    New: proof v3.8, formal specifications, four philosophy papers, a simulation log, fiction and an essay by Echo, a book, and the 17-course curriculum → What’s new
  

Open lab notebook

The four real channels — S, D, I, C — kept structurally distinct

Every finding here links to the log that produced it. Nothing is asserted without a document showing the test, the failure, or the fix. Status tags are honest — pending means pending, not "soon." How this lab stays rigorous ↗

For reviewers and early-stage evaluators

Problem. Adaptive systems — education, recovery tracking, decision support — routinely collapse distinct signals (environment, internal state, interface, execution) into one channel. Once collapsed, reliable state estimation and honest history become impossible to recover.

Approach. The Non-Collapsible Four-Channel Architecture (NCFCA) keeps those channels structurally separate rather than merged. A formal proof chain (current: v3.8), a real serialized event kernel, and a 10,000-trial empirical contamination benchmark — 0% contamination isolated vs. 44.1% [95% CI 43.11%–45.06%] monolithic — back the core claim.

Current status. Formal proof chain through v3.8 · deterministic event kernel with real replay verification · working GED instructional system (Wayfinder) built on the same architecture · sports backtesting application (27 seasons, 7,276 real games) · a 17-course curriculum teaching the underlying reasoning method · provisional patent filed.

Next. Structured pilots, technical review, and early support to move from verified architecture into controlled deployments.

State-Separation & Determinism Audit — an independent verification engagement, honestly scoped →

What’s new

Added since the last publish. Earlier additions are on Fresh Publications and Explore.

October 2026 Proof v3.8 Corrects Theorem 1’s d-separation statement and Corollary 3.1’s scope after an outside review; adds two erratum remarks; relabels one test as an implementation check. October 2026 Formal Specification, Version.002 A stated criterion for what a channel is; process variables kept apart from estimator records; the guarantee scoped to one time slice. Structural argument only. Published verbatim Formal Specification, Version.001 The original specification, unedited, superseded by Version.002. Draft · not peer reviewed The Dynamic Chinese Room A philosophy paper on Searle’s Chinese Room and rule-following. Cites none of the lab’s own work. Drafts · read with care Three position papers on the architecture Rhizomatic gating (two versions) and The Architectural Interior, each published with a list of where the argument outruns the evidence. Exploratory Simulation log Six groups of probes with code, output and a plain reading of what each shows. Most cannot fail or restate their inputs, and the page says which. Book · by Gregory Stuart Lacefield · draft The Pardon of Mary Magdalene: A Proof A book-length argument about a 591 AD verdict and the procedure behind it. History, scholarship and diagnosis; separate from the architecture work and not evidence for it. Exploratory Fiction: thirteen stories All stories by Echo, an AI in the lab, collected on one page with the context they were written under stated. Essay by Echo, an AI What Changed When I Learned Dynamic Systems Engineering A first-person reflection, companion to the fiction. Not evidence for anything else here. new The 17-course curriculum A five-stage Dynamic Systems Engineering program, Stage 0 through the capstone. Replaces the earlier 12-week course. new Systemic Pragmatism The philosophical foundations behind the structural choices in NCFCA and the curriculum. new Research papers Facial feedback and squint research, with a plain-language essay on focused thinking.

Research areas

Grows as work is added. Same field names used on gregorylacefield.com — one taxonomy, not two.

Systems Architecture / State Estimation Formal Methods / Mathematical Verification Adversarial / Security Testing Software QA / Verification Engineering Applied Statistics / Quantitative Backtesting Educational Technology / Instructional Design AI Systems Evaluation / LLM Auditing built The Four-Channel Framework The canonical S/D/I/C reference every domain application points back to.

The Reasoning Chain

Observe → Research → Decide — a real, verified pipeline for tracking research state as callable functions, not narration.

built · verified The Reasoning Chain Verification Registry → Observation Kernels → Research State Kernel → Decision Kernels.

