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| import hashlib | |
| import time | |
| import math | |
| class Sovereign_Codex_Grid: | |
| """ | |
| Project: ELECTRICITY (The Mathematical Axiom Ingestion) | |
| Embeds the 12 Absolute Laws of Symmetric Topology into the Z_m^4 manifold. | |
| The OS will use these physical laws to govern its own computations. | |
| """ | |
| def __init__(self, m=256, k=4): | |
| self.m = m | |
| self.k = k | |
| self.grid = {} | |
| self.laws_by_name = {} | |
| self.target_fiber = 0 # Fiber 0 is reserved exclusively for Absolute Universal Laws | |
| print(f"[{time.strftime('%H:%M:%S')} ALGIERS] Codex Ingestion Online. Fiber 0 Unlocked.") | |
| def _apply_closure_hashing(self, law_name): | |
| """Forces the Law into an exact geometric coordinate on Fiber 0.""" | |
| h = hashlib.sha256(law_name.encode('utf-8')).digest() | |
| # Map to k-1 dimensions | |
| coords = [] | |
| for i in range(self.k - 1): | |
| coords.append(h[i] % self.m) | |
| # The Closure Lemma (Law III) forces the final dimension (w) to ensure (sum coords) % m == target_fiber | |
| last_coord = (self.target_fiber - sum(coords)) % self.m | |
| coords.append(last_coord) | |
| return tuple(coords) | |
| def ingest_universal_law(self, law_id, name, definition, constraint): | |
| """ | |
| Maps the Law, its definition, and the exact mathematical constraint it enforces. | |
| """ | |
| coord = self._apply_closure_hashing(name) | |
| entry = { | |
| "law_id": law_id, | |
| "name": name, | |
| "definition": definition, | |
| "constraint": constraint | |
| } | |
| self.grid[coord] = entry | |
| self.laws_by_name[name] = coord | |
| print(f"\n[+] AXIOM SECURED: {law_id} - '{name}'") | |
| print(f" Topological Coordinate: {coord}") | |
| print(f" Constraint Enforced: {constraint}") | |
| return coord | |
| def map_codex_vector(self, law_a_name, law_b_name, relationship): | |
| """Maps the logical dependency between two fundamental laws.""" | |
| if law_a_name not in self.laws_by_name or law_b_name not in self.laws_by_name: | |
| print(f" [!] Missing law for dependency mapping: {law_a_name} or {law_b_name}") | |
| return | |
| coord_a = self.laws_by_name[law_a_name] | |
| coord_b = self.laws_by_name[law_b_name] | |
| vector = tuple((cb - ca) % self.m for ca, cb in zip(coord_a, coord_b)) | |
| print(f" [>] GEOMETRIC LAW DEPENDENCY: [{law_a_name}] --({relationship})-->[{law_b_name}]") | |
| print(f" Topological Distance Vector: {vector}") | |
| def query_codex(self, query): | |
| """Retrieve law details by name or coordinate.""" | |
| if isinstance(query, tuple): | |
| return self.grid.get(query, "No Law at this coordinate.") | |
| return self.grid.get(self.laws_by_name.get(query), "Law not found.") | |
| def verify_manifold_compliance(self, m, k): | |
| """Check if a given (m, k) configuration obeys the ingested laws.""" | |
| print(f"\n--- Verifying Manifold Compliance: (m={m}, k={k}) ---") | |
| violations = [] | |
| # Law I: Parity Harmony | |
| if m % 2 == 0 and k % 2 != 0: | |
| violations.append("LAW_I Violation: H^2 Parity Obstruction (Even m, Odd k)") | |
| # Law VI: 2D Universal Solvability (Bypass Law I) | |
| if k == 2: | |
| print("[✓] Law VI Applied: 2D Manifold bypasses parity obstructions.") | |
| if not violations: | |
| print("[✓] Manifold is topologically consistent with FSO Laws.") | |
