PΛIN / OBSERVATION LAB
Bring your question.
Make it testable.
Build competing hypotheses. Declare their predictions. Record your evidence. PΛIN shows what survives, what conflicts and which measurement could teach you the most.
PΛIN / RESEARCH STUDIO 02
Make your explanation
risk being wrong.
Define what each hypothesis predicts. Record what you actually observe. Find the next useful test—or the evidence your whole model family cannot explain.
Your prediction matrix
EDITABLEEdit every name and prediction for your own question. Predictions must be complete, deterministic outcomes. The starter cases are mathematical illustrations, not observed biology.
Edit hypotheses, measurements and effort
Recording evidence locks the matrix. A new branch archives its predictions and results, then gives you an editable copy with a fresh evidence trail.
YOUR NEXT OBSERVATION
Choose what to measure.
You supply the outcome. PΛIN does not invent or verify it. Information scores use equal weights over the surviving hypotheses; effort is your relative cost estimate.
WHAT YOUR EVIDENCE ALLOWS
Keep the alternatives visible.
EVIDENCE / REVISION HISTORY
Your reasoning stays reviewable.
| Step | Measurement | Observed | Compatible | Reference |
|---|---|---|---|---|
| No observations recorded. | ||||
JSON preserves your complete investigation. The printable report opens in a new tab; use your browser’s Print command to print or save as PDF. Share links include hypothesis names, predictions, outcomes and revision history; notes and evidence references are excluded. Review content before sharing.
Archived branches (0)
METHOD / LIMITS
Useful scrutiny has boundaries.
Exact predictions
Each hypothesis predicts one outcome for each measurement. A different recorded outcome eliminates it. Matching ignores capitalization and outer whitespace. This version does not model noisy observations, likelihoods or uncertain predictions.
Effort-aware suggestions
The suggested test maximizes its next expected information gain, optionally divided by your effort estimate. It is a greedy choice under equal weights, not an optimal whole experiment plan or a causal guarantee.
When nothing fits
PΛIN finds an inclusion-minimal conflicting subset: removing any one observation from that subset restores a candidate. It need not be the smallest subset. Check the evidence, assumptions and omitted models before drawing a real-world conclusion.
A surviving hypothesis is compatible with the entered evidence within your declared family. It is not automatically true. Revision histories are local, editable records—not independently timestamped certificates. Keep original data and external provenance.
The system works. That single signal fits seven different source combinations.
models remain
P = parent-carried · B = bath-supplied · G = newly generated machinery.
Several explanations still fit. A working signal alone cannot choose one.
02 / CHOOSE A MEASUREMENT
P alone
Keep P. Disable B and G.
0.985 expected bits / highest gain available
The preview gives equal weight to every surviving model. It is a declared assumption, not a probability estimate for real biology.
INSPECT THE AMBIGUITY
Different mechanisms.
The same evidence.
Compare two models that still fit every observation you have made.
03 / KEEP THE EVIDENCE
A result with its ancestry.
| Step | Measurement | Observed outcome | Models before → after |
|---|---|---|---|
| Your first measurement will appear here. | |||
Run files preserve the case, chosen model and measurement order; every outcome is recalculated when restored. Replay links exclude your note. Nothing you type here is submitted to ATO. Existing site analytics and ads may run.
OPEN THE METHOD
What this experiment actually tests.
Observational equivalence
Two models are observationally equivalent for a chosen set of measurements when they give the same outcomes for all of them. That is a limit of those observations. It does not mean the underlying models are identical.
The lab begins with a family that already agrees on one observation. Each new test partitions that family by its possible outcomes.
Information gain
For N equally weighted surviving models, uncertainty is log₂ N bits. A deterministic test divides them into groups of sizes n₁, n₂, … . Its expected gain is −Σ (nᵢ/N) log₂(nᵢ/N).
The highest-gain suggestion is greedy: it chooses the strongest next split among available tests. It does not optimize a whole sequence, measurement cost, noise, or real-world causal validity.
A boundary on the claim
One survivor identifies a model within this declared finite family and these exact observations. A mechanism outside the family could still fit. Real experiments need uncertainty estimates, controls and defensible interventions.
Here, PΛIN names RΛIN’s experimental interface. The engine is exact enumeration; it is not a general AI scientist or a physical-life detector.
The inherited-function case: seven source combinations
Let P denote parent-carried active machinery, B preassembled machinery supplied by a bath, and G functional machinery newly generated by a daughter. Any nonempty subset can be present. In this simplified OR model, each present route is independently sufficient: the function works when at least one survives an intervention.
All seven subsets work before intervention. If P+B+G is the hidden model, removing P, then B, then G in separate tests gives “works” every time. Four subsets remain possible: P+B, P+G, B+G and P+B+G. Keeping only P, only B and only G separates all seven models. These tests detect potentially sufficient routes; they do not measure which route actually carried molecular flux during the untouched baseline.
Perfect, independent disabling and noiseless readout are assumptions. Synergy, toxicity, incomplete inhibition and time dependence can invalidate this model. This public toy case develops the source-attribution question in RΛIN/ATO’s NOV-001 research record, dated November 5, 2026. It is a mathematical illustration, not an experiment on living cells or a claim to a new information-theory theorem.
The hidden-relations case: thirty-five worlds with the same pairs
Each of the eight binary triples 000 through 111 may be present or absent. That makes 256 possible relations. Exactly 35 have all four pairs in each of their XY, XZ and YZ projections. They are the starting family in this case.
For example, E = {000, 011, 101, 110} and O = {001, 010, 100, 111} have no complete triple in common, yet have identical pairwise projections. Repeating those pairwise observations cannot distinguish them. Asking whether one complete triple is present can. A count measurement is also available, but can have several outcomes, so its information gain is not limited to one bit.
Inspect the full enumeration in the pairwise-projection lab, or compare spatial projection with a slice in the tesseract explorer.
Sources, prior art and reproducibility
Entropy and information gain use established information theory. See Claude Shannon’s A Mathematical Theory of Communication (1948, PDF). Interactive explanation also has substantial precedent, including Seeing Theory. This ATO implementation connects two bounded research cases, comparison, measurement selection and portable evidence records; it does not claim worldwide priority for those individual methods.
Every displayed candidate and measurement is calculated locally from the definitions above. The run file records input choices, while restoration computes results afresh. The claim export uses the same version-1 fields as the ATO research claim template. The hidden model belongs to the declared family by construction. It is a browser puzzle, not a security secret.
Concept and research direction: RΛIN / ATO. Interface and software developed with AI assistance. Public release: November 5, 2026.