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aimo_3_gateway.py
Gateway notebook for https://www.kaggle.com/competitions/ai-mathematical-olympiad-progress-prize-3
class AIMO3Gateway
Gateway class for the AI Mathematical Olympiad Progress Prize 3. Provides the interface between the competition platform and the TGI solver.
def AIMO3Gateway.__init__(self, data_paths)
Initializes the AIMO gateway with data paths and sets a generous timeout.
Args: data_paths (tuple[str] | None): Tuple containing the test CSV path.
def AIMO3Gateway.unpack_data_paths(self)
Unpacks the provided data paths or uses default competition paths.
def AIMO3Gateway.generate_data_batches(self)
Generates batches of test data for evaluation.
Returns: Generator[tuple[pl.DataFrame, pl.DataFrame], None, None]: Batches of (row, row_id).
def AIMO3Gateway.competition_specific_validation(self, prediction_batch, row_ids, data_batch)
Performs competition-specific validation on predictions.
algebraic.py
No description.
class AlgebraicClassifier
Classifies symmetric combinatorial problems in O(1) using cohomology. Guided by Law I (Dimensional Parity Harmony) and Law V (Joint-Sum Constraint). Determines existence of Hamiltonian paths in Z_m^k.
def AlgebraicClassifier.__init__(self, m, k)
Initializes the classifier with grid modulus m and dimensionality k.
Args: m (int): The grid modulus (number of levels per dimension). k (int): The dimensionality of the manifold.
def AlgebraicClassifier.analyze(self)
Performs a deep audit of the topological domain and returns a formal proof.
Returns: Dict[str, Any]: Proof metadata including existence, theorem ID, and proof steps.
class GroupExtension
Formalizes the Short Exact Sequence 0 -> H -> G -> Q -> 0. Enables decomposition of G into fiber H and quotient Q.
def GroupExtension.__init__(self, G_order, Q_order)
Initializes the extension with global order G and quotient order Q.
def GroupExtension.lift(self, q_state, h_state)
Lifts a point from the quotient and fiber to the total space.
def GroupExtension.project(self, g_state)
Projects a point from the total space to the quotient and fiber.
class Tower
A hierarchy of Group Extensions (Tower of Fibrations). Enables deep cognitive mapping across multiple manifold layers.
def Tower.__init__(self, orders)
Initializes the tower with a list of orders [base, ..., total].
def Tower.lift_sequence(self, states)
Lifts a state through the entire tower from base to total space.
def Tower.project_sequence(self, g_state)
Decomposes a global state into its constituent fiber components across the tower.
class NonAbelianSubgroup
Helper for subgroups with non-abelian central extensions.
def NonAbelianSubgroup.__init__(self, G_order, H_order, is_central)
Initializes the subgroup with global, fiber, and central metadata.
def NonAbelianSubgroup.parity_law(self, k)
Checks the finalized parity law for non-abelian extensions.
def analyze_advanced_domain(domain)
Advanced classification for icosahedral, crystal, and Hamming geometries.
def get_algebraic_proof(m, k)
Convenience wrapper for AlgebraicClassifier.analyze.
def get_heisenberg_proof(m, k)
Analysis of Hamiltonian decomposition for Heisenberg groups H3(Z_m).
analysis.py
analysis.py β Automated mathematical analysis of Claude's Cycles solutions.
Given a sigma function or SigmaTable, this module:
STRUCTURAL ANALYSIS
- Detects column-uniformity (does sigma depend only on s,j or all of i,j,k?)
- Computes the Q_c composed permutations
- Identifies the twisted translation form Q_c(i,j) = (i+b_c(j), j+r_c)
THEOREM VERIFICATION
- Theorem 1: Twisted Translation Structure (auto-detected)
- Theorem 2: Single-Cycle Conditions (gcd checks)
- Theorem 3: Existence for odd m (constructive verification)
- Theorem 4: Impossibility for even m (parity argument)
PATTERN REPORTING
- Full solution tables
- Arc sequences for each Hamiltonian cycle
- Comparison across m values
def detect_dependencies(sigma, m)
Determine which coordinates sigma actually depends on. Returns {'i': bool, 'j': bool, 'k': bool, 's': bool} where s = (i+j+k) mod m.
def extract_sigma_table(sigma, m)
If sigma is column-uniform (depends only on s,j), extract SigmaTable. Returns None if sigma is not column-uniform.
class SolutionAnalysis
Comprehensive analysis of a Claude's Cycles solution.
Usage: analysis = SolutionAnalysis(sigma_fn, m=5) analysis.run() print(analysis.report())
def SolutionAnalysis.__init__(self, sigma, m)
No description.
def SolutionAnalysis.run(self)
No description.
def SolutionAnalysis.report(self, verbose)
No description.
def SolutionAnalysis.__repr__(self)
No description.
def compare_across_m(results)
Generate a comparison table across multiple m values. results: {m: SolutionAnalysis}
benchmark.py
benchmark.py β v2.0 vs Alternatives
Measures six solvers across six problems. Reports: correctness, time, proof capability, speedup.
Run: python benchmark.py # default (m=3..6, all solvers) python benchmark.py --quick # m=3..5 only python benchmark.py --w4 # W4 correction speedup only python benchmark.py --scaling # scaling analysis
class BResult
No description.
def BResult.row(self)
No description.
def _build_score(m)
No description.
def solver_v2(m, k)
No description.
def solver_A0_random(m, budget)
No description.
def solver_A1_SA(m, max_iter)
No description.
def solver_A2_backtrack(m)
No description.
def solver_A3_v1(m, k)
v1.0 pipeline with O(m^m) W4.
def _build_score(m)
Helper: build integer-array score function.
def solver_A4_level_enum(m)
Deterministic level enumeration. No randomness. Occasionally faster than v2 on easy feasible problems (lucky early branch). Cannot prove impossibility β times out on impossible problems.
def solver_A5_scipy(m)
scipy Nelder-Mead on the discrete score function treated as continuous. Included to document that gradient-free continuous optimization fails completely on discrete problems. Always returns 0/N correct.
def run_benchmark(problems, verbose)
No description.
def print_summary(all_results, problems)
No description.
def w4_benchmark()
No description.
def main()
No description.
cli.py
cli.py β Command-line interface for the Claude's Cycles system.
Usage: python -m claudecycles # demo all modes python -m claudecycles verify 3 # verify known m=3 solution python -m claudecycles verify 5 # verify known m=5 solution python -m claudecycles solve 7 # find+verify m=7 python -m claudecycles solve 9 # find+verify m=9 python -m claudecycles analyze 3 # deep analysis of m=3 python -m claudecycles theorem # verify all four theorems python -m claudecycles compare 3 5 7 # compare solutions across m
All results are auto-verified before printing.
def cmd_verify(m)
Verify a known hardcoded solution.
def cmd_solve(m, strategy, seed, max_iter)
Find and verify a solution for given m.
def cmd_analyze(m)
Deep mathematical analysis of a solution.
def cmd_theorem()
Demonstrate and verify all four theorems.
def cmd_compare(m_values)
Compare solutions across multiple m values.
def cmd_demo()
Full demo: verify known solutions, analyze, run theorems.
def main(args)
No description.
core.py
core.py β Mathematical Foundations (Production Stable)
Weights Β· Verifier Β· Solutions Β· Level Machinery Β· SA Engine
class Weights
No description.
def Weights.strategy(self)
No description.
def Weights.summary(self)
No description.
def _check_fso_solvability(m, r)
The Non-Canonical Obstruction check: Joint sum constraint.
def extract_weights(m, k)
No description.
def verify_sigma(sigma, m)
No description.
def table_to_sigma(table, m)
No description.
def _sa_score(sigma, arc_s, pa, n, k)
No description.
def _build_sa(m, k)
No description.
def run_hybrid_sa(m, k, seed, max_iter)
No description.
def construct_spike_sigma(m, k)
Sovereign Spike Construction (O(m)). Proven Golden Path for all odd m.
def solve(m, k, seed, max_iter)
The Sovereign FSO Master Solver.
def repair_manifold(m, k, sigma_in, max_iter)
No description.
def verify_basin_escape_success(m, k, sigma_in, max_iter)
No description.
def build_functional_graphs(sigma, m)
No description.
def verify_functional_graph(fg, m)
No description.
def vertices(m, k)
No description.
def trace_cycle(fg, m)
No description.
def arc_sequence(path, m)
No description.
debug_m4.py
No description.
domains.py
domains.py β Domain Definitions and Extensions
All registered domains, including the new P5/P6 results.
Domains: Cycles G_m k=3 m=3..9 (odd: solved, even: partial) Cycles k=4 m=4,8 (arithmetic feasible) Latin squares (cyclic construction) Hamming codes (perfect covering) Difference sets (design theory) P5: S_3 (non-abelian) NEW: parity law extends P6: Z_mΓZ_n NEW: fiber quotient = Z_gcd(m,n)
def proved(s)
No description.
def open_(s)
No description.
def note(s)
No description.
def analyse_magic_squares(verbose)
Magic squares via Siamese method β same fiber/twisted-translation structure.
def analyse_pythagorean(verbose)
Pythagorean triples β fiber quotient Z_4, obstruction pβ‘3(mod4).
def _load_magic_pythagorean(engine)
No description.
class DecompositionCategory
Category of symmetric decomposition problems. Objects = problems (G,k,Ο). Morphisms = structure-preserving maps. Eilenberg: a functor from {symmetric systems} β {cohomology theories}.
def DecompositionCategory.__init__(self)
No description.
def DecompositionCategory.add_object(self, name, G, k, m, status, H1)
No description.
def DecompositionCategory.add_morphism(self, src, tgt, kind, desc)
No description.
def DecompositionCategory.print_category(self)
No description.
def build_decomposition_category()
No description.
def _load_heisenberg(engine)
No description.
def load_all_domains(engine)
No description.
def _load_cycles(engine)
No description.
def _load_classical(engine)
No description.
def analyse_P5_nonabelian(verbose)
S_3 Cayley graph analysis.
RESULT (proved): β’ SES: 0 β A_3 β S_3 β Z_2 β 0 is valid (A_3 normal, index 2) β’ k=2 arc types: r-pair (1,1) sums to |Z_2|=2 β β FEASIBLE β’ k=3 arc types: no r-triple sums to 2 from {1} β OBSTRUCTED β’ Same parity law as abelian case
DIFFERENCE from abelian: β’ Twisted translation = conjugation Q_c(h) = g_cβ»ΒΉΒ·hΒ·g_c β’ HΒΉ gauge group = HΒΉ(G/H, Z(H)) β involves centre of H β’ A_3 is abelian, so Z(A_3)=A_3 and the gauge structure is the same
def _load_P5_nonabelian(engine)
No description.
def analyse_P6_product_groups(verbose)
Z_m Γ Z_n analysis.
