C1_scope
C1_scope fixes the title and claim boundary for the C-1 paper interpreting GCIC as nonlocal theta. Paper authors cite this definition to lock the exact scope before drafting theorems or postulates. The implementation is a direct string assignment with no further computation or dependencies.
claimThe scope string for claim C-1 is ``GCIC as Nonlocal Theta''.
background
This module freezes exact claim scopes for each paper so drafts reference resolved strings rather than placeholders. It distinguishes machine-checked theorems, labeled postulates, modeling definitions, and out-of-scope items. Papers covered include C-1 on GCIC as Nonlocal Theta and C-2 on consciousness as phi-boundary. Upstream structures such as the nuclear density tiers and 8-tick phases supply the discrete phi-ladder and periodicity conventions used across these boundaries.
proof idea
This is a one-line definition that assigns the literal string ``GCIC as Nonlocal Theta''.
why it matters in Recognition Science
The definition anchors the C-1 paper boundary inside the Recognition framework, ensuring consistent citation of inherited theorems while separating them from C-2 postulates such as automatic collapse at C greater than or equal to 1. It supports the overall forcing chain by clarifying what counts as proved versus postulated before any phi-boundary or consciousness Hamiltonian arguments are invoked. No open scaffolding questions are closed here.
scope and limits
- Does not contain any theorem statements or Lean proofs.
- Does not specify content for C-2 consciousness emergence or collapse thresholds.
- Does not include biological EEG predictions or death operators.
- Does not address SelectionRule mechanisms or MutualInfo derivations.
formal statement (Lean)
60def C1_scope : String := "GCIC as Nonlocal Theta"
proof body
Definition body.
61
62/-! ## C-2: Consciousness as φ-Boundary
63
64### Theorems (cite freely)
65- `ConsciousnessHamiltonian.lam_rec_pos` — recognition length > 0
66- `ConsciousnessHamiltonian.boundary_cost_nonneg` — BoundaryCost ≥ 0
67- `ConsciousnessHamiltonian.consciousness_emerges_at_cost_minimum` — local min + thresholds → DefiniteExperience
68- `CollapseSelection.collapse_is_R_hat_threshold` — C≥1 → definite pointer under R̂
69- All C-1 theorems (inherited)
70
71### Postulates (must label)
72- `RecognitionAxioms.r_hat_automatic_collapse` — automatic collapse at C≥1
73- `recognition_equals_twice_gravity_hypothesis` — C = 2A bridge (explicitly labeled)
74
75### Definitions (must declare)
76- `ConsciousnessH` — BoundaryCost + GravitationalDebt + MutualInfo
77- `DefiniteExperience` — C≥1 ∧ A≥1 ∧ local min of ConsciousnessH
78- `BoundaryCost` — τ · J(extent/λ_rec)
79
80### Known limitations (must acknowledge)
81- `SelectionRule` is currently constant 0 — no branch-selection mechanism proved
82- `MutualInfo` uses heuristic Dirac-overlap model, not derived
83- `GravitationalDebt` uses Newtonian potential model
84
85### Out of scope for C-2
86- Death operator (C-3)
87- Berry phase
88- Biological EEG predictions
89-/