Splitting a ∪ b into two random QFT groups destroys regular frequency reinforcement. Instead of interference bands the output collapses into a low noise floor with a handful of uneven spikes clustered off to one side. The transform is still unitary, but without a shared phase scaffold the two QFT domains never align, nothing interferes constructively. This run shows that once the Fourier space is partitioned improperly, the quantum computer has no route to build interference, randomness stays random, only reshuffled into scattered amplitude peaks.

When both a and b are placed into full superposition, phase-scrambled, and then run through two clean QFTs with no structure, the output no longer forms a ridge, just shallow, noisy oscillations. You can see unevenly spaced vertical and horizontal ripples. Without the aP + bQ phase oracle, the Fourier map has nothing to lock onto, so the landscape flattens into weak wave texture and noise.

Removing both QFTs and measuring the unordered a- and b-superposition produces uniform noise. No lanes, no valleys, no ridges. This shows the backend’s small local fluctuations from decoherence and readout drift. The absence of any geometry here shows how important the QFTs and the oracle-generated phase relation is for producing the interference lanes in the real 5-bit Shor-style run.

This Threejs visual renders the quantum interference landscape of the E = mc² 4-bit experiment, rendered as a wave surface. The green mesh represents the collective quantum amplitudes across all measured bitstring combinations, where peaks mark constructive interference along the predicted energy-mass relation. Red points show individual measurement outcomes from the backend, forming a probabilistic cloud around the ridge structure. The single yellow sphere highlights the correct modular slope k = 9, the point where the equation balanced most coherently. The measured surface is sine-animated to improve the view of interference geometry.

The Three-js visuals represent the measured output of a 6-bit Shor-style ECC-breaking experiment. The horizontal plane encodes all possible bitstring results as a 64 x 64 grid, where each coordinate (u, v) corresponds to the two quantum registers. The vertical spikes show the relative probability amplitude of each measured state. The green mesh surface encodes the full output distribution, while blue-highlighted vertices indicate states that satisfy the modular condition u + 42v ≡ 0 (mod 64), corresponding to valid solutions under the correct scalar key k = 42. Among these, the three most probable correct key outputs are marked with large yellow spheres. These spikes emerge from quantum interference in the modular exponentiation process. All red dots represent raw measurement outcomes, and their height reflects the frequency of observation. The measured surface is sine-animated to improve the view of interference geometry.

This Three.js render repeats the main quantum interference pattern from my 6-bit Shor-style ECC-breaking experiment. The horizontal plane encodes all possible bitstring results as a 64 x 64 grid, where each coordinate (u, v) corresponds to the two quantum registers. The vertical spikes show the relative probability amplitude of each measured state. The green mesh surface encodes the full output distribution, while blue-highlighted vertices indicate states that satisfy the modular condition u + 42v ≡ 0 (mod 64), corresponding to valid solutions under the correct scalar key k = 42. Among these, the three most probable correct key outputs are marked with large yellow spheres. These spikes emerge from quantum interference in the modular exponentiation process. All red dots represent raw measurement outcomes, and their height reflects the frequency of observation. The measured surface is sine-animated to improve the view of interference geometry.

This Threejs render displays three wave-like quantum interference surfaces generated from multiple 3-bit elliptic curve key-breaking experiments using a Shor-style attack. From left to right, the surfaces represent the flat implementation (left), the version with a single Bloch clock qubit (middle), and the version with two Bloch clocks in a chain (right). Each surface encodes bitstring probabilities into amplitude spikes, with red dots marking measurement intensities and blue lines showing the modular ridge defined by u + 7v ≡ 0 mod 8. The leftmost surface is less defined, with lower ridge amplitude and more phase noise. The center wave shows improved constructive interference and coherence from the introduction of a geometric timekeeper. The rightmost wave, with two Bloch clocks, exhibits the sharpest and cleanest interference ridge (highest blue spikes), reduced lateral noise, and a stronger signal-to-noise ratio, meaning increased fidelity through stacked temporal anchoring.

This Threejs render compares the quantum interference waveforms of my two Shor-style attack runs breaking a 3-bit elliptic curve key, the left shows the standard run, while the right shows the one that includes a Bloch clock qubit to segment computation over time. In the side view, the Bloch clock run has taller, more coherent interference fringes with denser red peaks, meaning stronger constructive interference and a later collapse in the computation timeline. The standard run appears noisier and shallower, showing earlier-stage measurement with less-developed phase structure. From the top view, the Bloch clock run shows structured, radial ridges and concentrated measurement clusters aligned to valid (a, b) modular residue classes, while the standard run is flatter and more diffuse. These show that the Bloch clock acts as a temporal-like filter, which allows only the more mature, high-fidelity slices of quantum evolution to be analyzed.

