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SMONADSINGLE MONAD · DUALITY OF TIME
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Explore 46 explanatory diagrams connecting SMM and DTT to records, nested time, phase, geometry, constants, and matter.

Figures in the article atlas connect generative histories with completed records, and make the mathematical steps in geometry, phase, constants and atomic models easier to follow. Their captions state whether they represent a conceptual scheme, a worked calculation or an idealized example.

Open a diagram at full size or continue into the associated article for its assumptions and derivation. The vector artwork remains sharp on small screens and when enlarged.

Six diagrams for the foundation guides

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A conceptual sequence from histories and completion to geometry, clocks, and matter.
From source to observable recordsA conceptual sequence from histories and completion to geometry, clocks, and matter. Read the explanation →
The paired readout ranks 1, 1, 2, 2, 3, 3, with the outer completion shown separately.
Six nested roles and outer completionThe paired readout ranks 1, 1, 2, 2, 3, 3, with the outer completion shown separately. Read the explanation →
A shared present reading becomes distinguishable under a later allowed test.
The same display can hide a differenceA shared present reading becomes distinguishable under a later allowed test. Read the explanation →
Ordinary and split-complex units obey different square laws and preserve different forms.
Circular phase and hyperbolic geometryOrdinary and split-complex units obey different square laws and preserve different forms. Read the explanation →
An exponential kernel records the effect of a hidden relaxing variable.
Eliminating a variable leaves memoryAn exponential kernel records the effect of a hidden relaxing variable. Read the explanation →
A common encoder gives a conditional ratio; a selected clock converts the matter coefficient.
Connecting records, clocks, and matterA common encoder gives a conditional ratio; a selected clock converts the matter coefficient. Read the explanation →

Diagrams from the atlas

All 40 figures →
A source generates two alternative curved histories; completion sends them to stable records. One source is a premise, while spatial and physical interpretations require further laws.
One source, histories, completed recordsConceptual reconstruction: composable source histories are tested and completed before a retained record becomes available. The source is not depicted as a point already located in space. Read the article →
Six nested rounded enclosures represent successive inner functional roles. Their ranks are 1,1,2,2,3,3. An arrow leaves the outermost inner enclosure toward a published record.
Six nested inner roles; one outer completionThe six inner roles are nested functional stages with readout ranks 1, 1, 2, 2, 3, 3. The outer completion publishes the resulting record. These are not seven independent time axes. Read the article →
Three receiver steps multiply the previous count by ten and add branch counts one, three, and seven, giving one, thirteen, and one hundred thirty-seven. The count expands as one hundred plus thirty plus seven.
A conditional receiver count: 1 → 13 → 137For the selected finite grammar Q(0) = 0 and Q(d) = 10Q(d−1) + (2ᵈ − 1), the depth-three output has 137 retained modes. Identifying 1/137 with an electromagnetic coupling needs additional response normalization and matching. Read the article →
A positive cone is shown as a triangle in the time-space section. An interior point is positive definite; boundary points have zero determinant.
Positive Hermitian records form a Lorentz coneWriting a Hermitian 2×2 record as X = tI + x·σ gives det X = t² − |x|². Positivity is equivalent to t ≥ |x|. The diagram is a two-dimensional section of the four-dimensional cone. Read the article →
An observed variable and a relaxing hidden variable exchange influence. Eliminating the hidden variable leaves an exponential memory kernel plotted against delay.
Eliminating a hidden variable produces memoryFor a linear relaxing hidden sector, substitution produces a Volterra memory term. An exponentially decaying kernel is the simplest example; its fast limit can yield local effective dissipation under additional assumptions. Read the article →
Horizontal bound-state energy levels lie at minus one, minus one-quarter, minus one-ninth and subsequent inverse squares, approaching the zero-energy continuum threshold.
The Coulomb spectrum is conditional on its HamiltonianFor the nonrelativistic Coulomb Hamiltonian, bound levels follow En = −E₀/n² and approach the continuum threshold. The diagram uses dimensionless E/E₀ and does not derive the coupling or supply radiative corrections. Read the article →

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The glossary explains the vocabulary; the reading paths connect the ideas; the source register points to the original arguments.

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