--- configs: - config_name: default data_files: omega_tensor.parquet - config_name: init_state data_files: init_state_tensor.parquet dataset_info: - config_name: default features: - name: op1 dtype: int64 - name: op2 dtype: int64 - name: op3 dtype: int64 - name: op4 dtype: int64 - name: op1_name dtype: string - name: op2_name dtype: string - name: op3_name dtype: string - name: op4_name dtype: string - name: halting_count dtype: int64 - name: omega dtype: float64 - name: has_swp dtype: bool - name: has_mov dtype: bool - name: has_and dtype: bool - name: has_shr dtype: bool - name: involution_count dtype: int64 - name: coupling dtype: string - name: avg_cycle dtype: float64 - name: max_cycle dtype: int64 - name: entropy_bits dtype: float64 - name: reachable_outputs dtype: int64 splits: - name: train num_examples: 38416 - config_name: init_state features: - name: op1 dtype: int8 - name: op2 dtype: int8 - name: op3 dtype: int8 - name: op4 dtype: int8 splits: - name: train num_examples: 38416 license: mit task_categories: - other tags: - halting-problem - computability - algorithmic-information-theory - exhaustive-enumeration - FPGA size_categories: - 1M= 8 were counted as halting. The computation used a Numba-JIT-compiled Python interpreter at 0.26 seconds per ISA (approximately 2.8 hours total for all 38,416 ISAs). Every halting count is exact. No sampling, no approximation, no estimation. ## Verification Known ISA values verified against independent FPGA silicon measurements and CPU cross-checks: - ISA-A (DEC SWP ADD XOR): 978,929 halting (dataset) = 978,929 (FPGA) = 978,929 (CPU) - ISA-B (NEG MOV SUB AND): 1,235,107 = 1,235,107 = 1,235,107 - ISA-G (SHR MOV SUB AND): 1,248,490 = 1,248,490 = 1,248,490 ## Contents — `init_state_tensor.parquet` 38,416 rows, one per ISA (same ISA space as `omega_tensor.parquet`). 260 columns: four opcode slots plus 256 halting counts, one per initial A value. | Column | Type | Description | |---|---|---| | op1-op4 | int8 | Operation IDs for opcodes 1-4 | | h_000 through h_255 | int32 | Halting counts at initial state (A=N, B=0) for N=0..255 | Join on (op1, op2, op3, op4) to recover names, cycle length, entropy, and structural columns from `omega_tensor.parquet`. The canonical value `omega` from that table equals `h_000 / 1,679,616`. ## Statistics — `init_state_tensor.parquet` - Total cells: 38,416 x 256 = 9,834,496 exact halting counts - Total program evaluations: ~16.5 billion - Omega(init=0) mean: 0.612418 (matches `omega_tensor.parquet`) - Omega(init=128) mean: 0.366431, range [0.236044, 0.681003] - Ratio Omega(0)/Omega(128): mean 1.7429, median 1.6430, range [0.8336, 3.1466] - 99.92% of ISAs have Omega(0) > Omega(128); 0.08% have the inverse (INC-dominant ISAs) - 7.91% of ISAs have a perfectly reflection-symmetric bowl (Omega(a) = Omega(256-a)) - No ISA has its Omega minimum at init_a = 128 exactly; 3.23% have argmin in [126, 130] - Bowl depth Omega(0) - Omega(min) ranges [0.058, 0.513], mean 0.260 ## Method — `init_state_tensor.parquet` Same interpreter and enumeration protocol as the canonical tensor, extended over all 256 values of the initial accumulator A (B held at 0). 9,834,496 (ISA, init_a) cells, each the exact halting count over the full 1,679,616-program space. Computed with the same Numba-JIT interpreter under an 18-worker multiprocessing pool, 110.3 wall hours, zero errors. Every count is exact. Cross-validation: for every ISA, the `h_000` column equals the canonical `halting_count` from `omega_tensor.parquet`. ## Citation Based on: [The Finite Halting Fraction Across Machine Models](https://github.com/CharlesCNorton/rime/blob/main/experiments/kolmogorov-omega/RESULTS.md)