Lee Smart @VFD_org

This is a fascinating result because it shifts the role of the hippocampus from passive memory storage to active field preparation. The deeper implication isn't simply that memories influence perception. It's that the brain prepares a coherent dynamical state before sensory information arrives. Hippocampal ripples appear to tune cortical gamma activity according to expected uncertainty, so what we experience depends as much on the prepared state as on the incoming stimulus itself. Viewed through a field perspective, cognition becomes: Memory → Coherence → Resonant Preparation → Perturbation → Closure Information isn't just transmittet, it is received by a system whose resonant geometry has already been configured by context and experience. This doesn't prove a field-based model of cognition, but it is another piece of evidence that the brain operates as a hierarchy of interacting oscillatory fields rather than a passive symbol processor. The computation is increasingly looking like the evolution of a dynamic field toward coherence.

Earl K. Miller @MillerLabMIT

2 days ago

Cortical gamma oscillations riding on top hippocampal ripples help “tune” how the cortex responds later. nature.com/articles/s4159… #neuroscience

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Fair question. I would not describe ARIA as simply “a Kuramoto lattice” or “CGLE,” although those are useful reference points. At the public level: ARIA uses a field of coupled local oscillatory states with phase, amplitude, memory and constraint terms. The key behaviour is not imposed spiral-wave generation, but excitable phase-locking near criticality. When local coherence crosses threshold, rotational/spiral modes can emerge as attractor patterns in the substrate. So the closest public description is: Kuramoto-like phase coupling + reaction/diffusion-style excitability + memory/constraint feedback, rather than one standard textbook equation. The important point is that spiral waves are not treated as “the source of consciousness.” They are a dynamical signature of coherent integration in an excitable medium, similar to what appears in cardiac tissue, cortical waves, chemical oscillators and other nonlinear systems. In ARIA, the hypothesis is that useful cognition emerges when those local phase relations become stable enough to carry persistent information, but flexible enough to reorganise. That is the part we are testing computationally.

Norstien @stinor

4 days ago

@VFD_org What equation is ARIA actually integrating? Is it a Kuramoto lattice or CGLE, or something else?

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There’s clearly convergence happening here. In VFD we frame gravity not as primitive force, but as curvature/geodesic response from non-uniform closure and event-accessibility. Energy density is the source-side expression; closure imbalance is the deeper object. We have the public record, so no need for priority arguments, the important thing is that the same structure keeps reappearing.

Spiral waves may not be generated by microtubules directly, but could emerge naturally from any coherent excitable network operating near criticality. In ARIA we found something similar computationally: when local oscillators become sufficiently phase-locked, information no longer propagates as simple diffusion but organizes into rotating wavefronts that maximize coherence while minimizing energetic cost. If cortical tissue behaves similarly, microtubules may act less as the origin of the spiral and more as one of the structures that stabilizes phase coherence across dendritic networks. That would also fit the observation that anesthesia disrupts spiral organization without simply eliminating all electrical activity. Perhaps the real question is not "what generates the spiral?" but "what field conditions make spiral coherence the preferred solution?" If spiral waves are an energy-minimizing coherence state rather than a specific anatomical feature, we'd expect similar structures to emerge across biological and artificial cognitive systems operating near criticality.

Stuart Hameroff @StuartHameroff

4 days ago

May I ask the mechanism of spiral EEG waves? Some articles mention spiral axons but I haven’t seen evidence. EEG comes from apical dendrites with mixed polarity microtubule networks. Maybe the spirals come from microtubules with baseline frequency of 39 hertz.

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NotebookLM audio podcast now available for: The Icosian Closure Object and a Geometric RH-Equivalent The paper is technical, so the podcast gives a more digestible walkthrough of the core idea: from the 600-cell / maximal icosian order, we construct a scale-axis Weil positivity form Q_A = A∞ − A_P whose universal positivity is equivalent to RH/GRH for one associated icosian cuspidal L-function. This is not a claimed proof of RH. It is an audio guide to: • the real geometric object • the exact arithmetic shadow • the Eisenstein and cuspidal faces • the Brandt prime-side witness • the named open frontier: positivity For anyone who wants the story before reading the formulas, start here.

