docs: convert LaTeX syntax to clean Unicode for Hugging Face Markdown rendering

MODEL_CARD.md

@@ -1,10 +1,11 @@
+
 # Model Card: InvariantOne-v1
 
 **Release Version:** `InvariantOne-v1` (Frozen Release)  
 **Date:** September 24, 2026  
 **License:** Apache-2.0  
 **Base Backbone:** `Qwen/Qwen3.5-4B-Base` (Revision `1001bb4d826a52d1f399e183466143f4da7b741b`, Native BF16)  
-**Primary Checkpoint:** $D_5$-L4 ($N_{\text{op}}=16$, Seed 42 Primary; Replicated across Seeds 43, 44)  
+**Primary Checkpoint:** D5-L4 (N_op=16, Seed 42 Primary; Replicated across Seeds 43, 44)  
 
 ---
 
@@ -14,8 +15,8 @@
 
 Standard autoregressive language models suffer from severe position, length, and order biases when evaluating multiple-choice candidate decisions. `InvariantOne-v1` solves this structural failure through a decoupled comparative architecture:
 1. **Candidate-Independent Scoring:** Each candidate action is scored independently conditioned on context, eliminating candidate order sensitivity and cross-option attention artifacts.
-2. **Analytic Distributional Equivariance:** Option-span pooled representations pass through a lightweight direct comparative projection head, producing logits normalized via softmax to guarantee exact permutation equivariance over candidate distributions ($\text{Mean TVD} = 0.000000$).
-3. **Upper-Layer Relational Pre-Adaptation:** Parameter-efficient adaptation (LoRA on layers 28–31) trained across a diverse relational operator universe ($N_{\text{op}}=16$) instills strong, transferable relational reasoning capabilities into the comparative readout.
+2. **Analytic Distributional Equivariance:** Option-span pooled representations pass through a lightweight direct comparative projection head, producing logits normalized via softmax to guarantee exact permutation equivariance over candidate distributions (Mean TVD = 0.000000).
+3. **Upper-Layer Relational Pre-Adaptation:** Parameter-efficient adaptation (LoRA on layers 28–31) trained across a diverse relational operator universe (N_op=16) instills strong, transferable relational reasoning capabilities into the comparative readout.
 
 ```
 Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
@@ -35,28 +36,28 @@ Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
 
 | Parameter | Specification |
 | :--- | :--- |
-| **Base Model** | `Qwen/Qwen3.5-4B-Base` (32 transformer layers, $d_{\text{model}} = 2560$) |
+| **Base Model** | `Qwen/Qwen3.5-4B-Base` (32 transformer layers, d_model = 2560) |
 | **Backbone Status** | Layers 0–27 strictly frozen (zero parameter updates) |
-| **Adaptation** | Low-Rank Adaptation (LoRA) on upper layers 28–31: $r = 8, \alpha = 16$ (layers 28–30: `in_proj_qkv`, `out_proj`; layer 31: `q_proj`, `v_proj`, `o_proj`) |
+| **Adaptation** | Low-Rank Adaptation (LoRA) on upper layers 28–31: r = 8, α = 16 (layers 28–30: `in_proj_qkv`, `out_proj`; layer 31: `q_proj`, `v_proj`, `o_proj`) |
 | **Active LoRA Parameters** | 585,728 parameters |
-| **Readout Head** | `DirectComparativeHead`: Linear($2560 \to 256$) $\to$ GELU $\to$ LayerNorm($256$) $\to$ Linear($256 \to 1$) |
+| **Readout Head** | `DirectComparativeHead`: Linear(2560 → 256) → GELU → LayerNorm(256) → Linear(256 → 1) |
 | **Active Head Parameters** | 722,177 parameters |
-| **Total Active Adapted Parameters** | 1,307,905 parameters ($<0.05\%$ of base model) |
+| **Total Active Adapted Parameters** | 1,307,905 parameters (<0.05% of base model) |
 | **Pooling Method** | Option-span mean pooling over candidate option token span |
-| **Scoring Scheme** | Independent candidate scoring with comparative readout: $P(y = i \mid x, \{o_k\}) = \frac{\exp(s_i / \tau^*)}{\sum_{j=1}^K \exp(s_j / \tau^*)}$ |
-| **Calibration Temperature** | $\tau^* = 1.0091$ (pre-calibrated on validation split) |
+| **Scoring Scheme** | Independent candidate scoring with comparative readout: `P(y = i | x, {o_k}) = exp(s_i / τ*) / Σ_j exp(s_j / τ*)` |
