The Sandbox, Hybrid Quantum-Tensor Probabilistic Computational Architecture (V0.8)
LICENSING:
This entire publication is licensed under CC BY 4.0 (Creative Commons Attribution 4.0 International) to it's author, Christofer Ford. 'The Sandbox', 'ND Wave Representation Theory', and all other sections, including any and all original hardware, software, data representation design and/or novel synthesis of pre-existing designs are licensed under Apache License 2.0.
Copyright 2025, 'The Sandbox' by Christofer Ford
'The Sandbox' is Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
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This release is entirely free, any outside source charging for this information is not the original, and should be reported for infringement unless following the licensing structure. To discuss this publication, the Sandbox design, or any contents therein you must credit the author (Christofer Ford), or you void the CC BY 4.0 License previously outlined, and are subject to be pursued for infringement. Additionally, any and all new/original patents made using any and all new/original Sandbox design elements or theories are licensed under Apache License 2.0, check previous sections for more information.
What if we could efficiently and accurately compute and even predict "hypercomputational" problems -like mRNA modeling?
I'm here to tell you we can, today, with technologies that already exist.
We have to take four of our most advanced technologies and combine them, while simultaneously redesigning almost everything about computation itself. And I have included Wave Representation Theory, to show how these technologies can actually be used in this design, without running into the efficiency errors present in current designs.
What if I said we're already doing this?
When we look at current AI Models, we see a very interesting and common event occur between them. It seems as if during an AI Model's training it improves linearly for a majority of the training and then suddenly "collapses" into a much simpler and more accurate model (Watch THIS video if you don't know what this is referring to)
What if we could replicate this phenomena with certainty? What new possibilities would open up for us?
The goal of this publication is to answer that question, not with another question, but with a design. A design, that can be made today, with real, currently existing technologies. This is called 'The Sandbox'. (CC BY 4.0, APL 2.0)
And to propose theories of the universe, not as factual descriptions, but as hypothesis seeking to be proven or disproven by scientific measure and study. They have predictions that can be measured first, and only then should they be taken seriously in any way. 'The Sandbox' should be able to help simulate and test these as well, pushing the boundaries of modern physics. (CC BY 4.0)
The Sandbox, Part 1: Hardware (CC BY 4.0, APL 2.0)
For the hardware of the Sandbox, we'll need to use these four technologies:
*Quantum Computing (QPU or Quantum Processing Unit, Qubits) - This is used to map out true random
*Thermodynamic Computing (PPU or Probabilistic Processing Unit, Pbits) - This is used to map out probabilities over Time
*Lightspeed Interconnects (LSI) - These are mandated by the speed and efficiency requirements of this design
*Classical Computing (referred to as CPU and/or Classical Board) - Necessary for integration between technologies and "foundational" architecture. MUST BE TERTIARY OR HIGHER, CANNOT BE BINARY. This is because the actual usefulness of the design comes from the Classical mapping information to AT LEAST 2 Qubits and 1 Pbit, any less and the design ceases to be useful.
We need a data pathway that looks something like this ('ND WRT'):
'SCALAR': Classical board receives information (this is taken from real world data of any type over Time or measured for Probability)
ALL Classical information across the entire system is considered the 'Scalar' (N) layer
'VECTOR': Information is routed through the LSI to be mapped to QPU in the form of a Hamiltonian
ALL Qubits are considered the 'Vector' (D) layer, also refereed to as Dynamic or Spatial layer (Qubit over Time/Pbit)
'TENSOR': QPU bits are mapped by the PPU for Chance and/or Time. When several Qubits are mapped against each other we can create new Qubits and Pbits based on their 'interactions over time', this allows us to 'go to the next dimension'. We aren't physically accessing higher dimensions, we have differing
ALL Pbits together are considered the 'Tensor' (T) layer,
What does 'predicting' or 'dimensional transfer' look like ('ND WRT')?
There are three layers here, my Multiversally Predictive Theory, which translates into the Sandbox design, which then translates into Sandbox Hardware. This relationship looks like:
MPT: Each dimension has an Abstract (N), Spatial (D), and Temporal (T) layer at the same 'dimensional level' as everything else. The Abstract Layer represents the underlying physical laws, for example the equations of General Relativity. The Spatial Layer represents the entire Abstract Layer as individual physical objects within 'larger systems', for example a planet or star being described by General Relativity. The Temporal Layer represents the entire Spatial Layer over Time or the 'larger systems' unique to the Temporal Layer, consisting of interactions between it's own base components and 'other larger systems' (e.g. a star's gravity locking planets into orbit around it).
