Publish trained Sofia Edge v0.1 with verified kernel controls

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NOTICE

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+Sofia Distilled v0.1
+Copyright 2026 Rootcastle Engineering & Innovation
+
+Sofia Edge contains newly trained NumPy model weights and original synthetic signal data.
+Sofia Chat contains modified pretrained weights derived from Qwen/Qwen2.5-0.5B-Instruct,
+copyright its respective authors, distributed under the Apache License 2.0.
+Pinned upstream revision: 7ae557604adf67be50417f59c2c2f167def9a775.
+
+The verifiable product-kernel method is informed by Batuhan Ayribas (2026),
+Quantum Artificial Intelligence with Verifiable Kernels:
+https://www.academia.edu/175377730/Quantum_Artificial_Intelligence_with_Verifiable_Kernels
+The implementation, signal-learning task, distillation extension, and new experimental
+results in this repository are separate from the manuscript's supplementary archive.

README.md

@@ -1,3 +1,68 @@
 ---
+language:
+- en
 license: apache-2.0
+tags:
+- sofia
+- numpy
+- knowledge-distillation
+- quantum-inspired
+- verifiable-kernels
+- synthetic-data
+- vibration-analysis
+- experimental
 ---
+
+# Sofia Edge Distilled v0.1
+
+A **trained 325-parameter NumPy classifier** for five synthetic vibration scenarios: healthy, imbalance, misalignment, bearing impulses and rubbing. The teacher is centred kernel ridge regression using a product-rotation kernel with an exact efficient classical evaluation.
+
+Developed by Rootcastle Engineering & Innovation. [Source and reproducible training](https://github.com/rootcastleco/sofia-distilled).
+
+## Training
+
+14 statistical/spectral features feed a 14 → 16 → 5 ReLU MLP. The teacher uses 600 fit examples and 200 validation examples; its 25-fit scale/penalty search is matched by an RBF control. After selection it is refitted on the 800 training/validation anchors. The student is trained for 120 epochs on 6,000 separately generated waveforms, with 1,000 student-validation examples for checkpoint selection.
+
+The student objective combines hard-label cross-entropy and temperature-2 teacher-target KL. A supervised-only student with identical initialization, data, architecture and optimization budget is retained as a control. Train-only standardization precedes fixed arctangent angle encoding for the teacher.
+
+## Held-out results
+
+| Model | Synthetic test accuracy / balanced accuracy |
+| --- | ---: |
+| Product-kernel teacher | 99.933% |
+| Matched-budget RBF teacher | 99.933% |
+| Distilled student | 99.933% |
+| Supervised-only student | 100.000% |
+
+The balanced test set has 1,500 examples. The distilled student reaches 100.000% on a separately generated shaft-frequency shift of 43–65 Hz, versus 18–42 Hz during training. These results concern easy analytical formulas, not machine diagnosis. The control outperforms distillation on the in-distribution accuracy measure; no distillation quality advantage is claimed.
+
+## Use
+
+Download this repository, then run its standalone loader:
+
+```python
+import numpy as np
+from inference import EdgeModel
+
+model = EdgeModel(".")
+signal = np.load("acceleration.npy", allow_pickle=False)
+result = model.predict_signal(signal, sample_rate=2048, shaft_hz=25)
+print(result)
+```
+
+Acceleration values must be in g. Training windows have 1,024 samples at 2,048 Hz. The loader validates feature order, dimensions, finiteness and the weight SHA-256 before inference.
+
+## Artifacts and provenance
+
+- `model.npz`: final float32 student parameters and training-only scaler.
+- `config.json`: exact ordered feature schema and weight digest.
+- `kernel_teacher.npz`: anchors, ridge coefficients, centring statistics and selected hyperparameters.
+- `dataset.npz`: all fit/validation/test feature matrices, labels and held-out scores.
+- `metrics.json`, `protocol.json`, `training_history.json`: measured results and run configuration.
+- `verification_report.json`: independent kernel and noise control experiments.
+
+The method follows [Quantum Artificial Intelligence with Verifiable Kernels](https://www.academia.edu/175377730/Quantum_Artificial_Intelligence_with_Verifiable_Kernels). Calculations use classical CPU hardware. Read `VERIFICATION.md` for exact scope.
+
+## Limitations
+
+No measured machine data, field validation or calibrated confidence. Softmax values are scores, not diagnostic certainty. The range check is a feature-distance heuristic. The model cannot validate arbitrary sensor placement, machines or units. It is intended for research and demonstration; it has no machinery actuation API. Only one Edge training seed was run. No quantum processor or quantum computational advantage is claimed.

