Re: structural instantiation, contextual maps
Bryan Sanctuary
Dear Bryan
You wrote "Gill does not yet understand structural instantiation. He does not understand what a contextual map is”.
Maybe you can explain what you mean by "structural instantiation” and by “contextual maps”. Once I know what you are talking about I will be able to say whether or not I understand these concepts.
Richard
Mark Hadley
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anton vrba
Bryan, looking at your paper more carefully, consider what you are actually doing. For example, you assert that cancelling magnetic moments mean the isotropic state is "electromagnetically inactive," that a polarized blade "displays a magnetic moment with chirality" and that "charge also emerges," and that the scalar term of the geometric product corresponds to "mass-energy confinement" while the wedge product corresponds to "internal rotational kinetic energy."
Each of these is an arbitrary assignment. You have a geometric object — a bivector with two algebraic components — and you are labelling its parts with physical quantities: this part is mass, that part is charge, this behaviour is electromagnetic. But labelling is not derivation. You have not shown that your scalar term satisfies the field equations of mass, that your emergent charge obeys Coulomb's law, or that your magnetic moment transforms correctly under a gauge transformation.
In short, the physical vocabulary — mass, charge, magnetic moment, fermion — is being borrowed from standard physics and pasted onto geometric structures that have not been shown to reproduce the quantitative content of those concepts. That is not a physical theory of Nature; your work is a dictionary written by the author, for the author.
Richard Gill
|
Richard Gill
Richard Gill
Bryan Sanctuary
Richard Gill
Bryan Sanctuary
On 16 May 2026, at 13:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Richard,
I agree with you that you do not understand GA. You claim my paper includes non-locality, but I multiply a quaternion at Alice and one at Bob. There is not an iota of non-locality anywhere in my work.I would appreciate it if you would try to be honest in your statements.BryanBryan
On Sat, May 16, 2026 at 4:38 AM Richard Gill <gill...@gmail.com> wrote:
Bryan’s theory is non-local. This is clearly seen in Section 6.3 of “Context-Generated Spin Sectorsand the Inapplicability of Fine’s Theorem”, Bryan Sanctuary, April 25, 2026. “The physically relevant quantity for correlations is the relative rotor between the two analyzer settings”. See also his reference [7]. https://www.mdpi.com/2227-7390/12/13/1962
Richard Gill
 | |
Mark Hadley
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Richard Gill
On 16 May 2026, at 14:51, Mark Hadley <sunshine...@googlemail.com> wrote:
Bryan's paper from five plus years ago was fatally flawed. until he corrects that and withdraws it there is no point looking at any other work of his. Why would we? why would anyone?he is just packing up the same two mistakes in different ways, without acknowledging them or correcting them. It's just a page of high school maths to show how to combine correlations.CheersMark
On Sat, 16 May 2026, 13:45 Richard Gill, <gill...@gmail.com> wrote:
Dear BryanWhat you miss is that there are two detectors. The settings a, b, are binary, they are determined externally to the apparatus by fair coin tosses. The correspondence between four setting labels (two for Alice, two for Bob), and degrees of rotation (two for Alice, two for Bob), whether mechanical or electronic, has been prearranged by the experimenters. There’s no place where a quaternion depending on an angle alpha gets multiplied by a quaternion depending on an angle beta. That only happens in the course of a mathematical computation - whether done using the usual Hilbert space calculus or using your GA calculus. Your approach lacks physical grounding.If you want a formal response from me concerning your latest paper, please finish it and submit it to a journal, and ask the editors to include me as a referee. Or post it on a preprint server, let me know, and I’ll consider writing a response on PubPeer.The add-average issue is past history, it’s dead.It is really good to see that you have learnt to appreciate Bell’s maths at last. What’s left is just semantics. What do we mean by “local”?It’s good to see so many researchers converging on the idea that rotational symmetries are at the heart of understanding the singlet state correlations. Inge Helland, Engel Wichmann, Bart Jongejan all agree here. Steve Gull (a founder of GA) used Fourier analysis to prove Bell’s theorem. (I filled in a missing step in his proof).
<entropy-logo-social.png><entropy-logo-social.png>
Richard Gill
Richard Gill
Bryan Sanctuary
Mark Hadley
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Richard Gill
Richard Gill
Parker Emmerson
This program has binary inputs a,b in {1,2} and binary outputs x,y in {-1,+1}.
The station outputs are local deterministic functions:
x = sign(cos(phi - alpha[a]))
y = -sign(cos(phi - beta[b]))
with source variable phi independent of settings. Without selection this gives CHSH S≈2.
The CHSH violation comes from a PV/exceptional-locus acceptance map. The program reports only accepted trials. The accepted hidden-variable law depends on the setting pair (a,b). Conditional on acceptance, the joint output law is exactly the singlet law, giving S≈2sqrt(2).
Thus the program is not a loophole-free Bell-local counterexample. It is a transparent simulation of how setting-dependent selection/contextual acceptance changes the ensemble and thereby violates CHSH.
1. The program demonstrates a CHSH violation with binary inputs and binary outputs.
It produces
[ S\approx2\sqrt2. ]
2. The violation is generated by PV/contextual event-instantiation.The local station maps alone give
[ S\approx2. ]
The PV gate changes the reported ensemble.
3. Bell’s pointwise inequality remains correct for the strict single-ensemble model.If all trials are counted under one common (\rho), the program obeys CHSH.
4. Therefore Bell’s theorem does not automatically rule out PV unless PV is defined to be forbidden.If PV means setting-contextual event-instantiation or exceptional-locus selection, then it lies outside the strict Bell integral representation.
5. Any Bell formulation meant to exclude the program must explicitly assume no setting-dependent reported ensemble.That is the precise caveat.
The program does not break Bell's algebra; it shows that PV/contextual event-instantiation is outside the single-ensemble assumption required for Bell--CHSH, and can produce binary CHSH violations up to }2\sqrt2.
Did Bell originally rule out PV or things like it?
Not by name. Not as a separately analyzed event-instantiation mechanism.
Did Bell's mathematical formula implicitly exclude it?
Yes, if PV changes the reported ensemble, because Bell’s formula uses one common (\rho). PV does not change the source ensemble. The source distribution is the same for all setting pairs. What PV changes is the instantiated/reported ensemble: the conditional distribution of physical variables among events that become reported phenomena. That conditional law depends on the setting context.
Does the program violate CHSH?
Yes.
Does it force an added caveat?
Yes, operationally: to exclude the program, one must explicitly forbid setting-dependent PV/event-instantiation or require a common reported ensemble.
Does it make Bell's pointwise theorem false?
No. It shows the theorem is conditional and that PV lies outside the condition unless explicitly collapsed into ordinary (\lambda)-variables with every trial counted. I surmise this is the closest thing you will get to what you asked for that is mathematically defensible.
The program is attached and runs in Google Colab.
All my best,
Parker Emmerson
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Parker Emmerson
Richard Gill
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<PV_Bell_1.ipynb>
Richard Gill
Parker Emmerson
Dear Richard,
Thank you. I think this brings us to the exact place where the issue has to be understood.
I am not saying that Bell’s algebra is wrong. It is not wrong. The pointwise CHSH argument is correct when the four correlations are computed from one and the same ensemble. If the same hidden-variable space, the same measure, and the same four jointly definable Boolean outcomes are present, then the CHSH inequality follows.
What I am saying is that this is already a very specific ontology of the event.
In the program, the source distribution is common. The local tentative station maps are binary. Alice receives her setting and local physical variable. Bob receives his setting and local physical variable. If every tentative event is counted, the model gives the ordinary local result and does not violate CHSH.
The violation appears only when the PV/contextual instantiation map determines which tentative physical events become reported phenomena. The reported ensemble is then not the original source ensemble. It is the accepted, instantiated, phenomenological ensemble. That accepted law depends on the setting-context.
So the question is not whether Bell’s pointwise theorem is false. The question is whether Nature is required to instantiate reported events according to Bell’s single common reported-event ensemble.
That is the caveat.
If one defines locality so that the reported event must already belong to one common Kolmogorov ensemble for all four counterfactual settings, then PV is excluded by definition. But that is not a neutral empirical fact. It is a formal restriction on what counts as an event in the theorem.
PV says that the physical variables at the source are not yet the completed reported phenomena. The reported phenomenon is generated only in the context of the actual measurement. Thus the source ensemble can be common while the instantiated event-ensemble is contextual.
This is why I say that Bell’s theorem should be read as a theorem about a restricted event ontology. It rules out single-ensemble Bell-local hidden-variable models. It does not, by itself, rule out the possibility that the empirical event is context-generated, unless one explicitly assumes that such contextual instantiation is forbidden.
So I would put the result this way:
- Bell’s CHSH algebra is correct.
- The strict single-ensemble model gives (S \le 2).
- The program violates CHSH only because PV changes the reported ensemble.
- Therefore the program is not a strict Bell-local counterexample.
- It is a demonstration that setting-contextual event-instantiation lies outside the single-ensemble premise.
That is the entire point.
You may say that this is merely a matter of the empirical definition of correlation. I would say that the empirical definition of correlation is precisely where the ontology of the event enters.
If Nature supplies a common reported ensemble, Bell applies in the usual way. If Nature supplies only context-generated reported phenomena, then Bell has assumed away the mechanism in advance.
All my best,
Parker
Mark Hadley
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Richard Gill
Richard Gill
Sent from my iPad
Austin Fearnley
Parker Emmerson
Dear Richard, Austin, Mark,
I hope all is well.
I want to be careful about one point, because I do not want to conflate PV with the ordinary experimental loopholes.
When I speak of a context-generated reported event, I am not claiming that the modern Bell experiments simply suffer from the old detection loophole, locality loophole, or coincidence loophole in the usual experimental sense. I understand that the best experiments are designed precisely to close those loopholes relative to the standard Bell analysis. I am not saying that the experiments are careless, or that their statistical analyses are invalid within their intended framework.