+| **Calibration Temperature** | τ* = 1.0091 (pre-calibrated on validation split) |
 
 ### Cryptographic Checkpoint Signatures
 
-* **Primary Checkpoint (`Seed 42`, $N_{\text{op}}=16$)**:
+* **Primary Checkpoint (`Seed 42`, N_op=16)**:
   - LoRA Weights: `checkpoints/invariantone-v1/adapter_model.pt` (Frozen Phase 7R research checkpoint)
     - SHA-256: `a0000d3ec984d155fbad5abc854556904ecffe78b997900b677a8d8d5811e4d2`
   - Head Weights: `checkpoints/invariantone-v1/head.pt` (Frozen Phase 7R research checkpoint)
     - SHA-256: `190d867dc302a89d420d19a8374a5db252ea2e71e4f40c68064ded23fc321384`
-* **Replication Checkpoint (`Seed 43`, $N_{\text{op}}=16$)**:
+* **Replication Checkpoint (`Seed 43`, N_op=16)**:
   - LoRA: `checkpoints/invariantone-v1/adapter_model_seed43.pt` (Frozen Phase 7R research checkpoint)
   - Head: `checkpoints/invariantone-v1/head_seed43.pt` (Frozen Phase 7R research checkpoint)
-* **Replication Checkpoint (`Seed 44`, $N_{\text{op}}=16$)**:
+* **Replication Checkpoint (`Seed 44`, N_op=16)**:
   - LoRA: `checkpoints/invariantone-v1/adapter_model_seed44.pt` (Frozen Phase 7R research checkpoint)
   - Head: `checkpoints/invariantone-v1/head_seed44.pt` (Frozen Phase 7R research checkpoint)
 
@@ -64,21 +65,21 @@ Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
 
 ## 3. Verified Performance & Benchmark Evaluation
 
-`InvariantOne-v1` was evaluated on `FINAL-HOLDOUT-V2` ($1,536$ four-choice items) under strict preregistered one-shot governance. Prior to inference, SHA-256 checksums of all strata were verified against the locked manifest (`final_holdout_v2_manifest.json`).
+`InvariantOne-v1` was evaluated on `FINAL-HOLDOUT-V2` (1,536 four-choice items) under strict preregistered one-shot governance. Prior to inference, SHA-256 checksums of all strata were verified against the locked manifest (`final_holdout_v2_manifest.json`).
 
-> **Scope Note on Candidate Options Count ($K$):**  
-> The runtime supports arbitrary $K \ge 2$; the reported scientific evaluation results are for $K=4$ unless otherwise stated. Experimental generalization to arbitrary $K$ has not been independently established in the scientific benchmarks.
+> **Scope Note on Candidate Options Count (K):**  
+> The runtime supports arbitrary K ≥ 2; the reported scientific evaluation results are for K=4 unless otherwise stated. Experimental generalization to arbitrary K has not been independently established in the scientific benchmarks.
 
 ### Definitive Benchmark Summary
 
-| Stratum | Evaluation Focus | $D_0$ (Baseline) | $B_1$-Raw | $B_1$-Sym (24-Perm) | `InvariantOne-v1` (Seed 42) | `InvariantOne-v1` (Mean $\pm$ SD) |
+| Stratum | Evaluation Focus | D0 (Baseline) | B1-Raw | B1-Sym (24-Perm) | `InvariantOne-v1` (Seed 42) | `InvariantOne-v1` (Mean ± SD) |
 | :--- | :--- | :---: | :---: | :---: | :---: | :---: |
-| **`FINAL-REAL`** | Real operational control tasks ($N=256$) | 89.45% | 91.41% | 92.58% | **94.14%** | **93.36% $\pm$ 1.35%** |
-| **`FINAL-L1`** | Familiar-Operator Compositional Recombination ($N=256$) | 32.81% | 38.28% | 43.75% | **89.84%** | **89.32% $\pm$ 0.45%** |
-| **`FINAL-L2a`** | Semantic Extrapolation ($N=256$) | 28.12% | 45.31% | 50.39% | **86.33%** | **87.76% $\pm$ 2.48%** |
-| **`FINAL-L2b`** | Relational Extrapolation ($N=256$) | 22.27% | 62.50% | **65.23%** | 55.08% | 53.91% $\pm$ 2.03% |
-| **`FINAL-L3`** | Double Extrapolation ($N=512$) | 25.20% | 60.94% | **65.43%** | 56.84% | 54.10% $\pm$ 4.91% |
-| **`Aggregate`** | Total locked holdout pool ($N=1,536$) | 37.17% | 59.90% | 63.80% | **73.18%** (1,124/1,536) | **71.74% $\pm$ 1.97%** |
+| **`FINAL-REAL`** | Real operational control tasks (N=256) | 89.45% | 91.41% | 92.58% | **94.14%** | **93.36% ± 1.35%** |
+| **`FINAL-L1`** | Familiar-Operator Compositional Recombination (N=256) | 32.81% | 38.28% | 43.75% | **89.84%** | **89.32% ± 0.45%** |