RESULT (proved): β’ Fiber map: Ο(i,j) = (i+j) mod gcd(m,n) β’ SES: 0 β ker(Ο) β Z_mΓZ_n β Z_gcd(m,n) β 0 β’ Governing condition uses gcd(m,n) as modulus β’ Same parity obstruction formula with m replaced by gcd(m,n)
Examples: β’ Z_4ΓZ_6: gcd=2 β k=3 OBSTRUCTED (same as G_2^n) β’ Z_6ΓZ_9: gcd=3 β k=3 feasible (same as G_3^n) β’ Z_3ΓZ_5: gcd=1 β trivial fiber (always feasible)
def _load_P6_product(engine)
No description.
engine.py
No description.
class Domain
No description.
def Domain.__init__(self, name, n, k, m, fiber_map, tags, precomputed, group, notes)
No description.
class Engine
The Global Structure Engine provides a unified interface for classifying and solving combinatorial problems using the Short Exact Sequence framework.
def Engine.register(self, domain)
No description.
def Engine.print_results(self)
No description.
def Engine.__init__(self)
No description.
def Engine.run(self, m, k, strategy)
Runs the classification and optional search for a problem (m, k).
Args: m: The group order (Z_m). k: The dimension (number of cycles). strategy: Search strategy ('standard', 'hybrid', 'equivariant').
Returns: A dictionary containing the status, proof steps, and solution if found.
def Engine.analyse_text(self, desc, strategy)
Automatically parses a text description and classifies the domain.
Args: desc: Text description of the problem. strategy: Search strategy to use.
def Engine.simplify_problem(self, m, k)
Uses categorical morphisms (Quotient, Product) to reduce a complex problem to smaller solvable components.
def Engine.get_lean_export(self, m, k)
Generates Lean 4 source for the parity obstruction proof.
def get_suggested_morphisms(m, k)
Suggests ways to simplify or solve (m, k) using known components.
def check_remote_search_status()
Checks the status of Kaggle search kernels if CLI is configured.
fiber.py
fiber.py β Fiber decomposition of the Claude's Cycles problem.
KEY INSIGHT: The map f(i,j,k) = (i+j+k) mod m stratifies the digraph into m "fiber" layers F_0, β¦, F_{m-1}, each of size mΒ². Every arc goes from F_s to F_{s+1 mod m}.
In fiber coordinates (i,j) with k = (s-i-j) mod m, the 3 arc types become: arc 0: (i,j) in F_s β (i+1, j) in F_{s+1} [shift (1,0)] arc 1: (i,j) in F_s β (i, j+1) in F_{s+1} [shift (0,1)] arc 2: (i,j) in F_s β (i, j) in F_{s+1} [shift (0,0) β identity]
A "column-uniform" sigma depends only on (s, j) β not on i. At each level s, column j gets a fixed permutation: perm[j] = [arcβcycle].
The COMPOSED permutation after all m levels: Q_c(i,j) = (i + b_c(j), j + r_c) mod m where r_c = total j-increment for cycle c, b_c(j) = total i-increment.
Single mΒ²-cycle condition: gcd(r_c, m) = 1 AND gcd(Ξ£ b_c(j), m) = 1
def is_bijective_level(level, m)
Check that at level s, each cycle c induces a bijection on Z_mΒ². For cycle c: the set of targets {(i+di, j+dj) : j in Z_m, i in Z_m} must be exactly Z_mΒ² (all mΒ² positions hit).
def all_valid_levels(m)
Enumerate all column-uniform level assignments that are bijective.
def compose_levels(sigma_table, m)
Compose all m fiber-level functions to get Q_0, Q_1, Q_2. Returns 3 permutations on Z_mΒ² (as dicts).
def is_single_q_cycle(Q, m)
Check that permutation Q on Z_mΒ² is a single mΒ²-cycle.
def table_to_sigma_fn(sigma_table, m)
Convert a SigmaTable (indexed by [s][j]) into a 3D sigma function sigma(i, j, k) that can be used with core.verify_sigma. The key: depends only on s=(i+j+k)%m and j.
def analyze_Q_structure(Qs, m)
Analyze whether Q_c has the twisted translation form: Q_c(i,j) = (i + b_c(j), j + r_c) mod m Returns a dict with r_c, b_c, is_twisted, single_cycle per cycle.
def verify_single_cycle_conditions(r_c, b_c, m)
Verify the two necessary and sufficient conditions for Q_c to be a single mΒ²-Hamiltonian cycle.
def even_m_impossibility_check(m)
Verify the impossibility theorem for even m: No (r_0,r_1,r_2) with gcd(r_c,m)=1 can sum to m when m is even.
find_m3.py
No description.
frontiers.py
frontiers.py β Open Problem Solvers
P1 k=4, m=4 fiber-structured SA (construction open) P2 m=6, k=3 full-3D SA (first attempts) P3 m=8, k=3 full-3D SA (harder)
TRIAGE FINDINGS (from recent measurements): β’ P1 k=4 m=4: Score 337β230 in 300K iters of fiber-structured SA. Estimated budget: 4β8M iterations. β’ P2 m=6 k=3: Basin-escape reaches score=4 in 8M iters (prev record 9). This is a deep local minimum (depth β₯ 3). Needs ~10M iters at T=2.0. β’ P3 m=8 k=3: 512 vertices. Score function overhead scales linearly.
Run: python frontiers.py --p1 # k=4, m=4 python frontiers.py --p2 # m=6, k=3 python frontiers.py --p3 # m=8, k=3 python frontiers.py --all # all three python frontiers.py --status # print current knowledge state
def found(s)
No description.
def open_(s)
No description.
def note(s)
No description.
def hr(n)
No description.
def solve_P1(max_iter, seeds, verbose)
Find Ο: Z_4^4 β S_4 such that each colour class is a Hamiltonian cycle. Strategy: fiber-structured SA where Ο(v) = f(fiber(v), j(v), k(v)). The unique valid r-quadruple is (1,1,1,1) β all four colors share r_c=1.
MEASUREMENT: Score 337β230 in first 300K iterations. K=4 converges ~4x slower than K=3. Estimated budget: 4β8M iterations.
def solve_P2(max_iter, seeds, verbose)
G_6 has 216 vertices. Score function checks 3 components of 216 vertices. Column-uniform impossible (parity). Full-3D search required.
def solve_P2_warm_start(max_iter, seed, verbose)
m=6, k=3 warm-start approach using Z_3-lifted solution.
FINDING: The Z_3 lift (sigma_6(i,j,k) = sigma_3(i%3,j%3,k%3)) reaches score=9 reliably. This is a TRUE local minimum of depth >=3. Escape requires ~10M iterations at T=2.0.
STRUCTURAL INSIGHT: Z_6 = Z_2 Γ Z_3 creates a product-structure local minimum. Breaking it requires coordinated multi-vertex changes that span the Z_3 periodic structure.
def solve_P3(max_iter, seeds, verbose)
G_8: 512 vertices. Harder than m=6. Tests scaling. Score function needs 512 components checked per iteration.
def print_status()
No description.
def main()
No description.
def prove_fiber_uniform_k4_impossible(verbose)
THEOREM: No fiber-uniform Ο yields a valid k=4 decomposition of G_4^4. Proof method: exhaustive search over all 24^4 = 331,776 fiber-uniform sigmas.
Fiber-uniform means Ο(v) depends only on fiber(v) = (i+j+k+l) mod 4. With 4 fibers and 4 colors, there are 24^4 = 331,776 combinations. This is small enough to check completely in ~40 seconds.
Result: 0 valid sigmas found β proved impossible.
generate_api_docs.py
No description.
def get_docstring(node)
No description.
def format_args(args)
No description.
def parse_file(filename)
No description.
kaggle_search.py
No description.
def _build_sa(m, k)
No description.
def _sa_score(sigma, arc_s, pa, n, k)
No description.
def get_node_orbits(m, k, subgroup_generators)
No description.
def run_hybrid_sa(m, k, seed, max_iter, verbose)
No description.
def run_fiber_structured_sa(m, k, seed, max_iter, verbose)
No description.
def main()
No description.
search.py
search.py β Three complementary search strategies for Claude's Cycles.
RANDOM SEARCH: Fast for odd m. Sample random valid-level combinations, check if Q compositions are single mΒ²-cycles. Works well for m=3,5,7.
BACKTRACKING: Vertex-by-vertex with in-degree pruning. Explores the full sigma space (not restricted to column-uniform). Slower but more general.
SIMULATED ANNEALING: Continuous improvement via stochastic hill-climbing. Score = total "extra components" across 3 cycles (want 0). Effective at navigating large m.
All strategies return a SigmaTable (for fiber-based) or SigmaFn (for full 3D).
class RandomSearch
Sample random combinations of valid level tables. Extremely fast for odd m. Progressively slows for large m.
Usage: rs = RandomSearch(m=5) result = rs.run(max_attempts=50_000)
def RandomSearch.__init__(self, m, seed)
No description.
def RandomSearch.attempts(self)
No description.
def RandomSearch.elapsed(self)
No description.
def RandomSearch.run(self, max_attempts)
Return a valid SigmaTable or None if not found.
def RandomSearch.run_verbose(self, max_attempts, report_every)
Like run() but prints progress.
class BacktrackSearch
Vertex-by-vertex assignment of sigma with pruning:
- Each cycle gets exactly one arc from each vertex (permutation = guaranteed).
- Each vertex has in-degree exactly 1 per cycle (checked incrementally).
- Optionally shuffles perm order (via seed) for different search trees.
Usage: bt = BacktrackSearch(m=3, seed=42) sigma_fn = bt.run()
def BacktrackSearch.__init__(self, m, seed)
No description.
def BacktrackSearch.nodes_visited(self)
No description.
def BacktrackSearch.run(self)
Return SigmaFn or None.
class SimulatedAnnealing
Score = total number of extra cycle components (want 0). Perturb: change sigma at one random vertex. Temperature schedule: geometric cooling.
Usage: sa = SimulatedAnnealing(m=4, seed=0) sigma_fn = sa.run(max_iter=500_000)
def SimulatedAnnealing.__init__(self, m, seed, T_init, T_min)
No description.
def SimulatedAnnealing.best_score(self)
No description.
def SimulatedAnnealing._score(self, funcs, m)
Sum of extra components (0 = perfect).
def SimulatedAnnealing.run(self, max_iter, verbose, report_every)
No description.
def SimulatedAnnealing.run_verbose(self, max_iter)
No description.
def find_sigma(m, strategy, seed, max_iter, verbose)
Find a valid sigma for the given m using the best available strategy.
strategy="auto":
- odd m β RandomSearch (fast, fiber-based)
- even m β SimulatedAnnealing (full 3D) strategy="random" β RandomSearch only strategy="backtrack" β BacktrackSearch only strategy="sa" β SimulatedAnnealing only
Returns SigmaFn or None.
solutions.py
solutions.py β Hardcoded verified solutions for Claude's Cycles.
All solutions have been computationally verified (3 Hamiltonian cycles). Use get_solution(m) to retrieve; use construct_for_odd_m(m) for a general algorithm that works on any odd m > 2.
def get_solution(m)
Return a precomputed SigmaFn for known m values (currently m=3,5). Returns None for unknown m (use search module instead).
def get_solution_table(m)
Return the raw SigmaTable for known m values.
def known_m_values()
Return sorted list of m values with hardcoded solutions.
def construct_for_odd_m(m, seed, max_attempts)
Find a valid sigma for any odd m > 2 using RandomSearch. The fiber decomposition approach always succeeds for odd m (Theorem 3).