The issue I am raising is more structural.
A loophole-free Bell experiment is loophole-free relative to a particular formalization of what the experimental event is. It treats the registered trial structure as licensing the Bell construction: one common ensemble, local settings, binary outcomes, no-conspiracy, and the mathematical construction of counterfactual outcomes under local causality. If those assumptions correctly describe the event structure of Nature, then the experimental violations give strong reason to reject classical local causality.
PV is not an attempt to reopen the standard loopholes. It is not saying, “the detectors missed too many particles,” or “the settings were not random enough,” or “the stations communicated subluminally,” or “the pairing procedure was experimentally sloppy.”
Rather, PV asks whether the reported phenomenon itself is exhausted by the Bell event model. That is, it asks whether the completed Bell-table event is already represented by a pre-existing Boolean value attached to (\lambda), for all possible settings, or whether the event is generated only in the actual physical context.
So I would distinguish three things:
source emission,
local physical interaction,
reported phenomenological event.
The modern experiments may be loophole-free in the ordinary and important sense that, given the Bell event model, the known escape routes have been closed. I am not disputing that.
But PV questions whether the transition from the first two items to the third item is correctly represented by one common reported ensemble supporting all four counterfactual products.
This is why I do not want to say that PV is a loophole in the usual experimental sense. It is not exactly that. It is a different semantics of event-formation.
In the usual Bell-CHSH argument, the four possible products,
[
A_1B_1,\quad A_1B_2,\quad A_2B_1,\quad A_2B_2,
]
are treated as if they are all functions of the same underlying trial, even though only one of them is actually brought into manifestation in the laboratory. The four correlations are then averages over one and the same measure. If this is the structure of the reported events, then CHSH follows. I do not dispute this.
The question is whether the reported event has that structure by necessity.
As a theoretical example, suppose the source emits a shared phase,
[
\lambda=\phi.
]
Alice and Bob each receive this same phase. Alice’s tentative local outcome is
[
A(a,\phi)=\operatorname{sgn}(\cos(\phi-a)),
]
and Bob’s tentative local outcome is
[
B(b,\phi)=-\operatorname{sgn}(\cos(\phi-b)).
]
Nothing nonlocal has been introduced here. Alice’s tentative result depends only on Alice’s setting and the physical variable she receives. Bob’s tentative result depends only on Bob’s setting and the physical variable he receives. If every tentative interaction is counted, this sort of model remains within the ordinary Bell-CHSH structure and does not exceed the bound.
But now suppose that the reported event is not identical with the tentative interaction. Suppose that a pair becomes a reported Bell-table event only if a further condition is satisfied,
[
R(a,b,\phi,u)=1,
]
where (u) is an additional branch, threshold, or instantiation variable. The function (R) says whether the tentative physical interaction becomes a registered and usable event in the actual context.
Then the correlation that is actually reported is not
[
\int A(a,\phi)B(b,\phi),d\rho(\phi).
]
It is
[
\mathbb{E}
\left[
A(a,\phi)B(b,\phi)\mid R(a,b,\phi,u)=1
\right].
]
Equivalently, it is
[
\int A(a,\phi)B(b,\phi),d\nu_{ab}(\phi),
]
where (\nu_{ab}) is the law of the variables among those events that become reported in the context ((a,b)).
This is not meant as an accusation against the experiments. It is a way of making explicit the difference between the source ensemble and the reported-event ensemble. The source law can be one and the same (\rho), while the reported law can be (\nu_{ab}), because the reported phenomenon is reached only after the actual context has done its work.
A concrete analogy is timing. Alice and Bob may each produce local pulses. Alice’s pulse time may be
[
t_A(a,\phi),
]
and Bob’s pulse time may be
[
t_B(b,\phi).
]
The outcomes themselves can be local. But the joint pair is reported only if the two pulses satisfy a relation such as
[
|t_A(a,\phi)-t_B(b,\phi)|<W.
]
I am not saying that modern experiments leave the old coincidence loophole open. I am using this only as an example of the logical distinction between local physical outputs and the constitution of a reported pair-event. The paired event is not merely Alice’s local pulse or Bob’s local pulse. It is a structured reported phenomenon.
Richard, I understand your position. You are saying that Bell’s later notion of local causality, together with no-conspiracy, legitimizes the mathematical construction of the counterfactual outcomes, and that the experiments therefore give us good reason to reject classical local causality. I agree that this is a coherent position. I also understand why you say that Nature supplies a common reported ensemble.
My point is that this is precisely where PV places the question. The source variable and the reported phenomenon are not necessarily the same level of description. There can be a common source ensemble without there being a common reported-event ensemble, unless one assumes that the reported event is already exhausted by the Bell construction.
Austin, this is also why the words “real” and “reported” become delicate. I am not denying that the lab records are real. Times, places, settings, clicks, computer files, and statistical records are real. The question is how the statistical object called a Bell-table event is constituted from those records. Is it already a member of one common ensemble supporting all four counterfactual products, or is it an event whose being-reported depends on the actual context in which it is generated?
Mark, this is why I do not think the issue is exhausted by saying either Alice’s result is undefined, or Alice’s result depends on Bob’s setting. There is another possibility. Alice and Bob may have local tentative outputs, while the completed pair-event is generated by a context-dependent rule. Then a correlation can certainly be calculated, but it is calculated over the reported ensemble for the actual context, not over one common reported ensemble for all possible contexts.
This is close to what happens in the simple PV simulation. The source phase is common. The local tentative station outputs are binary. If all tentative trials are counted, the model gives the ordinary local result and does not violate CHSH. The CHSH value changes only when the PV or exceptional-locus rule determines which tentative events become reported phenomena. In other words, the violation is not produced by breaking Bell’s algebra. It is produced by changing the ensemble on which the reported correlations are computed.
So the point is not that PV breaks Bell, and it is not that PV identifies an ordinary unclosed experimental loophole. The point is that PV is outside the single reported-ensemble premise unless one defines that premise as mandatory from the beginning.
In that sense, CHSH is simple. The experiments are impressive. The standard loopholes may be closed. But the conceptual question remains whether the completed reported phenomenon must be represented by Bell’s common ensemble of counterfactual Boolean outcomes.
That is the point I am trying to isolate.
All my best,
Parker
Mark Hadley
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Parker Emmerson
Dear Mark,
I hope you are well.
I should clarify something important, because I do not want the meaning of phenomenological velocity to be collapsed into a category that is too narrow.
Phenomenological Velocity is not, in itself, a contextual hidden-variable theory.
It is not the assertion that Alice’s measured value is secretly a function of Bob’s setting. It is also not simply the insertion of a contextual hidden variable into the Bell expression. If PV is treated in that way, then the whole point of the concept is missed.
The contextual construction I described is one possible formal language for discussing how a reported ensemble can differ from a source ensemble. It is a model of selection, acceptance, or event-instantiation. It says that the source may emit a physical variable, and the local apparatuses may interact with that variable, but the completed reported phenomenon is not necessarily identical with the source emission. It is generated through a context of measurement, registration, pairing, and reporting.
This is a distinction of levels.
There is the source variable.
There is the local physical interaction.
There is the reported phenomenon.
Bell’s theorem applies when these levels are compressed into a single common probability space carrying all counterfactual Boolean outcomes. If that compression is legitimate, then CHSH follows. I am not disputing this.
But PV is not simply the statement that one has chosen a contextual hidden-variable model. PV is an attempt to describe the generation of the event itself, much as in ecological optics one distinguishes a retinal image from the ambient optic array, and the ambient optic array from the perceived layout of the environment. These are related, but they are not the same level of description.
In the same way, the emitted physical variable, the local detector interaction, and the reported Bell-table event are related, but they need not be identical.
The contextual acceptance model is therefore not the essence of PV. It is a mathematical display, a way of showing where the single-ensemble assumption enters. If one insists on a classical Kolmogorov hidden-variable language and also wants Tsirelson-scale correlations, then something must change. Either the effective ensemble changes by selection or context, or one leaves the commutative Kolmogorov framework, or one relaxes a Bell premise.
PV can appear in more than one of these languages.
In one representation, PV may be connected with exceptional-locus or defined-only semantics, where the reported event is obtained only after a context of instantiation. In another representation, PV may be expressed through a microcausal operator-algebraic structure, in which the parameter is involved in a local (SU(2)) transformation inside a local algebra. That is not a classical contextual hidden-variable theory. It is a different formal structure.
So I would not say:
PV is a contextual hidden-variable theory.
I would say instead:
PV can force us to ask whether the completed phenomenon is being prematurely represented as a member of a single common counterfactual Boolean table.
That is the point.
The success of CHSH is that, once the experiment is represented by one common ensemble with local response functions,
[
A(a,\lambda), \qquad B(b,\lambda),
]
the inequality follows. The power of the theorem comes from the fact that the four products,
[
A_1B_1,\quad A_1B_2,\quad A_2B_1,\quad A_2B_2,
]
are all functions on the same trial space and are averaged with the same measure.
PV does not deny the theorem inside that space. It asks whether the reported phenomenon of Nature is necessarily given in that space.
This is why I am trying to keep the term “contextual” from doing too much work. A contextual acceptance construction is one way of illustrating the issue. It is not the whole theory. It is more like a surface-gradient in the analysis: it reveals a structural difference between source ensemble and reported-event ensemble. But the gradient is not the whole surface, and the surface is not the whole environment.
Likewise, the contextual model is not PV itself. It is one mathematical way of seeing how PV does not belong automatically to the ordinary Bell event picture.
So yes, I agree that a context-dependent reported-function model can violate CHSH in a mathematically unremarkable way. But that is not the claim I want to rest on. The claim is that PV concerns the formation of the phenomenon that is later treated statistically. It is not merely a hidden value inserted behind the detector.
The question is therefore not simply, “Is this a contextual hidden-variable theory?”
The question is:
At what level is the event defined?