+| **`FINAL-L2a`** | Semantic Extrapolation (N=256) | 28.12% | 45.31% | 50.39% | **86.33%** | **87.76% ± 2.48%** |
+| **`FINAL-L2b`** | Relational Extrapolation (N=256) | 22.27% | 62.50% | **65.23%** | 55.08% | 53.91% ± 2.03% |
+| **`FINAL-L3`** | Double Extrapolation (N=512) | 25.20% | 60.94% | **65.43%** | 56.84% | 54.10% ± 4.91% |
+| **`Aggregate`** | Total locked holdout pool (N=1,536) | 37.17% | 59.90% | 63.80% | **73.18%** (1,124/1,536) | **71.74% ± 1.97%** |
 
 ### Counterfactual Sensitivity & Minimal-Pair Tracking
 
@@ -94,30 +95,30 @@ Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
 ## 4. Invariance Guarantees & Systems Efficiency
 
 ### Structural Invariance Audit
-* **Distributional Equivariance**: Mean TVD = **$0.000000$**, Max TVD = **$0.000000$** across all 24 option permutations on 128 samples ($3,072$ evaluations).
-* **Top-1 Tie-Breaking Instability**: $1.56\%$ top-choice flips under permutation, caused strictly by floating-point precision ties at decision boundaries under argmax selection. The underlying probabilistic output distribution is strictly equivariant.
+* **Distributional Equivariance**: Mean TVD = **0.000000**, Max TVD = **0.000000** across all 24 option permutations on 128 samples (3,072 evaluations).
+* **Top-1 Tie-Breaking Instability**: 1.56% top-choice flips under permutation, caused strictly by floating-point precision ties at decision boundaries under argmax selection. The underlying probabilistic output distribution is strictly equivariant.
 
 ### Computational Efficiency (Measured on NVIDIA A100-SXM4-40GB)
 * **Benchmark Provenance Note:** A100 performance figures are from the frozen FINAL-HOLDOUT-V2 benchmarking run; release-wheel functionality was independently smoke-tested in a fresh Python 3.12 environment.
-* **Forward Passes**: 4 candidate forward passes per sample vs 24 full-context forward passes for $B_1$-Sym ($6.0\times$ reduction).
-* **Wall-Clock Latency**: **$83.71\text{ ms}$** vs **$425.31\text{ ms}$** ($B_1$-Sym) $\implies$ **$5.08\times$ speedup**.
-* **Throughput**: **$11.95\text{ samples/sec}$** vs **$2.35\text{ samples/sec}$** ($B_1$-Sym).
-* **Peak VRAM**: **$8,941.2\text{ MB}$** vs **$14,614.2\text{ MB}$** ($B_1$-Sym) $\implies$ **$38.8\%$ memory footprint reduction**.
+* **Forward Passes**: 4 candidate forward passes per sample vs 24 full-context forward passes for B1-Sym (6.0× reduction).
+* **Wall-Clock Latency**: **83.71 ms** vs **425.31 ms** (B1-Sym) ⟹ **5.08× speedup**.
+* **Throughput**: **11.95 samples/sec** vs **2.35 samples/sec** (B1-Sym).
+* **Peak VRAM**: **8,941.2 MB** vs **14,614.2 MB** (B1-Sym) ⟹ **38.8% memory footprint reduction**.
 
 ---
 
 ## 5. Capabilities vs Frontier Boundaries
 
 ### Confirmed Capabilities
-1. **Real-Task Decision Accuracy**: Outperforms unadapted baselines and 24-permutation causal scoring on real operational decision tasks ($94.14\%$).
-2. **Compositional Recombination**: Excels at counterfactual state tracking and rule execution for learned operator families ($89.84\%$ accuracy, $99.12\%$ override switch rate).
-3. **Semantic Domain Generalization**: Robustly transfers learned relational operators to completely novel technical and engineering domains ($86.33\%$, $+35.94$ points over $B_1$-Sym).
-4. **Order-Equivariant Efficiency**: Eliminates position bias with zero prompt permutation overhead, achieving $5.08\times$ lower latency than permutation averaging.
+1. **Real-Task Decision Accuracy**: Outperforms unadapted baselines and 24-permutation causal scoring on real operational decision tasks (94.14%).
+2. **Compositional Recombination**: Excels at counterfactual state tracking and rule execution for learned operator families (89.84% accuracy, 99.12% override switch rate).
+3. **Semantic Domain Generalization**: Robustly transfers learned relational operators to completely novel technical and engineering domains (86.33%, +35.94 points over B1-Sym).