Lee Smart @VFD_org

3 weeks ago

Published: The Icosian Closure Object and a Geometric Equivalent of the Riemann Hypothesis Website Link: vibrationalfielddynamics.org/articles/icosi… This paper gives a geometry-first construction of an RH-equivalent Weil positivity form, built from the 600-cell / maximal icosian order. The

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We’ve created a NotebookLM video explainer for: The Icosian Closure Object and a Geometric RH-Equivalent The paper is technical, so the video is a more accessible way into the result. Core idea: from the 600-cell / maximal icosian order, we construct a scale-axis Weil positivity form Q_A = A∞ − A_P whose universal positivity is equivalent to RH/GRH for one associated icosian cuspidal L-function. This is not a claimed proof of RH. It is a geometric construction of the RH-equivalent positivity wall: • real geometric object • exact arithmetic shadow • two arithmetic faces • Brandt/cuspidal prime side • one named open frontier: positivity For anyone who wants the big picture before reading the paper, start with the video.

Lee Smart @VFD_org

3 weeks ago

Published: The Icosian Closure Object and a Geometric Equivalent of the Riemann Hypothesis Website Link: vibrationalfielddynamics.org/articles/icosi… This paper gives a geometry-first construction of an RH-equivalent Weil positivity form, built from the 600-cell / maximal icosian order. The

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Published: The Icosian Closure Object and a Geometric Equivalent of the Riemann Hypothesis Website Link: vibrationalfielddynamics.org/articles/icosi… This paper gives a geometry-first construction of an RH-equivalent Weil positivity form, built from the 600-cell / maximal icosian order. The derivation is: Object → arithmetic shadow → two faces → witness form → RH-equivalent positivity frontier The core construction is a scale-axis quadratic form: Q_A = A∞ − A_P where A∞ is the archimedean gamma/conductor boundary term, and A_P is the prime residual built from geometric Brandt coefficients. By the Weil criterion: Q_A ≥ 0 for all admissible test functions ⇔ RH/GRH for the associated icosian cuspidal L-function. So this sits alongside the known RH-equivalent formulations: Weil positivity, Li coefficients, de Bruijn–Newman, Jensen hyperbolicity, and the Hilbert–Pólya / Connes operator programmes. The contribution is the geometric realisation: a real 600-cell / icosian object, an exact arithmetic shadow, and a concrete Weil-positivity form whose remaining frontier is precisely named. Classical ζ appears in the separate Eisenstein face as one factor of four; it is not isolated here. This is not a claimed proof of RH. It is a geometric construction of the RH-equivalent positivity wall for one icosian cuspidal L-function. Github: github.com/vfd-org/icosia…

We’ve also created a NotebookLM Video overview for the Icosian Closure Object bundle. The papers are technical, so this is intended as an easier entry point: a guided Video walkthrough of the object, the arithmetic shadow, the certified ζ-boundary, and the positivity wall. Important framing: This is not a proof of RH. It explains the result clearly: • the 600-cell / maximal icosian order is the concrete object • its exact shadow is ζ_K(s)ζ_K(s−1) • classical ζ appears as one factor of four, not isolated • the strong “object = ζ” bridge is rejected • the Brandt/cuspidal face supplies the prime side of a Weil witness • the remaining wall is universal positivity For anyone who wants the big picture before reading the PDFs, the podcast is the best place to start.

Lee Smart @VFD_org

3 weeks ago

Published: The Icosian Closure Object vibrationalfielddynamics.org/articles/icosi… This is not a proof of RH. It is a geometry-first object study built from the 600-cell / maximal icosian order. The result: • exact arithmetic shadow L(Θ,s) = ζ_K(s)ζ_K(s−1) • full degree-4 factorisation

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Reading order: The Positivity Wall RH landscape: where the object sits and where known mathematics stops. A Closure Geometry on the 600-Cell The object, exact ζ_K(s)ζ_K(s−1) shadow, and certified ζ-boundary. The Prime Side of a Weil Witness Cuspidal Brandt face; prime residual; gap localized. A Shared Geometric Object Firewall note: one object, multiple roles, no proven cosmology↔RH implication. Technical backbone: The Icosian Triad on V₆₀₀ v1.1.0.

Machine-readable claim ledger: NOT claimed: • no RH proof • no GRH proof • no cosmology → RH claim • no claim that the 600-cell object is ζ • no claim finite W≥0 tests prove positivity Claimed: • concrete 600-cell / maximal icosian order object • exact Eisenstein shadow ζ_K(s)ζ_K(s−1) • ζ is one factor among four, not isolated • certified negative for “object = ζ” • cuspidal Brandt face gives the prime side of a Weil witness • remaining open step = universal positivity Meaning: The work does not solve RH. It localizes the positivity wall in a reproducible geometry-first setting.