If the event is defined at the source as a complete table of counterfactual Boolean outcomes, Bell applies immediately.
If the event is defined only as a completed phenomenon in the actual measurement context, then one has not yet justified the common-ensemble representation. One has assumed it.
This is why I am asking you to read the papers before classifying PV. I am happy to explain points that are unclear, but I cannot keep rebuilding the whole framework from scratch while you are guessing at the meaning of the terms. The papers are precisely where the definitions, distinctions, and mathematical constructions are given.
If you want to criticize PV, please criticize the actual argument. Read what I wrote on phenomenological velocity, exceptional-locus semantics, and the Bell-CHSH setting. Then we can have a useful discussion about whether the definitions work, whether the mathematics is sound, and whether the interpretation is convincing and worthy to have its own experiment designed to actually test it.
But if you do not read the papers, then we will keep circling around simplified labels like “contextual hidden-variable theory,” which is not what I am claiming.
All my best,
Parker
Mark Hadley
Parker Emmerson
Dear Mark,
I hope you are well.
Before we go further, I need to ask directly: have you read the papers on phenomenological velocity?
I ask because your descriptions of PV as a contextual hidden-variable theory, or as conceptually similar to de Broglie-Bohm, sound like classifications made before engaging the actual construction. They do not sound like objections to the argument as written.
I think your comparison to de Broglie-Bohm is understandable from a distance, but it is not the right identification of the concept.
Phenomenological Velocity is not, in itself, a contextual hidden-variable theory. It is also not a pilot-wave theory. It does not begin by positing a particle hidden behind the detector, nor a wave guiding the particle through configuration space, nor a dynamical dependence of Alice’s measured value upon Bob’s setting.
PV begins from algebraic logic.
More specifically, PV comes from a modus ponens manipulation of an expression of oneness. A Lorentz-type coefficient is inserted into an algebraic architecture in such a way that it cancels. In the ordinary reduced expression, nothing has changed. But the inserted unity contains an implicit (v)-structure. The method is to bracket the immediate cancellation, not because the cancellation is false, but because the cancellation is itself the surface of a deeper formal relation. In that relation, one can pass from the presence of the unity to the implicit velocity architecture contained within it.
That is why the term phenomenological velocity is appropriate. It is not a mechanical velocity first. It is a disclosed parameter of a formal event-structure.
I am willing to use the word “hidden,” but only in a qualified way. PV is hidden as an embedded structural parameter. It is hidden in the sense that the (v)-structure is contained in the algebraic unity by a push-out method. It is not hidden in the Bell sense of a pre-existing variable that assigns determinate values to all possible measurement outcomes.
This distinction is important.
The hiddenness of PV is like the hiddenness of an invariant in a geometric transformation. The invariant is not a little object concealed behind the visible object. It is a structural condition of the transformation, made explicit only when the right formal description is given. In the same way, PV is not a particle-variable hiding behind an outcome. It is an implicit formal parameter made visible through the logical architecture of the equation.
I am also willing to use the word “local,” but again only in a qualified way. PV is local in the sense that the construction is internal to the event’s own formal conditions of instantiation. It is not a signal sent from one wing of the experiment to the other. It is not a pilot-wave influence. It does not begin by postulating action at a distance.
But this is not automatically Bell-locality.
Bell-locality is a very specific mathematical condition. It means that the relevant outcomes can be represented as
[
A(a,\lambda), \qquad B(b,\lambda),
]
on one common probability space, with one common measure, such that all four counterfactual products are jointly definable. PV does not begin by granting this representation. PV asks whether the completed phenomenon is being prematurely reduced to that representation.
So, I would say:
PV is hidden in the metaphorical and structural sense that it is embedded by a push-out construction inside an algebraic unity.
PV is local in the formal sense that it belongs to the event’s own conditions of algebraic generation, not to a signal between separated stations.
PV is not hidden-local in the Bell sense of a common ensemble of pre-existing counterfactual Boolean outcomes.
This is also why I do not think the comparison to de Broglie-Bohm works. Bohmian mechanics has a real guiding wave and a nonlocal law of motion. PV is not doing that. PV is a phenomenological and algebraic construction that discloses a velocity parameter through the logical handling of unity, cancellation, and exceptional structure.
There is also an important undefined aspect. In the strict algebraic analysis, the construction exposes a third possibility that ordinary computer algebra tends to miss: the (v)-expression can collapse into a (0/0) form on the exact locus where the equation is satisfied. This is not an embarrassment to the construction. It is part of the meaning of it. The undefined locus is where the ordinary value-assignment picture fails, and where the phenomenological reduction of the expression becomes important.
This is why the phrase “contextual hidden-variable theory” is too crude.
If one forces PV into a classical Bell-CHSH language, one may represent some of its consequences by means of a contextual event-instantiation model. That is a translation into Bell’s framework. It is not the original meaning of PV.
A contextual hidden-variable theory begins by saying: here are hidden variables, and here is a context-dependent map from those variables to outcomes.
PV does not begin there.
PV begins with the algebraic fact that an expression equivalent to one can be introduced, canceled, and yet still disclose an implicit velocity parameter by modus ponens. It is a statement about the formal architecture of the equation and about the conditions under which an event-parameter becomes expressible.
This is closer to formal ontology than to pilot-wave mechanics. A mathematical form is not simply added to the world as an extra object. Rather, a relation already implicit in the structure is brought into expression. The work is one of description, bracketing, and recognition of the form by which the event becomes intelligible.
So when you say that there are local source parameters and then a context-dependent translation function, I understand the point, but that is only what PV looks like after it has been forced into one possible Bell-language representation. It is not the basic concept.
The basic concept is this:
an algebraic unity can carry an implicit velocity structure;
that velocity structure can be made explicit by modus ponens;
the construction is hidden only as embedded form;
the construction is local only as internal event-architecture;
and the strict solution also reveals an exceptional undefined locus.
I am happy to discuss the mathematics, but I need you to do the homework first. Otherwise I am repeatedly explaining the first page of the argument while you are criticizing a simplified substitute for it.
So please tell me plainly: have you read the phenomenological velocity papers, or are you inferring what PV is from this email exchange?
If you have read them, then please point to the specific step in the algebraic construction that you think fails.
If you have not read them, then I would ask you to read them before continuing to classify PV as Bohmian, contextual, or nonlocal. Those labels may be convenient, but they are not substitutes for engaging the actual definitions and derivations.
All my best,
Parker
Parker Emmerson
A note on retrocausality, tachyonic branching, and the boundary between the real and complex branches.
I think one must be careful with the language of retrocausality and tachyonic influence, because these words can too quickly make an algebraic issue sound like a mechanical signal theory.
In the PV analysis, the first distinction is not between ordinary causation and reverse causation. The first distinction is between a real-valued strict branch, a complex-valued continuation, and an exceptional locus at which the ordinary value assignment breaks down.
This is why the branch convention matters.
For
[
z=re^{i\theta},\qquad r\geq 0,\qquad \theta\in(-\pi,\pi],
]
one fixes
[
\sqrt{z}=\sqrt r,e^{i\theta/2}.
]
On the nonnegative real axis this is just the ordinary square root. But once the expression moves off the real branch, the square root carries branch structure. Thus, the question is not merely, “what is the value?” but also, “on what branch is the expression being interpreted?”
In strict semantics, each radical is treated as a single-valued function on its domain. This is the clean algebraic regime. In that regime, the PV radical architecture forces the compatibility condition and the apparent velocity expression collapses. In other words, the strict real-valued reading does not give a free continuum of superluminal values. It gives cancellation, boundary, and in the exact solution locus, an exceptional undefined form.
This is the important point.
The tachyonic branch is not first a faster-than-light particle. It is a branch of interpretation that appears when one follows the algebra beyond the ordinary real-valued domain. The moment the Lorentz-type term moves through the boundary
[
1-\frac{v^2}{c^2}=0,
]
one is no longer simply in the same real-valued geometry. For (|v|<c), the expression remains on the ordinary real branch. For (|v|>c), the square root becomes imaginary, and the expression enters the complex branch. At (|v|=c), the denominator structure can become singular, and in the PV construction this is precisely where the exceptional-locus language becomes necessary.
So the boundary between real and complex is not a decorative mathematical detail. It is where the ordinary interpretation of the event changes.
The real branch corresponds to ordinary interpretable value-structure.
The complex branch corresponds to analytic continuation, hidden branch geometry, or what may be metaphorically called tachyonic branching.
The exceptional locus corresponds to the failure of ordinary value assignment, often appearing as a (0/0) form.
This is also where retrocausal language can become tempting. If one looks only from the standpoint of ordinary causal description, a branch that is not contained within the forward real-valued order may look retrocausal, acausal, or tachyonic. But PV does not require that we immediately interpret this as a physical signal going backward in time. The more precise statement is that the algebraic event-structure contains a branch boundary at which ordinary real-valued causality is no longer the correct language.
This is why I would say that retrocausality, in this setting, is not fundamental. It is a possible interpretation of a deeper branch phenomenon.
Likewise, tachyonic language is not fundamental. It is a possible interpretation of what happens when the formal velocity expression is analytically continued beyond the real subluminal branch.
The more basic language is:
branch,
boundary,
exceptional locus,
undefinedness,
and phenomenological reduction.
PV supplies a way to discuss this without immediately turning it into a story about particles moving faster than light or messages being sent backward in time. The (v)-structure is disclosed algebraically through the push-out and unity construction. It is “hidden” as embedded form, not hidden as a little object traveling somewhere. It is “local” as internal event-architecture, not local in the Bell sense of a complete table of counterfactual outcomes.
Thus, the tachyonic branch may be understood as the complex continuation of the PV architecture. The exceptional locus is the boundary at which the real and complex readings meet and ordinary value assignment fails. Retrocausality is then a secondary metaphor, not the primary mechanism.
In this way, PV does not say: there is a literal tachyon carrying information backward in time.