SHA256SUMS.json

@@ -0,0 +1,15 @@
+{
+  "config.json": "87b9743e903f14022505f0702cf98a1761aa5f0db803347b965a931adeb62c3b",
+  "dataset.npz": "9a7f781845a6874922954411372651d8b0201f4dfd7b1ce29c3973fc2418093c",
+  "inference.py": "292239e30984cfd8fea2311b31371ca0bdef4f94019f7356bfb401d5be8394fd",
+  "kernel_teacher.npz": "ecf9bdeff242776a1db37760cdc30f00ade66f06dbf8ef80a6df4b85bf55967f",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "metrics.json": "74981e0b8b7a698aeed7c8d15f2f060ea0e7a636c4be67d03496e76210b01c9b",
+  "model.npz": "4ca49061fee1dff9237793a9300c2509cf631b6aafcb242b48f4b17af043583a",
+  "NOTICE": "14c2f6fb1f5eebbdb1a031058214480a4ba8f24ae07eee24655b2af28035b6a5",
+  "protocol.json": "cede6dadafda44f20aaa3faec1a85599860f8da40637bc2edee262a79769d68f",
+  "README.md": "d9143a9b8a822a400d52efb78133ae03cd39ec4cbd475f8c19b9a7390a2f4434",
+  "training_history.json": "a373e944f57c20778604433dba242ce6a21a51125a4fe8bedbaae8f59ace2134",
+  "VERIFICATION.md": "c295c9b52f51defd50e0400e0d30d1d4d0c6fc40fec5e74cc82a3bd83d3e339a",
+  "verification_report.json": "6a49a1e2b9fd729951f143fb55119696883dc75564d85c51ecdfc48ea41208ec"
+}

VERIFICATION.md

@@ -0,0 +1,48 @@
+# Verification and evidence scope
+
+## Method source and scope
+
+[Quantum Artificial Intelligence with Verifiable Kernels](https://www.academia.edu/175377730/Quantum_Artificial_Intelligence_with_Verifiable_Kernels), Batuhan Ayribas, September 2026, informs the kernel controls. This repository contains an independently written adaptation. Its new random seeds and outputs are not the manuscript's original supplementary archive.
+
+All experiments here use classical numerical computation. A feature geometry described using quantum states can have a useful classical representation. Predictive scores alone do not establish quantum advantage.
+
+## Evidence map
+
+| Claim | Implementation | Retained evidence |
+| --- | --- | --- |
+| Product kernel equals a state-overlap calculation | `product_kernel`, `product_states` | `identity_audit`, parameterized tests |
+| Product kernel equals explicit classical features | `trig_features` | maximum discrepancy across dimensions 1, 2, 4, 6, 8 |
+| A shared terminal unitary preserves overlap | independent orthogonal matrices applied to state vectors | numerical discrepancy |
+| Global depolarization produces the specified affine kernel | independent density matrices | density-versus-affine discrepancy |
+| Matched regularization preserves exact centred ridge predictions | `CenteredRidge`, `depolarize` | prediction discrepancy, separate exact and shot results |
+| Finite-shot measurement does not inherit exact invariance | binomial SWAP simulation, positive training eigenspace | 30 replicates at each noise/shot condition |
+| Kernel teacher can be compressed into an Edge MLP | `kernel_training` | held-out predictions, supervised-only student control |
+| Chat representation alignment actually appears in the loss | `chat_training` | training configuration and validation kernel MSE |
+
+## Experiment protocol
+
+Each of three small classification tasks uses 30 independent train/validation/test datasets. Product and RBF models use 25 validation fits each; linear uses five. Hyperparameters are selected on validation labels and then refitted on the training/validation union. Test labels are reserved for final reporting. Intervals are pointwise percentile bootstraps over the simulator replicates, with 2,000 resamples. No multiplicity-adjusted significance claim is made.
+
+Finite-shot conditions use a separate fixed product model, a global state-depolarization channel, an ideal SWAP measurement estimator, and positive-eigenspace repair fitted using the training matrix. Negative overlap estimates are retained. No shot data are described as real device measurements.
+
+The protocol is saved and hashed before computation. `datasets_and_predictions.npz` retains inputs, labels and score arrays. `classification_rows.json` and `noise_rows.json` retain seed-level metrics.
+
+## Measured checks in the first local run
+
+| Identity | Maximum absolute discrepancy |
+| --- | ---: |
+| State overlap versus direct classical kernel | 1.55e-15 |
+| Explicit classical features versus direct kernel | 1.89e-15 |
+| Shared terminal unitary | 1.78e-15 |
+| Density-matrix global depolarization | 8.88e-16 |
+| Matched-regularization prediction | 1.37e-13 |
+
+These finite checks support the implementations at tested inputs; they do not replace mathematical proofs or certify a physical device. Original numerical reports, rather than rounded values in this document, are authoritative.
+
+## Model-specific boundaries
+
+Edge uses newly generated vibration formulas rather than recorded machinery data. Its angle encoding is a fixed `2 * atan` transformation after training-only feature standardization. Product-kernel and RBF teacher selection use identical scale/penalty budgets. The 325-parameter student combines hard-label cross-entropy with soft teacher targets. These targets are softened ridge scores, not calibrated probabilities.
+
+Chat uses pretrained Qwen blocks, a frozen shared embedding/head and trainable LoRA adapters. Its kernel term compares four-dimensional sketches of response representations against eight training-only teacher landmarks. The sketch and angle map are fixed. This is a heuristic representation-alignment objective. The manuscript's exact ridge-noise identity applies to its specified kernel learner, not to the transformer or its generated answers.
+
+The Chat test set contains different topic families from the training and validation sets. It still uses generated teacher answers as references. A lower teacher-reference cross-entropy is not a factuality, coding or safety benchmark. Broad quality and the separate effect of the kernel term require additional data, multiple training seeds, independent references and controlled ablations.

