Document init_state_tensor.parquet and add its config

README.md

@@ -1,49 +1,68 @@
 ---
+configs:
+  - config_name: default
+    data_files: omega_tensor.parquet
+  - config_name: init_state
+    data_files: init_state_tensor.parquet
 dataset_info:
-  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: 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
@@ -54,14 +73,19 @@ tags:
   - exhaustive-enumeration
   - FPGA
 size_categories:
-  - 10K<n<100K
+  - 1M<n<10M
 ---
 
 # Omega Tensor: Exact Halting Fractions for 38,416 Instruction Sets
 
 Exhaustive enumeration of all 1,679,616 programs of length 8 for every possible instruction set on a two-register, 8-bit, bounded machine with JNZ-to-zero control flow. Each row is one ISA. Each halting count is exact.
 
-## Contents
+The repository contains two tables:
+
+- `omega_tensor.parquet` (38,416 rows) — canonical single-initial-state table used in the paper, with the halting fraction at A=0, B=0 and cross-observable columns (cycle length, output entropy, reachability, structural flags).
+- `init_state_tensor.parquet` (38,416 rows, 260 columns) — extends the above to every initial A value in 0..255 at B=0. Halting counts only.
+
+## Contents — `omega_tensor.parquet`
 
 38,416 rows. Each row represents one ordered ISA defined by four opcode assignments (opcodes 1-4) drawn from 14 primitive operations. Opcode 0 is always INC. Opcode 5 is always JNZ.
 
@@ -79,7 +103,7 @@ Exhaustive enumeration of all 1,679,616 programs of length 8 for every possible
 | entropy_bits | float | Shannon entropy of the output distribution (bits) |
 | reachable_outputs | int | Number of distinct outputs produced by halting programs |
 
-## Statistics
+## Statistics — `omega_tensor.parquet`
 
 - Range: [0.290710, 0.816916]
 - Mean: 0.612418
@@ -109,6 +133,35 @@ Known ISA values verified against independent FPGA silicon measurements and 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)