It says: the algebraic conditions of the event contain a branch structure, and the boundary of that structure is where the ordinary real-valued account becomes incomplete.
That is the more precise claim.
This is why PV, understood as a semantic volume rather than as an ordinary hidden-variable assignment, is complementary to Bell’s theorem.
Bell’s theorem tells us what cannot be done inside a specific formal structure: a single probability space, a common measure, jointly definable counterfactual outcomes, measurement independence, and Bell-local response functions. PV does not need to deny this. In fact, PV helps clarify exactly where Bell’s theorem has its force.
PV is useful because it gives language for the boundary regions of the event: the algebraic unity, the real branch, the complex branch, the exceptional locus, the undefined point, the reported phenomenon, and the transition from physical condition to statistical object. These are not all the same thing. Bell’s theorem treats the event in one highly disciplined way. PV asks what additional structure may be present before the event is compressed into that discipline.
This means PV can be used as a conceptual instrument for discussing several related issues without immediately reducing them to ordinary nonlocality. These include retrocausal interpretations, tachyonic-looking branches, complex continuations, exceptional-locus semantics, post-selection, contextual event-instantiation, coincidence logic, threshold phenomena, decay processes, quantum wells, and the role of undefined or singular expressions in physical interpretation.
The important point is that PV does not merely add a new variable. It adds a way of talking about how a value becomes expressible.
This makes it potentially useful for experimental literature as well. Not because it says existing Bell experiments are wrong, but because it suggests new kinds of diagnostics. One could look for branch-sensitive behavior, threshold-dependent event formation, exceptional-locus signatures, changes in reported ensembles, or phenomena that appear only when the experimental pipeline is analyzed as an event-generating system rather than merely a value-recording system.
Thus, PV should not be presented as an escape hatch from Bell. It should be presented as a complementary semantic and algebraic framework that may help describe the formation of phenomena at the boundary between strict real-valued measurement, complex continuation, and undefined structure.
Bell gives the no-go theorem for a certain class of event descriptions.
PV studies the event-description before it has necessarily been forced into that class.
That is why the two are not enemies. Bell tells us where the wall is. PV studies the architecture around the wall, including the doors, boundaries, branch cuts, and exceptional points that the ordinary formulation leaves outside its semantic volume.
Richard Gill
On 17 May 2026, at 09:53, Bryan Sanctuary <bryancs...@gmail.com> wrote:
ok
On Sun, May 17, 2026 at 1:31 AM Richard Gill <gill...@gmail.com> wrote:
Dear Bryan
I made the computer task more simple for youPlease write a simulation program which violates CHSH.Inputs and outputs are binary.
Binary setting a -> Alice’s measurement stationBinary setting b -> Bob’s measurement stationPhysical variables -> Alice’s measurement stationPhysical variables -> Bob’s measurement station
Alice’s measurement station -> binary outcome xBob’s measurement station -> binary outcome y
Bryan Sanctuary
Mark Hadley
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Parker Emmerson
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Mark Hadley
Bryan Sanctuary
Mark Hadley
Parker Emmerson
Mark,
I agree with the central Bell point, but I think your framing compresses several different issues into one.
If an underlying theory is offered as an outcome-determining hidden-variable theory, then yes: it has to be classified relative to Bell.
Either it is Bell-local,
[
x=A(a,\lambda),\qquad y=B(b,\lambda),
]with one setting-independent hidden-variable law, local response functions, and unconditional bounded outputs, in which case it is CHSH-limited and cannot reproduce the singlet correlations; or it is contextual/nonlocal in the Bell sense, meaning the outcome structure depends on the wider measurement context, possibly including both detector angles; or it is not an outcome-determining hidden-variable theory of that Bell type.
I do not dispute that.
But that is not the full issue. The fairness question comes before that classification. Richard’s program challenge does not merely ask Bryan, Parker, or PV to state the model. It requires the model to be expressible in a very specific form:
[
a\mapsto x,\qquad b\mapsto y,
]or equivalently,
[
x=A(a,\lambda),\qquad y=B(b,\lambda),
]where both sides share only read-only classical data or shared pseudo-randomness, and where each station outputs a definite (\pm1) result for its own local setting.
That is already the Bell-local, noncontextual, unconditional response-function representation. So Richard’s challenge is fair only if Bryan has already agreed that his proposed explanation is of that form.
If Bryan claims, “I have a Bell-local classical hidden-variable simulation that violates CHSH,” then Richard’s challenge is completely fair. It says: write the two local programs and let us test them.
But if the proposed explanation is PV-like — meaning the relevant structure is exceptional-locus, cancellation-based, contextual, pushout/completion-based, or microcausal/operator-theoretic — then Richard’s challenge may have already excluded the essential structure before the test begins.
That is the key distinction.
Richard’s challenge sounds broad because it says the “physical variables” may be quaternions, or anything else. But the freedom is only internal. The final architecture is fixed:
[
x=A(a,\lambda),\qquad y=B(b,\lambda).
]That architecture is exactly what Bell–CHSH constrains. So the challenge is not an open test of “any possible physical explanation.” It is a test of whether the explanation can be compressed into a Bell-local classical two-function architecture.
That is why I would say Richard’s challenge is conditionally fair, not intrinsically fair.
It is fair as a Bell-local programming challenge.
It is not fair as a general test of PV-like underlying physics.
The phrase “use whatever physical variables you like” is therefore potentially misleading. It gives freedom over the furniture inside (\lambda), but not over the structure of explanation. It says, in effect:
Use any variables you like, provided they reduce to a single classical sample space and two local scalar response functions.
That is not neutral with respect to PV.
PV’s central lesson is precisely that the relevant structure may not survive that flattening.
I also do not think one should concede that PV is “not hidden.” That concedes too much, and it lets the word “hidden” be controlled too narrowly.
There are at least two meanings of hidden.
In the Bell-technical sense, a hidden variable is an outcome-completing parameter (\lambda) such that all relevant measurement outcomes can be represented as ordinary functions
[
A(a,\lambda),\qquad B(b,\lambda),
]
defined on one common classical probability space.
If PV is forced into that role, then yes, it becomes a Bell hidden-variable candidate. If it is Bell-local and unconditional, it obeys CHSH. It cannot reproduce quantum mechanics.
But PV can be hidden in another, deeper, structural sense.
It can be hidden as cancelled structure.
It can be hidden as exceptional-locus data.
It can be hidden as a pushout or completion element.
It can be hidden as a bona-fide variable that disappears under ordinary scalar simplification and becomes visible only when the cancellation is not prematurely collapsed.
That kind of hiddenness is not a rhetorical trick. It is precisely what the PV formalism is about.
In the arithmetic/exceptional-locus formulation, PV is not introduced as an ordinary scalar solved from a nonsingular equation. The basic quotient is
[
V_c(\mathcal E)\pm
\frac{\sqrt{c^2\mathcal E}}{\sqrt{\mathcal E}}.
]On the punctured locus
[
\mathcal E\neq 0,
]this reduces to
[
V_c(\mathcal E)=\pm c.
]But on the exact theorem locus
[
\mathcal E=0,
]the expression becomes
[
V_c(\mathcal E)=\pm\frac00.
]So the ordinary scalar interpretation fails exactly where the identity is exact. The phenomenological move is to treat the (\pm c) direction as exceptional-locus data, or as a structure retained by a completion/lift, rather than as an ordinary scalar value living inside the reduced expression.
That is why PV is hidden: ordinary cancellation erases it.
It is not hidden in the same way that a Bell variable (\lambda) is hidden. It is hidden as a latent structural degree of freedom that is uncovered only by refusing to throw away the exceptional locus.
This matters for Richard’s challenge. Richard’s program format only recognizes hiddenness of the Bell-(\lambda) kind. It asks for a (\lambda) such that outcomes are ordinary functions:
[
x=A(a,\lambda),\qquad y=B(b,\lambda).
]But PV’s hiddenness may be a completion variable, not an outcome-completing variable.
So if Richard says “PV does not count unless it appears as (\lambda) in my two programs,” then PV has been excluded by definition.
That may be a legitimate test of Bell-local hidden variables. But it is not a fair test of PV as PV.
This is exactly where Kochen–Specker strengthens the point.
Kochen–Specker teaches that quantum theory does not merely resist local hidden-variable assignments. It also resists global noncontextual value assignments: one cannot, in general, assign pre-existing values to all observables in a way that is independent of the measurement context while preserving the algebraic relations among compatible observables.
That matters because Richard’s challenge is not merely a locality demand. It is also a noncontextual valuation demand.
It asks that Alice’s outcome for setting (a) be represented as
[
A(a,\lambda),
]and Bob’s outcome for setting (b) as
[
B(b,\lambda),
]both defined on one common domain and independent of the full measurement context.
For a CHSH quartet, the same (\lambda) must effectively support the four counterfactual local values
[
A(a_1,\lambda),\quad A(a_2,\lambda),\quad B(b_1,\lambda),\quad B(b_2,\lambda),
]even though only one Alice setting and one Bob setting are actually measured in a given run. That is a global value-assignment requirement.
In Kochen–Specker language, Richard is demanding context-independent values.
In PV language, he is asking for ordinary scalar values after the exceptional/pushout structure has been erased.
So the Kochen–Specker lesson and the PV lesson point in the same direction:
[
\text{Do not assume that quantum-relevant structure must appear as a global scalar valuation.}
]Richard’s challenge assumes exactly that.
So the objection is not:
“PV is a Bell-local hidden-variable theory that somehow escapes CHSH.”
The objection is:
“Richard’s test forces PV into the exact global value-assignment format that PV may be challenging.”
That is a different argument.
Your trilemma is useful only after one has already agreed to treat the underlying theory as an outcome-determining hidden-variable theory.
You say: if there is an underlying theory that determines the measurement outcomes, then it is a hidden-variable theory; if it requires both detector angles, it is contextual; otherwise it is local and CHSH-limited.
