Existence is not reachability.
A goal can still be real after every path to it has closed. Reachability Labs measures when a process loses access to viable futures — before ordinary metrics can see it.
Every commitment spends futures. In real systems, going backward means rework, scrap, wasted compute, schedule slip, or a changed problem. Diagnostics are available now. Software is in development.
Bring a failing process. Get a receipt-backed analysis of where it loses the path, how it fails, and what changes are likely to help.
A diagnostic platform for boundary detection, trap analysis, and process comparison. Early-access and pilot conversations are welcome.
Oracle-verified trap analysis, confirmed scaling predictions, and a second combinatorial domain all support the core finding.
Most systems don't fail because the goal vanished. They fail because the route died first.
Classical maps tell you where valid outcomes exist. They do not tell you when a real process has already committed itself out of every workable route. By the time that failure is obvious, teams have already paid in rework, scrap, wasted compute, or schedule slip.
The gap between existence and reachability is the core object.
A route can close long before the goal disappears. That loss has its own geometry, hidden states, warning signs, and costs. The diagnostics are built to find it.
Paid diagnostics for processes that fail in ways ordinary metrics miss.
By the time failure is visible, teams may already have burned compute, material, time, or schedule. The work tells you where a process loses reachability, what kind of trap dominates, and what a realistic upgrade is likely to buy.
Diagnostic studies
Bring a solver, planner, search pipeline, optimizer, or comparable constructive process. Reachability Labs instruments the run, analyzes where and how the path closes, and returns a decision-grade report.
What you receive
A structured technical report, supporting plots and summaries, and a clear explanation of what is failing, what is merely noisy, and where process changes are most likely to matter.
Good fit if
- Your process keeps moving but still fails late.
- Local metrics look healthy while outcomes collapse.
- You have stronger variants and do not know what they actually buy.
- You need more than a benchmark score or a generic postmortem.
Constructive reachability software
The long-term product is a software platform for measuring constructive accessibility directly: boundary detection, trajectory diagnostics, trap analysis, variant comparison, and adapter-based transfer in one instrumented workflow.
How to engage now
Early adopters and pilot partners can start through diagnostic studies first. That path grounds the roadmap in real process failures, real reports, and validated instrumentation rather than speculative product claims.
Planned path: service-led development now, documented software release later, with publication-grade validation and a formal release track including JOSS.
How a diagnostic works.
Define the target. Instrument the process. Compare variants. Diagnose how a committed process reshapes its reachable future.
Landscape-side · structural
Results that give the same answer regardless of which process you use are candidates for structural claims about the problem itself. These are features of the constraint geometry, not your process.
Process-side · procedural
Results that shift when you change the process are tied to the interaction between your method and the problem. The diagnostic tells you which failures are structural and which your process can actually fix.
Where this applies
Different domains, same failure pattern: the target remains possible while the current process has already cut itself off from it. The same core diagnostic logic applies wherever a process builds toward valid outcomes under accumulating constraints.
SAT & constraint solving
The flagship 3-SAT work measures a sharp constructive accessibility boundary and resolves its fingerprint through bridge checks, rewind probes, and late-frontier diagnostics.
Why it matters: It shows the diagnostic object is real in a canonical benchmark with strong auditability.
Graph coloring
A second oracle-backed adapter already shows a large process-side collapse band inside an alive landscape, confirming that the process-versus-landscape distinction is not confined to SAT and that the measurement contract can transfer.
Why it matters: It validates the adapter program and transfer-calibration logic.
Compiler and EDA workflows
Register allocation, routing, proof search, and related workflows are all sequential constrained processes that can lose reachable futures before their surface diagnostics reveal why.
Why it matters: These are real engineering domains where hidden process failure has direct cost.
Scheduling and planning
Forward planners and schedulers commit to actions and resource allocations under accumulating constraints. They often fail for reasons that are visible only very late in the run.
Why it matters: The diagnostics translate naturally to process-side bottlenecks in planning systems.
Channel and frequency assignment
Conflict-constrained assignment domains, including graph-coloring-like formulations in communications, fit the same instrument logic well.
Why it matters: The existence of valid assignments and the reachability of them by a process are often very different things.
Emerging AI reasoning workflows
Structured decoding, planning-like inference, and sequential reasoning systems are natural future domains because they also accumulate commitments while local metrics remain incomplete.
Why it matters: The long-term product opportunity is likely larger than SAT itself.
Research that supports the offer.
The papers matter because they establish that the diagnostics are not guesswork. The current stack includes a flagship benchmark, a first validation lane, a process ladder, an internal theorem scaffold, and a second adapter showing that the core measurement logic transfers.
A measured constructive accessibility boundary in random 3-SAT
A sharp process-indexed boundary in a canonical benchmark, with late visible failure, exact-prefix deadness, trap depth, and strong within-instance path dependence.
See evidence ↓Exact-all-local and pool-stability checks
New validation runs keep the constructive boundary in the same narrow band, strengthening the case that the flagship signal is not just a pool artifact.
See validation ↓P1 shows that stronger forward processes can move the boundary
A stronger forward rung stays alive far beyond the baseline window, showing that added structure can move the accessibility boundary rather than merely smooth the curve.
Why the ladder matters ↓Graph coloring as a second oracle-backed adapter
A second combinatorial domain now shows the same deeper process-vs-landscape split with a different surface morphology, strengthening the adapter-first program.
