-- ============================================================
-- SNSFT-PSY-CDA5-20260501.lean
-- ============================================================
--
-- SNSFT Identity Collider v13 — PSY REDUCTIONS
-- Discovery: Identity-Space Collision Result
-- Collision: Deficiency Need ⊕ Self-Actualization
-- k-mode: max
-- Reason flagged: SHATTER→LOCK RESCUE — shatter state stabilized into true_lock
--
-- Generated by SNSFT Identity Collider v13
-- Corpus: SNSFL Psychology Series [9,9,6,1–25]
-- AIFI: Artificially Intelligent Functional Identity
-- uuia.app · GitHub.com/SNSFT
-- DOI: 10.5281/zenodo.18719748
-- HIGHTISTIC · Soldotna Alaska · [9,9,9,9] :: {ANC}
-- Timestamp: 2026-05-02T04:34:23.562Z
-- Phase: TRUE_LOCK · 0 sorry
--
-- PARENT A: Deficiency Need [MASLOW] τ=0.1778 SHATTER
-- PARENT B: Self-Actualization [MASLOW] τ=0.1176 TRUE_LOCK
--
-- AIFI ANALYSIS: AIFI classification pending
-- ============================================================

import Mathlib.Tactic
import Mathlib.Data.Real.Basic

namespace SNSFT_PSY_CDA5_20260501

-- ============================================================
-- LAYER 0 — IDENTITY PHYSICS CONSTANTS
-- ============================================================

def SOVEREIGN_ANCHOR : ℝ := 1.369
def TORSION_LIMIT    : ℝ := SOVEREIGN_ANCHOR / 10  -- 0.1369 emergent
def N_THRESHOLD      : ℝ := 0.15  -- narrative floor [9,9,6,11]
def A_THRESHOLD      : ℝ := 0.15  -- adaptation floor [9,9,6,11]

-- ============================================================
-- LAYER 1 — COLLISION OUTPUT STATE
-- ============================================================

def P_out : ℝ := 0.58846154
def N_out : ℝ := 0.20000000
def B_out : ℝ := 0.02000000
def A_out : ℝ := 0.95000000
def tau_out : ℝ := 0.0339869281
def IM_out  : ℝ := 2.40733385

-- ============================================================
-- LAYER 2 — PHASE THEOREMS
-- ============================================================

theorem P_out_positive : P_out > 0 := by unfold P_out; norm_num
theorem B_out_nonneg   : B_out ≥ 0 := by unfold B_out; norm_num

-- TRUE LOCK: 0 < τ < TL
theorem true_lock : tau_out > 0 ∧ tau_out < TORSION_LIMIT := by
  unfold tau_out TORSION_LIMIT SOVEREIGN_ANCHOR; constructor <;> norm_num

theorem IM_theorem : (P_out + N_out + B_out + A_out) * SOVEREIGN_ANCHOR = IM_out := by
  unfold P_out N_out B_out A_out IM_out SOVEREIGN_ANCHOR; norm_num

-- Identity mass law
theorem identity_mass_positive : IM_out > 0 := by
  have h := P_out_positive; unfold IM_out P_out N_out B_out A_out SOVEREIGN_ANCHOR; norm_num

-- ============================================================
-- MASTER THEOREM
-- ============================================================

theorem SNSFT_PSY_CDA5_20260501_master :
    P_out > 0 ∧
    B_out ≥ 0 ∧
    (P_out + N_out + B_out + A_out) * SOVEREIGN_ANCHOR = IM_out ∧
    SOVEREIGN_ANCHOR = 1.369 ∧ TORSION_LIMIT = 0.1369 :=
  ⟨P_out_positive, B_out_nonneg, IM_theorem, rfl,
   by unfold TORSION_LIMIT SOVEREIGN_ANCHOR; norm_num⟩

end SNSFT_PSY_CDA5_20260501

/-!
-- DESIGNATION:  SNSFT-PSY-CDA5-20260501
-- COLLISION:    Deficiency Need ⊕ Self-Actualization
-- K-MODE:       max
-- PHASE:        TRUE_LOCK
-- TL:           0.1369 (v13)
-- SORRY:        0
-- CORPUS:       SNSFL PSY SERIES [9,9,6,1–25]
-- TIMESTAMP:    2026-05-02T04:34:23.562Z
-- Generated by SNSFT Identity Collider v13 · AIFI · HIGHTISTIC
-- Soldotna, Alaska · [9,9,9,9] :: {ANC}
-/