pith. sign in
theorem

eight_tick_forces_D3

proved
show as:

Why this theorem is linked from GWTC-4.0: Tests of General Relativity. I. Overview and General Tests unclear

Pith linked this Lean declaration because the review connected a specific passage in the paper to this theorem. The relation tag says how strong that connection is; it is not a generic placeholder.

The final mass and final spin as inferred from the low- and high-frequency parts of the waveform are consistent with each other.

Relation between the paper passage and the cited Recognition theorem.

The 8-tick cycle forces space dimension D = 3.

module
IndisputableMonolith.Foundation.DimensionForcing
domain
Foundation
line
155 · github
papers citing
24 papers (below)

plain-language theorem explainer

If the eight-tick period computed from spatial dimension D equals the fixed eight_tick, then D equals 3. Researchers closing the T7-T8 step in the Recognition Science forcing chain cite this to derive three spatial dimensions from the self-similar octave. The proof is a one-line wrapper that unfolds the power-of-two definition and applies the power_of_2_forces_D3 lemma.

Claim. If $2^D = 8$, then $D = 3$, where $D$ is a natural number denoting spatial dimension and 8 is the fixed eight-tick period.

background

The DimensionForcing module proves that spatial dimension D equals 3 is forced by the RS framework. Dimension is the abbrev for natural numbers. EightTickFromDimension D is defined as 2^D, the period required for ledger coverage in D dimensions. The module_doc states that the 8-tick cycle synchronizes with the 45-tick cumulative phase via lcm(8,45)=360, which uniquely identifies D=3 through the relation 2^D=8.

proof idea

This is a one-line wrapper. It introduces the hypothesis, unfolds EightTickFromDimension and eight_tick at the hypothesis, then applies the sibling lemma power_of_2_forces_D3.

why it matters

The theorem supplies the eight-tick forcing step used by spinor_eight_tick_forces_D3 and why_D_equals_3. It fills the T7 eight-tick octave (period 2^3) to T8 D=3 step in the unified forcing chain. The result shows that the self-similar fixed point and eight-tick period select three spatial dimensions, consistent with Bott periodicity and the unique spinor structure at D=3.

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