Follow your curiosity through a city of signals, learning, poetry, and proof. Every discovery has another way in.
THE FINITE CORE125→47Explore the mathematics. Keep its boundaries visible.
CONSTELLATION MAPChoose a district · drag to orbit
A shared home for your existing worlds.EXPLORE / EXPERIMENT / VERIFY
YOUR FIRST DISCOVERY
A signal finds its shape.
Change a signal. Make a prediction. Watch what remains. Then inspect the evidence.
Explore
Predict
Experiment
Inspect
TOUCH THE MATHEMATICS 02 / SIGNAL GARDEN
Watch a signal find what stays.
Seven spectral sectors. Two retained. Change the initial overlap and see how the filter reshapes the signal.
SPECTRAL LANDSCAPESTEP 0
Conditional fidelity—
Success probability—
Complement norm—
Unnormalized sector population after filtering
Sector
Dimension
Population
Selection
FROM YOUR ATTACHED QGNN CODE EXACT COMPRESSED SIMULATION
Evolve inside the retained carrier.
Four graph-derived quantum gates change a fixed retained input while preserving its norm. Move an angle and watch the observable respond. These controls are separate from the spectral filter above.
47 RETAINED COORDINATESLOADING
Observable expectation—
State norm—
Norm error—
Inspect the 47 populations
Coordinates in the supplied retained eigenbasis, not torus-node addresses
Coordinate
Population
WHAT YOU ARE SEEING
Retention and contraction.
The filter leaves the J = 2 and J = 5 sectors unchanged and contracts the other sectors. The complement norm is bounded by (15/17)n times its initial norm. Conditional fidelity is undefined when the selected overlap is zero.
LEARN BY CHANGING THINGS 03 / NEURAL LAB
Teach a boundary. See learning happen.
A small neural network learns from synthetic points. Predict, train, compare—and keep neural accuracy separate from spectral projection.
DECISION FIELDREADY
Epoch0
Training accuracy—
Mean squared error—
A real trainer, a clear boundary.
This browser lab runs deterministic gradient training on synthetic data. Its training accuracy does not measure performance on unseen real-world data. The existing ENTRAIN instrument includes an additional feature encoding and E47 projection monitor; the Signal Garden here is a separate experiment.
Inspect every training point and prediction
All 128 synthetic points: inputs, labels, and current predictions
Point
X
Y
Label
Probability
Prediction
MANY WORLDS, ONE WAY IN 04 / ATLAS
Your instruments. Connected.
Explore the existing surfaces. Each destination keeps its own purpose and evidence boundary.
CURIOSITY WITH A TRACE 05 / EVIDENCE
See how we know.
Inputs, assumptions, sources, and limits stay attached to each experiment.
FINITE MATHEMATICS
The spectral core
H = V₂ ⊗ V₂ ⊗ V₂, dimension 125. K = (C − 6I)(C − 30I). ker K has dimension 47. Γ = I − K²/99144.
The browser Signal Garden computes seven-sector norm observables. It does not reconstruct phases, compile quantum gates, or run on quantum hardware.
Replay files contain validated inputs. Imported results are recomputed. Saved progress stays on this browser unless you export it.
FOR HUMAN & MACHINE READERS
A common contract
Stable identifiers, explicit scope, versioned inputs, and attributable sources. Machines can inspect the same experiment without interpreting the visual scene.