+4. **Order-Equivariant Efficiency**: Eliminates position bias with zero prompt permutation overhead, achieving 5.08× lower latency than permutation averaging.
 
 ### Localized Frontier Limitations
-1. **Zero-Shot Novel Operator Grammars**: Performance drops to $55.08\%$ on $L_{2b}$ and $56.84\%$ on $L_3$. While $D_5$ rescues independent candidate comparative scoring from near-chance baseline failure ($D_0 = 25.20\%$, $\Delta = +31.64$ points), exhaustive permutation-averaged full-context causal inference ($B_1$-Sym $= 65.43\%$) retains an $8.59$-point advantage on completely novel relational operators.
+1. **Zero-Shot Novel Operator Grammars**: Performance drops to 55.08% on L_2b and 56.84% on L_3. While D5 rescues independent candidate comparative scoring from near-chance baseline failure (D0 = 25.20%, Δ = +31.64 points), exhaustive permutation-averaged full-context causal inference (B1-Sym = 65.43%) retains an 8.59-point advantage on completely novel relational operators.
 2. **Mechanistic Hypothesis**: The observed advantage is consistent with a benefit from joint full-context token processing, but the evaluation does not establish this as the unique causal mechanism.
-3. **Capacity Ceiling ($N_{\text{op}}=16$ vs $N_{\text{op}}=32$)**: Training with 32 operator families saturates held-out transfer ($+1.37\%$ on $L_3$, $p=0.2075$) while causing substantial in-distribution catastrophic degradation on $L_1$ ($75.52\%$ vs $89.32\%$). $N_{\text{op}}=16$ was selected as the frozen Pareto operating point under the fixed D5-L4 adaptation budget.
+3. **Capacity Ceiling (N_op=16 vs N_op=32)**: Training with 32 operator families saturates held-out transfer (+1.37% on L_3, p=0.2075) while causing substantial in-distribution catastrophic degradation on L_1 (75.52% vs 89.32%). N_op=16 was selected as the frozen Pareto operating point under the fixed D5-L4 adaptation budget.
 
 ---
 

README.md

@@ -12,13 +12,14 @@ tags:
 - qwen
 ---
 
+
 # Model Card: InvariantOne-v1
 
 **Release Version:** `InvariantOne-v1` (Frozen Release)  
 **Date:** September 24, 2026  
 **License:** Apache-2.0  
 **Base Backbone:** `Qwen/Qwen3.5-4B-Base` (Revision `1001bb4d826a52d1f399e183466143f4da7b741b`, Native BF16)  
-**Primary Checkpoint:** $D_5$-L4 ($N_{\text{op}}=16$, Seed 42 Primary; Replicated across Seeds 43, 44)  
+**Primary Checkpoint:** D5-L4 (N_op=16, Seed 42 Primary; Replicated across Seeds 43, 44)  
 
 ---
 
@@ -28,8 +29,8 @@ tags:
 
 Standard autoregressive language models suffer from severe position, length, and order biases when evaluating multiple-choice candidate decisions. `InvariantOne-v1` solves this structural failure through a decoupled comparative architecture:
 1. **Candidate-Independent Scoring:** Each candidate action is scored independently conditioned on context, eliminating candidate order sensitivity and cross-option attention artifacts.
-2. **Analytic Distributional Equivariance:** Option-span pooled representations pass through a lightweight direct comparative projection head, producing logits normalized via softmax to guarantee exact permutation equivariance over candidate distributions ($\text{Mean TVD} = 0.000000$).
-3. **Upper-Layer Relational Pre-Adaptation:** Parameter-efficient adaptation (LoRA on layers 28–31) trained across a diverse relational operator universe ($N_{\text{op}}=16$) instills strong, transferable relational reasoning capabilities into the comparative readout.
+2. **Analytic Distributional Equivariance:** Option-span pooled representations pass through a lightweight direct comparative projection head, producing logits normalized via softmax to guarantee exact permutation equivariance over candidate distributions (Mean TVD = 0.000000).
+3. **Upper-Layer Relational Pre-Adaptation:** Parameter-efficient adaptation (LoRA on layers 28–31) trained across a diverse relational operator universe (N_op=16) instills strong, transferable relational reasoning capabilities into the comparative readout.
 