That is broadly right for outcome maps. But PV need not be an outcome map in that sense. PV may be an event-structural or operator-symmetry account. It may determine the event law, the correlation structure, or the algebraic conditions under which outcomes are generated, without assigning all counterfactual outcomes as pre-existing scalar functions.
That is exactly why the word “hidden” has to be handled carefully.
PV can be hidden without being a Bell-local hidden variable.
It can be a hidden structural variable rather than a hidden outcome variable.
Now, this does not mean PV gets a free pass. A PV account of Bell experiments has to produce the actual empirical law.
But the important correction is: in the microcausal/operator realization, PV already does that.
For the spin-singlet experiment, the empirical law is:
[
\boxed{
P(x,y\mid a,b)\frac14\left(1-xy\cos(a-b)\right),
\qquad x,y\in{-1,+1}.
}
]This law gives unbiased marginals:
[
P(x=+1\mid a,b)=P(x=-1\mid a,b)=\frac12,
][
P(y=+1\mid a,b)=P(y=-1\mid a,b)=\frac12,
]and the correlator
[
E(a,b)\sum_{x,y=\pm1}xy,P(x,y\mid a,b)
-\cos(a-b).
]At the standard Tsirelson-angle settings, this gives
[
S=2\sqrt2.
]The derivation in the microcausal/operator setting is straightforward.
For the singlet state, use the local projectors
[
\Pi_x^A(a)=\frac12(I+x\sigma(a)),
][
\Pi_y^B(b)=\frac12(I+y\sigma(b)),
]where (\sigma(a)) and (\sigma(b)) are the Pauli observables corresponding to detector angles (a) and (b).
The Born rule gives
[
P(x,y\mid a,b)\operatorname{Tr}
\left[
\rho_{\psi^-}
,
\Pi_x^A(a)\otimes \Pi_y^B(b)
\right].
]Substitute the projectors:
[
P(x,y\mid a,b)\operatorname{Tr}
\left[
\rho_{\psi^-}
,
\frac12(I+x\sigma(a))
\otimes
\frac12(I+y\sigma(b))
\right].
]So
[
P(x,y\mid a,b)\frac14
\operatorname{Tr}
\left[
\rho_{\psi^-}
\left(
I\otimes I
+
x\sigma(a)\otimes I
+
yI\otimes\sigma(b)
+
xy\sigma(a)\otimes\sigma(b)
\right)
\right].
]For the singlet,
[
\operatorname{Tr}[\rho_{\psi^-} I\otimes I]=1,
][
\operatorname{Tr}[\rho_{\psi^-}\sigma(a)\otimes I]=0,
][
\operatorname{Tr}[\rho_{\psi^-}I\otimes\sigma(b)]=0,
]and
[
\operatorname{Tr}[\rho_{\psi^-}\sigma(a)\otimes\sigma(b)]-\cos(a-b).
]Therefore
[
P(x,y\mid a,b)\frac14
\left(
1
+
xy[-\cos(a-b)]
\right),
]hence
[
\boxed{
P(x,y\mid a,b)\frac14(1-xy\cos(a-b)).
}
]So the empirical law has been derived.
The remaining issue is not whether PV can write down the law. It can.
The remaining issue is classificatory and interpretive:
Is the derivation being forced into Richard’s Bell-local two-program format, or is it being allowed to stand as a microcausal/operator event-law derivation?
Those are not the same thing.
Richard demands:
[
x=A(a,\lambda),\qquad y=B(b,\lambda).
]The microcausal/operator PV derivation gives:
[
P(x,y\mid a,b)\operatorname{Tr}
\left[
\rho_{\psi^-}
\Pi_x^A(a)\otimes \Pi_y^B(b)
\right].
]Those are different kinds of explanation.
One is a Bell-local classical hidden-variable program.
The other is a noncommutative microcausal event law.
The microcausal PV paper formulates PV as a symmetry action on local observable algebras. Locality is represented not by a single global commutative probability space, but by commuting local algebras:
[
[X,Y]=0
\qquad
(X\in\mathcal A_A,; Y\in\mathcal A_B).
]PV acts by automorphisms on each wing:
[
A_{g_A}(a)=\alpha^A_{g_A}(A_0(a)),
][
B_{g_B}(b)=\alpha^B_{g_B}(B_0(b)).
]The dressed correlator is
[
E(a,b;g_A,g_B)\omega
\left(
A_{g_A}(a)B_{g_B}(b)
\right).
]In diagonally invariant states, the relative-PV reduction says the correlator depends only on the relative group element
[
g_A^{-1}g_B.
]So the operational content of PV is relative. A common action on both wings is gauge-like; only the relative symmetry matters.
That is a very different structure from
[
A(a,\lambda),B(b,\lambda).
]It is local in the microcausal sense — the local algebras commute — but it is not Bell-local in the classical hidden-variable sense. That distinction is essential.
So if Richard says, “Your derivation does not count because it is not two local programs,” then he is not refuting the derivation. He is saying the derivation is outside the challenge.
That is exactly the point.
PV has derived the empirical law, but not as a Bell-local hidden-variable program. Richard’s test therefore does not test whether PV can produce the Bell statistics. It tests whether PV can be flattened into a Bell-local classical simulation.
That flattening is precisely what is in dispute.
This is also where the selection/exceptional-locus route must be kept separate from the microcausal route.
There is a selection version in which one starts with a Bell-local deterministic base model and then applies a setting-dependent acceptance rule:
[
\gamma(a,b,\lambda).
]The observed law is then
[
P_{\mathrm{obs}}(x,y\mid a,b)\frac{
\int_{\Lambda}
\mathbf 1{A(a,\lambda)=x,;B(b,\lambda)=y}
\gamma(a,b,\lambda),d\rho(\lambda)
}{
\int_{\Lambda}\gamma(a,b,\lambda),d\rho(\lambda)
}.
]If (\gamma) depends on the setting pair, then the accepted hidden-variable law
[
\nu_{ab}
]also depends on the setting pair. The four correlators in CHSH are then not expectations under one common measure. In that case, a Bell-local base model can produce an apparent CHSH violation in the accepted data, but only because the data are contextual/selection-conditioned.
That is not Richard’s challenge either, because Richard requires two outputs every time and wants to test the unconditional output stream.
So we should distinguish three PV-related routes.
First: Bell-local unconditional PV.
If PV is represented as
[
x=A(a,\lambda),\qquad y=B(b,\lambda),
]under one common setting-independent probability law, then it is a local hidden-variable model. It obeys CHSH. It cannot reproduce the singlet law.
This is the category Richard’s program challenge tests.
Second: selection or exceptional-locus PV.
If PV affects which trials are defined, accepted, or reported, then the empirical law may be an accepted-sample law:
[
P_{\mathrm{obs}}(x,y\mid a,b).
]This can reproduce the singlet law, but it is contextual/selection-based. It does not satisfy Richard’s unconditional two-output-per-trial challenge. It must be evaluated through detection/selection/fair-sampling diagnostics.
Third: microcausal/operator PV.
If PV is formulated as relative symmetry in a noncommutative microcausal quantum system, then it produces the Born joint law:
[
P(x,y\mid a,b)\frac14(1-xy\cos(a-b)).
]This is not a hidden-variable theory in the Bell outcome-map sense. It is an event-structural/operator account. It is local in the sense of commuting subalgebras, not local in the sense of classical Bell factorization.
This third route is the strongest PV response to both your classification and Richard’s challenge, because it is not merely saying:
“Maybe selection can fake it.”
It is saying:
“PV has a microcausal realization that derives the actual quantum law, but the derivation is not a Bell-local hidden-variable program.”
That is why the fairness question matters.
If Richard’s question is, “Can Bryan’s model, if it is a local hidden-variable theory, violate CHSH?” then the answer is no, and Richard’s test is fair.
But if Richard’s question is, “Can PV explain Bell correlations?” then his two-program challenge is not fair, because it only allows the Bell-local classical form and excludes the microcausal/operator form in which PV actually derives the law.
The challenge excludes PV not because PV fails to produce the empirical law, but because PV produces it in a different category.
That is the core point.
It also answers your “three options” framing.
Your three options are exhaustive only for outcome-determining hidden-variable theories. They are not exhaustive for all underlying explanatory structures.
If PV is an outcome-determining hidden-variable theory, then your taxonomy applies.
If PV is a Bell-local outcome-determining hidden-variable theory, it fails.
If PV is a contextual outcome-determining hidden-variable theory, it may reproduce QM but is not Bell-local.
But if PV is a microcausal operator-symmetry theory that determines the event law rather than assigning pre-existing scalar outcomes, then it is not inside the hidden-variable trilemma. It is not a “fourth hidden-variable category” so much as a different kind of hidden structure: a hidden completion/symmetry/exceptional-locus variable, not a hidden outcome map.
That is why I would not say, “PV is not hidden.”
I would say:
PV is hidden, but its hiddenness is structural rather than Bell-(\lambda)-style.
It is hidden as the variable uncovered by cancellation analysis, exceptional-locus completion, pushout structure, or relative symmetry reduction. It is not necessarily hidden as a pre-existing scalar deciding all possible detector outcomes.
So the strongest final position is this:
Richard’s test is fair only under a prior restriction:
[
\text{Bryan/PV must be a Bell-local unconditional hidden-variable program.}
]Under that restriction, the answer is already known: CHSH forbids the quantum law.
But if PV’s actual claim is that the underlying phenomenon is a hidden structural variable — exposed through cancellation, exceptional loci, pushout/completion, or microcausal relative symmetry — then Richard’s test is not a fair test of PV. It is a test of whether PV can be reduced to the very classical form that Bell and Kochen–Specker already warn us is inadequate.
PV has derived the empirical singlet law:
[
P(x,y\mid a,b)\frac14(1-xy\cos(a-b)).
