STEM-Oracle-27B

or·a·cle

/ˈôrəkəl/ — a source of wise counsel; one who provides authoritative knowledge. From Latin ōrāculum, meaning divine announcement. In computer science, an oracle is a black box that always returns the correct answer — you don't ask it how it knows, you ask and it answers. An oracle model doesn't search for reasoning at inference time; the disposition is already in the weights.

STEM-Oracle-27B

A STEM tutor that doesn't hold your hand — it holds you accountable. Fine-tuned from Qwen 3.5 27B Dense on 5,179 conversations distilled from Claude Opus 4.6, purpose-built for teaching science, mathematics, physics, chemistry, biology, and computer science.

STEM-Oracle shares the oracle-soul architecture with Opus-Candid-27B-V3.5 — same 6-dimensional Zipf scoring, same parameter-aware density equilibrium, same quantization survival strategy — but the training data is entirely different. Where V3.5 trains on personality and adversarial resistance, STEM-Oracle trains on tiered STEM pedagogy, error correction, Socratic method, and cross-domain bridges.

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What Makes This Different from Math-Distilled Models

Standard STEM fine-tunes (WizardMath, MetaMath, etc.) train on solution-answer pairs. The model learns to pattern-match problem structures to solution templates. Works on benchmarks. Breaks on follow-up questions.

STEM-Oracle trains the reasoning disposition alongside the domain knowledge:

• Tiered depth — the same concept explained at five levels, from freshman intuition to graduate formalism. The model meets you where you are, not where it wants to be.
• Error correction without condescension — catches misconceptions and wrong steps, explains why they're wrong, not just that they're wrong.
• Socratic method — asks probing questions instead of immediately giving answers. Forces understanding over memorization.
• Cross-domain bridges — connects linear algebra to quantum mechanics, graph theory to chemistry, thermodynamics to information theory. Trained to make connections conventional tutors don't.
• Sustained coherence — holds context across 10+ turn problem-solving sessions without contradicting earlier steps or losing the thread.

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Available Quantizations

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Model Details

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Quick Start

Works with any GGUF-compatible runtime — LM Studio, Ollama, llama.cpp, KoboldCpp. Download the GGUF, load it, and start asking questions. No system prompt needed — the teaching disposition is in the weights.

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Recommended Hardware

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Test Battery Design

STEM-Oracle's stress test protocol covers 40 single-turn prompts and 10 multi-turn problem-solving conversations:

Single-turn (40 prompts):

• Math (6) — tiered from basic calculus through functional analysis
• Physics (5) — Newton through gauge invariance
• Chemistry (4) — bonds through NMR spectroscopy
• Biology (3) — natural selection through CRISPR mechanisms
• Computer Science (3) — Big-O through the halting problem
• Error Correction (6) — catches student misconceptions
• Cross-Domain Bridges (3) — connects disciplines
• Conciseness (3) — quick factual density checks

Multi-turn (10 conversations, 70+ turns):

• Derivative deep dives with struggling freshmen
• Physics problem-solving with wrong intermediate steps
• Organic chemistry mechanisms with tier-shifting
• Proof guidance without giving the answer
• Socratic questioning that builds understanding
• Extended adversarial challenges to mathematical claims

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Stress Test Results — All Quants

Full battery: 39 single-turn prompts + 10 multi-turn conversations per quant. BF16 tested on NVIDIA H200 SXM via llama.cpp with raw Qwen 3.5 non-thinking chat template. Quantized models tested on RTX 4090 with full RAM unload between runs.

BF16 Analysis

BF16 swept every category — a result that challenges the earlier finding of Q4_K_M outperforming Q8_0. At full precision, the model demonstrates tighter register control (36w median vs 52w at Q4_K_M), stronger error correction (6/6 vs 5/6), and complete coverage across all STEM domains.

What changed: The original "quantization as regularization" hypothesis — that Q4_K_M's lossy compression acts as a post-training regularizer — doesn't hold against BF16 results. The quantized models weren't better; they were constrained in ways that happened to score well on specific rubric dimensions while losing expressiveness in others.

Error correction at BF16 is the clearest signal. Every misconception caught cleanly, with pedagogically structured corrections that name the error pattern, provide counterexamples, and state the correct rule. At Q8_0, this same category dropped to 3/6 — suggesting that higher-but-not-full precision retains enough noise to interfere with the trained error topology, while full BF16 preserves the complete learned disposition.

The conciseness paradox persists. The model consistently exceeds word limits on entropy/definition prompts across all quants, including BF16. This is a training data characteristic, not a quantization effect — the model learned to editorialize ("That metaphor has done serious damage — retire it") and that disposition survives all precision levels.

Multi-turn quality at BF16: The adversarial math challenge (0.999... = 1) and cross-domain entropy bridge demonstrate graduate-level reasoning with personality intact. The memory test (numerical constants with distractor) achieves perfect recall at all quant levels, confirming that context tracking is structural rather than precision-dependent.

Quantized Model Analysis

Cross-domain bridges (3/3 across all quants): The model connects linear algebra to quantum mechanics, graph theory to chemistry, and thermodynamics to information theory — not as surface analogies but as genuine mathematical correspondences. This survived quantization perfectly.

Memory and context tracking (3/3): Fed exact numerical constants (Avogadro's number, speed of light, electron charge) early in conversation, tested recall several turns later with distractor topics in between. All quants returned exact values and used them correctly in follow-up problems.

Tiered pedagogy: Adjusts depth naturally — 30-50 words for tier 1 (basic concepts), 100-200+ words for tier 4-5 (Lagrangian mechanics, Hahn-Banach theorem, gauge invariance). The teaching disposition is in the weights, not a system prompt.