config.json

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+{
+  "model_type": "sofia-edge-mlp",
+  "version": "0.1.0",
+  "role": "product-kernel-distilled-student",
+  "feature_schema": "sofia.synthetic-vibration.v1",
+  "feature_names": [
+    "log_rms",
+    "log_peak",
+    "kurtosis",
+    "crest_factor",
+    "shaft_energy",
+    "second_harmonic_energy",
+    "third_harmonic_energy",
+    "fourth_harmonic_energy",
+    "high_frequency_energy",
+    "spectral_flatness",
+    "spectral_entropy",
+    "envelope_kurtosis",
+    "log_envelope_rms",
+    "zero_crossing_rate"
+  ],
+  "labels": [
+    "healthy",
+    "imbalance",
+    "misalignment",
+    "bearing_impulses",
+    "rubbing"
+  ],
+  "dimensions": [
+    14,
+    16,
+    5
+  ],
+  "input_unit": "g",
+  "weights_sha256": "4ca49061fee1dff9237793a9300c2509cf631b6aafcb242b48f4b17af043583a",
+  "parameter_count": 325,
+  "training_data": "analytical synthetic waveforms only",
+  "sample_rate_hz": 2048,
+  "window_size": 1024,
+  "training_shaft_hz": [
+    18,
+    42
+  ]
+}

dataset.npz

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9a7f781845a6874922954411372651d8b0201f4dfd7b1ce29c3973fc2418093c
+size 1479936