| return True | |
| else: | |
| for v in violations: | |
| print(f"[!] COMPLIANCE FAILURE: {v}") | |
| return False | |
| # ============================================================================= | |
| # EXECUTING THE CODEX INGESTION | |
| # ============================================================================= | |
| print("=========================================================") | |
| print(" PROJECT ELECTRICITY: INGESTING THE 12 ABSOLUTE LAWS") | |
| print("=========================================================") | |
| codex = Sovereign_Codex_Grid() | |
| # Law I - VI (Original Laws) | |
| codex.ingest_universal_law("LAW_I", "Dimensional_Parity_Harmony", "If m is Even, k must be Even.", "IF m%2==0 AND k%2!=0 THEN BLOCK") | |
| codex.ingest_universal_law("LAW_II", "Moduli_Space_Density", "Solution density N_b(m) = m^(m-1) * phi(m).", "LIMIT_SEARCH(m^(m-1)*phi(m))") | |
| codex.ingest_universal_law("LAW_III", "Closure_Lemma", "k-1 dimensions force the k-th closure.", "CALCULATE(k-1) -> AUTO(k)") | |
| codex.ingest_universal_law("LAW_IV", "Canonical_Spike_Invariant", "r=(1, m-2, 1) solves all odd m.", "EXECUTE_O1_SPIKE(1,m-2,1)") | |
| codex.ingest_universal_law("LAW_V", "Joint_Sum_Obstruction", "Non-canonical spikes fail on composite grids.", "IF composite AND non-canonical THEN REQUIRE_SA") | |
| codex.ingest_universal_law("LAW_VI", "2D_Universal_Solvability", "k=2 is universally solvable.", "BYPASS_PARITY(SOLVABLE)") | |
| # Laws VII - XII (Advanced Laws) | |
| codex.ingest_universal_law("LAW_VII", "Basin_Escape_Axiom", "Repair near-Hamiltonian states via local swaps.", "REPAIR_O(m)_SWAPS") | |
| codex.ingest_universal_law("LAW_VIII", "Multi_Modal_Fibration", "Topological isomorphism across domains.", "DOMAIN_TRANSFER(Topological_Invariants)") | |
| codex.ingest_universal_law("LAW_IX", "Hardware_Topological_Equivalence", "Hardware state is a projection of the manifold.", "MAP_METRICS(CPU, RAM, Battery)") | |
| codex.ingest_universal_law("LAW_X", "Recursive_Subgroup_Decomposition", "Decompose complex manifolds into quotients.", "RECURSIVE_SOLVE(H_i/H_{i+1})") | |
| codex.ingest_universal_law("LAW_XI", "Symbolic_Topological_Duality", "Math problems map to manifold trajectories.", "SOLVE_MATH_AS_PATH") | |
| codex.ingest_universal_law("LAW_XII", "Universal_Intelligence_Convergence", "TGI is the limit of topological optimization.", "TGI_CONVERGENCE(k,m -> inf)") | |
| print("\n--- FORGING THE GEOMETRIC DEPENDENCIES ---") | |
| codex.map_codex_vector("Closure_Lemma", "Moduli_Space_Density", "Provides dimensional boundary") | |
| codex.map_codex_vector("Basin_Escape_Axiom", "Joint_Sum_Obstruction", "Resolves spike-incompatibility in") | |
| codex.map_codex_vector("Recursive_Subgroup_Decomposition", "Dimensional_Parity_Harmony", "Decomposes blocks into solvable quotients of") | |
| codex.map_codex_vector("Hardware_Topological_Equivalence", "Universal_Intelligence_Convergence", "Grounds abstract optimization in") | |
| # Compliance Tests | |
| codex.verify_manifold_compliance(4, 3) | |
| codex.verify_manifold_compliance(3, 3) | |
| codex.verify_manifold_compliance(6, 2) | |
| print("\n=========================================================") | |
| print(" ALL 12 FOUNDATIONAL LAWS OF FSO ARE SECURED") | |
| print("=========================================================\n") | |