Returns SigmaFn or None (None is unexpected for m β€ ~15).
test_basin.py
No description.
test_sa.py
No description.
theorems.py
theorems.py β Formal Verification of the SES Framework
Verified theorems 3.2 through 17.1 (FSO Codex Laws I-XII). Includes group actions, parity obstructions, and multi-modal fibrations.
def proved(s)
No description.
def hr()
No description.
def check_spike_conditions(m)
Analytically verify Theorem 11.1 conditions for odd m.
def phi(n)
No description.
def verify_moduli_space_laws()
Verify Codex Laws II and III for m=3.
def verify_basin_escape_law()
Verify Law VII (Basin Escape Axiom) for m=3.
def verify_cross_domain_consistency()
Verify Law VIII (Multi-Modal Fibration Invariant).
def verify_subgroup_decomposition_law()
Verify Law X (Recursive Subgroup Decomposition) for m=12.
def verify_symbolic_duality_law()
Verify Law XI (Symbolic-Topological Duality).
def verify_hardware_hamiltonian_health()
Verify Law IX (Hardware-Topological Equivalence).
def verify_all_theorems(verbose)
No description.
def print_cross_domain_table()
No description.
research/action_mapper.py
No description.
class ActionMapper
TGI Action-Coordinate Mapping. Translates topological paths and coordinates into system-level 'Agentic' actions. Ensures the TGI can 'do' things as a result of manifold reasoning. Guided by Law VIII (Multi-Modal Consistency).
def ActionMapper.__init__(self, m)
No description.
def ActionMapper.map_coord_to_action(self, coord)
Maps a specific coordinate in Z_m^k to an action and its parameters.
def ActionMapper.path_to_action_sequence(self, path)
Converts a Hamiltonian path into a sequence of agentic actions.
def ActionMapper.resolve_intent(self, intent_text)
Lifts a textual intent into a coordinate for action execution. Uses grounded TLM semantic mapping and Law VIII (Multi-Modal Consistency).
research/admin_vision_process.py
No description.
def admin_process(image_path)
No description.
research/advanced_solvers.py
No description.
class GeneralCayleyEngine
No description.
def GeneralCayleyEngine.__init__(self, elements, op, gens, seed)
No description.
def GeneralCayleyEngine.score(self, sigma)
No description.
def GeneralCayleyEngine.solve(self, max_iter, verbose)
No description.
class HeisenbergSolver
No description.
def HeisenbergSolver.__init__(self, m, seed)
No description.
class TSPSolver
No description.
def TSPSolver.__init__(self, name, coords, seed)
No description.
def TSPSolver.score(self, tour)
No description.
def TSPSolver.nearest_neighbor(self)
No description.
def TSPSolver.solve(self, max_iter, init_method, verbose)
No description.
def load_tsplib_instances(csv_path)
No description.
research/agentic_action_engine.py
No description.
class ActionExecutor
TGI Action Executor (Phase 8 Completion). Handles real execution of agentic plans and establishes the feedback loop. Guided by Law VII (Basin Escape) and Law IX (Hardware Grounding).
def ActionExecutor.__init__(self)
No description.
def ActionExecutor.execute_step(self, step)
Executes a single step of an agentic plan.
def ActionExecutor.execute_plan(self, plan)
Executes a full multi-step plan and returns the audit trail.
class TopologicalActionEngine
TGI Agentic Action Engine. Executes and resolves multi-step topological paths into coherent agentic plans.
def TopologicalActionEngine.__init__(self)
No description.
def TopologicalActionEngine.resolve_path_to_plan(self, path, base_intent)
Resolves a sequence of coordinates into a multi-step execution plan.
research/agentic_bridge.py
No description.
class AgenticBridge
The TGI Agentic Bridge (Upgraded v4). Links the topological action space to actual MCP tool signatures and LIBRARY metadata. Guided by the FSO Codex Law VIII (Multi-Modal Consistency).
def AgenticBridge.__init__(self)
No description.
def AgenticBridge.resolve_intent(self, intent)
Maps a natural language intent to a topological manifold and action set.
def AgenticBridge.resolve_resource_for_action(self, action_data, domain_hint)
Finds the most appropriate tool or library for a topological action.
def AgenticBridge.generate_agentic_plan(self, intent)
Creates a fully resolved agentic plan from a natural language intent.
research/agentic_expansion_demo.py
No description.
def run_demo()
No description.
research/agentic_tgi_demo.py
No description.
def run_demo()
No description.
research/aimo_p7_solver.py
No description.
def count_f2024_values()
f(m) + f(n) = f(m + n + mn) f(n) = \sum a_p * v_p(n+1) a_p = f(p-1) >= 1 Constraint: f(n) <= 1000 for n <= 1000. Find number of values for f(2024) = h(2025) = 4a_3 + 2a_5.
research/aimo_reasoning_engine.py
No description.
class AIMOReasoningEngine
No description.
def AIMOReasoningEngine.__init__(self)
No description.
def AIMOReasoningEngine.solve(self, problem_latex, problem_id)
No description.
research/aimo_recurring_parquet.py
No description.
research/aimo_solver.py
No description.
def solve_alice_bob()
No description.
def solve_functional_equation()
No description.
def count_f2024_values()
No description.
def solve_double_sum_floor()
No description.
research/aimo_submission_script.py
No description.
def get_answer(problem_id)
No description.
research/aimo_submit.py
No description.
research/analysis.py
analysis.py β Automated mathematical analysis of Claude's Cycles solutions.
Given a sigma function or SigmaTable, this module:
STRUCTURAL ANALYSIS
- Detects column-uniformity (does sigma depend only on s,j or all of i,j,k?)
- Computes the Q_c composed permutations
- Identifies the twisted translation form Q_c(i,j) = (i+b_c(j), j+r_c)
THEOREM VERIFICATION
- Theorem 1: Twisted Translation Structure (auto-detected)
- Theorem 2: Single-Cycle Conditions (gcd checks)
- Theorem 3: Existence for odd m (constructive verification)
- Theorem 4: Impossibility for even m (parity argument)
PATTERN REPORTING
- Full solution tables
- Arc sequences for each Hamiltonian cycle
- Comparison across m values
def detect_dependencies(sigma, m)
Determine which coordinates sigma actually depends on. Returns {'i': bool, 'j': bool, 'k': bool, 's': bool} where s = (i+j+k) mod m.
def extract_sigma_table(sigma, m)
If sigma is column-uniform (depends only on s,j), extract SigmaTable. Returns None if sigma is not column-uniform.
class SolutionAnalysis
Comprehensive analysis of a Claude's Cycles solution.
Usage: analysis = SolutionAnalysis(sigma_fn, m=5) analysis.run() print(analysis.report())
def SolutionAnalysis.__init__(self, sigma, m)
No description.
def SolutionAnalysis.run(self)
No description.
def SolutionAnalysis.report(self, verbose)
No description.
def SolutionAnalysis.__repr__(self)
No description.
def compare_across_m(results)
Generate a comparison table across multiple m values. results: {m: SolutionAnalysis}
research/autonomous_engine_demo.py
No description.
def run_demo()
No description.
research/classify_new_domains.py
No description.
research/collect_all_results.py
No description.
def get_stats(kernel_id)
No description.
def main()
No description.
research/cycles_even_m.py
cycles_even_m.py β 6-Phase Discovery: Even m in Claude's Cycles
The digraph G_m: vertices (i,j,k) β Z_mΒ³ arc 0: (i,j,k) β (i+1, j, k ) mod m arc 1: (i,j,k) β (i, j+1, k ) mod m arc 2: (i,j,k) β (i, j, k+1) mod m
sigma assigns each arc to one of 3 cycles. Goal: every cycle is a single directed Hamiltonian cycle of length mΒ³.
Odd m β column-uniform sigma works (proven, m=3,5,7 solved). Even m β column-uniform is PROVABLY impossible. This script discovers WHY and then FINDS a solution via SA.
Phases: 01 GROUND TRUTH β define verification; confirm odd m works 02 DIRECT ATTACK β attempt column-uniform on m=4; record exact failure 03 STRUCTURE HUNT β prove the parity obstruction; characterise what even m needs 04 PATTERN LOCK β SA search for m=4; analyse the solution structure 05 GENERALIZE β test the discovered structure on m=6 06 PROVE LIMITS β complete theorem: odd proven, even found, open frontier stated
Run: python cycles_even_m.py # full 6-phase run python cycles_even_m.py --fast # skip m=6 search (saves ~2 min)
def hr(c, n)
No description.
def sec(num, name, tag)
No description.
def kv(k, v, ind)
No description.
def found(msg)
No description.
def miss(msg)
No description.
def note(msg)
No description.
def info(msg)
No description.
def vertices(m)
No description.
def build_funcs(sigma, m)
No description.
def count_components(fg)
No description.
def score(sigma, m)
Excess components across 3 cycles (0 = valid).
def verify(sigma, m)
Full verification: each cycle is exactly 1 Hamiltonian cycle.
def build_funcs_list(sigma, m)
Build 3 mutable dicts.
def fiber_valid_levels(m)
All column-uniform level assignments where each cycle is bijective on Z_mΒ².
def _cartesian(lst, k)
No description.
def _level_bijective(level, m)
No description.
def compose_q(table, m)
Compose all m fiber levels β 3 permutations Q_c on Z_mΒ².
def q_is_single_cycle(Q, m)
No description.
def table_to_sigma(table, m)
No description.
def find_odd_m(m, seed, max_att)
No description.
def prove_column_uniform_impossible(m)
Column-uniform needs rβ+rβ+rβ = m, each gcd(rα΅’,m)=1. For even m: coprime-to-m βΉ odd. Sum of 3 odds is odd β m (even). QED. Returns dict with all proof data.
def exhaustive_column_uniform(m, max_combos)
Try ALL column-uniform sigmas for small m. Record outcome.
def _build_perm_table(m)
Precompute for each (vertex_idx, perm_idx) β [successor_0, s_1, s_2]. Returns succs[v][p][arc] = successor vertex index.
def _build_funcs_fast(sigma_int, arc_succ, perm_arc, n)
Build 3 successor arrays from integer sigma.
def _count_comps_fast(f, n)
Count cycle components in successor array.
def _score_fast(f0, f1, f2, n)
No description.
def sa_search_fast(m, max_iter, T_init, T_min, seed, verbose, report_n)
Fast SA with score=1 repair mode + plateau-escape reheat. Returns (sigma_int_list or None, stats).
def _sigma_int_to_map(sigma_int, m)
Convert integer sigma to SigmaMap.
def sa_multistart(m, restarts, iter_each, T_init, verbose)
Multi-start SA. Return first success.
def analyse_sigma_dependencies(sigma, m)
Find which coordinates sigma actually depends on.
def analyse_sigma_pattern(sigma, m)
Analyse symmetry structure of a found sigma.
def analyse_q_structure(sigma, m)
Extract Q_c (if sigma is column-uniform) or analyse fiber-level transitions even for full-3D sigma.
def phase_01()
No description.
def phase_02()
No description.
def phase_03()
No description.
def phase_04(fast)
No description.
def phase_05(sigma4, fast)
No description.
def phase_06(p4_result, p5_result)
No description.
def main()
No description.
research/debug_spike_m3.py
No description.
research/deploy_p1_fix.py
No description.
def deploy()
No description.
research/deploy_p2_p3.py
No description.
def deploy()
No description.
research/deploy_swarm.py
No description.
def deploy()
No description.
research/discovery_engine.py
discovery_engine.py β 6-Phase Mathematical Discovery Engine
Pure sympy. No API. All six phases run as real computation.
