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module module moderate

IndisputableMonolith.Foundation.CoherenceExponentUniqueness

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The CoherenceExponentUniqueness module defines the Fibonacci deficit k_fib(D) = 2^D - D and proves that the coherence exponent equals 5 uniquely at D=3 by isolating the sole point of agreement between deficit functions. Researchers tracing the forcing chain from T0 to T8 would cite these results to fix both the exponent and spatial dimension. The argument relies on explicit equality checks and case analysis at small integer D values.

claim$k_{fib}(D) := 2^D - D$, together with the statement that the coherence exponent is uniquely 5 when the dimension D equals 3.

background

The module introduces deficit functions that compare exponential growth against linear terms to isolate a unique exponent value. The Fibonacci deficit is given explicitly as k_fib(D) = 2^D - D. Companion definitions include k_int together with lemmas that test agreement or disagreement of these functions at successive small integers D.

proof idea

The module first defines k_fib and k_int, then establishes disagreement at D=1,2,4, agreement at D=3, equality of both functions to 5 at D=3, and finally the uniqueness of the exponent at D=3. All steps proceed by direct evaluation on a finite set of integers.

why it matters in Recognition Science

This module supplies the uniqueness result that fixes the coherence exponent at 5 when D=3, thereby supporting the eight-tick octave (T7) and the emergence of three spatial dimensions (T8) in the forcing chain. It feeds downstream statements on the mass ladder and the native-unit constants.

scope and limits

declarations in this module (16)