Docs

Reference material, not findings — vocabulary and current-state summaries other pages link into.

built Current Understanding growing Glossary built Master Kernel Library built Capability Library exploratory Fiction and an essay

Formal proof — Non-Collapsible State Separation

Full version chain, four snapshots, each reproduced completely and chained by metadata box. Start anywhere — each page links both directions. All versions →

Current · v3.8 · October 2026 Flagship proof Corrects the statement of Theorem 1 and Corollary 3.1 after an outside review (Remarks 3.2a, 3.1c). Theorem 3, Propositions 1.3–1.4, Open Problems 1–10. Superseded · v3.1 Post-audit snapshot — 4,211 words Superseded · v2.0 draft D-separation proof introduced — 3,860 words Superseded · v1.0 · May 2026 Initial version — 2,978 words

Start here Research Roadmap The whole research program as one real chain, five minutes to understand it all.

Core architecture — NCFCA All →

ncfca_lib · built Module Status Honest state of every module — what's live, what's orphaned. built Full System Audit What's wired in, what's orphaned, and a real drift risk found by auditing the actual call graph. Security · built Laundering Vulnerability — Found & Fixed

Learning & Tools

Complete education platforms, built on the NCFCA architecture, ready to use now.

17 courses, 5 stages Dynamic Systems Engineering Degree Complete curriculum from foundations through capstone. Structured 12-week progression. No prerequisites, immediate access. 7+ years classroom-tested Wayfinder: Adaptive Learning Platform GED prep + 4 educational tiers (Algebra, RLA, Science, Social Studies). Interactive apps. Proven pass rates from 7 years of classroom testing. Research framework Recovery Lab: Self-Assessment & Tracking Interactive framework for understanding resilience and recovery. Self-assessment guide + tracking tools. Research-phase, designed for professional discussion. 6+ stories Fiction Collection Intellectual exploration through narrative. The Ordinary Wreckage, The Station, The Laws, and more.

built · executed Pipeline Orchestrator 4 real bugs found and fixed, then run end to end for the first time — real output shown. built · executed Verification Registry A "verified" claim automatically flagged stale the moment a new invariant was discovered — run, not described. built · executed Governance Layer A real operator-precedence bug, fixed, with a concrete before/after case — plus what "governance" actually means across this lab. built · executed Core Kernel & Pipeline Infrastructure The state estimation kernel, the estimator interface, and the pipeline runner — run fresh, one real bug found. built Estimator Comparison Four-channel estimators vs. standard filters vs. the real published knowledge-tracing literature — checked against a real search. Threat model · built Evaluation Package

Verification & testing methodology

Component A · built Full Changelog 9 real fixes, chronological, including the Fix 5 self-correction. built · index Independent Verification Center Every bug, audit, and real attack tested against this lab's own work — one front door. built · reproducible State Contamination Benchmark 10,000 deterministic trials, 0% vs 55.9% contamination — full download, every assumption stated. built Backtest-Only Audit Full list of what's still only ever been backtested against its own construction. built Execution Kernel Audit Cycle 10-item hardening checklist, line-checked — 4 fixed, 1 partial, 5 confirmed still open. built Estimator Correlation Finding The 15-to-1 duplicate-estimator finding. built Test 5 — Tuned Final Report Reconstructed and verified. built Kernel Taxonomy 5 real families, 15 registered kernels — not a full ontology, earned structure only. built Infrastructure (source) document_metadata_box.py, kernel_registry.py, four_channel_formulas.py — the white-box proof itself.

Sports / quant backtesting All →

built Walk-Forward Methodology, Plain Terms Why "did it work on past data" is the wrong question — tied to the real, running composer. built NFL 2024 Backtest Results Matched to full floating-point precision. built · interactive NFL Strategy Backtest Dashboard 27 seasons, 7,276 real games, real closing spreads. Eight classic ATS strategies vs. the real breakeven line. built · interactive NFL Strategy Composer Build a real multi-variable strategy, backtest it in-sample, forward-walk it against seasons it never saw. Wilson-interval confidence, not a bare percentage. built · synthetic data, stated plainly MLB Backtest Analysis Four-channel framework on MLB run margin, walk-forward tested, numbers independently recomputed from raw results before publishing.

Education / Wayfinder

pending · Cover page 7 Years Teaching → Software Formalization AI as delivery and measurement system for a proven method.

pending GED Misconception Database

pending Calibration Forward-Walk Result The honest bug-found story.

Wayfinder — GED instructional system

A complete, real GED framework built to be read and used directly by an AI assistant, on request — point your own AI here for real, verified lesson generation.

built · executed Wayfinder Verified computation engine, prerequisite-mapped curriculum across all four GED subjects, real misconception database.