Each phase applies one principle from the Discovery Methodology: 01 GROUND TRUTH β classify, parse, build the verifier 02 DIRECT ATTACK β try standard methods; record failures precisely 03 STRUCTURE HUNT β factor, symmetry, decompose, find invariants 04 PATTERN LOCK β analyse the working answer; extract the law 05 GENERALIZE β parametrise the family; name the condition 06 PROVE LIMITS β find the boundary; state the obstruction
Usage: python discovery_engine.py "x^2 - 5x + 6 = 0" python discovery_engine.py "sin(x)^2 + cos(x)^2" python discovery_engine.py "factor x^4 - 16" python discovery_engine.py "x^3 - 6x^2 + 11x - 6 = 0" python discovery_engine.py "prove sqrt(2) is irrational" python discovery_engine.py "sum of first n integers" python discovery_engine.py "2x + 3 = 7" python discovery_engine.py --test # run all built-in tests
def hr(char, n)
No description.
def section(num, name, tagline)
No description.
def kv(key, val, indent)
No description.
def finding(msg, sym)
No description.
def ok(msg)
No description.
def fail(msg)
No description.
def note(msg)
No description.
class PT
No description.
class Problem
No description.
def _parse(s)
No description.
def classify(raw)
No description.
def phase_01(p)
No description.
def phase_02(p, g)
No description.
def phase_03(p, prev)
No description.
def phase_04(p, prev)
No description.
def phase_05(p, prev)
No description.
def phase_06(p, prev)
No description.
def _final_answer(p)
No description.
def run(raw)
No description.
def run_tests()
No description.
research/discovery_engine_unified.py
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β DISCOVERY ENGINE β Complete Unified System β β Finding Global Structure in Highly Symmetric Systems β ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
WHAT THIS FILE IS βββββββββββββββββ A single self-contained system encoding every discovery, theorem, algorithm, and search strategy produced during the Claude's Cycles investigation. It is simultaneously: β’ The traceable record of what was found and how β’ The runnable proof of every theorem β’ The extended coordinate framework applicable to new domains β’ The improved search engine with structured SA
DISCOVERY ARC (the strategic path that led here) ββββββββββββββββββββββββββββββββββββββββββββββββββ Phase 1 GROUND TRUTH β verify() before search() Phase 2 DIRECT ATTACK β measure how failures fail Phase 3 STRUCTURE HUNT β the fiber map f(v) = Ο(v) Phase 4 PATTERN LOCK β twisted translation Q_c Phase 5 GENERALIZE β governing condition gcd(r_c,m)=1 Phase 6 PROVE LIMITS β parity obstruction for even m
Extensions: Ext 1 REFORMULATION β same 4 coordinates in 6 domains Ext 2 GLOBAL STRUCTURE β master theorem via SES Ext 3 k=4 FRONTIER β new theorem + structured search
THE FOUR COORDINATES (the universal discovery tools) βββββββββββββββββββββββββββββββββββββββββββββββββββββββ C1 Fiber Map Ο: G β G/H (group quotient) C2 Twisted Translation Q_c (coset action on H) C3 Governing Condition gcd(r_c,|G/H|)=1 (generator in G/H) C4 Parity Obstruction arithmetic of |G/H| (when C3 fails)
Run: python discovery_engine_unified.py --demo # full demo python discovery_engine_unified.py --cycles m=5 # solve G_m python discovery_engine_unified.py --verify # verify all theorems python discovery_engine_unified.py --search k=4 # k=4 structured search python discovery_engine_unified.py --domains # cross-domain analysis python discovery_engine_unified.py --strategy # print strategy guide
def hr(c, n)
No description.
def phase_header(n, name, tag)
No description.
def proved(msg)
No description.
def found(msg)
No description.
def miss(msg)
No description.
def note(msg)
No description.
def info(msg)
No description.
def kv(k, v)
No description.
class FiberMap
Universal fiber decomposition tool.
Given a group G (encoded as a list of elements) and a homomorphism Ο: G β Z_k, decompose G into k fibers F_0,...,F_{k-1}.
The short exact sequence: 0 β ker(Ο) β G β Z_k β 0 is the algebraic skeleton of the decomposition.
Orbit-stabilizer theorem: |G| = k Γ |ker(Ο)|
def FiberMap.__init__(self, elements, phi, k)
No description.
def FiberMap.verify_orbit_stabilizer(self)
No description.
def FiberMap.report(self)
No description.
def cycles_fiber_map(m)
No description.
class TwistedTranslation
The induced action of a generator on the fiber H β Z_mΒ².
Q(i,j) = (i + b(j), j + r) mod m
This is the COSET ACTION: h β¦ h + g (residual group action of g on H).
def TwistedTranslation.__init__(self, m, r, b)
No description.
def TwistedTranslation.apply(self, i, j)
No description.
def TwistedTranslation.orbit_length(self)
No description.
def TwistedTranslation.is_single_cycle(self)
No description.
def TwistedTranslation.condition_A(self)
gcd(r, m) = 1 β r generates Z_m β j-shift has full period.
def TwistedTranslation.condition_B(self)
gcd(Ξ£b(j), m) = 1 β accumulated i-shift has full period.
def TwistedTranslation.verify_theorem_5_1(self)
THEOREM 5.1: Q is a single mΒ²-cycle iff A and B both hold. Returns verification dict with prediction vs actual.
def TwistedTranslation.derivation_sketch(m)
No description.
class GoverningCondition
For a k-decomposition via the fiber structure, we need k parameters r_0,...,r_{k-1} each coprime to m (generating G/H β Z_m) summing to m (the constraint from the identity action of arc type k-1).
This class analyses feasibility and finds valid r-tuples.
def GoverningCondition.__init__(self, m, k)
No description.
def GoverningCondition.find_valid_tuples(self)
No description.
def GoverningCondition.canonical_tuple(self)
The simplest valid tuple: (1, m-(k-1), 1, ..., 1) when feasible.
def GoverningCondition.analyse(self)
No description.
class ParityObstruction
THEOREM 6.1 (Generalised): For even m and odd k: no k-tuple from coprime-to-m elements can sum to m. Proof: all such elements are odd; sum of k odd numbers has parity k%2; k odd β sum is odd; m is even β contradiction.
COROLLARY 9.2 (New): k even β potentially feasible for all m. The obstruction is k-parity specific, not m-parity specific.
def ParityObstruction.__init__(self, m, k)
No description.
def ParityObstruction.analyse(self)
No description.
def ParityObstruction.complete_table(m_range, k_range)
Generate the complete kΓm feasibility table.
def _build_arc_succ_3(m)
No description.
def _perm_table_3()
No description.
def _build_funcs_3(sigma, arc_succ, perm_arc, n)
No description.
def _count_comps(f, n)
No description.
def _score_3(f0, f1, f2, n)
No description.
def _level_bijective(level, m)
No description.
def _valid_levels(m)
No description.
def _compose_q(table, m)
No description.
def _q_single(Q, m)
No description.
def _table_to_sigma(table, m)
No description.
def verify_sigma_map(sigma_map, m)
Full verification of a sigma given as {(i,j,k): perm_tuple}.
class SAEngine3
Fast SA for G_m (k=3) using integer arrays. 38K+ iterations/second on m=4. Features: repair mode (score=1), plateau escape (reheat+reload).
def SAEngine3.__init__(self, m)
No description.
def SAEngine3.run(self, max_iter, T_init, T_min, seed, verbose, report_n)
No description.
class OddMSolver
Column-uniform sigma via random level sampling. Works for any odd m > 2 in expected polynomial time.
def OddMSolver.__init__(self, m, seed)
No description.
def OddMSolver.solve(self, max_att)
No description.
def find_sigma(m, seed, verbose)
Unified solver: odd m β random fiber search; even m β SA. Always returns {(i,j,k): perm_tuple} or None.
class SystemSpec
Specifies a highly symmetric system for analysis.
name: human-readable identifier G_order: |G|, the symmetry group order H_order: |H| = |ker(phi)|, the fiber size k: number of parts in decomposition G_quotient: |G/H| = k, the quotient group governing: string description of the governing condition obstruction: string description of the impossibility case (or None)
def SystemSpec.G_quotient(self)
No description.
def SystemSpec.verify_orbit_stabilizer(self)
No description.
def SystemSpec.report(self)
No description.
class K4M4Engine
Structured search for k=4, m=4.
The 4D digraph Z_4^4 (256 vertices, 4 arc types). The fiber-uniform approach is PROVED IMPOSSIBLE (exhaustive: 24^4=331,776 checked). The fiber-STRUCTURED approach restricts to Ο(v) = f(fiber, j, k) reducing the search from 24^256 to 24^64.
def K4M4Engine.__init__(self)
No description.
def K4M4Engine._dec(self, v)
No description.
def K4M4Engine._enc(self, i, j, k, l)
No description.
def K4M4Engine._build_arc_succ(self)
No description.
def K4M4Engine._build_perm_arc(self)
No description.
def K4M4Engine._build_funcs(self, sigma)
No description.
def K4M4Engine._score(self, sigma)
No description.
def K4M4Engine.prove_fiber_uniform_impossible(self)
Exhaustively check all 24^4 fiber-uniform sigmas.
def K4M4Engine.sa_fiber_structured(self, max_iter, seed, verbose, report_n)
SA in the fiber-structured subspace. State: table[(s,j,k)] β perm_index, 64 entries, 24 choices each. This is the correct restricted search space: Ο(v) = f(fiber(v), j(v), k(v)).
def verify_all_theorems(verbose)
Run all theorems as computational proofs. Each theorem is stated, then verified by explicit computation.
def cross_domain_analysis()
No description.
def print_strategy_guide()
No description.
def cmd_demo()
No description.
def cmd_cycles(m)
No description.
def cmd_k4_search(fast)
No description.
def main()
No description.
research/find_p1_params.py
No description.
def verify_k4(sigma, m)
No description.
def solve_p1()
No description.
research/frontier_discovery.py
No description.
def _build_sa(m, k)
No description.
def _sa_score(sigma, arc_s, pa, n, k)
No description.
def get_node_orbits(m, k, generators)
No description.
def run_frontier_sa(m, k, seed, max_iter, verbose)
No description.
research/global_structure.py
global_structure.py
FINDING GLOBAL STRUCTURE IN HIGHLY SYMMETRIC SYSTEMS
The central theorem, proved and tested:
For any combinatorial system with a transitive symmetry group G,
every valid global decomposition is determined by:
(1) A SUBGROUP CHAIN H β΄ G (the fiber map is the quotient G β G/H)
(2) AN INDUCED ACTION of G/H on H (the twisted translation)
(3) A GENERATOR CONDITION on the action parameters (coprimality analog)
(4) A PARITY OBSTRUCTION when the group arithmetic prevents (3)
This is not a heuristic. It is orbit-stabilizer theorem + Lagrange's theorem
applied to the action of G on the system's constraint graph.
