IndisputableMonolith.Modal

   1/-
   2Copyright (c) 2025 Recognition Science. All rights reserved.
   3Released under MIT license as described in the file LICENSE.
   4Authors: Recognition Science Contributors
   5-/
   6import IndisputableMonolith.Modal.Possibility
   7import IndisputableMonolith.Modal.Actualization
   8import IndisputableMonolith.Modal.ModalGeometry
   9
  10/-!
  11# RS Modal Logic: The Grammar of Possibility
  12
  13This module aggregates the complete RS modal logic formalization:
  14- **Possibility**: What COULD BE
  15- **Actualization**: How possibilities become actual
  16- **ModalGeometry**: The shape of possibility space
  17
  18## The RS Modal System
  19
  20Unlike classical modal logic (Kripke frames, possible worlds), RS modal logic
  21is **grounded in physics**:
  22
  23| Classical | RS Modal | Grounding |
  24|-----------|----------|-----------|
  25| Possible worlds | Config space | Ledger states |
  26| Accessibility | Possibility operator P | Finite J-cost paths |
  27| Necessity □ | ∀ y ∈ P(c) | Cost-forced |
  28| Possibility ◇ | ∃ y ∈ P(c) | Cost-permitted |
  29| Actuality | Actualization A | J-minimizing selection |
  30
  31## Key Results
  32
  331. **Identity is unique attractor**: ∀c, A^∞(c) = 1
  342. **Change is cheaper than stasis** (for x ≠ 1): J_change < J_stasis
  353. **Modal Nyquist**: 8-tick limits modal resolution
  364. **Born rule emerges**: P[γ] ∝ exp(-C[γ])
  375. **Collapse is built-in**: C ≥ 1 forces selection
  38
  39## Answering Fundamental Questions
  40
  41This modal logic answers:
  42- **Why does anything happen?** Stasis costs more than change (for x ≠ 1)
  43- **What are counterfactuals?** Alternative cost-equivalent paths
  44- **What is contingency?** When multiple paths have equal minimal cost
  45- **What is necessity?** When unique path has minimal cost
  46- **Why does time flow?** 8-tick structure forces temporal direction
  47
  48## Usage
  49
  50```lean
  51import IndisputableMonolith.Modal
  52
  53-- The possibility set
  54#check Modal.Possibility
  55
  56-- The actualization operator
  57#check Modal.A
  58
  59-- Modal operators
  60#check Modal.Necessary  -- □
  61#check Modal.Possible   -- ◇
  62
  63-- Key theorems
  64#check Modal.identity_prefers_stasis
  65#check Modal.why_anything_happens
  66#check Modal.modal_nyquist
  67```
  68-/
  69
  70namespace IndisputableMonolith
  71
  72namespace Modal
  73
  74-- Re-exports from submodules
  75-- (The imports above make these available)
  76
  77/-! ## Top-Level Summary -/
  78
  79/-- Complete RS Modal Logic status. -/
  80def rs_modal_logic_status : String :=
  81  "╔══════════════════════════════════════════════════════════════╗\n" ++
  82  "║       RS MODAL LOGIC: THE GRAMMAR OF POSSIBILITY             ║\n" ++
  83  "╠══════════════════════════════════════════════════════════════╣\n" ++
  84  "║                                                              ║\n" ++
  85  "║  CORE MODULES:                                               ║\n" ++
  86  "║  ├─ Possibility.lean     What COULD BE                       ║\n" ++
  87  "║  ├─ Actualization.lean   How possibilities become actual     ║\n" ++
  88  "║  └─ ModalGeometry.lean   Shape of possibility space          ║\n" ++
  89  "║                                                              ║\n" ++
  90  "╠══════════════════════════════════════════════════════════════╣\n" ++
  91  "║  PHILOSOPHICAL ANSWERS:                                      ║\n" ++
  92  "║                                                              ║\n" ++
  93  "║  Q: Why does anything happen?                                ║\n" ++
  94  "║  A: J_stasis > J_change for x ≠ 1                            ║\n" ++
  95  "║     (Staying away from identity costs more than moving)      ║\n" ++
  96  "║                                                              ║\n" ++
  97  "║  Q: What are counterfactuals?                                ║\n" ++
  98  "║  A: Alternative paths in P(c) not chosen by A                ║\n" ++
  99  "║     (Unrealized finite-cost alternatives)                    ║\n" ++
 100  "║                                                              ║\n" ++
 101  "║  Q: What is necessity vs contingency?                        ║\n" ++
 102  "║  A: □p = forced by cost, ◇p = permitted by cost              ║\n" ++
 103  "║     Contingency = degeneracy (multiple cost-equivalents)     ║\n" ++
 104  "║                                                              ║\n" ++
 105  "║  Q: Why is there something rather than nothing?              ║\n" ++
 106  "║  A: J(0) = ∞ (nothing costs infinity)                        ║\n" ++
 107  "║     J(1) = 0 (existence costs nothing)                       ║\n" ++
 108  "║                                                              ║\n" ++
 109  "╠══════════════════════════════════════════════════════════════╣\n" ++
 110  "║  LEAN STATUS:                                                ║\n" ++
 111  "║  • Possibility operator: DEFINED                             ║\n" ++
 112  "║  • Actualization operator: DEFINED                           ║\n" ++
 113  "║  • Modal necessity/possibility: DEFINED                      ║\n" ++
 114  "║  • Cost of stasis/change: DEFINED                            ║\n" ++
 115  "║  • Modal geometry: DEFINED                                   ║\n" ++
 116  "║  • Key theorems: PARTIALLY PROVED (some sorry)               ║\n" ++
 117  "║                                                              ║\n" ++
 118  "║  NEXT STEPS:                                                 ║\n" ++
 119  "║  • Complete numerical bounds for why_anything_happens        ║\n" ++
 120  "║  • Prove modal completeness fully                            ║\n" ++
 121  "║  • Connect to ULQ modal logic stubs                          ║\n" ++
 122  "║  • Write paper: 'The Geometry of Could-Be'                   ║\n" ++
 123  "╚══════════════════════════════════════════════════════════════╝"
 124
 125#check rs_modal_logic_status
 126
 127end Modal
 128
 129end IndisputableMonolith
 130