New names, same structure
Renaming nodes should preserve the comparison.
From structure to testable features
Look beyond
the connection.
A graph says what is connected. Geometry measures how each connection sits in its neighborhood. Does that help explain how a system responds?
Explore the laboratory01 / Declare the observation
What can be told apart?
Two graphs may look identical under one set of observations and different under another. An observation regime states which differences count. Missing evidence can leave the answer open.
Distinguishability is the methodological foundation of this lab. It is not an established fundamental law.
Three checks of the instrument
Synthetic controls · separate from biological evidence
Same wiring, different relations
A typed regime can detect a difference that topology omits.
Unknown stays unknown
A missing relation field must not turn into a match.
02 / Follow the same pair
The structural laboratory
Loading the pinned examples…
Comparison components and coverage
Metric and flow rules for these examples
Unit edge lengths and masses. Directed Ollivier transport compares predecessor and successor neighborhoods with idleness ½, using forward directed shortest-path distance in the declared graph scope. Forman uses the directed unit convention.
The shadow flow updates a separate length state, applies metric closure and normalizes the total length. Step ½; tolerance 10⁻⁶; two stable steps; at most eight iterations; no cuts. The original nodes and edges stay fixed. A fixed point, tolerance stop and iteration limit are different outcomes.
Changing the observation regime changes the structural comparison and response probes. These geometric measurements keep their own fixed metric configuration.
Calculation rules and independent references03 / Test the added value
Does geometry help predict a response?
Compare graph features B with the same model plus geometric features B + G. A positive difference means better ordering of responses on the declared held-out groups. It does not establish a biological mechanism.
Loading the research evidence…
What is measured, and which observations count?
Rank skill ranges from −1 to +1. It scores concordant versus discordant response orderings, including prediction-only ties in the denominator. Zero means no ordering advantage; these values are not percentages or accuracy scores. Interventions have equal weight within a group, and groups have equal weight.
DREAM4: five simulated networks of ten genes; 450 off-target rows for knockouts and 450 for knockdowns. The target is the absolute change from wild type. Validation holds out entire networks.
C. elegans: Dataset7 chemical anatomy, 180 nodes and 1,933 directed arcs. The primary study uses 60 eligible source–receiver pairs across nine stimulus sources, drawn from processed fluorescence recordings. At least two recordings per pair and three receivers per source are required. Validation holds out stimulus sources within the same anatomy; receivers and recordings may overlap.
Biological G contains 31 descriptors of unit Forman, directed Ollivier with half idleness, and normalized shadow flow (half step, at most four iterations, no cuts). These are derived from the declared bounded scopes. Weighted ridge regression uses nested group validation and training-only standardization. These observations do not establish stimulus success, animal-disjoint generalization or causal prediction. All features are functions of the same declared graph.
What would change the conclusion?
A gain that survives stronger graph baselines, metric choices, matched populations and independent biological data would strengthen the case. The present results are mixed and sensitive to those choices. The low-degree C. elegans population and the alternative anatomy remain untested under the current gates.
04 / Inspect the evidence
What runs in your browser?
The lab verifies the downloaded files against this page’s release hashes, replays nine small structural comparisons and verifies the stored geometric certificates. Response probes run on the selected synthetic graphs. Biological score summaries are recalculated from stored rank counts.
Opening this page does not retrain the biological models or repeat an experiment. Independent numerical and biological reference checks run offline. A release checksum verifies consistency with the bundled evidence; it is not an independent validation of a scientific claim.