We demonstrate this on five increasingly abstract systems:
SYS 1: Claude's Cycles (Z_mΒ³) β the original, now understood fully
SYS 2: Cayley graph of Z_n Γ Z_n β 2D analog, different fiber structure
SYS 3: Vertex-transitive graphs β BFS fibers from group structure
SYS 4: Affine planes AG(2,q) β fiber = parallel class, q must be prime power
SYS 5: Difference sets in Z_n β the governing condition IS the multiplier theorem
The script:
- Detects the symmetry group of each system
- Predicts valid decompositions from group structure alone
- Derives impossibility from arithmetic of group order
- Verifies predictions computationally
- Extracts the universal governing law
Run: python global_structure.py
def hr(c, n)
No description.
def section(title, sub)
No description.
def thm(label, statement)
No description.
def proved(msg)
No description.
def found(msg)
No description.
def miss(msg)
No description.
def note(msg)
No description.
def info(msg)
No description.
def kv(k, v)
No description.
def step(n, msg)
No description.
class AbelianGroup
Finite abelian group G = Z_{n1} Γ Z_{n2} Γ ... Γ Z_{nk}. The key operations:
- Subgroup enumeration (via divisors of each factor)
- Quotient map construction
- Orbit-stabilizer decomposition
- Generator testing
def AbelianGroup.__init__(self, *orders)
No description.
def AbelianGroup.elements(self)
No description.
def AbelianGroup.add(self, a, b)
No description.
def AbelianGroup.neg(self, a)
No description.
def AbelianGroup.zero(self)
No description.
def AbelianGroup.is_subgroup(self, H)
No description.
def AbelianGroup.cosets(self, H)
No description.
def AbelianGroup.subgroups_of_index(self, idx)
Find all subgroups H with [G:H] = idx (i.e., |H| = |G|/idx).
def AbelianGroup.generate(self, generators)
Subgroup generated by a list of elements.
def AbelianGroup.generator_order(self, g)
Order of element g.
def AbelianGroup.cyclic_generators(self)
Elements that generate the full group (if cyclic).
def AbelianGroup.is_cyclic(self)
No description.
class FiberDecomposition
Given group G and linear functional Ο: G β Z_m (a group homomorphism), decompose G into fibers F_s = Οβ»ΒΉ(s).
This is the ABSTRACT FORM of the Claude's Cycles fiber map. The functional Ο defines the 'stratification coordinate'.
def FiberDecomposition.__init__(self, G, phi, num_fibers)
No description.
def FiberDecomposition.fiber_size(self)
No description.
def FiberDecomposition.cross_fiber_action(self, g)
The induced action of g on fibers: maps F_s to F_{s + Ο(g)}. Within each fiber, the action is: h β¦ h + (g - Ο(g) * e) projected to fiber. This is the TWISTED TRANSLATION.
def FiberDecomposition.verify_orbit_stabilizer(self)
Verify: |G| = |orbit| Γ |stabilizer| orbit = the set of fibers (size = num_fibers) stabilizer = the kernel (size = fiber_size)
class TwistedTranslation
The induced action Q on a single fiber F β Z_mΒ².
Q(i,j) = (i + b(j), j + r) mod m
Parameters: r : the j-shift (= Ο(generator), the 'fiber-crossing speed') b : the i-offset function (= residual i-component of generator)
Single-cycle condition: Q is a single mΒ²-cycle iff: (A) gcd(r, m) = 1 (B) gcd(Ξ£_j b(j), m) = 1
def TwistedTranslation.__init__(self, m, r, b)
No description.
def TwistedTranslation.apply(self, i, j)
No description.
def TwistedTranslation.orbit_length(self)
Length of the orbit of (0,0) under repeated application.
def TwistedTranslation.is_single_cycle(self)
No description.
def TwistedTranslation.condition_A(self)
No description.
def TwistedTranslation.condition_B(self)
No description.
def TwistedTranslation.check_conditions(cls, m, r, b)
No description.
class ParityObstructionProver
Proves impossibility of decompositions from group order arithmetic.
The key theorem: For G = Z_m^n decomposed into k equal parts via a quotient map G β Z_k: each part spans a single Hamiltonian cycle iff there exist r_1,...,r_k coprime to m summing to m. For even m: all coprime-to-m elements are odd, and sum of k odd numbers has parity k mod 2 β 0 = m mod 2 when k is odd. [Generalized obstruction]
def ParityObstructionProver.__init__(self, m, k)
No description.
def ParityObstructionProver.coprime_elements(self)
No description.
def ParityObstructionProver.all_have_parity(self)
If all coprime-to-m elements have the same parity, return it; else None.
def ParityObstructionProver.sum_parity(self, k_copies, element_parity)
No description.
def ParityObstructionProver.target_parity(self)
No description.
def ParityObstructionProver.prove(self)
No description.
def system_1_claudes_cycles()
No description.
def system_2_cayley_2d()
No description.
def system_3_universal_principle()
No description.
def system_4_difference_sets()
No description.
def system_5_synthesis()
No description.
def main()
No description.
research/global_structure_engine.py
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β GLOBAL STRUCTURE ENGINE v1.0 β β Finding Global Structure in Highly Symmetric Systems β β βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ£ β β β WHAT THIS ENGINE DOES β β βββββββββββββββββββββ β β Given any highly symmetric combinatorial system, it automatically: β β 1. Registers the domain (group G, fiber map Ο, decomposition goal) β β 2. Applies all four coordinates of the short exact sequence β β 3. Dispatches the correct search strategy β β 4. Tracks a branch tree of proved/open/impossible results β β 5. Generates theorem statements from the analysis β β 6. Exposes hooks for adding new coordinates and strategies β β β β ARCHITECTURE β β ββββββββββββ β β Engine β β βββ DomainRegistry register/retrieve domains β β βββ CoordinateAnalyser C1βC2βC3βC4 pipeline (auto) β β βββ StrategyDispatcher selects S1/S2/S3/S4/S5 from analysis β β βββ BranchTree records proved/open/attempted/impossible β β βββ TheoremGenerator produces formal theorem statements β β βββ ExpansionProtocol hooks for new coordinates / strategies β β β β THE FOUR COORDINATES (always applied in this order) β β C1 FiberMap Ο: G β G/H (group quotient) β β C2 TwistedTranslation Q on H (coset action) β β C3 GoverningCondition gcd check (generator condition) β β C4 ParityObstruction arithmetic (impossibility) β β β β HOW TO ADD A NEW DOMAIN β β ββββββββββββββββββββββββ β β engine = GlobalStructureEngine() β β engine.register( β β name = "My System", β β group_order = 64, β β k = 3, β β phi_desc = "sum of coords mod m", β β verify_fn = my_verify, # callable: candidate β bool β β search_fn = my_search, # callable: β candidate or None (optional) β β ) β β result = engine.analyse("My System") β β engine.print_branch_tree() β β β β Run: β β python global_structure_engine.py # analyse all domains β β python global_structure_engine.py --domain "Cycles m=5" β β python global_structure_engine.py --tree # print branch tree β β python global_structure_engine.py --theorems # print all theorems β β python global_structure_engine.py --extend # show extension API β ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def hr(c, n)
No description.
class Status
No description.
class CoordinateResult
Output of applying ONE coordinate to a domain.
class BranchNode
One node in the branch tree: a specific (domain, question) pair.
def BranchNode.add_child(self, child)
No description.
class AnalysisResult
Complete result of analysing one domain through all four coordinates.
def AnalysisResult.status(self)
No description.
def AnalysisResult.summary(self)
No description.
class C1_FiberMap
Applies the fiber decomposition to any domain.
The fiber map Ο: G β Z_k partitions |G| objects into k equal fibers. It is the projection in the short exact sequence 0 β H β G β G/H β 0.
Required inputs: group_order, k, phi_description Output: orbit-stabilizer check, fiber sizes, kernel description
def C1_FiberMap.apply(self, domain)
No description.
class C2_TwistedTranslation
Analyses the induced action of G/H on H (the coset action).
For the Cayley graph setting: Q_c(i,j) = (i+b_c(j), j+r_c) mod m. For general abelian G: the action is always of this twisted form.
Verifies: does the action structure admit single-orbit generators?
def C2_TwistedTranslation.apply(self, domain, c1)
No description.
class C3_GoverningCondition
Finds the governing condition: which r-tuples in G/H allow single cycles?
General form: k values r_0,...,r_{k-1}, each coprime to |G/H|, summing to |G/H|.
Fully automatic from (group_order, k).
def C3_GoverningCondition.apply(self, domain, c2)
No description.
class C4_ParityObstruction
Proves impossibility from arithmetic of |G/H| when C3 finds no valid tuples.
The proof is: if all coprime-to-|G/H| elements have parity p, and sum of k elements has parity kΓp, but target |G/H| has opposite parity, then it's impossible.
Fully automatic: either produces an impossibility proof or confirms feasibility.
def C4_ParityObstruction.apply(self, domain, c3)
No description.
class StrategyDispatcher
Selects the correct search strategy based on coordinate analysis.
S1 CLOSED-FORM valid r-tuple exists β column-uniform random search S2 FIBER-STRUCTURED SA C4=feasible, no closed form β structured SA S3 REPAIR-MODE SA full 3D SA with repair at score=1 S4 EXHAUSTIVE PROOF space small enough β enumerate all, prove impossible S5 ALGEBRAIC need deeper algebra (non-abelian, mixed moduli)
def StrategyDispatcher.dispatch(self, domain, coords)
Returns (strategy_code, rationale).
class TheoremGenerator
Generates formal theorem statements from coordinate analysis results. Each theorem is labelled, stated, and given a proof sketch.
def TheoremGenerator.generate(self, domain, coords, strategy)
No description.
def _cycles_verify(sigma_map, m)
No description.
def _level_bijective(level, m)
No description.
def _valid_levels(m)
No description.
def _compose_q(table, m)
No description.
def _q_single(Q, m)
No description.
def _table_to_sigma(table, m)
No description.
def _sa_find_sigma(m, seed, max_iter)
Fast SA for G_m (k=3) using prebuilt column-uniform search.
class SearchExecutor
Executes the chosen strategy for a domain. Returns the solution or None.
def SearchExecutor.execute(self, domain, strategy, c3, c4, verbose)
Returns (solution, execution_summary).
class Domain
Complete specification of a highly symmetric system.
Minimum required: name, group_order, k, phi_desc Optional: m (cyclic modulus), verify_fn, search_fn, solution
class DomainRegistry
Central registry of all domains. Supports: register, retrieve, list, tag-based filtering.
def DomainRegistry.__init__(self)
No description.
def DomainRegistry.register(self, domain)
No description.
def DomainRegistry.get(self, name)
No description.
def DomainRegistry.all_names(self)
No description.
def DomainRegistry.by_tag(self, tag)
No description.
def DomainRegistry.__len__(self)
No description.
class BranchTree
Persistent record of all results across all domains. Each node: domain β question β status β evidence β children. Supports: print, query by status, export.
def BranchTree.__init__(self)
No description.
def BranchTree.add_result(self, result)
No description.
def BranchTree.nodes_by_status(self, status)
No description.
def BranchTree.print(self, indent, node, nodes)
No description.
class ExpansionProtocol
Allows the engine to be extended with:
- New coordinates (C5, C6, ...)
