`inevitability`

proved

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module: IndisputableMonolith.Foundation.InevitabilityStructure
domain: Foundation
line: 172 · github
papers citing: 2 papers (below)

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IndisputableMonolith.Foundation.InevitabilityStructure on GitHub at line 172.

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formal source

 169
 170    **STATUS**: THEOREM (logical reduction to gates)
 171    **IMPORTANCE**: This is the central uniqueness theorem of Recognition Science. -/
 172theorem inevitability (F : AlternativeFramework)
 173    (h_zero : zero_parameter F)
 174    (h_obs : F.derives_observables) :
 175    (F.cost = RS_framework.cost ∧ F.selection = RS_framework.selection) ∨
 176    (∃ g ∈ all_gates, violates_gate F g) := by
 177  by_cases h_rs : (F.cost = RS_framework.cost ∧ F.selection = RS_framework.selection)
 178  · left; exact h_rs
 179  · right
 180    -- h_rs : ¬(F.cost = RS_framework.cost ∧ F.selection = RS_framework.selection)
 181    -- Split on whether costs match
 182    by_cases h_cost : F.cost = RS_framework.cost
 183    · -- Costs match, so selection must differ
 184      have h_sel : F.selection ≠ RS_framework.selection := by
 185        intro h_sel_eq
 186        exact h_rs ⟨h_cost, h_sel_eq⟩
 187      use gate_selection_rule
 188      constructor
 189      · simp [all_gates]
 190      · unfold violates_gate
 191        simp [gate_selection_rule, h_sel]
 192    · -- Costs differ
 193      use gate_cost_uniqueness
 194      constructor
 195      · simp [all_gates]
 196      · unfold violates_gate
 197        simp [gate_cost_uniqueness, h_cost]
 198
 199/-! ## The Choke Point Analysis -/
 200
 201/-- A choke point is a place where alternatives can hide unless proven closed. -/
 202structure ChokePoint where

papers checked against this theorem (showing 2 of 2)

Mixup on example pairs improves neural network generalization
unclear · 1710.09412

"Our experiments on the ImageNet-2012, CIFAR-10, CIFAR-100, Google commands and UCI datasets show that mixup improves the generalization of state-of-the-art neural network architectures."
Self-distillation turns feedback into denser RL signals
unclear · 2601.20802

"The SDPO gradient is a (negated) logit-level policy gradient where the advantages are estimated using the self-teacher."