, 桥接假设, 法向双曲不变流形, トランスフォーマー力学, B2 structure preservation, NHIM, 分野横断的監査, Разложение на двойственные многообразия, Таксономия отказов, Hierarchical Compression, 重力波リングダウン, 階層的圧縮, \Гравитационно-волновой звон, layered framework, entropy reduction, B1 admissibility, Иерархическое сжатие, الضغط الهرمي, Мостовые предположения, regularity conditions
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