This Threejs render visualizes the quantum interference pattern resulting from my arXiv 5-bit elliptic curve key-breaking experiment using a Shor-style attack. The 32x32 wave mesh represents the full outcome space of the two 5-qubit registers (a, b), with each grid cell corresponding to a measured (u, v) bitstring from the QFT output. The wave height and ripple intensity are scaled to the relative count of each bitstring, revealing where quantum probability concentrated. A diagonal structure, emerging from the condition u + kv ≡ 0 mod 32, appears as an oscillating ridge aligned to the secret key k = 7, visually encoding the modular relation exploited by the Shor-style attack. Green and blue grid colors separate background from target modular lines, while red dots rise with amplitude to show shot density. The three most probable correct key outputs are marked with large yellow spheres.

This Three.js render repeats the main quantum interference pattern from my arXiv 5-bit elliptic-curve key-breaking experiment using a Shor-style attack. The 32x32 wave mesh mirrors the (a, b) register space, with each cell showing a measured (u, v) bitstring from the QFT output. Wave height and ripple intensity follow raw counts, showing the repeated ridge structure u + kv ≡ 0 (mod 32) aligned with the secret key k = 7. Green and blue grids mark modular regions, red dots rise with amplitude, and the three most probable key outputs appear as yellow spheres.

This Three.js render visualizes the idealized backend result (~10⁻⁶ - 10⁻⁷), showing how the full interference pattern would appear on a high-fidelity quantum computer. The 32×32 wave mesh represents the complete run space, with every correct modular line sharply defined and minimal noise across the field. The ridge u + kv ≡ 0 (mod 32) remains dominant, marking the recovered key k = 7, while the background tail reveals the residual quantum structure beneath the noise floor.

This Threejs render represents the quantum interference pattern from executing a a Shor-style attack to break a 4-bit elliptic curve key. Each point on the 16x16 grid corresponds to a bitstring outcome from the quantum Fourier transform of registers a and b, where the x- and z-axes denote the values u and v. The green mesh encodes the relative shot frequencies as dynamic wave amplitudes, while red spheres indicate the actual measurement counts, rising higher for more frequent outcomes. A blue diagonal marks the modular condition u + 7v ≡ 0 mod 16. The emergence of strong signal amplitude along this diagonal confirms successful quantum extraction of the hidden scalar.

This Threejs render shows the green wave maps |11> probabilities across the 10 x 10 lattice for the Twistor‑Casimir Coupling (100 Qubits) experiment, high peaks show where the three‑slice Twistor shear reinforces, low troughs where it cancels. Red orbs, scaled by pair‑creation rate ρ_c, show the edge corridors that emit most |11 > Casimir pairs, showing the shear steers vacuum energy while keeping channels independent.

This Threejs render displays the output of the Dynamic Casimir Photon Emission circuit. Each 60-bit result string is checked for symmetric |11⟩ events between qubits i and 59 - i, which signify the spontaneous creation of virtual photon pairs from vacuum fluctuations. The grid maps these pair events spatially, with the height and wave amplitude indicating how often a given symmetric pair was excited during the experiment. Brightness and red dot elevation reflect the strength of the Casimir signal at that spatial location.

Visualizing bitstring frequencies from the Breaking a 3-Bit Elliptic Curve Key circuit using Threejs. This render shows a Shor-style attack output over the order-8 elliptic curve subgroup. The green wave surface encodes measurement probabilities for each (u, v) register pair. Blue peaks show outcomes along the interference diagonal u ≡ v mod 8, revealing the correct discrete log scalar k = 7. Red dots mark only the valid observed measurement outcomes.

Visualizing bitstring frequencies from the Topological Chimeric Spinor Projection circuit using Threejs. Each square tile in the field corresponds to a distinct bucket of measurement results. The first three bits of a 7-bit read-out choose the tile’s column (0 - 7) and the remaining four bits choose its row (0 - 15), producing an 8 x 16 grid. Within a tile the wire-frame surface rises in proportion to the number of counts recorded for that bucket, so taller ripples mean a higher probability for that bit pattern.

