Numerical Civilizations — unmarked bronze counting board. Mini AI Labs visual system.
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VISUAL SYSTEM · MINI AI LABS
Near-black laboratory. Cyan live · bronze Λ-ghost · mint lock. No type on stills.
Record: CITY-LABS-VISUAL-SYSTEM-20260915.
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NEW · LINGUISTICS BUREAU UNIVERSAL TRANSLATOR
Universal Translator — Invariant Grammar Lab turns this exhibit into an interactive Bureau station: natural language → typed invariant packet → target rendering, while the existing numerical dialects retain exact round-trip certification.
Launch mini lab · Python source · Drive station 06
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Canonical Drive monograph — Civilizational Radix Translation Engine
Dual Horizon Mathematics — From the Sphinx Pair to Base 5, 12, 20, and 60
This synthesis links the pyramid-register exhibit to the clock-math branch through the exact translation invariant $D_cT_{b\to c}E_b(X)=X$ and the antipodal involution $A_b(k)=k+b/2\pmod b$ for even radix $b$.
The Quinary Family of Engineering Pyramids, Revision C — Exact Validation Monograph · Machine certificate
The certificate preserves the distinction among top place value $b^n$, register cardinality $b^T$, register range $0,\ldots,b^T-1$, and the repunit $(b^T-1)/(b-1)$. Bases 5, 10, 12, and 60 remain representational dialects of one radix-independent square-pyramid geometry. The submitted seed strengthens the existing PYR, TMP, and B5-125 citizens without creating duplicate pages.
Canonical monograph: Theoretical Modular Mathematics And Pyramid Construction.
The civilizational dialect exhibits now use the corrected Revision C distinctions between top place value, register cardinality, range, representational dialect, and invariant structure. The deterministic Python renderer is the publication witness; it certifies arithmetic and finite verification only. Historical and engineering interpretations remain separately bounded.
Decimal Civilizations Hall
Decimal and positional mathematics rendered in civilizational continuity: survey, grid, zero, modular assembly, and administrative infrastructure.
This monograph traces the continuity by which civilizations converted numeral systems and modular arithmetic into measurement, calendrics, surveying, proportion, administration, and architecture. It distinguishes radix from modular structure and treats each tradition as a formal mathematical dialect embedded in material culture.
$$ \boxed{\text{number system}\rightarrow\text{measurement}\rightarrow\text{geometry}\rightarrow\text{architecture}} $$