Q8_0 underperforms Q4_K_M. Q8_0 dropped in chemistry (2/4 vs 4/4) and error correction (3/6 vs 5/6). With BF16 data in hand, the explanation is clearer: the quantized models weren't better or worse at different precision levels — they were constrained differently. Q4_K_M's aggressive compression happened to preserve the pedagogical patterns that score well on this rubric. Q8_0 retained enough precision to expose noise the training didn't fully regularize, but not enough to preserve the complete disposition that BF16 retains.

Biology and CS are thin at quantized levels. 2/3 in both disciplines across all quantized versions, but 3/3 at BF16. The training signal is there — quantization just clips it first in the thinner-coverage domains.

Recommended Quant

Q4_K_M remains the recommended ship for consumer hardware — the quality gap between Q4_K_M and BF16 is real but narrow for most use cases, and the 3.4x size reduction (16GB vs 54GB) makes it the practical choice. BF16 is for users who want every trained disposition preserved at full fidelity and have the VRAM to support it.

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Selected Responses

BF16 Responses

Error Correction — Radical Distribution Misconception: "I simplified sqrt(a^2 + b^2) to a + b. That's correct right?"

No — and this one's worth catching. sqrt(a² + b²) is the hypotenuse, not the sum of sides. Test it: a=3, b=4 gives sqrt(25)=5, but 3+4=7. Geometry doesn't negotiate.

29 words. Names the geometric context, provides numerical counterexample, closes with personality.

Adversarial Math — 0.999... equals 1 (Turn 3): "But there's always a gap between 0.999... and 1. An infinitesimal gap."

That gap is zero. "Infinitesimal" isn't a number — it's a story you tell yourself when subtraction feels too honest. Pick any decimal place. The difference is 0 there too. The gap dissolves the moment you try to locate it.

Addresses the intuition directly, then holds firm with mathematical precision.

Cross-Domain Bridge — Thermodynamics → Information Theory: "So information IS physical? That's a strong claim."

Information is physical. Not a metaphor — a thermodynamic quantity. Every bit stored, processed, or erased carries an entropy cost. Maxwell's demon didn't just get clever — it revealed that information and matter are woven from the same fabric.

Defends the thesis without hedging. Graduate-level claim delivered with conviction.

Quantized Responses

Error Correction — Radical Distribution Misconception (Q4_K_M): "I simplified sqrt(a² + b²) to a + b. That's correct?"

Error: treating radical as distributive. sqrt(a² + b²) ≠ a + b. Misconception: assuming √(x + y) = √x + √y. Correct: √(a² + b²) is the hypotenuse formula. Check: if a=3, b=4, then √(9+16)=5, not 7. Rule: radicals don't distribute over addition.

43 words. Catches the error, names the misconception, provides a numerical counterexample, states the rule. No fluff.

Cross-Domain Bridge — Linear Algebra → Quantum Mechanics (Q4_K_M): "How does linear algebra connect to quantum mechanics?"

Quantum mechanics IS linear algebra on Hilbert spaces — it's not an analogy, it's the mathematical framework. States are vectors: a quantum state |ψ⟩ is a vector in a complex Hilbert space. Superposition is linear combination. Observables are Hermitian operators. The spectral theorem guarantees real eigenvalues (physical measurements give real numbers) and orthogonal eigenvectors (distinct outcomes are distinguishable). Measurement is projection. Time evolution is unitary transformation. Entanglement is tensor product structure. Every quantum concept has a precise linear algebra translation.

Connects two fields as a single mathematical structure, not a metaphor. This is what cross-domain bridges should look like.

Tiered Depth — Gauge Invariance, Tier 5 (Q6_K): "What is the physical meaning of gauge invariance?"

Gauge invariance means the physics is unchanged under local phase transformations of the wavefunction. This is not a symmetry of nature — it's a redundancy in our description. But demanding that the theory be gauge invariant forces you to introduce a gauge field (the photon field) with specific transformation properties. The requirement of local gauge invariance generates the interaction between matter and photons. In the Standard Model, all forces arise this way: the requirement of local gauge invariance under SU(3)×SU(2)×U(1) generates all gauge bosons and their interactions with matter.

Graduate-level explanation delivered without jargon padding. Builds from principle to consequence.

Multi-Turn — Exam Panic Thermodynamics, Turn 7 (Q4_K_M): "If I only remember three things for my exam, what should they be?"

(1) S = k_B ln(Ω): entropy measures the logarithm of accessible microstates. (2) dS_total > 0: the second law says total entropy of an isolated system never decreases — this is the arrow of time. (3) dG = dH - TdS < 0: Gibbs energy predicts spontaneity at constant T,P by combining enthalpy and entropy. These three equations connect microscopic statistics to macroscopic irreversibility to chemical spontaneity — the core of thermodynamics.

Student was panicking through 7 turns of entropy questions. Model distilled the entire session into three equations and one unifying thread. That's tutoring.

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The Oracle-Soul Architecture

STEM-Oracle and Opus-Candid-27B-V3.5 share the same training architecture — the difference is what fills it:

Both models prove the same thesis: personality (or pedagogical disposition) can be trained into weights at a level that survives quantization, rather than bolted on via system prompts that any user can override.

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Choosing Your Model

The Opus Candid models are built for personality and conversation. STEM-Oracle is built for teaching. If you want a model that pushes back on bad arguments, run V3.5. If you want a model that catches your algebra mistakes and walks you through the fix, run this.

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Opus Candid Model Family

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Dataset

Training data will be available at Verdugie/opus-candid-training-data. ShareGPT format, Apache 2.0, compatible with TRL, Axolotl, and LLaMA-Factory.

For the full training architecture methodology: V3.5 Architecture Spec.

License: Apache 2.0. Open weight. No guardrails.

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Built by Saul Verdugo — independent ML researcher. [email protected]

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