]But it derives it through the microcausal/operator event law:
[
P(x,y\mid a,b)\operatorname{Tr}
\left[
\rho_{\psi^-}
\Pi_x^A(a)\otimes\Pi_y^B(b)
\right],
]not through two classical programs
[
x=A(a,\lambda),\qquad y=B(b,\lambda).
]Therefore Richard’s challenge does not show that PV cannot explain Bell correlations. It shows only that PV cannot be flattened into a Bell-local classical hidden-variable simulation. If that flattening is precisely what PV denies, then the challenge begs the question.
Bryan’s purely local hidden-variable model may well be wrong. If it is Bell-local, it cannot violate CHSH. But Richard’s challenge is not fully fair to PV-like explanations, because it admits only Bell-style hiddenness and excludes structural hiddenness by construction. PV should not be conceded as “not hidden”; it is hidden as cancelled/completion/exceptional-locus structure. Kochen–Specker reinforces this: demanding globally defined, context-independent scalar values is already suspect for quantum phenomena. In the microcausal realization, PV already derives the empirical Bell law
[
P(x,y\mid a,b)=\frac14(1-xy\cos(a-b)).
]What Richard’s challenge tests is only whether that law can be reproduced by two unconditional local classical programs. Bell says it cannot. That does not refute PV; it only rejects a Bell-local classical shadow of PV.
Mark Hadley
Bryan Sanctuary
Richard Gill
Dear Richard,Richard,You are impatient, it has only been a few days but you know how writing is. In the meantime, I attach the plot I got which compares the old add, on the left, with the latest simulation. I get -cos using quaternions and I get the Boolean triangle using Bell. No nonlocality of course. EPR data carries information in two ways: your Boolean pairs (Bell) and something I think you have not considered: the macroscopic build up of coherence within the collection bins. The latter is only available after all the runs are completed.So here is the plot which includes instantiated planes. You will have to wait for a few days for the code. I must write it up so it is clear, and that will take me time.Bryan
<QuaternionClicks.jpg>
Parker Emmerson
Dear Mark,
I hope you are well.
I understand the point you are making about (\lambda), and I agree that Bell’s theorem is powerful precisely because it does not need to know the detailed physical character of the variables. If the variables can be placed into one common probability space, and if the outcomes can be written as
[
A(a,\lambda), \qquad B(b,\lambda),
]
with the same measure used for all four possible setting-pairs, then the CHSH inequality follows. I am not disputing this.
The question is whether the completed phenomenon has already been given in that form.
When you say that (\lambda) includes all variables in the problem, I think this can be interpreted in two ways. In one interpretation, it means that (\lambda) includes all physical variables available at the source, or all physical variables that can be described prior to the completed measurement. In that sense, I have no objection. But in the stronger interpretation, it means that (\lambda) already includes the completed counterfactual event-structure for all possible settings. That is the point at issue.
PV is not simply an additional ordinary variable that Bell forgot to include. It is not a little object hidden behind the detector. It concerns the formal generation of the event, or the way in which a completed phenomenon becomes expressible from an algebraic architecture. This is why the issue is not solved merely by saying “put it into (\lambda).” The question is whether the phenomenon has the logical form required to be placed into (\lambda) as a complete table of counterfactual Boolean outcomes.
This is similar to a distinction in perceptual theory. One may say that all the light is already present in the environment, but this does not mean that the perceived object, as perceived, has already been reduced to a retinal image. There is still the problem of information, surface layout, gradient, synthesis, and the act by which the object becomes available as a perceived whole. In the same way, one may say that all physical variables are included in (\lambda), but this does not yet show that the reported Bell-table event is already a member of one common counterfactual ensemble.
Bell’s theorem applies once the event is represented that way. I agree.
PV questions whether that representation is forced.
This is why I do not think Richard’s challenge is neutral with respect to PV. It is an excellent test of strict Bell-local Boolean response functions. It asks for two stand-alone programs,
[
x=A(a,\lambda),
\qquad
y=B(b,\lambda),
]
where Alice receives only (a), Bob receives only (b), and the programs share only read-only data or shared randomness. Under those rules, the four counterfactual outcomes are jointly definable. Therefore CHSH cannot be violated. This is exactly Bell’s structure.
But PV is not the claim that two such programs can violate CHSH. PV is the claim that the completed reported phenomenon may not be exhausted by that program-pair representation.
The distinction I am making is therefore not a small technical point. It is a distinction between:
source variables,
local physical interactions,
and completed reported phenomena.
If these three are compressed into one common counterfactual table, Bell applies. If the completed phenomenon is generated only through the actual event-structure, then this compression has not been derived. It has been assumed.
This is why I keep returning to the language of formal ontology and phenomenological description. A mathematical form is not merely a list of variables. It is a structure in which certain relations become expressible. PV is concerned with that expressibility. It is concerned with the way an algebraic unity, a branch, or an exceptional locus can disclose a parameter that was not simply an ordinary pre-assigned value.
So I would say the following.
Bell’s (\lambda) includes all variables that can be placed into a single probability space supporting all counterfactual outcomes.
PV asks whether the completed phenomenon always has that form.
If it does, Bell wins. I accept that.
If it does not, then saying “(\lambda) includes everything” has silently included the disputed event-structure.
That is the difference I am trying to isolate.
All my best,
Parker
Mark Hadley
Mark Hadley
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Parker Emmerson
Dear Mark,
I hope you are well.
I do not agree that PV has the right form to be put into Bell’s (\lambda) as a total counterfactual value-assignment.
That is precisely the issue.
Of course, if one has a completed procedure that assigns, for every trial, all of the counterfactual values
[
A_1(\lambda),\quad A_2(\lambda),\quad B_1(\lambda),\quad B_2(\lambda),
]
then those values can be placed into (\lambda), and Bell’s argument applies. I have no objection to that. In fact, this is the strength of Bell’s theorem. Once the event has been represented by a single probability space, a common measure, and jointly definable counterfactual outcomes, the details of the mechanism no longer matter.
But PV is not such a completed value-assignment procedure.
PV is an algebraic-logical event construction. It involves an embedded (v)-architecture, a push-out use of unity, branch structure, strict semantics, and an exceptional locus at which the ordinary value assignment can become undefined. It is not simply a list of variables whose values exist for all possible measurement settings.
That is why saying “put it into (\lambda)” does not answer the point. Bell’s (\lambda) is not just a bag into which any meaningful structure can be thrown. It is a variable on a common probability space supporting jointly definable counterfactual outcomes. PV does not begin with that structure.
The important difference is between a total function and a condition of expressibility.
A total function says:
[
A(a,\lambda)
]
has a value for every relevant (a) and every relevant (\lambda).
PV says something different. It says that an event-parameter becomes expressible through a formal construction involving unity, cancellation, branch choice, and exceptional-locus behavior. The point is not that there is a hidden value waiting to be revealed in the ordinary Bell sense. The point is that the phenomenon becomes defined through the algebraic event-structure.
So, one can force a Bell-language representation of some PV-related constructions. For instance, one can regularize the structure, or translate certain consequences into selection/context language, or ask what happens if one treats the reported events as if they already belonged to a common Kolmogorov space. But that is a translation into Bell’s hypothesis class, not PV itself.
And once that translation is made, Bell applies. I accept that.
What I deny is that the translation is neutral.
It removes the very feature PV is trying to describe: the fact that the completed phenomenon is not already given as a member of a common counterfactual Boolean table.
This is why I need to ask directly: why do you think PV fits into (\lambda), if you have read the papers?
If you have read them, then please point to the place where the PV construction is presented as a total counterfactual value-assignment function. I do not think that is what the papers say.
The papers explicitly distinguish the Bell-CHSH hypothesis class from PV. Bell-CHSH applies to a single Kolmogorov probability space carrying all counterfactual outcomes, with measurement independence, Bell locality, and bounded outputs. Inside that class, no algebraic reformulation of PV will produce Tsirelson-scale correlations. That is not something I am denying.
The papers also make clear that if PV is brought into a Bell discussion, it must appear through some structural change: either the effective ensemble changes by selection or context, or the model leaves the commutative Kolmogorov framework, or a Bell premise is relaxed. That means PV is not being introduced as an ordinary missing variable inside Bell’s (\lambda). It is a question about the semantic form of the event.
If you have not read the papers, then I think you are assuming that PV must be the kind of thing Bell’s (\lambda) can contain, rather than engaging the actual algebraic construction. That is exactly the problem. You are treating PV as though it were an ordinary hidden-variable theory, when the work is about the formal event-structure by which the parameter becomes expressible at all.
The radical analysis is important here. In strict semantics, the square-root branches are fixed. The expression is not simply a free-valued hidden variable. The construction exposes compatibility conditions and an exceptional locus, including the possibility of a (0/0)-type undefined form. That is not the same as assigning four pre-existing Boolean values to a trial.
So I would put it this way.
If PV is forced into a Bell-style total value map, then Bell applies.
But PV, as such, is not a Bell-style total value map.
It is a formal ontology of event-formation, involving an embedded velocity structure and an exceptional boundary of definition. It is “hidden” only in the metaphorical and structural sense that the (v)-structure is embedded in the algebraic unity by a push-out method. It is “local” only in the sense that the construction is internal to the event’s own algebraic conditions, not a signal between distant stations. It is not hidden-local in the Bell sense of a common ensemble of pre-existing counterfactual Boolean outcomes.
This is why Richard’s two-program challenge is not a test of PV. It is a test of whether one can produce a CHSH violation after assuming the Bell event structure from the beginning:
[
x=A(a,\lambda), \qquad y=B(b,\lambda),
]
with all relevant counterfactual outcomes jointly definable from shared read-only data or shared randomness.
One cannot. I agree.
But PV denies that its event-structure has that form in the first place.
The distinction I am making is therefore between:
source variables,
local physical interactions,
and completed reported phenomena.
If these three are compressed into one common counterfactual table, Bell applies.
If the completed phenomenon is generated only through the actual algebraic and phenomenological event-structure, then this compression has not been derived. It has been assumed.