inference.py

@@ -0,0 +1,178 @@
+"""NumPy signal classifier and reproducible synthetic waveform specification."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from itertools import pairwise
+from pathlib import Path
+
+import numpy as np
+
+LABELS = ("healthy", "imbalance", "misalignment", "bearing_impulses", "rubbing")
+FEATURE_NAMES = (
+    "log_rms",
+    "log_peak",
+    "kurtosis",
+    "crest_factor",
+    "shaft_energy",
+    "second_harmonic_energy",
+    "third_harmonic_energy",
+    "fourth_harmonic_energy",
+    "high_frequency_energy",
+    "spectral_flatness",
+    "spectral_entropy",
+    "envelope_kurtosis",
+    "log_envelope_rms",
+    "zero_crossing_rate",
+)
+SCHEMA = "sofia.synthetic-vibration.v1"
+
+
+def softmax(logits: np.ndarray, temperature: float = 1.0) -> np.ndarray:
+    z = logits / temperature
+    z = z - z.max(axis=-1, keepdims=True)
+    ex = np.exp(z)
+    return ex / ex.sum(axis=-1, keepdims=True)
+
+
+def extract_features(signal: np.ndarray, sample_rate: float, shaft_hz: float) -> np.ndarray:
+    """14 dimensionless/log features; amplitude input must be acceleration in g."""
+    x = np.asarray(signal, dtype=np.float64)
+    if x.ndim != 1 or x.size < 128 or not np.isfinite(x).all():
+        raise ValueError("signal must be a finite 1-D waveform with at least 128 samples")
+    if not np.isfinite(sample_rate) or sample_rate <= 0:
+        raise ValueError("sample_rate must be positive and finite")
+    if not np.isfinite(shaft_hz) or not 0 < shaft_hz < sample_rate / 10:
+        raise ValueError("shaft_hz must be positive and below sample_rate / 10")
+    x = x - x.mean()
+    eps = 1e-12
+    rms = np.sqrt(np.mean(x * x))
+    peak = np.max(np.abs(x))
+    if rms < 1e-9:
+        raise ValueError("constant or zero-energy signals cannot be classified")
+    power = np.abs(np.fft.rfft(x * np.hanning(x.size))) ** 2
+    freq = np.fft.rfftfreq(x.size, 1 / sample_rate)
+    total = power.sum() + eps
+    width = max(2 * sample_rate / x.size, shaft_hz * 0.12)
+    bands = [power[np.abs(freq - k * shaft_hz) < width].sum() / total for k in range(1, 5)]
+    dist = power / total
+    analytic_filter = np.zeros(x.size)
+    analytic_filter[0] = 1
+    analytic_filter[1 : (x.size + 1) // 2] = 2
+    if x.size % 2 == 0:
+        analytic_filter[x.size // 2] = 1
+    envelope = np.abs(np.fft.ifft(np.fft.fft(x) * analytic_filter))
+    env_center = envelope - envelope.mean()
+    env_var = np.mean(env_center**2)
+    return np.asarray(
+        [
+            np.log(rms + eps),
+            np.log(peak + eps),
+            np.mean(x**4) / (rms**4 + eps),
+            peak / rms,
+            *bands,
+            power[freq > sample_rate * 0.2].sum() / total,
+            np.exp(np.mean(np.log(power + eps))) / (power.mean() + eps),
+            -np.sum(dist * np.log(dist + eps)) / np.log(power.size),
+            np.mean(env_center**4) / (env_var**2 + eps),
+            np.log(np.sqrt(np.mean(envelope**2)) + eps),
+            np.mean(x[1:] * x[:-1] < 0),
+        ],
+        dtype=np.float64,
+    )
+
+
+def waveform(
+    label: int,
+    rng: np.random.Generator,
+    *,
+    shaft_hz: float,
+    sample_rate: float = 2048,
+    size: int = 1024,
+) -> np.ndarray:
+    """Analytical toy scenarios, not a simulation validated against real machinery."""
+    if label not in range(len(LABELS)):
+        raise ValueError("unknown scenario")
+    t = np.arange(size) / sample_rate
+    phase = rng.uniform(0, 2 * np.pi, 4)
+    fundamental = rng.uniform(0.15, 0.35)
+    second = rng.uniform(0.01, 0.04)
+    third = rng.uniform(0.005, 0.02)
+    if label == 1:
+        fundamental *= rng.uniform(3.0, 6.0)
+    if label == 2:
+        second = fundamental * rng.uniform(0.9, 1.8)
+        third = fundamental * rng.uniform(0.3, 0.8)
