mp_physical
plain-language theorem explainer
The Meta-Principle that nothing cannot recognize itself is restated as three cost statements: defect diverges to infinity as x approaches 0 from above, exactly one positive real has zero defect, and that real equals 1. Researchers deriving ontology from J-cost minimization cite it to replace assumed existence with a selection outcome. The proof is a term-mode constructor that directly assembles nothing_cannot_exist, rs_exists_unique, and a projection from rs_exists_unique_one.
Claim. Let defect denote the J-cost functional on positive reals. Then $ (∀ C ∈ ℝ, ∃ ε > 0, ∀ x ∈ ℝ, (0 < x ∧ x < ε) → C < defect(x)) ∧ (∃! x ∈ ℝ, 0 < x ∧ defect(x) = 0) ∧ (∀ x ∈ ℝ, (0 < x ∧ defect(x) = 0) → x = 1) $.
background
RSExists(x) holds when x > 0 and defect(x) = 0, where defect coincides with the J-cost functional; this makes existence the outcome of cost minimization rather than a primitive predicate. The module treats existence and truth as verifiable selection results under the Recognition Composition Law, with the rule that x exists precisely when defect collapses to zero under coercive projection. Upstream, nothing_cannot_exist states that for any real bound C there is ε > 0 such that defect(x) > C whenever 0 < x < ε, while the sibling rs_exists_unique asserts that the zero-defect point is unique.
proof idea
The proof is a term-mode constructor that packages three upstream results without further tactics: the first conjunct is supplied directly by nothing_cannot_exist, the second by rs_exists_unique, and the third by a lambda that applies the left-to-right direction of rs_exists_unique_one to any RSExists hypothesis.
why it matters
This declaration derives the Meta-Principle inside the cost foundation, replacing a logical tautology with a physical statement about non-selectability of the zero configuration. It anchors the operational ontology of RSExists and RSTrue, linking the forcing chain (T0-T8) to concrete existence at unity. No downstream uses are recorded, but the result closes the step from LawOfExistence to physical selection.
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