 ```
 Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
@@ -49,28 +50,28 @@ Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
 
 | Parameter | Specification |
 | :--- | :--- |
-| **Base Model** | `Qwen/Qwen3.5-4B-Base` (32 transformer layers, $d_{\text{model}} = 2560$) |
+| **Base Model** | `Qwen/Qwen3.5-4B-Base` (32 transformer layers, d_model = 2560) |
 | **Backbone Status** | Layers 0–27 strictly frozen (zero parameter updates) |
-| **Adaptation** | Low-Rank Adaptation (LoRA) on upper layers 28–31: $r = 8, \alpha = 16$ (layers 28–30: `in_proj_qkv`, `out_proj`; layer 31: `q_proj`, `v_proj`, `o_proj`) |
+| **Adaptation** | Low-Rank Adaptation (LoRA) on upper layers 28–31: r = 8, α = 16 (layers 28–30: `in_proj_qkv`, `out_proj`; layer 31: `q_proj`, `v_proj`, `o_proj`) |
 | **Active LoRA Parameters** | 585,728 parameters |
-| **Readout Head** | `DirectComparativeHead`: Linear($2560 \to 256$) $\to$ GELU $\to$ LayerNorm($256$) $\to$ Linear($256 \to 1$) |
+| **Readout Head** | `DirectComparativeHead`: Linear(2560 → 256) → GELU → LayerNorm(256) → Linear(256 → 1) |
 | **Active Head Parameters** | 722,177 parameters |
-| **Total Active Adapted Parameters** | 1,307,905 parameters ($<0.05\%$ of base model) |
+| **Total Active Adapted Parameters** | 1,307,905 parameters (<0.05% of base model) |
 | **Pooling Method** | Option-span mean pooling over candidate option token span |
-| **Scoring Scheme** | Independent candidate scoring with comparative readout: $P(y = i \mid x, \{o_k\}) = \frac{\exp(s_i / \tau^*)}{\sum_{j=1}^K \exp(s_j / \tau^*)}$ |
-| **Calibration Temperature** | $\tau^* = 1.0091$ (pre-calibrated on validation split) |
+| **Scoring Scheme** | Independent candidate scoring with comparative readout: `P(y = i | x, {o_k}) = exp(s_i / τ*) / Σ_j exp(s_j / τ*)` |
+| **Calibration Temperature** | τ* = 1.0091 (pre-calibrated on validation split) |
 