+    x = (
+        fundamental * np.sin(2 * np.pi * shaft_hz * t + phase[0])
+        + second * np.sin(4 * np.pi * shaft_hz * t + phase[1])
+        + third * np.sin(6 * np.pi * shaft_hz * t + phase[2])
+    )
+    x += rng.normal(0, rng.uniform(0.005, 0.025), size)
+    if label == 3:
+        period = sample_rate / (shaft_hz * rng.uniform(4.4, 5.2))
+        for start in np.arange(rng.uniform(0, period), size, period):
+            lag = np.arange(size - int(start)) / sample_rate
+            pulse = rng.uniform(0.7, 1.8) * np.exp(-lag * rng.uniform(180, 350))
+            x[int(start) :] += pulse * np.sin(2 * np.pi * rng.uniform(500, 750) * lag)
+    if label == 4:
+        x += rng.uniform(0.2, 0.5) * np.sin(2 * np.pi * shaft_hz * t + phase[3]) ** 3
+        x += rng.normal(0, rng.uniform(0.10, 0.22), size)
+    return x * rng.uniform(0.8, 1.2)
+
+
+class EdgeModel:
+    """Load verified, pickle-free weights and classify a signal or feature matrix."""
+
+    def __init__(self, folder: str | Path):
+        folder = Path(folder)
+        self.config = json.loads((folder / "config.json").read_text(encoding="utf-8"))
+        if self.config.get("feature_schema") != SCHEMA:
+            raise ValueError("unsupported feature schema")
+        if self.config.get("feature_names") != list(FEATURE_NAMES):
+            raise ValueError("feature ordering mismatch")
+        path = folder / "model.npz"
+        if hashlib.sha256(path.read_bytes()).hexdigest() != self.config["weights_sha256"]:
+            raise ValueError("weights failed SHA-256 verification")
+        with np.load(path, allow_pickle=False) as archive:
+            self.weights = {k: archive[k].copy() for k in archive.files}
+        dims = self.config["dimensions"]
+        if dims[0] != len(FEATURE_NAMES) or dims[-1] != len(LABELS):
+            raise ValueError("invalid input/output dimensions")
+        for i, (a, b) in enumerate(pairwise(dims)):
+            if self.weights[f"w{i}"].shape != (a, b) or self.weights[f"b{i}"].shape != (b,):
+                raise ValueError("invalid weight dimensions")
+        for name in ("mean", "scale"):
+            if self.weights[name].shape != (len(FEATURE_NAMES),):
+                raise ValueError("invalid scaler dimensions")
+        if not all(np.isfinite(v).all() for v in self.weights.values()):
+            raise ValueError("non-finite model parameters")
+        if (self.weights["scale"] <= 0).any():
+            raise ValueError("invalid feature scale")
+
+    def predict_features(self, features: np.ndarray) -> np.ndarray:
+        x = np.asarray(features, dtype=np.float64)
+        if x.ndim not in (1, 2) or x.shape[-1] != len(FEATURE_NAMES):
+            raise ValueError("expected 14 features per sample")
+        if not np.isfinite(x).all():
+            raise ValueError("features must be finite")
+        h = (x - self.weights["mean"]) / self.weights["scale"]
+        for i in range(len(self.config["dimensions"]) - 1):
+            h = h @ self.weights[f"w{i}"] + self.weights[f"b{i}"]
+            if i < len(self.config["dimensions"]) - 2:
+                h = np.maximum(h, 0)
+        return softmax(h)
+
+    def predict_signal(self, signal: np.ndarray, sample_rate: float, shaft_hz: float) -> dict:
+        features = extract_features(signal, sample_rate, shaft_hz)
+        p = self.predict_features(features)
+        z = np.abs((features - self.weights["mean"]) / self.weights["scale"])
+        return {
+            "label": LABELS[int(p.argmax())],
+            "probabilities": dict(zip(LABELS, p.tolist())),
+            "max_probability": float(p.max()),
+            "out_of_training_range": bool((z > 6).any()),
+            "feature_schema": SCHEMA,
+            "status": "experimental_synthetic_only",
+        }

