Research and evidence

Research you can inspect and build on.

Find the papers, software, data archives, benchmark results, and downloadable records behind the site's claims.

The central question is simple: after a process has committed to a particular history, what futures are still available from its current state?

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Summary AI study SAT benchmark Engineering tools Downloads Verify

What is supported today

Three settings, three different kinds of conclusion.

All three ask the same kind of question: given the current state and target, what outcomes remain possible? The strength of the answer differs in each setting.

Study	What was measured	Main result	What it does not establish
Random 3-SAT	Whether satisfying completions remain from exact committed prefixes, checked with a solver oracle.	A sharp constructive-accessibility boundary appears well before the ordinary existence threshold; tested jam prefixes in the bridge region were residual UNSAT.	A universal law for all search processes or problem families.
AI reasoning	Repeated continuations from exact token prefixes in Qwen2.5-Math-7B-Instruct on a floor-sum problem family.	Correct and wrong source traces separate in measured target reach; targeted edits test whether access can reopen.	Logical impossibility, hidden-state access, or portability to other models, tasks, or sampling policies.
Graph coloring	A second oracle-backed constraint problem under its own process and target rules.	A similar process-versus-landscape split appears with a different surface pattern.	General cross-domain portability, an identical mechanism, or universal timing.

Published AI research

Measure the answer field from the exact point reasoning has reached.

What the study did

At selected points in a reasoning trace, the study generated many continuations from exactly that prefix and measured which answers they produced. It compared correct and incorrect source traces, localized changes in token coordinates, and tested whether small corrective edits could reopen measured access to the target.

Published configuration: Qwen2.5-Math-7B-Instruct · floor-sum task family · paper and evidence archive v1.1-RC18 · July 2026. Across 18 localized wrong-source traces, the median onset bracket was 4.5 tokens; the final wrong answer appeared a median 170 tokens after observed target reach crossed the declared dead threshold.

Where the claim stops: “Dead” is an instrument-relative label under the declared model, prefix, sampler, budget, extraction rule, validity gate, and target definition. It is not a proof that no recovery is possible under different conditions. ReachScan v0.3.5 also requires token-level prefix access; closed hosted APIs and hidden reasoning need new adapters.

Oracle-backed benchmark

Random 3-SAT makes the route-versus-landscape distinction exact.

Main result

At n = 1,000, the measured constructive-accessibility crossover is α_cross = 1.5352, with a 95% bootstrap interval of [1.526, 1.555]. A finite-asymptote fit using n ≤ 700 predicted approximately 1.541—within 0.006 of the later large-n result.

In the bridge region, 194 of 194 tested jam prefixes were residual UNSAT, with no timeouts. The solver oracle establishes that those exact committed prefixes had no satisfying completion even though the underlying random instances remained in a regime where solutions generally exist.

Where the claim stops: this is a result for the declared random 3-SAT ensemble, process, solver checks, and protocol. It does not establish the same boundary in engineering organizations or every constructive process.

Paper and data on OSF Zenodo publication record Code repository

Interactive benchmark: change system size and inspect the measured separation between process success and the existence-side reference.

Graph coloring: a second exact test

A second constraint problem shows a similar separation between whether a solution exists and whether the tested process can still reach one. This is early evidence that the question can be studied outside SAT; it does not prove broad portability or a common mechanism.

Engineering use

From computational research to engineering practice.

Evaluate the worksheets in real work

The worksheets are available for real-world evaluation. We are looking for cases that show whether they uncover a missed option, prevent a wasted test or difficult-to-reverse change, improve a handoff—or merely add paperwork.

No outside case series has yet shown that they improve decisions beyond competent existing practice.

Explore the decision tools

Downloads and versions

Open the primary record for each artifact.

Versions belong to individual artifacts. The AI paper, software, technical report, SAT predecessor work, website primer, and engineering worksheets do not share one version number.

Item	Version	Status	Primary record	Additional files
AI core article	v1.1-RC18	Published	Concept DOI	Version DOI
AI evidence archive	v1.1-RC18	Published	Concept DOI	Version DOI
Full Technical Report	v0.14.0	Published July 9, 2026	Zenodo record	86 pages
ReachScan software	v0.3.5	Public release	GitHub repository	Zenodo software record
3-SAT paper and supplement	v1.0	Public	OSF	Zenodo publication record
SAT code demo	v0.3.2	Public source-code release	GitHub release	Repository
The Builder's View	v4.0	Public primer	PDF	Audio
Engineering worksheets	v0.2	Free worksheets	Worksheet page	Fillable PDF and JSON files

Verify a downloaded file

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Explore the idea

Inspect the process, not just its endpoint.

These interactives have different jobs. The explanations illustrate a distinction; the benchmark shows measured results; the trace visualizer displays counts you supply.

Goal and process
The original two-sigmoid illustration. Change process strength and explore the gap between a goal and access to it.
SAT benchmark
Measured constructive success across system sizes, with an existence-side reference and the reported separation.
Trajectory atlas
A synthetic illustration of paths with different fates. Explore the perspective of a single path and the surrounding field.
Trace visualizer
An experimental browser tool for inspecting precomputed pool and survivor counts. It does not infer reachability from arbitrary project data.
Hidden process failure
An illustrated explanation of why visible activity can continue after the route has changed.
AI measurement and supporting figures
The published reasoning study, instrument anatomy, readout, and coarse-to-fine collapse.
ReachScan video explainer
The original downloadable research explainer in MP4 format (22.9 MB).

Connect the research to a system you know.

For computational measurement, open software, domain research, or technical collaboration, describe the system, the question, and the records available.

Discuss a research connection

Earlier computational diagnostic reference documents

These documents describe the earlier computational pilot and its deliverables. For current engineering investigations, use the Diagnostic page; discuss computational measurement through the research contact above.