Your initial statement "The name physical reality is used to display the universe with everything that exists and moves therein." is appreciated as a attempt to clarify semantic interpretive errors... but what fundamentally constitutes Physical?... motion??... some theoretical minimum unit of Energy (QE)???
What fundamental property do we assign to any one of "everything" to verify the one as Physical?
If Physical is undefined one can not eliminate the potential for Metaphysical... i.e. other than physical.
I utilize Metaphysical in my essay to differentiate from Physical "in terms of Physically measureable properties... i.e. sound, light, electromagnetic potential, chemical reaction, quantum particle choreographies, etc.... but are all PHENOMENA processes Physical?" ~ sl FQXi Essay
If you are speaking of "structure" as being a Spatial construct?... I agree that "deeper layers will reveal "an increasingly simpler structure"... and may I add, that structural form follows function?
To the degree that one is speaking of a Spatial geometry model, a predicted observation does not constrain the observation to a single geometry model, nor does it necessarily verify all aspects of a theory inferred from a specified "bench" geometry model that resolves the observed prediction.
That is to say, that direct observation of a gravitational radiation wave, does not verify Einstein's rubber sheet (2D plane) geometry model as the definitive resolve of Space/Energy/Time computational geometry models.
I do agree that the foundation revealed "must force the development of reality in the selected direction"... i.e. initial conditions are the primary selection criteria of emergence, and in that no Physical Energy Choreographies existed at initial differentiation of Space by Energy, a unique Spatial logic/information quantization by a unified volume unit... i.e. Einstein's concept of a unified 3D field geometry... is a "Good guess"... REF: TOPIC: A Universe Made of Stories by Philip Gibbs
... as is the requirement for initial Emission Distribution "equal in all directions from a single point." ~ sl FQXi Essay
"It is not that something is being created from nothing, it is that undifferentiated potential information is being differentiated as minimum units of Space/Energy/Time/Information" ~ sl FQXi Essay
If we observe that "the growth process provides restrictions" those restriction must be supported by the underlying "bench" geometry structure utilized as the initial emission/propagation logic.
That is to say that, to the degree that one is speaking of any process in terms of equations extracted from a specified "bench" geometry model, to verify that the specified "bench" geometry model resolves the observed process, the visual kinematic chain for the theoretical derivation, from the observed geometry, back to the specified "bench" geometry model in which the process is nimated... i.e. given dynamics... must be verifiably unbroken.
Digital CAD/SIM models can facilitate highly complex visual verification... i.e. if the coded simulation does not visually emulate the observed process, then the Mathematics is not verifiable.
In that mathematical theories of Space/Energy/Time, at least in principle, are derived from an observed and/or intellectually visualized Spatial geometry model, the quest for a "potential candidate for the foundation of physical reality" is now being pursued at a most fundamental Mathematical level... i.e. as comparative investigations of underlying geometries that support initial Emission Distribution "equal in all directions from a single point".
REF: UQS Origin Singularity Geometry http://www.uqsmatrixmechanix.com/UQST-TVNH.php
With permissions supported/granted by the Unified Quantization of Spherical Singularity (UQS) geometry... I have for over 20 years utilized a conventional computer to quantize a unified field geometry environment... i.e. as a Unified Quantization of a Singularity (UQS)... and am currently developing/coding a UQS Virtual Quantum Lab/Game that utilizes a UQS CAD Environment to digitally visual animate, Emission expansion of pulsed minimum units of Energy (QE)... i.e. digital sprites... for distribution/propagation analysis.
REF: UQS Data Bus http://www.uqsmatrixmechanix.com/UQDB.php
You state that there are "only three number systems", but all three can be derived from geometry coordinate systems, so why convert the concept of Spatial distribution to a number system, when we now have the digital tools to project the concept directly onto the visual "bench" geometry... i.e. the CAD environment provides "The base model (which) acts as a storage space for dynamic geometric data.", and the SIM interface utilizes timestamped events in the CAD environment to tell a "dynamic story".