kernel_teacher.npz

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+version https://git-lfs.github.com/spec/v1
+oid sha256:ecf9bdeff242776a1db37760cdc30f00ade66f06dbf8ef80a6df4b85bf55967f
+size 130562

metrics.json

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+{
+  "protocol_sha256": "cede6dadafda44f20aaa3faec1a85599860f8da40637bc2edee262a79769d68f",
+  "teacher_selected_scale": 0.5,
+  "teacher_selected_penalty": 0.0001,
+  "teacher_validation_balanced_accuracy": 1.0,
+  "teacher_test_balanced_accuracy": 0.9993333333333332,
+  "teacher_ood_balanced_accuracy": 1.0,
+  "rbf_selected": [
+    0.25,
+    0.01
+  ],
+  "rbf_validation_balanced_accuracy": 1.0,
+  "rbf_test_balanced_accuracy": 0.9993333333333332,
+  "student": {
+    "accuracy": 0.9993333333333333,
+    "macro_f1": 0.9993333314814763,
+    "cross_entropy": 0.29937443104218475,
+    "confusion_matrix": [
+      [
+        300,
+        0,
+        0,
+        0,
+        0
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+        300,
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+      [
+        0,
+        0,
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+        300
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+    ],
+    "per_class_f1": {
+      "healthy": 0.9983361064891847,
+      "imbalance": 0.998330550918197,
+      "misalignment": 1.0,
+      "bearing_impulses": 1.0,
+      "rubbing": 1.0
+    }
+  },
+  "supervised_control": {
+    "accuracy": 1.0,
+    "macro_f1": 1.0,
+    "cross_entropy": 0.0009983560894549599,
+    "confusion_matrix": [
+      [
+        300,
+        0,
+        0,
+        0,
+        0
+      ],
+      [
+        0,
+        300,
+        0,
+        0,
+        0
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+      [
+        0,
+        0,
+        300,
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+        0
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+        0,
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+        300,
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+        300
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+    "per_class_f1": {
+      "healthy": 1.0,
+      "imbalance": 1.0,
+      "misalignment": 1.0,
+      "bearing_impulses": 1.0,
+      "rubbing": 1.0
+    }
+  },
+  "ood_student": {
+    "accuracy": 1.0,
+    "macro_f1": 1.0,
+    "cross_entropy": 0.3101353251954706,
+    "confusion_matrix": [
+      [
+        300,
+        0,
+        0,
+        0,
+        0
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+      [
+        0,
+        300,
+        0,
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+        0
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+      [
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+        300
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+    "per_class_f1": {
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+      "imbalance": 1.0,
+      "misalignment": 1.0,
+      "bearing_impulses": 1.0,
+      "rubbing": 1.0
+    }
+  },
+  "student_teacher_agreement": 1.0,
+  "student_parameters": 325,
+  "teacher_anchor_count": 800,
+  "quantum_hardware": false,
+  "limitations": [
+    "Synthetic scenarios only; no field diagnostic validation",
+    "Kernel has an exact efficient classical equivalent",
+    "One model-training seed; no inferential benefit claim for distillation",
+    "Scores/softmax are not calibrated confidence"
+  ]
+}

model.npz

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+version https://git-lfs.github.com/spec/v1
+oid sha256:4ca49061fee1dff9237793a9300c2509cf631b6aafcb242b48f4b17af043583a
+size 2860

protocol.json

@@ -0,0 +1,31 @@
+{
+  "method": "product-rotation centred kernel ridge teacher + neural KL distillation",
+  "source": "https://www.academia.edu/175377730/Quantum_Artificial_Intelligence_with_Verifiable_Kernels",
+  "scales": [
+    0.25,
+    0.5,
+    1.0,
+    2.0,
+    4.0
+  ],
+  "ridge_penalties": [
+    1.0,
+    0.1,
+    0.01,
+    0.001,
+    0.0001
+  ],
+  "epochs": 120,
+  "seed": 20261008,
+  "teacher_fit": 600,
+  "teacher_validation": 200,
+  "student_train": 6000,
+  "student_validation": 1000,
+  "test": 1500,
+  "ood_test": 1500,
+  "selection": "teacher: first best validation balanced accuracy; student: minimum validation CE",
+  "neural_temperature": 2.0,
+  "kernel_score_temperature": 0.5,
+  "alpha": 0.7,
+  "quantum_hardware": false
+}

training_history.json

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verification_report.json

@@ -0,0 +1,228 @@
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+  "quantum_hardware": false,
+  "interpretation": "Any product-kernel performance is shared by its exact classical equivalent; no quantum advantage claim",
+  "scope": "independent adapted implementation; not a reproduction of original seed-level archive",
+  "intervals": "pointwise percentile bootstrap over independent simulator replicates; 2000 resamples; no significance testing"
+}