 ### Cryptographic Checkpoint Signatures
 
-* **Primary Checkpoint (`Seed 42`, $N_{\text{op}}=16$)**:
+* **Primary Checkpoint (`Seed 42`, N_op=16)**:
   - LoRA Weights: `checkpoints/invariantone-v1/adapter_model.pt` (Frozen Phase 7R research checkpoint)
     - SHA-256: `a0000d3ec984d155fbad5abc854556904ecffe78b997900b677a8d8d5811e4d2`
   - Head Weights: `checkpoints/invariantone-v1/head.pt` (Frozen Phase 7R research checkpoint)
     - SHA-256: `190d867dc302a89d420d19a8374a5db252ea2e71e4f40c68064ded23fc321384`
-* **Replication Checkpoint (`Seed 43`, $N_{\text{op}}=16$)**:
+* **Replication Checkpoint (`Seed 43`, N_op=16)**:
   - LoRA: `checkpoints/invariantone-v1/adapter_model_seed43.pt` (Frozen Phase 7R research checkpoint)
   - Head: `checkpoints/invariantone-v1/head_seed43.pt` (Frozen Phase 7R research checkpoint)
-* **Replication Checkpoint (`Seed 44`, $N_{\text{op}}=16$)**:
+* **Replication Checkpoint (`Seed 44`, N_op=16)**:
   - LoRA: `checkpoints/invariantone-v1/adapter_model_seed44.pt` (Frozen Phase 7R research checkpoint)
   - Head: `checkpoints/invariantone-v1/head_seed44.pt` (Frozen Phase 7R research checkpoint)
 
@@ -78,21 +79,21 @@ Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
 
 ## 3. Verified Performance & Benchmark Evaluation
 
-`InvariantOne-v1` was evaluated on `FINAL-HOLDOUT-V2` ($1,536$ four-choice items) under strict preregistered one-shot governance. Prior to inference, SHA-256 checksums of all strata were verified against the locked manifest (`final_holdout_v2_manifest.json`).
+`InvariantOne-v1` was evaluated on `FINAL-HOLDOUT-V2` (1,536 four-choice items) under strict preregistered one-shot governance. Prior to inference, SHA-256 checksums of all strata were verified against the locked manifest (`final_holdout_v2_manifest.json`).
 
-> **Scope Note on Candidate Options Count ($K$):**  
-> The runtime supports arbitrary $K \ge 2$; the reported scientific evaluation results are for $K=4$ unless otherwise stated. Experimental generalization to arbitrary $K$ has not been independently established in the scientific benchmarks.
+> **Scope Note on Candidate Options Count (K):**  
+> The runtime supports arbitrary K ≥ 2; the reported scientific evaluation results are for K=4 unless otherwise stated. Experimental generalization to arbitrary K has not been independently established in the scientific benchmarks.
 
