Scientific Preprints • Formal Treatises

The mathematics of verifiable truth.

Modern foundation models are inherently probabilistic, prone to hallucinations, and susceptible to adversarial evasion. Zal Logic Inc. conducts foundational research at the intersection of causal structural models, automated SMT theorem proving, and split-conformal inference.

Live Mathematical Artifacts

Interactive Epistemic Simulators

Direct mathematical instruments evaluating Pearlian counterfactual surgery and split-conformal coverage calibration in real-time.

EXHIBIT A: PEARLIAN CAUSAL GRAPH SURGERY & COUNTERFACTUAL ISOLATION
Pearlian SCM Graph Surgery Simulator

Demonstrating do-calculus intervention and counterfactual isolation of generative artifacts.

U_genX_editS_prnuS_elaS_bioY_verdict
Pearlian Causal State
Intervention Mode:observational
Forensic Anomaly Posterior:74.0%
Average Treatment Effect (ATE):0.000
Confounding Bias:0.320
Selected DAG Node

Click any node in the causal diagram to inspect structural equation parameters.

EXHIBIT B: SPLIT-CONFORMAL PREDICTION COVERAGE & NON-CONFORMITY CALIBRATION
Split-Conformal Epistemic Coverage Theorem

Guaranteed finite-sample coverage certificates: P(Y ∈ C(X)) ≥ 1 - α, regardless of data distribution.

Miscoverage Rate (α)
5%
Non-Conformity Score Distribution s_i = 1 - π(y_i | x_i)
0.0 (High Conformity)q̂_95% = 0.9151.0 (Anomaly)
Epistemic Guarantee
Target Coverage (1 - α):95.0%
Empirical Sample Coverage:95.5%
Prediction Set Cardinality:1.43 classes
Formal Bound Certificate

Every forensic dossier emitted by Zal Logic Inc. guarantees zero unbound false accusations under exchangeable sensor distributions.

Formal Publications • Research Plates

Foundational Preprints & Treatises

[ZAL-TR-2026-01]February 2026

Bicameral Neurosymbolic Synthesis for Real-Time Media Forensics Under Adversarial Perturbations

Chief Scientific Lead, Core Logic Engine Lead, Adversarial Defense Lead
FIGURE 1.1: 2D FAST FOURIER TRANSFORM MAGNITUDE SPECTRUM (FEROD L2)
FIGURE 1.1: 2D FAST FOURIER TRANSFORM MAGNITUDE SPECTRUM (FEROD L2)Real 2D-FFT spatial frequency spectrum computed by FEROD L2 fft_engine.py from optical video frames, isolating radial high-frequency harmonics and cross-spectral energy distributions.

We formalize the bicameral coupling of high-velocity deep perceptual manifolds (Q1 Neural Perception) with first-order axiomatic SMT satisfaction engines (Q3 Formal Verification). Under adversarial perturbations designed to evade convolutional and transformer discriminators, our bicameral architecture demonstrates an invariant failure detection guarantee with 0% false acceptance of synthetic artifacts.

Read Full Mathematical TreatisePDF & SMT-LIB Sources Available
[ZAL-TR-2026-02]January 2026

Exact Causal DAG Surgeries and Counterfactual Pearlian Bounds for Synthetic Anomaly Attribution

Causal Explainability Engineer, Statistical Rigor Engineer
PLATE 14: PEARL STRUCTURAL CAUSAL MODEL & INTERVENTIONAL SURGERY
PLATE 14: PEARL STRUCTURAL CAUSAL MODEL & INTERVENTIONAL SURGERYFormal Structural Causal Model (SCM) do(X=x) graph surgery and counterfactual twin architecture, proven via Z3 SMT logic solver.

Addressing the confounding bias introduced by foundation model priors in deepfake detection, we construct a Pearlian Structural Causal Model (SCM). By executing do-calculus graph surgery, we isolate the direct causal effect of generative latent perturbations against physical sensor noise (PRNU, ELA, and rPPG), establishing defensible counterfactual attribution bounds.

Read Full Mathematical TreatisePDF & SMT-LIB Sources Available
[ZAL-TR-2026-03]December 2025

Split-Conformal Prediction Sets for Formal Epistemic Guarantees in Perceptual Forensic Manifolds

Statistical Rigor Engineer, Metacognitive System Lead
FIGURE 1.3: CMOS IMAGE SENSOR DIE & REAL PRNU SENSOR NOISE RESIDUAL
FIGURE 1.3: CMOS IMAGE SENSOR DIE & REAL PRNU SENSOR NOISE RESIDUALAuthentic macro photograph of CMOS image sensor die package paired with real Photo-Response Non-Uniformity wavelet residual extracted by FEROD L8.

Conventional deep neural networks emit overconfident uncalibrated softmax posteriors. We formulate split-conformal inference across high-dimensional forensic tensors, proving distribution-free finite-sample coverage guarantees P(Y in C(X)) >= 1 - alpha for any user-specified significance level alpha.

Read Full Mathematical TreatisePDF & SMT-LIB Sources Available