In MPT, there are these two ideas, and this is how they transfer:
Total Measured State (TMS) - The entire measured state of the 'dimensional level', the entire Abstract, Spatial, and Temporal Layers specific to that 'dimensional level'. In Sandbox terms, this refers to all information in the Sandbox, including the Classical, Quantum, and Thermodynamic layers. Or all the 'data' within the Sandbox.
Singularity - This refers to multiple of the Spatial, Quantum. or Vector Layer interacting with each other over the Temporal, Thermodynamic, or Tensor Layer to form new variables. It is called this because this is supposed to come after the TMS, when the entire measured system has 'collapsed' into it's simplest applicable form. From this 'state of collapse/simplicity', new variables for the Abstract, Classical, and Scalar Layer.
Dimensions are defined as Bit numbers, if we have 3 Qubits and 1 Pbit this effectively represents 3 'dimensions' over 1 'Time dimension' or in other words '4D SpaceTime' represented by 3 spatial (Vector) Qubits over 1 Time (Tensor) Pbit.
The reason we have to 'start in Tertiary' with 2 Qubits and 1 Pbit is because this is the minimum required to map out Qubits against each other with Pbits. Any less, and the design becomes functionally redundant.
3N (the N representing Variable Number) refers to the Scalar Classical Information Layer that is encoded onto the Qubits, or in other words all classical information mapped to Qubits. This is the 'input' of the system.
3D refers to the Vector or Quantum Layer or in other words the 3 Qubits that represent our 'variables'. This does NOT include the Pbits. This is the 'measurement' of the system.
3T refers to the Tensor or Thermodynamic Layer, up to 3 Pbits (or whatever the equivalent 'dimension number' is) that map out the 'probability/interaction' of the Qubits AND the additional Pbit that represents Time. There's N + 1 Pbits, one for each Qubit and one for Time. This is the 'prediction' of the system.
Let's use 2D as an example, go up to 3D, and then see what 'predictions' are and how we map them. We take the Scalar layer, 2N, and input all information from it into the Vector layer, 2D, before mapping these over Time and Chance with the Tensor layer (2T, one for Time and one for Chance of the two Vector layers interacting).
At the Tensor layer, we take each Pbit that maps out the chance of 2 or more Qubits/Vector layers interacting, and we record the classical information from these as our "predictions', notably we can measure several 'predictions' for each Pbit used. One Pbit might encode the interactions between 3 Qubits, giving us 9 new 'predictions'.
When the QPU and the PPU are using the same number of 'bits', we have to take the Pbits and 'collapse' them into a single Pbit. This single Pbit can then make 'predictions' that can add back more bits, effectively allowing for the accuracy of the computation to improve generationally, or with each iteration.
These real world technologies already incorporate some of these ideas:
-3D Photonic-CMOS design (Xintian Tina Wang, Columbia University School of Engineering and Applied Science)
-Xanadu's Photonic Quantum Computers
The Sandbox, Part 2: 'ND Wave Representation Theory' or 'ND WRT' (CC BY 4.0, APL 2.0)
This 3D data representation method (Ian Scheffler, Stanford University) serves as an in-depth look into the basis behind the 'ND Wave Representation Theory', and how we can achieve these designs in reality. It serves as an effective "glance" into what this technology could be like, and offers significantly more than 'The Sandbox' in terms of certified expertise -in reference to it's author- and practical methods of building this. How the Sandbox differs fundamentally from this approach is that it doesn't stop at 3D, the Sandbox allows transition all the way into 4, 5, or even 6 "dimensions", where the final number of "dimensions" is simply uncapped. (dimensions in this case are the number of Qubit/Vector variables plus the number of PBit/Tensor variables.)
To achieve the '3D' effect (more specifically 2D over Time, or the Tertiary BASE layer), we start with multiple 'systems' -consisting of 2 outputs- mapped against each other. In the Sandbox, this means we take two Qubits at different points in T and 'collapse' them into their measurements. We then take the collapsed Qubits (in other words the new data output) and map them with the PPU's PBits. We can either use one PBit to represent one Time variable -this makes our model match the 1D flow of time we perceive- or, we can use up to as many PBits as there are Qubits, effectively representing NT (N being the dimension number or Qubit number and T represents each of these Qubits over their own Pbit) or N Outputs over Time. We have to do the ladder to achieve 'dimensional transfer', when we map out N Probabilities over Time their interactions create new Probabilities that can't be fully described by the previous system.