 ### Definitive Benchmark Summary
 
-| Stratum | Evaluation Focus | $D_0$ (Baseline) | $B_1$-Raw | $B_1$-Sym (24-Perm) | `InvariantOne-v1` (Seed 42) | `InvariantOne-v1` (Mean $\pm$ SD) |
+| Stratum | Evaluation Focus | D0 (Baseline) | B1-Raw | B1-Sym (24-Perm) | `InvariantOne-v1` (Seed 42) | `InvariantOne-v1` (Mean ± SD) |
 | :--- | :--- | :---: | :---: | :---: | :---: | :---: |
-| **`FINAL-REAL`** | Real operational control tasks ($N=256$) | 89.45% | 91.41% | 92.58% | **94.14%** | **93.36% $\pm$ 1.35%** |
-| **`FINAL-L1`** | Familiar-Operator Compositional Recombination ($N=256$) | 32.81% | 38.28% | 43.75% | **89.84%** | **89.32% $\pm$ 0.45%** |
-| **`FINAL-L2a`** | Semantic Extrapolation ($N=256$) | 28.12% | 45.31% | 50.39% | **86.33%** | **87.76% $\pm$ 2.48%** |
-| **`FINAL-L2b`** | Relational Extrapolation ($N=256$) | 22.27% | 62.50% | **65.23%** | 55.08% | 53.91% $\pm$ 2.03% |
-| **`FINAL-L3`** | Double Extrapolation ($N=512$) | 25.20% | 60.94% | **65.43%** | 56.84% | 54.10% $\pm$ 4.91% |
-| **`Aggregate`** | Total locked holdout pool ($N=1,536$) | 37.17% | 59.90% | 63.80% | **73.18%** (1,124/1,536) | **71.74% $\pm$ 1.97%** |
+| **`FINAL-REAL`** | Real operational control tasks (N=256) | 89.45% | 91.41% | 92.58% | **94.14%** | **93.36% ± 1.35%** |
+| **`FINAL-L1`** | Familiar-Operator Compositional Recombination (N=256) | 32.81% | 38.28% | 43.75% | **89.84%** | **89.32% ± 0.45%** |
+| **`FINAL-L2a`** | Semantic Extrapolation (N=256) | 28.12% | 45.31% | 50.39% | **86.33%** | **87.76% ± 2.48%** |
+| **`FINAL-L2b`** | Relational Extrapolation (N=256) | 22.27% | 62.50% | **65.23%** | 55.08% | 53.91% ± 2.03% |
+| **`FINAL-L3`** | Double Extrapolation (N=512) | 25.20% | 60.94% | **65.43%** | 56.84% | 54.10% ± 4.91% |
+| **`Aggregate`** | Total locked holdout pool (N=1,536) | 37.17% | 59.90% | 63.80% | **73.18%** (1,124/1,536) | **71.74% ± 1.97%** |
 
 ### Counterfactual Sensitivity & Minimal-Pair Tracking
 
@@ -108,30 +109,30 @@ Context + Option_i ---> [Qwen3.5-4B (Frozen Layers 0-27 + LoRA Layers 28-31)]
 ## 4. Invariance Guarantees & Systems Efficiency
 
 ### Structural Invariance Audit
-* **Distributional Equivariance**: Mean TVD = **$0.000000$**, Max TVD = **$0.000000$** across all 24 option permutations on 128 samples ($3,072$ evaluations).
-* **Top-1 Tie-Breaking Instability**: $1.56\%$ top-choice flips under permutation, caused strictly by floating-point precision ties at decision boundaries under argmax selection. The underlying probabilistic output distribution is strictly equivariant.
+* **Distributional Equivariance**: Mean TVD = **0.000000**, Max TVD = **0.000000** across all 24 option permutations on 128 samples (3,072 evaluations).
+* **Top-1 Tie-Breaking Instability**: 1.56% top-choice flips under permutation, caused strictly by floating-point precision ties at decision boundaries under argmax selection. The underlying probabilistic output distribution is strictly equivariant.
 
 ### Computational Efficiency (Measured on NVIDIA A100-SXM4-40GB)
 * **Benchmark Provenance Note:** A100 performance figures are from the frozen FINAL-HOLDOUT-V2 benchmarking run; release-wheel functionality was independently smoke-tested in a fresh Python 3.12 environment.
-* **Forward Passes**: 4 candidate forward passes per sample vs 24 full-context forward passes for $B_1$-Sym ($6.0\times$ reduction).
-* **Wall-Clock Latency**: **$83.71\text{ ms}$** vs **$425.31\text{ ms}$** ($B_1$-Sym) $\implies$ **$5.08\times$ speedup**.
-* **Throughput**: **$11.95\text{ samples/sec}$** vs **$2.35\text{ samples/sec}$** ($B_1$-Sym).
-* **Peak VRAM**: **$8,941.2\text{ MB}$** vs **$14,614.2\text{ MB}$** ($B_1$-Sym) $\implies$ **$38.8\%$ memory footprint reduction**.
+* **Forward Passes**: 4 candidate forward passes per sample vs 24 full-context forward passes for B1-Sym (6.0× reduction).
+* **Wall-Clock Latency**: **83.71 ms** vs **425.31 ms** (B1-Sym) ⟹ **5.08× speedup**.
+* **Throughput**: **11.95 samples/sec** vs **2.35 samples/sec** (B1-Sym).
+* **Peak VRAM**: **8,941.2 MB** vs **14,614.2 MB** (B1-Sym) ⟹ **38.8% memory footprint reduction**.
 
