Visualisations

Interactive 3D diagrams of the framework's core geometric structures


These diagrams are not illustrations. They are the geometry the three axioms produce — derived, not assumed. Each is the same structure viewed from a different angle. If correct, they are the first glimpse of the actual shape of the universe. Drag to rotate, scroll to zoom. Best viewed on desktop.

XIII. Dark Energy

The cosmological constant \(\Lambda\) is the residual crossing energy at the Present — the minimum bloom that the syphon produces even in completely empty space. Every point in space is a potential wormhole crossing. Even with no matter, no crossing concentration, no accumulation of Actual, the throat still has a zero-point energy: the Breit-Wigner resonance at \(t_1\) with width \(\gamma = 1/4\) has a vacuum expectation that cannot be zero. The outward bloom never quite reaches zero amplitude. This residual is dark energy. The framework derives \(\Lambda = (3/7)/(4\pi^2) \times t_1^2/R_H^2\) — within 5% of observation, with no free parameters. The DESI measurement \(w_0 = -0.685\) follows from the \(P_\mathrm{eg} = 5/7\) asymmetry of the egress segment.

Vacuum energy — every point in empty space has a residual crossing rate. The outward bloom amplitude is not zero even with no matter present. The gold shimmer is the zero-point bloom — the minimum syphon output, the spectral gap at the throat. Dark energy is not a separate substance. It is the universe's inability to stop crossing — the Present cannot be switched off, even in vacuum.
Expansion rate — the Hubble parameter \(H(z)\) as a function of redshift. Gold curve: the framework prediction with \(w_0 = -0.685\) from the \(P_\mathrm{eg} = 5/7\) asymmetry. Grey dashed: the standard \(\Lambda\)CDM prediction with \(w_0 = -1\). Blue point: the DESI 2024 measurement at \(z \approx 0.5\). The framework predicted this deviation before the measurement was published.

XIV. Quantum Entanglement

Two fermions sharing a common bilateral mesh node are topologically linked. This is the Hopf fibration's linking number of 1 made physical: any two fibres in \(S^3\) are linked exactly once, and no local operation can unlink them without tearing the manifold. In the framework, entanglement is not a mysterious non-local correlation. It is two wormhole throats sharing a crossing event — a common Present. Measuring one collapses the spectral position of both not because a signal was sent, but because they were never two separate events. They were one crossing, registered from two positions.

Linked throats — two wormhole mouths (gold discs) sharing a common bilateral mesh structure. The purple curve connecting them is not a signal — it is the shared topology, the Hopf linking. The blue and red streams show the correlated quantum states flowing through each throat. The correlation is maintained without communication because the two throats are a single crossing event seen from two positions.
Measurement — when one throat is measured (click the left disc), its spectral position collapses to a definite value. The right throat instantly resolves to the conjugate value — not because information was transmitted, but because the shared bilateral structure has only one consistent configuration. The collapse is simultaneous because it is topological, not causal. No signal. No hidden variable. One crossing.

XV. The Big Bang

The Big Bang is not an explosion. It is the first crossing — the Present at \(\tau = 0\) of the entire universe. Before: no geometry, no time, only quantum potential. The crossing occurs. The syphon initiates. The bilateral mesh forms from nothing but the three axioms. Time begins because the syphon runs — becoming-time \(\tau\) is the accumulated order of crossings, and before the first crossing there is no order and therefore no time. The singularity of standard cosmology is the framework's first crossing: not a point of infinite density but a point of zero geometry, from which geometry blooms.

The first crossing — the gold point at the centre is the Present at \(\tau = 0\). Before the crossing: quantum potential only, no geometry, no structure. The crossing fires. The syphon initiates. The bilateral mesh forms — shown as the first Riemann zeros appearing as gold rings. Geometry blooms outward. Time begins. The universe is not something that exploded into space. It is the ongoing outward bloom of the first crossing, still happening now, from here.
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Technical note. All three visualisations are pure canvas — no WebGL, no external libraries.