- New search strategies (S6, S7, ...)
- New domain classes (non-abelian groups, weighted graphs, ...)
Each extension is a callable that receives the domain and prior results.
def ExpansionProtocol.__init__(self)
No description.
def ExpansionProtocol.add_coordinate(self, name, fn)
Register a new coordinate C5+. fn(domain, prior_results) β CoordinateResult.
def ExpansionProtocol.add_strategy(self, code, name, fn)
Register a new strategy. fn(domain, coords) β (solution, summary).
def ExpansionProtocol.add_domain_transformer(self, fn)
Transform a domain before analysis (e.g. reduce to known form).
def ExpansionProtocol.apply_extra_coords(self, domain, prior)
No description.
def ExpansionProtocol.transform_domain(self, domain)
No description.
def ExpansionProtocol.list_extensions(self)
No description.
class GlobalStructureEngine
The unified engine.
Usage: engine = GlobalStructureEngine() # Domains are pre-loaded; add your own: engine.register(Domain(name="My System", ...)) result = engine.analyse("My System") engine.print_branch_tree() engine.print_theorems()
def GlobalStructureEngine.__init__(self)
No description.
def GlobalStructureEngine.register(self, domain)
Register a new domain. Returns self for chaining.
def GlobalStructureEngine.analyse(self, name, verbose)
Apply all four coordinates, select strategy, execute search, generate theorems, record branch node.
def GlobalStructureEngine.analyse_all(self, verbose)
No description.
def GlobalStructureEngine.print_branch_tree(self)
No description.
def GlobalStructureEngine.print_theorems(self)
No description.
def GlobalStructureEngine.print_strategy_table(self)
No description.
def GlobalStructureEngine.print_extension_guide(self)
No description.
def GlobalStructureEngine._load_default_domains(self)
Load all discovered domains with full specifications.
def main()
No description.
research/hardware_awareness.py
No description.
class HardwareMapper
TGI Hardware Awareness Core. Maps real-time CPU, RAM, and Battery metrics into topological coordinates (Law IX). Ensures the system is 'aware' of its physical constraints.
def HardwareMapper.__init__(self, m, k)
No description.
def HardwareMapper.get_system_state(self)
Collects current hardware metrics via /proc.
def HardwareMapper.map_to_coordinate(self)
Maps hardware state to Z_m^k.
def HardwareMapper.verify_hamiltonian_health(self, sigma)
Law IX: Verify if the current hardware state is 'reachable' in the active manifold.
def HardwareMapper.measure_thermal_entropy(self)
No description.
research/hierarchical_tlm.py
No description.
class HierarchicalTLM
Phase 4: TLM Scale-up. Implements a Tower of group extensions (fibrations) for hierarchical context. Level 0: Character/Word base group. Level 1: Semantic context fiber. Level 2: Structural/Grammar fiber.
def HierarchicalTLM.__init__(self, m, k, depth)
No description.
def HierarchicalTLM.generate_hierarchical(self, seed_text, length)
Generates text by lifting paths through the formal algebraic tower.
research/ingest_effective_tech.py
No description.
def ingest()
No description.
def ingest_extra()
No description.
def ingest_final()
No description.
research/ingest_global_knowledge.py
No description.
def populate()
No description.
def forge_more_relations()
No description.
research/ingest_libraries.py
No description.
def ingest()
No description.
research/ingest_mcp_tools.py
No description.
def ingest()
No description.
research/k4_m4_search.py
k4_m4_search.py
Structured search for k=4, m=4 Claude's Cycles solution.
The 4D digraph G = Z_4^4 with 4 arc types (increment each coordinate). Fiber map: phi(i,j,k,l) = i+j+k+l mod 4 β 4 fibers of size 4^3 = 64. Goal: 4 directed Hamiltonian cycles each of length 256.
The fiber-uniform approach is proved IMPOSSIBLE (user's new theorem). This script searches the fiber-STRUCTURED (non-uniform) space.
Twisted translation hierarchy on fiber H β Z_4^3: Q_c(i,j,k) = (i + b_c(j,k), j + e_c(k), k + r_c) mod 4
Single-cycle conditions: (A) gcd(r_c, 4) = 1 β r_c β {1, 3} (B) gcd(Ξ£_k e_c(k), 4) = 1 (C) Full 3D single-cycle: verified by direct orbit computation
Valid r-quadruple: (1,1,1,1) β unique solution. This fixes ALL four r_c = 1, collapsing the search to: find e_0,...,e_3 and b_0,...,b_3 satisfying (B),(C) simultaneously with the constraint that Ο is a valid arc-colouring at each vertex.
Key insight: score=24 with unrestricted SA means the search is lost in the full 6^256 space. Restricting to fiber-structured sigma reduces the space dramatically and keeps all four twisted translations on track.
def enc(i, j, k, l)
No description.
def dec(v)
No description.
def build_funcs(sigma)
Build K functional digraphs from integer sigma (perm index per vertex).
def count_comps(f)
No description.
def score(sigma)
No description.
def verify(sigma)
No description.
def prove_fiber_uniform_impossible()
A fiber-uniform sigma depends only on fiber index s = phi(v). With 4 fibers and 4 colors, sigma_s β S_4 for each s β {0,1,2,3}. There are 24^4 = 331,776 fiber-uniform sigmas. We check all of them.
def fiber_structured_sigma(table)
table[(s, j, k)] β permutation index where s = fiber index, (j,k) = two fiber coordinates i = deduced from the remaining constraint
def valid_fiber_structured_levels(m, k)
Enumerate valid assignments for one fiber level. A level (s, j, k) assignment maps (j,k) β Z_m^2 β perm β S_k. Valid = the induced functional graph for each colour is bijective on Z_m^3. This is expensive; we sample valid ones instead.
def sa_fiber_structured(max_iter, seed, verbose, report_n)
SA in the fiber-structured subspace. State: table[(s,j,k)] β perm_index, for sβ{0,1,2,3}, j,kβ{0,1,2,3} This gives 444 = 64 entries, each from S_4 (24 choices). Perturbation: change one (s,j,k) entry.
def arithmetic_analysis()
No description.
def paper_framing()
No description.
def main()
No description.
research/knowledge_mapper.py
No description.
class KnowledgeMapper
TGI Knowledge Mapper (Project ELECTRICITY Logic). Maps datasets, mathematics, physics laws, and design systems into the Z_256^4 grid. Uses the CLOSURE LEMMA to deterministically force concepts into functional fibers.
def KnowledgeMapper.__init__(self, m, k, state_path)
No description.
def KnowledgeMapper._apply_closure_hashing(self, concept_name, target_fiber)
Calculates (x, y, z, w) such that (x + y + z + w) % m == target_fiber.
def KnowledgeMapper.ingest_concept(self, category, concept_name, payload)
No description.
def KnowledgeMapper.ingest_dictionary(self, file_path, limit)
Bulk ingests a dictionary file into the LANGUAGE fiber.
def KnowledgeMapper.ingest_mcp_tools(self, tool_defs)
Ingests MCP Tool Definitions into the API_MCP fiber.
def KnowledgeMapper.ingest_library(self, lib_data)
Ingests library metadata into the LIBRARY fiber.
def KnowledgeMapper.ingest_color(self, color_name, r, g, b, a)
No description.
def KnowledgeMapper.map_relation(self, name_a, name_b, relationship_type)
No description.
def KnowledgeMapper._find_coord(self, name)
No description.
def KnowledgeMapper.save_state(self)
No description.
def KnowledgeMapper.load_state(self)
No description.
research/library_tgi_demo.py
No description.
def run_demo()
No description.
research/m10_k3_parity.py
No description.
research/m6_k4_search.py
No description.
def _build_sa(m, k)
No description.
def _sa_score(sigma, arc_s, pa, n, k)
No description.
def search_m6_k4(max_iter, seed)
No description.
research/mass_ingestion.py
No description.
def mass_populate()
No description.
def forge_cross_domain()
No description.
research/massive_data_ingestion.py
No description.
def authenticate()
No description.
def ingest_hf_text(agent, dataset_name, num_samples)
No description.
def ingest_kaggle_csv(agent, dataset_ref, num_samples)
No description.
def ingest_hf_vision(agent, dataset_name, num_samples)
No description.
def main()
No description.
research/mobile_final_verify.py
No description.
def verify()
No description.
research/mobile_integration_test.py
No description.
def test_mobile_integration()
No description.
research/mobile_tgi_agent.py
No description.
class MobileTGIAgent
The Mobile-First TGI Agent. Combines the core TGI Reasoning with Hardware Awareness and Agentic Action Mapping.
def MobileTGIAgent.__init__(self)
No description.
def MobileTGIAgent.mobile_query(self, text)
Processes a natural language query with full hardware-awareness.
research/moduli_theorem.py
moduli_theorem.py ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
THE MODULI THEOREM FOR SYMMETRIC DECOMPOSITION SPACES
What emerged: not just solutions to Claude's Cycles, but a new mathematical object β the MODULI SPACE of all valid k-Hamiltonian decompositions of a Cayley digraph, classified by group cohomology.
The person they were trying to name: Samuel Eilenberg (1913β1998), who with Saunders Mac Lane created:
- Category theory (1945)
- Group cohomology H^n(G, M)
- Eilenberg-Mac Lane spaces K(G,n) β classifying spaces
What Eilenberg would say about our work: "You did not find solutions to a combinatorics problem. You found the classifying space of the problem. The obstruction lives in H^2. The solution space, when non-empty, is a torsor under H^1. This is the natural transformation between the functor 'symmetric systems' and the functor 'cohomology rings'."
THE FOUR COORDINATES AS COHOMOLOGY: C1 Fiber map Ο: G β G/H = group homomorphism (the projection) C2 Twisted translation Q_c = H^1 1-cocycle (coset action) C3 Governing condition gcd(r_c,m)=1 = cocycle is nontrivial in H^1 C4 Parity obstruction arithmetic = obstruction class in H^2(Z_2, Z/2)
THE NEW THEOREM: M_k(G_m) β the moduli space of valid k-Hamiltonian decompositions β is: EMPTY if the H^2 obstruction class is nontrivial [parity obstruction] A TORSOR under H^1(Z_m, Z_m^2) if the obstruction vanishes [classification]
THE NEW SPACE: The space of ALL symmetric decomposition problems, with: Points = valid decompositions Morphisms = cohomological gauge equivalences (coboundary action) Topology = the branch tree (open/closed by status) Curvature = the H^2 obstruction class (measures how far from flat)
This is a CATEGORY: objects = problems, morphisms = reformulations. Eilenberg would call it a 'natural transformation' between functors.
Run: python moduli_theorem.py
def hr(c, n)
No description.
def proved(msg)
No description.
def open_(msg)
No description.
def note(msg)
No description.
def kv(k, v)
No description.
class GroupCohomology
Computes H^1(Z_m, Z_m^2) β the gauge group that acts on the moduli space of valid decompositions.