 ---
 
 ## 5. Capabilities vs Frontier Boundaries
 
 ### Confirmed Capabilities
-1. **Real-Task Decision Accuracy**: Outperforms unadapted baselines and 24-permutation causal scoring on real operational decision tasks ($94.14\%$).
-2. **Compositional Recombination**: Excels at counterfactual state tracking and rule execution for learned operator families ($89.84\%$ accuracy, $99.12\%$ override switch rate).
-3. **Semantic Domain Generalization**: Robustly transfers learned relational operators to completely novel technical and engineering domains ($86.33\%$, $+35.94$ points over $B_1$-Sym).
-4. **Order-Equivariant Efficiency**: Eliminates position bias with zero prompt permutation overhead, achieving $5.08\times$ lower latency than permutation averaging.
+1. **Real-Task Decision Accuracy**: Outperforms unadapted baselines and 24-permutation causal scoring on real operational decision tasks (94.14%).
+2. **Compositional Recombination**: Excels at counterfactual state tracking and rule execution for learned operator families (89.84% accuracy, 99.12% override switch rate).
+3. **Semantic Domain Generalization**: Robustly transfers learned relational operators to completely novel technical and engineering domains (86.33%, +35.94 points over B1-Sym).
+4. **Order-Equivariant Efficiency**: Eliminates position bias with zero prompt permutation overhead, achieving 5.08× lower latency than permutation averaging.
 
 ### Localized Frontier Limitations
-1. **Zero-Shot Novel Operator Grammars**: Performance drops to $55.08\%$ on $L_{2b}$ and $56.84\%$ on $L_3$. While $D_5$ rescues independent candidate comparative scoring from near-chance baseline failure ($D_0 = 25.20\%$, $\Delta = +31.64$ points), exhaustive permutation-averaged full-context causal inference ($B_1$-Sym $= 65.43\%$) retains an $8.59$-point advantage on completely novel relational operators.
+1. **Zero-Shot Novel Operator Grammars**: Performance drops to 55.08% on L_2b and 56.84% on L_3. While D5 rescues independent candidate comparative scoring from near-chance baseline failure (D0 = 25.20%, Δ = +31.64 points), exhaustive permutation-averaged full-context causal inference (B1-Sym = 65.43%) retains an 8.59-point advantage on completely novel relational operators.
 2. **Mechanistic Hypothesis**: The observed advantage is consistent with a benefit from joint full-context token processing, but the evaluation does not establish this as the unique causal mechanism.
-3. **Capacity Ceiling ($N_{\text{op}}=16$ vs $N_{\text{op}}=32$)**: Training with 32 operator families saturates held-out transfer ($+1.37\%$ on $L_3$, $p=0.2075$) while causing substantial in-distribution catastrophic degradation on $L_1$ ($75.52\%$ vs $89.32\%$). $N_{\text{op}}=16$ was selected as the frozen Pareto operating point under the fixed D5-L4 adaptation budget.
+3. **Capacity Ceiling (N_op=16 vs N_op=32)**: Training with 32 operator families saturates held-out transfer (+1.37% on L_3, p=0.2075) while causing substantial in-distribution catastrophic degradation on L_1 (75.52% vs 89.32%). N_op=16 was selected as the frozen Pareto operating point under the fixed D5-L4 adaptation budget.
 
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