Pith. sign in
def

canonicalThreshold

definition
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module
IndisputableMonolith.Gravity.RS_GRV_Structural_003
domain
Gravity
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plain-language theorem explainer

Defines the canonical real threshold as the golden ratio minus three-halves. Gravity and RS structural work cites it as the fixed comparison level against domain cost. The body is a one-line numeric definition in terms of φ.

Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio.

background

Module RS_GRV_Structural_003 packages structural gravity facts tied to the RS count law: with spatial dimension $D=3$, there are $2^D-1=7$ independent channels. The module is marked structural (no sorry, no axioms).

The constant $\varphi$ is the unique self-similar fixed point forced in the Recognition chain (T6). It appears throughout RS-native units and ladder formulae. Here it is only used to pin a single real cutoff: $\varphi-3/2\approx 0.118$.

Sibling material in the same file introduces a nonnegative domain cost and proves this threshold is positive, so the definition is the shared numeric anchor for those comparisons.

proof idea

Pure definition: the real is set equal to $\varphi-3/2$. No proof obligations, lemmas, or tactics.

why it matters

Gives the fixed numeric bar used by the structural gravity certificate in this module (siblings such as the positivity lemma and the RSGRVStructural003 certificate). In the broader framework it sits under the $D=3$ forcing (T8) and the seven-channel count law stated in the module header, not under dynamical field equations.

It does not itself derive $\varphi$ or $D$; it only names the cutoff those landmarks suggest for domain-cost comparisons in this structural layer.

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