For *example (demonstrated for 2020 to 2024 below), if I map out the Inflation, Median Income, Median Rent, and Quality of Life of America over Time now I can get a rough map of how the four values influenced each other over the sample period.
Our result is an 'ND' representation of the system we have mapped out. Made out of 4 Qubits (at this stage effectively representing the 'superposition' of all outputs for any possible value) and 1 Pbit (thermodynamic bit mapping out Time)
If we now add more Pbits, these new ones representing the interaction between the Qubits, we can make unique and novel insights and even 'predictions' into what will happen if current trends continue and which actions taken now will result in the most favorable future outcomes.
We can map each system in increasing layers of complexity or 'higher dimensions', and then gradually collapse these higher dimensions into this base template:
Probability of X vs Probability of Y / Time
In other words, we can see the chance that 2 predictions happen against each other over Time. So if I wanted to map out "Does X creature die or continue at T?" I can model as much of the creature as possible through the Sandbox and then use this method to collapse it down into the binary probability of the desired event occurring over Time. Finally, this approach is by nature universal, meaning any individual, entity, group, or field should be able to take advantage of it.
The Sandbox Part 3, Example of Functionality (CC BY 4.0)
You might have read this entire article to here (or skipped through to here) and wondered: "How exactly is this useful to reality even if we can 'compute across dimensional transfers'?" The strength of this design is that when we map out several real world variables over Time we can now see how they interact with each other, and even the chance of any interaction happening. This section is meant to show how this approach is useful, even without 'The Sandbox' itself.
THESE ARE EXAMPLES OF FUNCTIONALITY, NOT WHAT FULL IMPLEMENTATION BY PROFESSIONALS WOULD BE LIKE. THESE EXAMPLES MAY BE INACCURATE, AND THEIR ONLY PROPOSED USE IS TO SEE THE METHOD OF PROBLEM SOLVING USED THAT CAN BE APPLIED UNIVERSALLY TO ANY FIELD, AND/OR SERVE AS TEMPLATES FOR FULLER IMPLEMENTATION OF 'THE SANDBOX' ITSELF.
(In other words, these examples are mere 'child's play' compared to what this design is really capable of.)
For this example we'll take these variables between 2020 and 2024 (before, during, and after the global pandemic's effect)
-Inflation (Annual Inflation Rate in %, and Change from Previous in %)
-Average/Median Rent Price (Raw value in $, and Change from Previous in %)
-Average/Median Household Income (Raw value in $ and Change from Previous in $)
-'Quality of Life' (QoL) in the US
And we intend to find;
Whether 'Quality of Life' in the US has gone up or down in the five year period, and what changes in the other variables occurred before, during, and after the global pandemic that could have potentially caused this?
First, let's get our variables:
2020:
Inflation: 1.4%, Change = -0.9%
Median Rent: 1,185$, Change = +3.12%
Income: 81,580$, Change -1,680$
2021:
Inflation: 7%, Change +5.6%
Median Rent: 1,265$, Change +6.76%
Median Income: 81,270$, Change -310$
2022:
Inflation: 6.5%, Change -0.5%
Median Rent: 1,341$, Change = 6.03%
Median Income: 79,500$, Change -1,770$
2023:
Inflation: 3.4%, Change -2.9%
Median Rent: 1,448$, Change +7.95%
Median Income: 82,690$, Change +3,190$
2024:
Inflation: AIR = 2.9%, CIR = -0.5%
Median Rent: RAC = 1,535$, CAC = 5.11%
Median Income: 83,730$, +1,040$
Now when we look at the (last recorded) Quality of Life for each year:
2020: 48.2%, down by 7.1% form 2019 (55.3%)
2021: 55.1%, up by 6.9% from 2020
2022: 51.2%, down by 3.9% from 2021
2023: 52.2%, up by 1% from 2022
2024: 48.9%, down by 3.3% from 2023
And we see these patterns emerge:
2019 -> 2020: Quality of Life has decreased significantly (-7.1%)
Inflation was actually down this year (-0.9%), and it wasn't very high the previous (2.3% in 2019 vs 1.4% in 2020). So why did the QoL drop?