Utilization of CAD/SIM analysis has shown that there is not just one "story that explains why the elementary particle constantly deforms its living space and why the particle possesses a quantity of mass."... i.e. UQS Emission CAD/SIM utilizing an 6 axis Equal Quantization Quaternion CAD environment Space/Energy/Time/Info model, tells the same story.
I have browsed the Hilbert Book Project, and I admire your directions to resolve a plausible Mathematical model, but you do admit, your numeric conversion process has "become quite complicated", and you have stated simplicity as a verification parameter of foundational fundamentality,
Not only is it complicated, it has not produced a verifiable mechanism for initial emergence of the minimum units of Energy (QE) required for animating the cosmos.
I herein reiterate statements from my review of TOPIC: A Universe Made of Stories by Philip GibbsPhilip Gibbs:
"With regard to "guessing correctly the answer to questions like 'what is "fundamental?'", the "stories" are ancient... REF: TOPIC Indra's Net - Holomorphic Fundamentalness by Cristinel Stoica ... and although such "stories" are prolific, multi-epoch, and multi-cultural, requirement for a logic reduction is a common element."~ sl
"However, cognitive abilities to resolve a Math model of a logic reduction of "fundamental" are apparently emergent...REF: TOPIC: How to Empirically Confirm a Rational Theory of Fundamentals by Jack H. James ... and application of Math semantics to an invalid logic reduction of "fundamental" have often muddied the cognitive waters."~ sl
'The Spatial Singularity quantization is fundamental to all derived Spatial relationships/logic. "~ sl
"In that evolution is driven by the "What is fundamental? quest, then technology is also, and development of digital tools has been reciprocated with a cognitive enhancement, in the form of a more precise Mathematical model of Indra's net "cast in all directions"... i.e. resolve of an Origin Spherical Singularity Geometry, which supports infinite minimum unified volume unit shell closure expansion as a valid CAD environment/field quantization... has now been added to the "stories", and a pulsed Emission of minimum quanta of Energy (QE), is being digitally simulated/animated within the virtual environment.
REF: UQS Origin Singularity Geometry http://www.uqsmatrixmechanix.com/UQST-TVNH.php "~ sl
"UQS is not a theory, it is a digital CAD/SIM virtual reality constructed on a logic reduction... i.e. an Origin Emission equal in all Spatial directions from a single point."~ sl
"Better than a guess?""~ sl
Hans, without revealing a verifiable property of "Physical", you state that "Only the application of deduction can expose the parts of the physical reality that resist observation."
Is deduction a Physical Information Energy process?
"Although they are in many cases stimulated by Physical processes, are mental info processes... i.e. conceptualization, realization, dreams, visualization, intuition, etc.... established on Metaphysical scale bit differentiated streams? "~ sl FQXi Essay
I agree that "The interplay of measurements and deduction can bring about the necessary confidence." in a theory, or in a digital virtual reality model.
In that "Much of the physical reality is inaccessible to measurement.", and "In that case, deduction remains the only way of approach.", I highly recommend that one verify the "bench" Origin Singularity geometry form follows function, for a pulsed minimum unit of Energy (QE) Emission, equal in all directions from a single Origin Source, before applying the artifice of the equationist to "everything", or anything, else.
As per my interpretation of World Science Festival: Topic: "Limits of Understanding" https://www.youtube.com/watch?v=DfY-DRsE86s, the instability w/ current Space/Energy/Time/Info Physics, is as a consequence of the current instability of Mathematics.
My assessment is that the APPARENT current instability of Math is as a consequence of a geometry coordinate system, in which the fundamental Spatial relationships of the geometry do not support application of minimum units of Energy/Space/Time/Info, to Space/Energy/Time/Info analysis.
Thanks Hans, for sharing your insights and thus making an opportunity for comment... I would read with attention your comments on my essay entry Title: Knowledge Base (KB) Access as Fundamental to Info Processor Intelligence.
Will return to rate after I read as many essays as I have time.