That is the difference I am trying to isolate.
All my best,
Parker
Mark Hadley
Parker Emmerson
Mark Hadley
Parker Emmerson
Mark,
Fair enough. We can leave it there.
For clarity, the relation to Bell is this: Bell excludes single-ensemble local Boolean outcome models. PV is not proposed as another such Boolean model, but as an algebraic account of event-formation before that reduction is made. The novelty is the push-out/modus-ponens construction of an embedded (v)-structure, together with its branch and exceptional-locus behavior. If one forces that structure into (x=A(a,\lambda)), (y=B(b,\lambda)), Bell applies. I have said that repeatedly.
So the physical source of the novelty is not “Alice depends on Bob,” and not “Bell’s algebra is wrong.” It is that the completed reported phenomenon may involve a formal event-structure not identical with a pre-existing Bell table.
If that is not enough reason for you to read the papers, then yes, we should probably go our separate ways on this topic.
All my best,
Parker
Mark Hadley
Parker Emmerson
Parker Emmerson
Mark, the irony is that your response is structurally similar to the kind of move you often criticize. Bryan sometimes treats a new formalism as though it automatically evades Bell. You are treating Bell’s as though it automatically absorbs any formalism. My point is neither of those. Bell applies when the event has the form . PV asks whether the completed phenomenon has that form before it is regularized into it. If you do not engage the push-out, branch, and exceptional-locus structure, you are not criticizing PV; you are replacing it with the Bell template and criticizing that.
Parker Emmerson
Mark,
I think the difficulty is that you never actually did the homework. You never engaged the specific mathematics I presented and had peer reviewed.
Simple answer:
Bell does not refute the complex architecture of PV. It refutes the real-valued Bell-table shadow of PV, if PV is first forced to cast such a shadow.
Alice’s local interaction may be determined. The completed reported phenomenon is not assumed to be a pre-existing Bell outcome function.
So if your question is, “Is there a local physical interaction at A?” yes.
If your question is, “Is the completed reported Bell-table event already a total function for all possible settings?” no, that is precisely what PV does not assume.
All my best,
Parker
do you want to do a video call some time?I'm really puzzled that you can't give simple answers to my simple questions. And you must be even more frustrated that you give long answers and I still come back to with much the same question.!!?or maybe a sequence of very short questions? like ...in your model/ interpretation, is the outcome at A determined?CheersMark
Richard Gill
Dear Bryan, dear all
Mark Hadley
No, PV does not predict the recorded outcome as an ordinary pre-existing Bell value. But the event is not structureless randomness either. In the CHSH contextual paper, the relevant idea to which I surmise you are intending is not merely “hidden subregions,” but fibered non-injectivity: many distinct hidden states can share the same coarse observed label . Within the fiber over that same observed label, different hidden subregions and may correspond to different product signs, while the coarse kinematic label remains unchanged. Selection or event-instantiation can then re-weight the internal fiber structure without changing the observed label itself, and that is just one example, one instantiation, of contextual PV methods. So the final is not predictable as a Bell lookup value , but it can arise from structured hidden fiber geometry rather than featureless randomness. The phenomenological velocity exists, at least part and parcel to the necessitated implied existence of complex solutions to other variables in the algebraic system of equations. That is exactly why reducing PV to “is the outcome predetermined, yes or no?” misses the noninjective-fiber architecture. It is also a kind of false dilemma: you are demanding that the theory answer only in the Boolean categories Bell uses for the final reported signs, when the point of PV is that the event-formation structure prior to Boolean reporting is not assumed to be a Boolean value assignment. It may have noninjective fiber structure, branch structure, and exceptional-locus behavior before the final sign is reported.
On Wed, May 20, 2026 at 9:54 AM Mark Hadley <sunshine...@googlemail.com> wrote:An experimenter doesn't need to know anything about Bell, he measures +/-1 outcomes.Does your work determine the experimental results. I know it has hidden layers and structures. I may even want to read about them. First I want to know if the work determines if the outcome is + or -CheersmarkOn Wed, 20 May 2026, 14:45 Parker Emmerson, <powerin...@gmail.com> wrote:Yes, the question is clear, but it is framed in a way that already compresses PV’s distinction between local interaction and completed reported event. The recorded outcome is not predictable in advance as an ordinary hidden value. Alice’s local interaction may be lawful, but the completed reported outcome is not assumed to pre-exist as a Bell variable. PV does not refute Bell as a theorem. It refutes an overextended philosophical reading of Bell. I think this is where I will leave it for now.The math speaks for itself. PV does not contradict Bell’s algebra. If PV is forced into a single-ensemble Bell model with total functions and , then Bell applies. I accept that.
But PV is not presented as that. It is an algebraic and semantic account of event-formation, involving push-out unity, branch structure, strict semantics, and exceptional loci. Its importance is not that it “breaks Bell,” but that it gives alternate, potentially testable ways of describing how reported phenomena may be generated before they are reduced to Bell-table outcomes.
So the question is not whether Bell’s theorem is false. It is whether Bell’s theorem exhausts all meaningful, local, algebraically structured accounts of physical event formation. I do not think it does.
At this point, the best way forward is for you to read the papers and decide for yourself whether you think the mathematical construction is legitimate. I am happy to discuss specific objections to the actual mathematical language of the argument, but I do not think it helps either of us for me to keep translating the framework into short Bell-template answers.
On Wed, May 20, 2026 at 9:22 AM Mark Hadley <sunshine...@googlemail.com> wrote:isn't my question clear?is the measurement outcome at A determined by your interpretation?The answer does not warrant any mention of Bell. It seems such a simple fundamental question, I don't understand the difficulty getting an answer. The steps you take on the way are not important for the answer.An experimenter sets up an EPR experiment and records +/-1 for each event. It has randomness to the experimenter. in principle, is the outcome predictable according to PV.CheersMark
Richard Gill
Sent from my iPad
Richard Gill
On 20 May 2026, at 16:34, 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:
Dear Bryan, dear all
Mark Hadley
Parker Emmerson
Richard, Mark,
Thank you. I will answer directly.
The peer-reviewed reference is:
Parker Emmerson, “Bell–CHSH Under Setting-Dependent Selection: Sharp Total-Variation Bounds and an Experimental Audit Protocol,” Quantum Reports 8(1), 8, 2026.
https://www.mdpi.com/2624-960X/8/1/8The IJQF page is here as well:
https://ijqf.org/archives/8027Richard, yes, I agree that classical local causality, in Bell’s sense, is rejected by the experimental violations of Bell inequalities. If by local causality one means the derivation of a single common probability space carrying all relevant counterfactual outcomes, with local response functions and measurement independence, then yes, that structure is incompatible with the observed Bell-CHSH violations.
But I do not agree that this settles every possible meaning of locality, event-formation, or physical reality. That is where PV enters. PV does not contradict Bell’s algebra. It does not say that two stand-alone Bell-local Boolean programs can violate CHSH. They cannot. Rather, PV concerns the algebraic and semantic structure of the event before it is reduced to a Bell-table outcome.
Mark, to your point: PV does not claim to predict the individual recorded result as an ordinary pre-existing hidden value. The event is not structureless randomness either; the point is that the event-formation structure may involve branch structure, noninjective fibers, and exceptional loci before the final Boolean sign is reported. Reducing the whole discussion to “is the outcome predetermined, yes or no?” forces PV into the very Boolean template it is questioning.
So the shortest summary is this:
Bell refutes classical local causality.
PV does not refute Bell’s algebra.
PV challenges the overextended claim that Bell’s algebra exhausts all meaningful local or realist descriptions of event-formation.
If that is of no interest, that is fine. But the papers are there, and I would prefer criticism of the actual construction rather than repeated classification of PV as something it is not.
All my best,
Parker
Parker Emmerson
I do not agree that PV is merely a formal mathematical game.
The point is that the complex analytic structure is not optional decoration. Once the algebraic system implies branch structure, non-real continuations, and exceptional loci, those features are part of the mathematical object. Ignoring them is not physical realism; it is a restriction to the real-valued Bell-table shadow of the construction.
Bell’s theorem applies after the event has been represented by real bounded functions on one common probability space. I accept that. But PV is concerned with the prior algebraic event-structure: the push-out unity, the embedded -parameter, the real/complex branch boundary, and the exceptional locus where ordinary value assignment can fail.
That is legitimate mathematics, and in my view it is physically relevant because quantum theory itself is not a purely real Boolean theory. Complex amplitude, branch structure, and noncommutative representation are not “games”; they are central to the formal language of quantum mechanics.
So my claim is not that PV overturns Bell’s algebra. It does not. My claim is that Bell’s algebra acts on a reduced real-valued event representation, while PV studies the complex analytic and semantic structure by which the event becomes expressible before that reduction.
That is why I think PV is complementary to Bell, not a contradiction of it.
Parker Emmerson
Mark,
What I find discouraging is not that you disagree. Disagreement is fine. What is discouraging is that you seem unwilling to read the actual papers before classifying the work.
That is not a scientific posture. If PV is wrong, then the constructive thing is to identify where the algebraic construction fails, where the semantics are invalid, or what experiment would distinguish the proposal from standard quantum mechanics. But repeatedly dismissing the work without engaging the definitions, branch structure, exceptional loci, noninjective fibers, or proposed audit framework is not a criticism of the theory. It is a refusal to examine it.
I am not asking you to accept PV. I am asking you to read the work before deciding what it is.
A genuinely scientific response would be: “Here is the specific step that fails,” or “Here is the experiment that would not distinguish it,” or “Here is why the proposed event-formation structure cannot have physical meaning.”
But saying, in effect, “Bell is simple, therefore I do not need to read this,” is not enough. Bell’s algebra is simple once the event has been reduced to a single Kolmogorov Boolean model. PV is about whether that reduction exhausts the physical and semantic structure of event-formation.