Visualizing bitstring frequencies from the Twistor-Entangled Quantum Repetition circuit using Threejs. Each green wave represents the relative frequency (amplitude) of a specific 3-bit classical bitstring result observed after running the circuit. Higher peaks mean higher counts (probability) in that region. Top Row (Back, Left to Right): 011 -> 2983 counts, 101 -> 2628 counts, 100 -> 562 counts, 001 -> 545 counts. Bottom Row (Front, Left to Right): 111 -> 625 counts, 010 -> 541 counts, 000 -> 132 counts, 110 -> 176 counts.

Visualizing bitstring frequencies from the Twistor-Encoded Error Geometry circuit using Threejs. Each panel represents a different quantum error applied to either a Twistor-encoded or Flat (unencoded) state. The wave height corresponds to the relative frequency of each 2-qubit output (00, 01, 10, 11).Wave Graph Order (Left-to-Right, Top-to-Bottom): X(Twistor), X(Flat), Z(Twistor), Z(Flat), Y(Twistor), Y(Flat), CZ(Twistor), CZ(Flat), Depolarizing(Twistor), Depolarizing(Flat).

Visualizing bitstring frequencies from the Non-Twistor-Encoded (same gate count randomized) Quantum State Stabilization circuit using Threejs. Wave Graph Legend: (Top) Shots: 0, Shots: 1024, Shots: 2048, (Bottom) Shots: 4096, Shots: 8192, Shots: 16384.

Visualizing bitstring frequencies from the Twistor-Encoded Quantum State Stabilization circuit using Threejs. Wave Graph Legend: (Top) Shots: 0, Shots: 1024, Shots: 2048, (Bottom) Shots: 4096, Shots: 8192, Shots: 16384.

Visualizing the bitstring frequencies of the second non-Twister teleportation circuit using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Twister-Inspired Teleportation circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Quantum Timekeeping Using a Bloch Clock circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Entanglement Dynamics (c⁴/G = 1.0) circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Entanglement Dynamics (c⁴/G = 0.5) circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Entanglement Dynamics (c⁴/G = 0.1) circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Twister-Inspired Error Correction circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Exploration of Penrose Twistor Space circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Navier-Stokes via Carleman Linearization circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Quantum Optimization of Protein Folding Pathways circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

Visualizing the Multi-Layer Retrocausal Encryption circuit bitstring frequencies using Threejs. This visual takes the measured bitstring counts from a quantum circuit and maps them to wave amplitudes on a 3D grid. Each vertex height reflects the normalized frequency of a bitstring, animated over time using sine and cosine functions. The result shows how quantum output probabilities form an evolving interference landscape.

This is the same Threejs wave visualization circuit with no IBM quantum JSON backend results loaded. This is the starting state before measurments are loaded.

This is the only Threejs render on this page this is not from direct results on a quantum IBM machine, this render comes from theory and speculation. In 2020, Sir Roger Penrose was awarded the Nobel Prize in Physics for his studies of black holes, specifically for proving that ‘black hole formation is a robust prediction of the general theory of relativity.’ His work showed that, if Einstein’s theory is correct, the formation of black holes is an inevitable consequence of gravitational collapse. Penrose’s black hole proof relies on the behavior of null geodesic congruences, or networks of light paths through spacetime, which form the mathematical foundation of his singularity theorem. In Twistor-inspired formulations, the geometry of black holes, such as the Kerr solution, can be described using Robinson congruences. These are shear-free, geodesic networks of light rays that characterize the spacetime structure, particularly around regions like the event horizon and ergosphere. Using the math of Twistor Theory, I made a Threejs visualization of a Robinson Congruence. The Robinson congruence is a three‑parameter family of null geodesics tied to a non‑null Twistor (in Twistor Theory terms, a null light ray in spacetime). Each closed loop is an integral curve of the Poynting vector of an electromagnetic Hopf knot, a topologically nontrivial Maxwell solution whose field lines are linked circles. The roots of this go back to Alfred Rañada’s 1889 discovery of electromagnetic knots, solutions built from Hopf maps whose field lines are linked, and to Roger Penrose’s Twistor Theory of the 1960s, which identified light rays with points in a complex projective space. The Robinson congruence, first studied by Ivor Robinson in the early 1960s, associates to each non‑null Twistor a shear-free, null geodesic congruence in Minkowski space. The render constructs and visualizes a three-dimensional bundle of closed curves, the Robinson congruence, each of which is an integral curve of a null Poynting vector derived from a non‑null twistor solution of Maxwell’s equations. Rather than static lines, this Threejs visual embeds a luminous pulse shader on semi‑transparent tubes and animates its parameter so that glowing packets travel along each loop in the precise direction dictated by the underlying electromagnetic field.