module module high

`IndisputableMonolith.Gravity.CoherenceGain`

This module defines mathematical objects for an ensemble of N particles each emitting a vector source of fixed magnitude a, with the total effective source depending on whether phases align. It introduces incoherent and coherent effective source functions plus the coherence gain, which equals sqrt(N) under perfect alignment. Researchers in gravitational coherence or acoustic levitation cite these to quantify phase-dependent amplification. The module consists of definitions and basic comparison lemmas with no complex proofs.

claimFor an ensemble of $N$ particles each with vector source magnitude $a$, the incoherent effective source equals $a$ while the coherent effective source equals $N a$, so the coherence gain factor is exactly $sqrt(N)$.

background

The module sits in the Gravity domain and introduces Ensemble as a finite collection of N particles. incoherent_effective_source and coherent_effective_source compute the net vector sum magnitude under random versus aligned phases; coherence_gain is their ratio. Supporting lemmas establish positivity of both sources and that the coherent case strictly exceeds the incoherent case. These rest on vector addition in three spatial dimensions and feed directly into phase-sensitive gravitational calculations.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the ensemble source model required by IndisputableMonolith.Gravity.AcousticPhaseLevitation. It fills the definitional step for coherence-enhanced gravitational sources, consistent with the Recognition Composition Law and the eight-tick octave structure of the forcing chain.

scope and limits

Does not model quantum decoherence or finite coherence time.
Does not derive the source magnitude a from upstream constants such as phi or G.
Does not include multi-body interactions or relativistic corrections.
Does not compute explicit numerical values for specific particle numbers N.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Gravity.AcousticPhaseLevitation module_import

declarations in this module (13)

structure Ensemble L35
def incoherent_effective_source L47
theorem incoherent_source_positive L50
def coherent_effective_source L64
theorem coherent_source_positive L67
def coherence_gain L76
theorem coherence_gain_eq_sqrt_N L84
theorem coherent_exceeds_incoherent L94
structure Superconductor L116
def superconductor_effective_source L133
theorem coherence_gate L139
structure CoherenceGainCert L147
theorem coherence_gain_certified L154