See domains ↓Internal theorem scaffold: a parallel theorem program continues to formalize hidden structural state, delayed manifestation, and the distinction between landscape-side existence and process-side reachability. See the benchmark view in Evidence.
The shortest useful vocabulary for what this work is measuring.
Start here if the language is new. The goal is to make the problem legible in plain terms first and technical terms second.
In the figures, the goal is the valid endpoint, the process is the method, and reachability is the live relation between them. The gap and benchmark figures are viability-space views. The atlas is a local-state view of the same deeper object.
Opacity is symmetric. A doomed path is dead but cannot tell — it keeps moving, locally healthy, while its prefix has no satisfying completion. A surviving path is alive but cannot tell — it occupies a local state where most of its neighbors are already dead. Toggle between them: same formula, same local view, opposite truths. Three objects measure what is happening: G (forfeiture — how much available future commitment has spent), W or C (the doomed interval or its surviving corridor dual), and O (opacity — the information gap between local state and ground truth).
From single path to population. G·W·O shows one trajectory at a time. The atlas below shows fifty at once — on the same formula. Press play and watch: they stay bundled for most of construction, then diverge violently in the final steps. Toggle "Reveal doomed paths" to see which ones were already dead before they knew it.
Map and route
A maze can still have exits even after the route you are on can no longer reach any of them. The map can stay alive while the route dies.
Existence is not reachability
A goal can remain valid after the current process has lost the route to it. Reachability asks whether this process can still get from here to a valid completion.
Hidden failure
A process can keep moving after its viable future is already gone. Local signals may look healthy even when the route is already dead.
Hidden survival and trap depth
The opposite can happen too: a route can look doomed while a narrow pass still exists. Some failures are shallow mistakes; others are deep structural traps.
The ladder
Stronger processes get more sight, more inference, more correction, more reversibility, or some combination. The ladder asks what each added capability actually buys.
Adapters
K-SAT and graph coloring are calibrated domains, not the whole story. The point is to measure the same deeper object across different terrains.
Commitment changes the future
Each committed step realizes structure while narrowing the futures that remain reachable. That is why path history matters, why local health can mislead, and why going backward is rarely free.
Validated. Oracle-verified. Receipt-backed.
The research-facing benchmark view. This is the benchmark projection of the same goal–process split used elsewhere on the site. The orange curve is measured A0 constructive success. The teal curve is the existence-side reference. The shaded band is the existence–accessibility gap. Toggle system size to see how the boundary sharpens. Drag to measure the separation at any matched success rate.
Nine system sizes through n = 1,000 anchor the flagship result. Oracle-verified trap analysis, bounded rewind, trajectory-space diagnostics, a confirmed scaling prediction, and a second combinatorial domain all support the same deeper claim: the goal can remain valid after the process has lost the route.
Where to start
Artifact ledger
Public artifacts, versions, and mirrors. The site is the hub — OSF, GitHub, Zenodo, and arXiv are the mirrored destinations.
| Artifact | Version | Status | Primary | Mirrors |
|---|---|---|---|---|
| Flagship paper Constructive Accessibility from Committed Prefixes in Random 3-SAT |
v1.0 | Public | OSF | Zenodo · arXiv forthcoming |
| Public demo Runnable constructive accessibility diagnostic |
v0.1 | Public | GitHub | Zenodo release forthcoming |
| Interactive figures Epistemic, G·W·O, scientific benchmark, and trajectory atlas figures |
v4–v6 | Public | Website | GitHub |
| Supplement Extended data, validation runs, coloring adapter |
v1.0 | Public | OSF | Zenodo |
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About Reachability Labs
Reachability Labs grew out of a process engineering background and a research program that kept arriving at the same question: why do well-instrumented processes still fail in ways their own metrics cannot explain?
The answer turned out to be structural. A process can lose access to viable futures long before any local signal reveals the loss. Behind that result is a broader thesis: each committed step realizes structure while narrowing the futures that remain reachable. The diagnostics, the research, and the software direction all follow from that finding — measured first in random 3-SAT with oracle-verified trap analysis, then extended to graph coloring, and now being built into a general-purpose diagnostic methodology.
The work spans computational combinatorics, constraint satisfaction, process diagnostics, and the emerging theory of constructive accessibility. At the core is a simple claim: success and failure are coarse labels on a deeper event — committed transformation and the futures it leaves behind. The lab is currently a focused research-and-services operation. The intention is to grow it as the methodology and software mature.
Bring a process, not a perfect story.
If your process keeps moving but outcomes still collapse, the fastest path is a diagnostic engagement. If you are interested in the coming software, ask about early access or pilot partnerships.
Good fit if: your process keeps moving but fails late, local metrics still look healthy while outcomes collapse, you are comparing stronger variants and do not know what they actually buy, or you need more than a benchmark score.
Diagnostic engagement
Bring a process, not a perfect story. The work can begin from your current implementation and current uncertainty.
- A runnable process: solver, planner, optimizer, decoder, scheduler, or similar system
- Your definition of success or valid completion
- Some description of the constraint structure
- What you have already tried and where it broke
Software and pilots
The software direction is real and in progress. Reach out if you want early access, a pilot relationship, or to discuss what deployment would need to look like for your domain.
- Early-access and pilot conversations
- Software roadmap questions
- Research-backed product development
- Selected research and grant conversations