The Mathematical City · Unified Interface

Mini AI Labs

Ten live labs. One Citadel Gateway.

Central Citadel · Gateway

SEE

Machine certificates — results, residuals, and provenance.

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STRUCTURE → INVARIANCE → DYNAMICS → MEMORY → MEASUREMENT → PREDICTION → FLOW → IDENTITY → BUILD → SOAR → STRUCTURE

SPECTRA

Structure

What structure is there?

E0/E1 substrate; visualization layer

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Fold

Invariance

What survives transformation?

E2 visualization / challenge layer

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Murmuration

Dynamics

How does structure move and reorganize?

E1/E2 depending on reconstruction vs synthetic trajectory

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Mnemosyne

Memory

What did we know, and when did we know it?

Commit / reveal / provenance discipline

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Density

Measurement

What can we reconstruct from incomplete observation?

E2 visualization; measurement only

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Horizon

Prediction

What invariant comes next?

E2 synthetic prospective forecast

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Wave

Flow

How does coherent structure evolve in a fluid?

E2 simulation; 2D periodic fluid dynamics

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Identity

Persistence

What remains the same as the system changes?

E2/structural transport lab; TIP projector metrics

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BUILD

Construction

How does structure assemble around an invariant?

Kinetic contraction lab; documented reference core

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SOAR

Restoration

Can an invariant sector be restored and deliberately transformed without leaving itself?

E47 control, programming and restoration lab

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OCTET PACKET · CROSS-LAB HANDOFF

Executable order:

spectra → fold → density → murmuration → horizon → mnemosyne → wave → identity → spectra_reveal → score

Horizon is sealed by Mnemosyne before Wave. Wave evolves or perturbs the carrier. Identity scores persistence. SPECTRA remeasures the realized invariant. The declared scorer closes the packet.

Packet schema Machine self-test Registry JSON

MNEMOSYNE · OPEN SEAL UTILITY

Legacy seal/verify actions remain backward compatible. Packet actions are stateless and store nothing.

Evidence boundaries remain typed per lab. The packet carries provenance and integrity metadata but performs no evidence-class promotion.