Executable research programme · finite numerical laboratory

Global Geometry Lab

Compose local relations. Measure the world they make.

Local rule compatibility iteration scale global geometry

One model, three directions

Generate, design, and recognize geometry

The presets share the same metric-measure-cell-complex engine. Their application names are disclosed interpretations of that common mathematics.

01

Forward

Iterate a finite-radius rule and measure the global trajectory.

02

Inverse

Give local curvature feedback a target satisfying the necessary Gauss–Bonnet sum.

03

Recognition

Compute descriptors of a supplied finite complex and expose what local observations cannot identify.

Interactive finite model

Local rule chamber

Exact finite identity Finite numerical estimate Research target Application analogy
Forward —

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Topologyexact
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Curvature closureidentity
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Effective dimensionestimate
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Global responseestimate
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Generated worldIntrinsic geometry comes from local lengths; screen position is a view.
low signal middle signal high signal
Current finite geometry A graph or triangular complex colored by its current local field or curvature error.

Select a vertex to inspect local state or target error.

Dimensional profileDimension is measured across scale, not assigned once.
Finite-scale dimension profile Volume-growth, spectral, and walk-dimension estimates from microscopic to macroscopic observation scales.

Move the observation-scale control to compare each estimator on its own normalized logarithmic scale.

1Neighbourhoodlocal data
2Compositionpaths and loops
3Global observablemetric, topology, dimension
observable universality test

Compare two microscopic worlds

Replay this preset with a different seed at the same time and compare topology, spectrum, and dimension signatures. Agreement is finite observable collapse—not proof of isometry or a continuum universality class.

Topology
not compared
Dimension profile distance
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Spectral signature distance
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The comparison is deterministic and matched by preset, parameters, step, and observation schedule.

Programmable configuration and reproducibility record

The editor accepts the closed schema only; it never evaluates code.

Finite-run record

Core / analysis schema
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Step / time
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Vertices / edges / faces
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Method
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Replay id
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Application map

The mathematics transfers; the claims do not

Each preset exposes the same local-to-global mechanism while preserving the boundary between a mathematical model and an empirical application.