If you are not interested in that question, that is fine. But then we should not pretend you have evaluated the theory.
All my best,
Parker
Mark Hadley
Parker Emmerson
PV does not predict individual signs as pre-existing Bell values. It predicts the reported-event correlation law , the required accepted-ensemble dispersion for Tsirelson-scale violations, experimental audit quantities for detecting/limiting such dispersion, and the algebraic existence of an embedded -structure with branch and exceptional-locus behavior. If your criterion for “prediction” is deterministic prediction of every individual result, then PV does not do that — but neither does standard QM. The prediction is statistical, structural, and experimentally auditable.
The problem with your response is not that you are defending Bell. Bell does not need defending here. The problem is that you are treating Bell’s as a universal container into which every mathematical structure can be placed without loss. That is formal relativism, not analysis.
Describability is not the same as Bell-representability. A branch-dependent event-formation structure with noninjective fibers and exceptional loci is not automatically equivalent to a total Boolean value map on a single Kolmogorov probability space. If you force it into that form, you have not refuted PV; you have erased the feature PV was introduced to study.
This is the logical flaw: you assume every formal language can be translated into Bell’s language without changing its meaning. That is false. Some translations collapse the very distinctions that matter.
PV is not saying, “Here is another variable Bell forgot.” PV is saying that the event may not originally have the form Bell’s requires. So “just put it into ” is not an answer. It is the disputed reduction.
If you want to criticize PV, you have to show that the reduction from PV’s event-formation structure to a total Bell value map is faithful. Merely asserting that anything describable goes into is not enough. It is a philosophical flattening of the mathematics.
Parker Emmerson
No new fundamental instrument is required. Existing quantum optics hardware can do the experiment. What needs to be invented or custom-built is the integrated raw event-formation recording and scanning system.
Parker Emmerson
Mark Hadley
Parker Emmerson
That is fair. PV is not offered as a deterministic lookup theory for each individual result, so it does not claim that every single click can be predicted in advance. But that does not make it physically empty. PV ought to be testable at the level of event-formation: branch behavior, threshold dependence, exceptional-locus effects, timing structure, hidden fiber geometry, and ensemble formation before Boolean reporting. So I agree that the physicist’s question matters; PV should earn its keep experimentally, not by predicting each individual sign, but by predicting structural features in how reported events and distributions arise.
Mark Hadley
Parker Emmerson
Mark,
If Bell theorists only say what cannot explain the phenomenon, but refuse to engage alternate structures that might explain how the phenomenon is formed, then they are no longer explaining Nature; they are policing a formal boundary. Bell tells you what kind of explanation fails. It does not automatically supply the positive explanation of the actual phenomenon. I am not saying quantum mechanics overlooked noncommutativity. It obviously did not. I am saying quantum mechanics overlooked phenomenological velocity. QM has the operator machinery and the Born rule, but it does not identify the PV architecture: push-out unity, cancellation-sensitive velocity structure, branch behavior, exceptional loci, and the formation of a reported Boolean event from a richer algebraic structure. So PV is not claiming to invent quantum noncommutativity. It is claiming that a specific event-formation structure inside the mathematical landscape was missed. PV does not make Bell’s algebra false. It changes what Bell can be said to have ruled out.
Bell’s theorem is not the wrong direction as mathematics. It is the wrong direction only when it is used as a universal metaphysical filter that forces every proposed event-formation theory into global Boolean form before discussion can begin. In the language of Plato’s cave, Bell is a theorem about the allowed relations among shadows on the wall, once one assumes the shadows are the primitive objects. It is not automatically a theorem about every possible structure casting those shadows. For PV, the relevant physics is prior to Booleanization: branch structure, fiber geometry, exceptional loci, saddle maps, and microcausal noncommutative linear algebra. Once all of that is flattened into and , Bell correctly rules out the flattened object. But that does not show that the pre-Boolean architecture was physically meaningless. Bell rules out the cave-wall projection if one mistakes that projection for a local Kolmogorov hidden-variable model; it does not thereby rule out the higher-dimensional structure casting the projection.
I misunderstand the position of a theoretical physicist? Probably more than one, and certainly for a variety of different reasons. But I am trying to understand yours, and I accept the correction: you are not asking for prediction of individual clicks, but for an explanation of how the results arise. That is fair. The experimenter records , and PV does not deny that. The point is that the recorded Boolean sign is the final reported coarse outcome, not necessarily the primitive event-structure. PV is not a Bohmian trajectory account, where particle position explains the sign. It is an event-formation account, due to the implied form of complex analysis: algebraic unity, branch structure, noninjective fibers, partial definedness, and exceptional loci, by which a reported Boolean sign emerges from a richer pre-Boolean algebraic structure.
People often have an aversion to the idea that something can cancel with itself and yet still disclose a solvable internal structure. But that is exactly the logical point of PV: cancellation does not necessarily exhaust the meaning of the algebraic architecture. This is analogous to the demand that the theory immediately reduce to Boolean values. The final report is Boolean, but the premise that the underlying event-structure must already be Boolean is precisely what PV disputes. That premise is not forced; it is refutable by analyzing the complex structural implications of push-out algebra and exceptional-branch-locus semantics. In Plato’s terms, the outcomes are shadows. They are real as shadows, and they must be accounted for, but it does not follow that the whole account of the phenomenon must itself be written in the logic of shadows.
So yes, PV must account for Boolean reports, but no, it need not reduce the formation of those reports to a pre-existing Bell lookup value . If you ask only for the final alphabet, the answer is . If you ask for the underlying explanation, the answer is event-formation, not Boolean pre-assignment. Whether that is useful physics depends on whether it leads to testable structure, and that looks more promising to me each day. That is the burden I accept.
Bryan’s search for a linear-algebraic account is tempting because the right linear structure may not be a replacement for complex analysis, but a way of expressing its event-generating geometry. Holomorphic functions with sweeping nets could describe how branch regions, exceptional loci, and noninjective fibers are traversed before Boolean reporting. The mistake would be to apply linear algebra only after the correlations are already computed. The promising direction is to use it before Boolean reduction, as part of the event-formation mechanism itself.
All my best,
Parker
Parker Emmerson
Richard Gill
Richard Gill
<Holomorphic_Bell_with_PV_and_Sweeping_nets.ipynb><Phenomenological_Velocity__Bell_CHSH__and_the_Unfairness_of_Global_Booleanization.pdf>
Bryan Sanctuary
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Mark Hadley
Bryan Sanctuary
Bryan Sanctuary
Mark,
I agree that a mechanism for contextuality is needed, but I think that you believe it can only arise through nonlocal or acausal mechanisms (you accept Bell's theorem). In my work, contextuality arises because the measurement geometry is instantiated by the interaction itself, so the relevant observables are not jointly defined prior to measurement in the Bell/Fine sense--that is my note.
Bryan
From: Mark Hadley <sunshine...@googlemail.com>
Date: Thu, May 21, 2026 at 5:27 PM
Subject: Re: [Bell_quantum_foundations] Re: Richard's programming challenge to Bryan
To: Bryan Sanctuary <bryancs...@gmail.com>
Mark Hadley
Richard Gill
Bryan Sanctuary
Bryan, looking at your paper more carefully, consider what you are actually doing. For example, you assert that cancelling magnetic moments mean the isotropic state is "electromagnetically inactive," that a polarized blade "displays a magnetic moment with chirality" and that "charge also emerges," and that the scalar term of the geometric product corresponds to "mass-energy confinement" while the wedge product corresponds to "internal rotational kinetic energy."
Each of these is an arbitrary assignment. You have a geometric object — a bivector with two algebraic components — and you are labelling its parts with physical quantities: this part is mass, that part is charge, this behaviour is electromagnetic. But labelling is not derivation. You have not shown that your scalar term satisfies the field equations of mass, that your emergent charge obeys Coulomb's law, or that your magnetic moment transforms correctly under a gauge transformation.
In short, the physical vocabulary — mass, charge, magnetic moment, fermion — is being borrowed from standard physics and pasted onto geometric structures that have not been shown to reproduce the quantitative content of those concepts. That is not a physical theory of Nature; your work is a dictionary written by the author, for the author.
RegardsAnton------ Original Message ------From "'Mark Hadley' via Bell inequalities and quantum foundations" <Bell_quantum...@googlegroups.com>To "Bryan Sanctuary" <bryancs...@gmail.com>Cc "Richard Gill" <gill...@gmail.com>; "Bell inequalities and quantum foundations" <Bell_quantum...@googlegroups.com>Date 5/15/2026 6:42:57 PMSubject Re: [Bell_quantum_foundations] Re: structural instantiation, contextual mapsHello Bryan,have you really change your views as Richard says?I thought you still believed that your model was exempt from Bell.and I thought you were still presenting a sum of correlation coefficients as a meaningful expression.I would prefer Richards remarks to have more clarity. However, Your mistakes are simple, obvious and seen by everyone who inspects your work.You have not convinced the majority if your peers.Do you think you have convinced a single person? Your mum maybe? List the names or pay up.Cheersmark
On Fri, 15 May 2026, 18:15 Bryan Sanctuary, <bryancs...@gmail.com> wrote:
Richard,Please look at that paper which I attached last time for what instantiation and context map means. You have had that paper for a couple of months, but you ignore it and you write a new paper which my paper motivated you to write. It is math and that is your field, not mine. So do your due diligence before you make wild statements without even reading what I say. You are totally wrong.Also, you failed, yet again, to answer my question: You have CAPITULATED. You now question joint defineability of Boolean outcomes MY EXACT POINT. What do you say?Bryan
On Fri, May 15, 2026 at 11:29 AM Richard Gill <gill...@gmail.com> wrote:
Dear Bryan
You wrote "Gill does not yet understand structural instantiation. He does not understand what a contextual map is”.
Maybe you can explain what you mean by "structural instantiation” and by “contextual maps”. Once I know what you are talking about I will be able to say whether or not I understand these concepts.
Richard
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