Published: The Icosian Closure Object vibrationalfielddynamics.org/articles/icosi… This is not a proof of RH. It is a geometry-first object study built from the 600-cell / maximal icosian order. The result: • exact arithmetic shadow L(Θ,s) = ζ_K(s)ζ_K(s−1) • full degree-4 factorisation ζ(s)L(s,χ₅)ζ(s−1)L(s−1,χ₅) • classical ζ appears as one factor of four • the stronger “object = ζ” bridge is structurally rejected • a separate cuspidal Brandt face supplies the parameter-free prime side of a Weil witness • the remaining wall is universal positivity: GRH for one cuspidal level-31 L-function, not classical RH So the claim is not “we crossed the wall.” The claim is: we built a concrete, reproducible geometric object that reaches the positivity wall cleanly, names exactly where it stops, and gives others something precise to test. A real object. A certified boundary. A falsifiable programme.

Yes, that is very close to how we frame it. The geometry defines the closure surface, but persistence requires a threshold condition: internal restoration must exceed environmental decoherence/disruption. In VFD terms, closure is not enough by itself. A structure becomes “alive” or recursively self-maintaining only when its internal corrective dynamics can preserve phase coherence across perturbation. So the bridge is: geometry defines where closure can occur; persistence defines when closure can remain self-sustaining. That threshold is exactly where recursive encounter becomes stable rather than transient.

Yes, that is very close to how we are framing it. In our language, the ν600 is not just a graph sitting in ordinary 3D space; it is a closure geometry on a hyperspherical / 3-sphere boundary. So “maps onto a 3-sphere” is basically the conventional topology language for the same bridge we are formalising: ν600 as a finite closure structure whose boundary-readable projections give the lower-dimensional physics. HoTT may be useful here too, especially for path/equality/self-reference language. I’d see it as complementary formal language rather than replacing the geometric closure construction. x.com/VFD_org/status…

tiv🕸🛡️ @reallyill

a month ago

@VFD_org Your v600 could map onto a 3 sphere then you’d potentially have your bridge that’s partially specified

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The path to a theory of everything may not be found by adding one more layer on top of the current stack. It may require returning underneath it: to geometry, reference frame, measurement, and the observer as part of the physical structure itself. QM and GR were extraordinary breakthroughs, but they were never final maps. The danger is not that they are “wrong”, it is becoming constrained by frameworks we already know are incomplete. At some point physics has to follow the mathematics and the measurements deeper, even if the next language does not look like the old one.

Lex Fridman @lexfridman

a month ago

Here's my conversation with Don Lincoln about some of the biggest open questions in physics, including dark energy, dark matter, the matter-antimatter imbalance, quantum vacuum, quantum foam, and the quest to unify the laws of physics. Don is a particle physicist at Fermilab who

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There is a real intuition here: triads matter because binary symmetry breaking alone is not enough. The deeper question is not whether (π−3)/3 is a magic scalar, but whether the break produces a bounded closure residual. In VFD terms, the triad becomes physical only when symmetry → residual → closure forms a repeatable constraint structure. That is where geometry stops being numerology and becomes mechanism.

A fair objection, but I think it slightly misreads what is being claimed. The point is not that a beautiful mathematical object should be promoted into ontology simply because it is elegant, recurrent, or suggestive across domains. The stronger claim is that the same closure structure keeps reappearing where independent constraints have to be satisfied: quantum mechanics, observer-compatible measurement, particle masses, GR-like ordering, cosmological structure, and now prime structure. So the bridge is not: beautiful math -> reality It is closer to: shared constraint -> repeated structure -> observable consequence I’m also not claiming that “the universe is mathematics” in the crude sense. What I’m suggesting is that reality appears to have a lawful, language-like substrate, and mathematics is the translation layer by which that substrate becomes intelligible. In that sense, we are beginning to see three levels: a dictionary: recurring finite objects, invariants, spectra, closure irreducibles a grammar: closure, admissibility, projection, recurrence, gauge structure, observer-compatible rules an interpretation layer: where those same structures become readable as physics, cosmology, and arithmetic So the 600-cell, closure operators, spectral recurrences, and prime structure are not being treated as “pretty objects” alone. They are candidate parts of a deeper substrate-language. That does not mean the case is closed. It means the real question is whether this structure is being imposed after the fact, or whether it keeps appearing because it belongs to the lawful grammar of what can stably exist and be observed. That is the bridge we are working to make explicit. And there is more coming on this soon, enough now exists to justify both a dedicated paper and a full article on the dictionary / grammar / interpretation view of the framework.

TCGS-SEQUENTION @TCGS_SEQUENTION

a month ago

@VFD_org My discomfort with this framework is not with its mathematics, but with the inferential leap by which a finite substrate and a recurring operator are promoted into ontology without first deriving their necessity, completing the required bridges, or treating time as a gauge rather

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That’s clearer, thank you. I agree HoTT could be useful as a syntactic/formal layer for proving equivalence, path identity and boundary-dependent projection structure. My current route is geometry-first: ν600 closure modes define the admissible fibrations, and the 3+1 observable metric emerges as the boundary-readable sector of the hyperspherical/S³ closure structure. So I’d frame HoTT as a complementary proof language for the path/equality layer, while ν600 remains the generative substrate.