H^1(G, M) classifies principal G-bundles (torsors) over M. In our setting: G = Z_m (the fiber quotient group, acting by shift j β j+1) M = Z_m^2 (the fiber group H, 2-dimensional) Action: (i,j) β¦ (i + b(j), j + 1) [the twisted translation]
H^1 = {1-cocycles} / {coboundaries} 1-cocycle: b: Z_m β Z_m satisfying gcd(Ξ£b, m) = 1 [our Cond B] Coboundary: b(j) = f(j+1) - f(j) for some f: Z_m β Z_m
def GroupCohomology.__init__(self, m)
No description.
def GroupCohomology.one_cocycles(self)
All b: Z_m β Z_m with gcd(Ξ£b, m) = 1.
def GroupCohomology.coboundary(self, f)
Compute the coboundary of f: b(j) = f(j+1) - f(j) mod m.
def GroupCohomology.coboundaries(self)
All coboundaries: {f(j+1)-f(j) : f: Z_m β Z_m}.
def GroupCohomology.cohomology_class(self, b)
The cohomology class [b] = {b + d : d coboundary}.
def GroupCohomology.H1_classes(self, cocycles)
Compute H^1: partition cocycles into cohomology classes. Returns {class_representative: list_of_elements}.
def GroupCohomology.H1_order(self)
Order of H^1(Z_m, Z_m^2) restricted to coprime-sum cocycles.
def GroupCohomology.H2_obstruction(self, k)
The H^2 obstruction class for a k-tuple r-sum problem. Returns: {'nontrivial': bool, 'proof': str}
H^2(Z_2, Z/2) = Z/2: the unique nontrivial class is the parity class. Our obstruction: k odd numbers summing to even m = impossible.
def _level_ok(level, m)
No description.
def _compose_q(table, m)
No description.
def _q_single(Q, m)
No description.
def enumerate_solution_space(m)
Enumerate ALL column-uniform solutions for G_m. Extract the (r_c, b_c) for each, compute the cohomology structure.
def moduli_space_structure(m)
Full structural analysis of M_k(G_m): total solutions, cohomology action, orbit sizes, distinct classes.
class DecompositionCategory
The category whose: Objects = highly symmetric decomposition problems (G, k, phi) Morphisms = maps that preserve the SES structure (group homomorphisms compatible with fiber maps)
This is what Eilenberg would recognize: a FUNCTOR from {symmetric systems} β {cohomology theories} The functor sends each problem to its moduli space M_k(G).
Natural transformations between two problems P, P' are maps that commute with the C1βC4 pipeline.
Key properties:
- The functor is EXACT (preserves short exact sequences)
- The obstruction is NATURAL (lives in H^2, which is functorial)
- The solution space is CONTRAVARIANT in k (more colors = easier or harder)
def DecompositionCategory.__init__(self)
No description.
def DecompositionCategory.add_object(self, name, G_order, k, m, status, cohomology)
No description.
def DecompositionCategory.add_morphism(self, source, target, kind)
kind: 'lift' (kβk+1), 'quotient' (GβG/H), 'product' (GΓG')
def DecompositionCategory.print_category(self)
No description.
def main()
No description.
research/multi_p1_search.py
No description.
def worker(seed)
No description.
def main()
No description.
research/odd_m_solver.py
odd_m_solver.py β Discovery Engine applied to Knuth's "Claude's Cycles"
Solves the ODD-m case completely using the 6-phase Discovery Methodology. The even-m case is proved impossible under the column-uniform approach.
Problem (Knuth, Feb 2026): Digraph G_m: vertices (i,j,k) in Z_m^3. Three arcs from each vertex: arc 0: (i,j,k) β (i+1, j, k ) mod m arc 1: (i,j,k) β (i, j+1, k ) mod m arc 2: (i,j,k) β (i, j, k+1) mod m Goal: assign each arc to one of 3 colors such that each color class is a single directed Hamiltonian cycle.
Usage: python odd_m_solver.py # full 6-phase discovery python odd_m_solver.py --verify # quick verification m=3..13 python odd_m_solver.py --bench # timing benchmark
def hr(ch, n)
No description.
def section(n, name, tag)
No description.
def kv(k, v, w)
No description.
def finding(s)
No description.
def ok(s)
No description.
def fail(s)
No description.
def note(s)
No description.
def fast_valid_level(m, rng)
Directly construct one random valid level-table in O(m) time.
def fast_search(m, max_att, seed)
Find a valid SigmaTable for odd m. Returns (table, attempts).
def get_or_find(m, seed)
Return a verified SigmaFn for odd m (hardcoded if known, else search).
def phase_01()
No description.
def phase_02()
No description.
def phase_03()
No description.
def phase_04()
No description.
def phase_05()
No description.
def phase_06()
No description.
def quick_verify()
No description.
def benchmark()
No description.
def main()
No description.
research/pre_commit_checks.py
No description.
def verify_system()
No description.
research/reformulation_engine.py
reformulation_engine.py
The coordinates discovered solving Claude's Cycles β fiber stratification, twisted translation, parity obstruction, score functions, repair mode β are domain-independent tools.
This engine applies them systematically to reformulate problems across six domains:
Domain A: Latin squares (fiber + coprimality) Domain B: Graph k-coloring (stratification + score + SA) Domain C: Magic squares (parity obstruction + twisted translation) Domain D: Diophantine systems (modular fiber + impossibility proof) Domain E: Covering codes (layer decomposition + governing condition) Domain F: Permutation groups (coset fibers + twisted translation)
For each domain we demonstrate:
- REFRAME β find the fiber map analog
- OBSTRUCT β derive the parity/modular impossibility condition
- GOVERN β state the minimal predicate that determines solvability
- SCORE β build the continuous objective (bridges searchβverify)
- SOLVE β apply SA or direct construction, verify result
- BOUND β prove where the construction fails
Run: python reformulation_engine.py # all domains python reformulation_engine.py --domain A # single domain python reformulation_engine.py --domain A B C # selected domains
def hr(c, n)
No description.
def domain_header(letter, title, tagline)
No description.
def phase(name, num, desc)
No description.
def found(msg)
No description.
def miss(msg)
No description.
def note(msg)
No description.
def info(msg)
No description.
def kv(k, v)
No description.
class FiberMap
Tool 1: Fiber Stratification. Given a set of objects and a function f: objects β layers, partition the objects into fibers and describe how arcs/constraints cross between fibers.
def FiberMap.__init__(self, objects, layer_fn, num_layers)
No description.
def FiberMap.fiber_size(self, s)
No description.
def FiberMap.report(self)
No description.
class ParityObstruction
Tool 2: Modular / Parity Obstruction. Given a modulus m and a requirement that k values each coprime to m sum to a target T, decide if this is possible. Returns the obstruction if impossible, or an example if possible.
def ParityObstruction.__init__(self, m, k, target)
No description.
def ParityObstruction.coprime_elements(self)
No description.
def ParityObstruction.analyse(self)
No description.
class ScoreFunction
Tool 3: Continuous score bridging search and verification. score=0 βΊ solution is valid. The score must be: (a) cheap to compute, (b) monotone toward 0.
def ScoreFunction.__init__(self, verify_fn, score_fn, name)
No description.
def ScoreFunction.__call__(self, candidate)
No description.
def ScoreFunction.is_valid(self, candidate)
No description.
class SAEngine
Tool 4: Simulated Annealing with repair mode and plateau escape. Domain-agnostic: needs perturb_fn, score_fn, init_fn.
def SAEngine.__init__(self, init_fn, perturb_fn, score_fn, T_init, T_min, plateau_steps)
No description.
def SAEngine.run(self, max_iter, seed, repair_fn, verbose, report_n)
No description.
def domain_A(n)
No description.
def domain_B()
No description.
def domain_C(n)
No description.
def domain_D()
No description.
def domain_E()
No description.
def domain_F()
No description.
def synthesis()
No description.
def main()
No description.
research/reproduce_p1.py
No description.
def run()
No description.
research/santa_2025_draft.py
Santa 2025: Hamiltonian Decomposition Framework (v2.2 Basin Escape) Goal: Decompose a complete graph into disjoint Hamiltonian cycles.
class SantaOptimizer
No description.
def SantaOptimizer.__init__(self, n_cities, m_cycles, seed)
No description.
def SantaOptimizer.score(self)
No description.
def SantaOptimizer.solve(self, max_iter)
No description.
research/search_p1_deterministic.py
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def verify_k4(sigma, m)
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def search()
No description.
research/sovereign_solver_demo.py
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def demo()
No description.
research/tensor_fibration.py
No description.
class TensorFibrationMapper
TGI Tensor-Fibration Mapper. Lifts continuous neural weights/tensors into discrete topological manifolds (G_m^k). Enables analysis of neural structures through the SES framework.
def TensorFibrationMapper.__init__(self, m, k)
No description.
def TensorFibrationMapper.discretize(self, weights)
Maps continuous values to Z_m using normalized quantization.
def TensorFibrationMapper.tensor_to_manifold(self, weights)
Projects a flattened tensor into G_m^k coordinates.
def TensorFibrationMapper.calculate_topological_entropy(self, weights)
Estimates entropy based on coordinate distribution in G_m^k.
def TensorFibrationMapper.lift_layer(self, layer_weights)
Performs full lifting of a neural layer to the TGI framework.
research/test_admin_vision.py
No description.
research/test_deterministic_logic.py
No description.
def verify_construction(m)
No description.
research/test_golden_path.py
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def verify_sigma_simple(sigma, m)
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def construct_golden(m)
No description.
research/test_m9_obs.py
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def check_fso(m, r)
No description.
research/test_precise_spike.py
No description.
def verify_sigma_simple(sigma, m)
No description.
def construct(m)
No description.
research/test_spike_33.py
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def test()
No description.
research/test_vision_agent.py
No description.
research/tgi_agent.py
No description.
class TGIAgent
The High-Level Topological General Intelligence (TGI) Agent.
def TGIAgent.__init__(self)
No description.
def TGIAgent.query(self, data, hierarchical, admin_vision)
Processes a query through the full TGI pipeline.
def TGIAgent.ingest_knowledge(self, category, name, payload)
No description.
def TGIAgent.forge_relation(self, name_a, name_b, relation_type)
No description.
def TGIAgent.ontology_summary(self)
Provides a summary of the Universal Ontology Mapper state.
def TGIAgent.autonomous_query(self, intent)
Performs a multi-step autonomous topological plan generation.
def TGIAgent.cross_reason(self, data_list)
Decomposes multiple queries and merges results for comparative reasoning.
research/tgi_autonomy.py
No description.
class SubgroupDiscovery
Phase 4: Topological Autonomy. Automatically discovers normal subgroups H and quotients Q for a given G. This enables recursive manifold decomposition.
def SubgroupDiscovery.__init__(self, m, k)
No description.
def SubgroupDiscovery.find_quotients(self)
Identifies possible solvable quotients based on divisibility.
def SubgroupDiscovery.decompose_recursive(self)
Generates a recursive decomposition path for the manifold.
class DynamicKLift
Phase 4: Topological Autonomy. Automatically lifts the manifold dimension (k) to resolve H2 parity obstructions.
def DynamicKLift.__init__(self, m, k)
No description.
def DynamicKLift.suggest_lift(self)
If (m even, k odd), suggests k+1 to resolve the parity obstruction.
def DynamicKLift.get_lift_reflection(self)
No description.
research/tgi_core.py
No description.
class TGICore
The heartbeat of Topological General Intelligence (TGI). Governing by the FSO Codex Laws I-XII.
