fso_codex_ingestion.py

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")