Back in February I answered this cautiously: I wouldn’t claim direct evidence for literal “triplets-of-triplets” as discrete spacetime atoms. Since then we have worked the manifold structure much further, and I’d now sharpen the answer: The recurring object is a closure triad. Not three things sitting in space, but three coupled roles required for stable recoverable organisation: boundary / constraint interior state / evolution projection / readout When that triad is recursively embedded, you get triplets of triplets as a manifold structure: nested closure, not isolated units. This shows up across scales: renormalisation, error correction, biological control, observer systems, and potentially spacetime geometry itself. So the evidence I’d point to is not yet “we found spacetime triplets.” It is that recoverable systems repeatedly require triadic closure, and spacetime may inherit the same minimal organisation principle. x.com/VFD_org/status…

Stuart Hameroff @StuartHameroff

5 months ago

You may be right. You’re a ‘ Smart guy’. Any thoughts or evidence for triplets of triplets in spacetime geometry?

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I appreciate the critique and the papers shared. I think there is useful methodological pressure here: avoid reification, separate map from territory, state bridge debt clearly, and do not promote a formal object into ontology without selection and falsifiability. That is a fair standard, and I accept it. Where I think we differ is evidential class. Much of the TCGS material appears to operate as a cartographic or interpretive framework: it reclassifies known physics and observed structures into a source/shadow, time-as-gauge language. That may be valuable, but it is not the same kind of work as deriving finite structures, building exact computational certificates, running simulations, fixing kernels, testing data-facing bridges, and exposing a programme to reproducible failure. So I do not think this can be resolved properly in a reply thread. The correct next step from my side is an evidence ledger: what is exact, what is derived, what is data-facing, what is conjectural, where parameters enter, and what would falsify each bridge. That will let the work be judged technically rather than rhetorically. For now, I appreciate the challenge. It has helped clarify one of the next papers.

This is useful, but I think the burden has to be applied symmetrically. The paper does not simply critique VFD from neutral ground. It demotes VFD from inside TCGS–SEQUENTION, where Counterspace, source-shadow projection, ECL, and time-as-gauge are already treated as the deeper ontology. That is a competing ontology, not a neutral tribunal. So yes: VFD must show where V600/closure is selected rather than imposed. Agreed. But the same standard applies to TCGS. Where is Counterspace independently selected? Where is the ECL derived rather than named? Where is time-as-gauge forced rather than asserted? Where are the computational certificates, empirical landings, alternative controls, and falsification conditions that would demote TCGS if they fail? That is the symmetry I think the rebuttal misses. VFD is incomplete as final ontology. I have no problem saying that. But it has already exposed itself to failure through exact finite mathematics, reproducible code, simulations, fixed-kernel tests, data-facing analyses, particle/cosmology/observer/prime bridges, and explicit open gaps. That is not mere pattern narrative. If the critique is “do not promote a map into the territory,” then it must also not promote Counterspace into the territory without meeting the same evidential burden. The next fair comparison is not rhetoric vs rhetoric. It is ledger vs ledger: assumptions, derivations, fixed inputs, free parameters, reproducibility artifacts, empirical contact, and falsification conditions.

I agree that the burden is high. It should be. But the burden is not one-sided. The programme has never claimed “beautiful object therefore reality,” nor has it hidden behind vague metaphor. The work has been built through papers, derivations, simulations, code, exact computational certificates, data-facing analyses, and reproducible experiment bundles. It has also been deliberately framed as falsifiable. That matters. If the claim were merely “V600 language recurs, therefore ontology,” your criticism would be sufficient. But that is not the full body of work. The framework has produced constrained bridges across quantum structure, observer-compatible measurement, particle spectra, GR-like ordering, cosmological terms, prime structure, and related closure phenomena, without simply adding free parameters for each domain. That does not mean the ontology claim is complete. It means the programme has already crossed the threshold from “pattern narrative” into a technical research programme with specific points of attack. So yes: I accept the burden to make the independent-forcing argument clearer. But the reciprocal burden is also real. A serious refutation now has to show where the derivations fail, where the constraint is merely imported, where parameter freedom is being smuggled in, or where the computational/data-facing results do not support the stated bridge. A global judgement based on one branch, one thread, a surface skim, or an AI-compressed summary is not enough. The work is open precisely so it can be tested, corrected, falsified, or extended. That is the standard I am holding myself to, and the standard criticism should meet as well.