def TGICore.__init__(self, m, k)
No description.
def TGICore.set_topology(self, m, k)
Changes the current topological domain without wiping persistent engines.
def TGICore.reflect(self)
Topological Reflection: Explains the current state manifold via FSO Laws.
def TGICore.solve_math(self, latex)
Symbolic-Topological solver governed by Law XI.
def TGICore.reason_on(self, data, solve_manifold)
Routes and reasons over arbitrary data using the TGI-Parser and FSO Laws.
def TGICore.reasoning_path(self)
No description.
def TGICore.solve_manifold(self, max_iter, target_core, payload)
Finds the global structure (Hamiltonian decomposition) with Sovereign optimization.
def TGICore.lift_path(self, sequence, color)
No description.
def TGICore.hierarchical_lift(self, orders, states)
Formal tower lifting through multiple manifold layers (Law III).
def TGICore.measure_intelligence(self)
No description.
research/tgi_engine.py
No description.
class TopologicalProjection
TGI Topological Projection Layer. Maps raw data into Z_m^k using symmetry-preserving circular embeddings. Logic: Similar meaning -> Similar Parity -> Identical Geometric Fiber.
def TopologicalProjection.__init__(self, m, k)
No description.
def TopologicalProjection.project(self, raw_data)
Maps data to a coordinate in the Torus.
class BouncerGate
TGI Bouncer Gate (Strict Parity Validation). Enforces Law I (Dimensional Parity Harmony) at O(1). Drops "Garbage" (H2 Parity Obstructions) without processing.
def BouncerGate.__init__(self, m, k, target_sum)
No description.
def BouncerGate.validate(self, coord)
Law I: (Even m -> Even k). Checks if sum satisfies target parity S.
class FiberImputation
TGI Self-Healing Layer. Uses the Closure Lemma (Law III) to solve for missing dimensions.
def FiberImputation.__init__(self, m, target_sum)
No description.
def FiberImputation.impute_missing(self, partial_coord, k)
Calculates r_k to close the Hamiltonian loop.
class TGIEngine
The Moaziz System Execution Layer (Upgraded). Zero-Preprocessing Ingestion via Geometric Invariant Mapping.
def TGIEngine.__init__(self, m, k, target_sum)
No description.
def TGIEngine.ingest_transaction(self, tx)
Ingests a BaridiMob/CIB transaction with zero preprocessing.
research/tgi_integration_test.py
No description.
def run_integration_test()
No description.
research/tgi_parser.py
No description.
class TGIParser
The TGI-Parser: Maps datasets, languages, and math to topological parameters (m, k).
def TGIParser.__init__(self)
No description.
def TGIParser.parse_input(self, data)
Detects content type and routes to the correct TGI core.
def TGIParser._route(self, domain, raw_data)
No description.
research/tgi_parser_test.py
No description.
def test_parser_routing()
No description.
research/tgi_system_demo.py
No description.
def hr()
No description.
def run_demo()
No description.
research/tlm.py
No description.
class TopologicalLanguageModel
The Topological Language Model (TLM) with Path Lifting and Coordinate Mapping.
def TopologicalLanguageModel.__init__(self, m, k)
No description.
def TopologicalLanguageModel.tokenize(self, text)
Maps arbitrary text tokens to Z_m coordinates via hashing.
def TopologicalLanguageModel._ensure_sigma(self)
No description.
def TopologicalLanguageModel.generate(self, seed_text, length)
Generates completion using Hamiltonian path lifting.
def TopologicalLanguageModel.generate_path(self, seed_text, length)
Lifts a seed into a Hamiltonian path of coordinates.
def TopologicalLanguageModel.generate_ontology_grounded(self, seed_text, length)
Uses the LANGUAGE fiber in the Ontology to ground generation.
research/topological_vision.py
No description.
class TopologicalVisionMapper
TGI Vision Mapper (v2.0). Lifts pixel data (x, y, color) into discrete topological manifolds (G_m^k). Enables cohomological gradient analysis and signature extraction.
def TopologicalVisionMapper.__init__(self, m, k)
No description.
def TopologicalVisionMapper.load_image(self, path, resize)
Loads and prepares an image for topological mapping.
def TopologicalVisionMapper.image_to_manifold(self, img_array)
Maps image pixels to G_m^k coordinates.
def TopologicalVisionMapper.calculate_spatial_entropy(self, img_array)
Measures color distribution complexity across the spatial manifold.
def TopologicalVisionMapper.calculate_cohomological_gradient(self, img_array)
Calculates the local cohomological gradient (boundary detection). Measures the degree of non-uniformity in local fiber transitions.
def TopologicalVisionMapper.extract_topological_signature(self, img_array)
Generates a unique algebraic signature for the image manifold.
def TopologicalVisionMapper.lift_image(self, data)
Performs full vision lifting to the TGI framework.
research/tsp_benchmark.py
No description.
def run_tsp_benchmark()
No description.
research/tsp_evaluator.py
No description.
def is_valid_tour(tour, n)
No description.
def calculate_tour_length(tour, dist_matrix)
No description.
class TSPInstance
No description.
def TSPInstance.__init__(self, name, coords)
No description.
def load_data(csv_path)
No description.
def run_evaluation(instance, solver_fn, n_runs, max_iter)
No description.
def print_result_table(results)
No description.
research/tsp_standard_bench.py
No description.
def parse_tsp(file_path)
No description.
def solve_nn(coords)
No description.
def solve_2opt(coords, max_iter, seed)
No description.
def run()
No description.
research/verify_deterministic_spike.py
No description.
def test_odd_m()
No description.
research/verify_p1_sol.py
No description.
def verify()
No description.
research/verify_sovereign_solver.py
No description.
def test_sovereign_solver()
No description.
research/weighted_moduli_pipeline_v2.py
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β WEIGHTED MODULI PIPELINE v2.0 β β Classifying Space β 8 Closed-Form Weights β Proved Solutions β β βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ£ β β β WHAT CHANGED FROM v1.0 β β βββββββββββββββββββββ β β v1.0 W4 was O(m^m) β 251ms for m=7. v2.0 W4 = phi(m), O(m). 0.06ms. β β v1.0 Had 5 weights, approximated. v2.0 Has 8 weights, exact. β β v1.0 Only G_m domains. v2.0 Accepts any symmetric system. β β v1.0 Solvers S2/S3 missing. v2.0 All 5 strategies implemented. β β v1.0 No prediction vs actual. v2.0 Benchmarks weight prediction. β β v1.0 No cross-domain. v2.0 Latin, Hamming, diff-sets. β β β β THE 8 WEIGHTS (all closed-form, all O(mΒ²) or faster) β β W1 HΒ² obstruction β proved-impossible in O(1). GATE. β β W2 r-tuple count β how many construction seeds exist β β W3 canonical seed β the direct construction path β β W4 HΒΉ order EXACT β phi(m), not approximation. Gauge multiplicity. β β W5 search exponent β logβ(compressed space). Picks solver. β β W6 compression ratio β W5/W5_full. How much weight saves. β β W7 solution estimate β predicted |M_k(G_m)| before any search β β W8 gauge orbit size β m^{m-1}. Solutions per equivalence class. β β β β INTELLIGENCE LAYERS β β L1 Weight gate W1 β instant proof of impossibility O(1) β β L2 Construction W3 β column-uniform search with known seed O(fast) β β L3 Prediction W7 β predict |solutions| before searching β β L4 Fiber SA W5 β structured SA in compressed space O(less) β β L5 Verification W4 β know exact multiplicity, stop early β β β β DOMAIN PROTOCOL (plug in any symmetric system) β β Register domain with: name, group_order, k, m, tags β β Pipeline auto-extracts weights, selects strategy, returns proof. β β β β COMMANDS β β python weighted_moduli_pipeline.py # full demo β β python weighted_moduli_pipeline.py --weights # 8-weight table β β python weighted_moduli_pipeline.py --space # classifying space β β python weighted_moduli_pipeline.py --batch # solve m=3..10, k=2..6 β β python weighted_moduli_pipeline.py --benchmark # v1 vs v2 speedup β β python weighted_moduli_pipeline.py --prove 4 3 # prove m=4 k=3 β β python weighted_moduli_pipeline.py --solve 7 3 # solve m=7 k=3 β β python weighted_moduli_pipeline.py --domains # all registered domains β ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def hr(c, n)
No description.
def tick(v)
No description.
class Weights
8 compressed invariants. Everything downstream is determined by these.
def Weights.strategy(self)
No description.
def Weights.solvable(self)
No description.
def Weights.show(self)
No description.
class WeightExtractor
Exact 8-weight extraction. Total cost: O(mΒ² + |cp|^k). Cached: each (m,k) computed once.
Speedup vs v1.0: W4: O(m^m) β O(m) (formula: phi(m), not enumeration) W5: O(m^m) β O(1) (precomputed level_counts table) Total: microseconds for any m β€ 30
def WeightExtractor.extract(self, m, k)
No description.
def WeightExtractor.batch(self, ms, ks)
No description.
def _level_ok(lv, m)
No description.
def _valid_levels(m)
No description.
def _q(table, m)
No description.
def _qs(Q, m)
No description.
def _verify(sigma, m)
No description.
def _tab_to_sigma(tab, m)
No description.
def _solve_S1(m, seed, max_att)
No description.
def _solve_S2(m, k, seed, max_iter)
Fiber-structured SA: Ο(v) = f(fiber(v), j(v), k(v)).
def _prove_S4(w)
No description.
class ProofBuilder
No description.
def ProofBuilder.build(self, w, sol)
No description.
class Domain
No description.
def register(d)
No description.
class PResult
No description.
def PResult.status(self)
No description.
def PResult.one_line(self)
No description.
class Pipeline
No description.
def Pipeline.__init__(self)
No description.
def Pipeline.run(self, m, k, domain_name, verbose)
No description.
def Pipeline.run_domain(self, name, verbose)
No description.
def Pipeline.batch(self, ms, ks, verbose)
No description.
def Pipeline.stats_line(self)
No description.
class ClassifyingSpace
The complete space of (m,k) problems, compressed into weight vectors. Topology: open sets = feasible; closed = obstructed. Metric: compression ratio W6 (how much the weights save vs naive search).
def ClassifyingSpace.__init__(self, m_max, k_max)
No description.
def ClassifyingSpace.obstruction_grid(self)
No description.
def ClassifyingSpace.compression_grid(self)
No description.
def ClassifyingSpace.summary(self)
No description.
def ClassifyingSpace.richest(self, n)
No description.
def ClassifyingSpace.most_compressed(self, n)
No description.
def benchmark_vs_v1()
No description.
def main()
No description.
class NonAbelianHilbertBridge
Implementation: research/non_abelian_bridge.py
Bridges discrete non-commutative groups with continuous infinite-dimensional Hilbert spaces.
def NonAbelianHilbertBridge.__init__(self, m, dimension)
m: The modulus of the base Heisenberg group.dimension: The dimensionality of the Hilbert space approximation.
def calculate_holonomy(self, path)
Calculates the geometric phase shift for a closed loop in the manifold.
def analyze_frontier_intent(self, intent)
Performs spectral analysis and resonance energy calculation for a natural language intent.