Median Rent increased (+3.12%), but not as much as any other year for the sample period
Median Income decreased significantly (-1,680$), but is this decrease enough to explain the QoL decrease?
2020 -> 2021: Quality of Life has increased significantly (+6.9%)
Inflation increased significantly (+5.6%)
Median Rent is up (+6.76%),
Median Income is down (-310$)
Notably, it seems as if the Quality of Life almost entirely 'bounced back' from the low of the previous year, despite all of these appearing to 'get worse' this year. What other variables can we add to this now that would explain this 'discrepancy'?
2021 -> 2022: Quality of Life has decreased (-3.9%)
Inflation is down slightly (-0.5%), despite the Quality of Life becoming worse over the time period. This isn't very unexpected as the decrease in Inflation wasn't very substantial.
Median Rent increased relatively significantly (+6.09%), possibly showing some of the reason for the corresponding decrease in Quality of Life
Median Income decreased (-1,770$), more so than any other year of the sample period. This provides more explanation to why the Quality of Life may have decreased.
2022 -> 2023: Quality of Life has increased slightly (+1%)
Inflation has decreased significantly (-2.9%), which seems to have benefitted the Quality of Life
Median Rent has increased (+5.11%), but not as much as other years in the sample period, potentially explaining why the Quality of Life didn't increase more than 1%
Median Income increased significantly (+3,190$) and more so than all other years in the sample period. I believe this almost definitely helped the Quality of Life increase.
2023 -> 2024: Quality of Life is down again, but not by very much (-3.3%)
Inflation decreased again (-0.5%), but not nearly as much as the last year, seeming to even out a bit
Median Rent increased here (+5.11%), however not as much as other years.
Despite the Quality of Life becoming worse between 2023 and 2024, the Median Income increased notably (+1,040$) showing the Median Income isn't tied directly to Quality of Life
The most important conclusion we come to:
This is not a full picture of the complex dynamic within the US over the given time period, it is simply a foundation to be added to with more and more variables through the Sandbox. We can see the inaccuracy in cases like 2021, where the Quality of Life increased despite all other variables seeming to 'get worse'.
Subsequent versions of this release and other releases will contain and expand upon these theories (CC BY 4.0):
Unified Dynamic Field Theory (UDFT)
A 'universal' theory, attempting to unify modern physics elegantly into one self-contained theory. The core idea is assuming that Gravity and Dark Matter are the same force, hypothetically transmitted through a field similar to the Higgs Boson field (omnipresent, but not Scalar), with properties of force carrying fields like the Electromagnetic/EM Field (localized but Vector), in other words what the Sandbox model defines as a 'full Tensor Field', hereby referred to as the Gravitational Tensor Field (GTF).
Additionally, Entropy and Dark Energy are both seen as the 'thermodynamic relaxation' of the underlying Gravitational Tensor Field, being the physical manifestation of the 'ordered reaction'(s) within the GTF 'breaking down over Time'. Gravitational forces are bypassed and pushed against, until the underlying 'ordered reaction' (planets, stars, black holes, any gravitationally ordered stellar body) is 'fully broken down' (planetary destruction, super/hypernova, hawking radiation)
THE PREDICTION TO TEST FOR:
"The Universal Expansion Rate should in some way directly increase the 'coolness' of the Thermodynamic profile in Hawking Radiation over Time"
Cited sources / design references
Sources Cited + Design References (in order of appearance):
Grokking or "The most complex model we actually understand"
Example problem for "mRNA Mapping"
Xanadu's Photonic Quantum Computers
"This New 3D Chip Could Shatter the “Memory Wall” Holding Back AI"
Sources for the 'Example of Functionality':
iProperty Management Average Rent by Year
US Federal Census Bureau: Real Median Household Income in the United States
Gallup National Health and Wellbeing Index
Licenses
CC BY 4.0 - This license applies to this entire publication.
APL 2.0 - This license applies to any and all designs or synthesis of design showcased here.
AI Summary and Other Use Examples:
As with all others, these examples are NOT fully accurate -as in, they are not proposed as 'full pictures', they lack enough data to be considered accurate- and are NOT proposed as such. Fact check all examples shown extensively.
-US Democracy Health over Time
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