Topoboard Labs

Topology Comparison

Same local rule. Different underlying space.

Purpose

What changes when topology changes?

Compare discrete topological dynamics across spaces while preserving the model, local rule, fixed parameters, seed plan, initial-condition family, and observable set.

Comparison mode
synchronized
Total runs
0
Worker
pending
Current Run
-
1

Select model

2

Reference and comparison topologies

Choose one reference topology and one or more comparison topologies. Incompatible entries are disabled with a reason.

3

Initial condition mapping

4

Local rule and fixed parameters

Same local rule means the same rule function is applied to each topology's local adjacency structure.

5

Seed plan

6

Observables and detectors

Select standard model observables and topology-sensitive event detectors. Detector outputs are labeled by exactness and confidence.

Topology-sensitive event detectors

7

Run synchronized comparison

Configure the comparison before running.
    8

    Comparison dashboard

    Observable comparison

    Difference view

    Seam and cycle overlay

    9

    Topology invariant table

    Topology Invariant Value Exactness Method
    10

    Event timeline

    Step Topology Event type Confidence Exactness
    11

    Topology-sensitive divergence score

    A normalized difference between observable time series under the same model, rule, seed plan, and mapping method. It is exploratory and not a universal physical invariant.

    Reference Comparison Observable Distance method Value Confidence
    12

    Export comparison dataset

    Exports include app version, topology hashes, fixed parameters, mapping method, seeds, observables, event detectors, exactness labels, warnings, and reproducibility notes.