The paper has three parts. In the first part ExtOSR, an extended version of Ontic Structural Realism, will be introduced. ExtOSR considers structural properties as ontological primitives, where structural properties are understood as comprising both relational and structurally derived intrinsic properties or structure invariants. It is argued that ExtOSR is best suited to accommodate gauge symmetry invariants and zero value properties. In the second part, ExtOSR will be given a Humean shape by considering structures as categorical and (...) global. It will be laid out how such structures serve to reconstruct non-essential structural kinds and laws. In the third part Humean structural realism will be defended against the threat of quidditism. (shrink)

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. While it is incompatible with conventional foundations, it is a powerful addition to homotopy (...) type theory. It also gives the new system of foundations a distinctly structural character. (shrink)

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the univalence axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. This powerful addition to homotopy type theory gives the new system of foundations a (...) distinctly structural character. (shrink)

We introduce the Invariance Maintenance Condition (IMC), a formal criterion identifying the class of systems that actively maintain structural invariants under perturbation at measurable cost. The IMC is derived from constraint geometry and is substrate-agnostic: it applies wherever a system satisfies four conditions — endogenous recursion, coupled and attributable maintenance cost, a pre-specified transformation group, and an independently falsifiable invariant. We characterize five failure modes that delineate the framework's boundary and distinguish inapplicability from predictive failure. The IMC generates (...) cross-domain predictions — including intervention transfer efficacy, precursor variance signatures before structural collapse, and hysteresis asymmetry in recovery trajectories — that are not derivable from within any single discipline. We identify three categories of disciplines relative to the IMC: those whose own formalisms already entail the conditions, those partially satisfying them, and those structurally incompatible with them. The framework is offered as a falsifiable research tool, not a unifying theory. (shrink)

Eino Kaila's thought occupies a curious position within the logical empiricist movement. Along with Hans Reichenbach, Herbert Feigl, and the early Moritz Schlick, Kaila advocates a realist approach towards science and the project of a “scientific world conception”. This realist approach was chiefly directed at both Kantianism and Poincaréan conventionalism. The case in point was the theory of measurement. According to Kaila, the foundations of physical reality are characterized by the existence of invariant systems of relations, which he called structures. (...) In a certain sense, these invariant structures, he maintained, are constituted in the act of measuring. By “constitution”, however, Kaila meant neither the dependency of the objects of measurement on a priori concepts (or Kantian categories) nor their being effected by conventional stipulations in a Poincaréan sense. He held that invariant structures are, quite literally, real: they exist prior to and independently of our theoretical capacity. By executing measurements, invariant structures are detected and objectively determinable by laws of nature. (shrink)

This paper proposes a theory of representation centered on invariance as the constitutive condition of objectivity. Any objective representational system functions as a sieve: it stabilizes identity by enforcing invariance over a structured possibility space. I demonstrate that binary relational representation under global invariance forces exactly four exhaustive stability profiles, determined by whether each argument position behaves as instance-like or role-like under substitution. These four profiles appear across representational systems: as fundamental verbs in natural language (IS, HAS, (...) MEANS, CAUSES), as arithmetic operations in mathematics (addition, multiplication, subtraction, division), and as interaction roles in physics. This convergence is not analogical but necessary: the four-fold emerges from the constraint structure of objective binary relational representation itself. (shrink)

Excerpts from Robert Nozick's "Invariances" Necessary truths are invariant across all possible worlds, contingent ones across only some.

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property (...) is first order. (shrink)

This study proposes the formalization of a structural model entitled Narrative Architecture of Textual Invariance (ANIT), characterized by the complete reorganization of a literary work without any alteration to its textual materiality. The study demonstrates that modifying the structural order of narrative segments may generate distinct interpretive experiences while fully preserving each original textual unit. The central hypothesis maintains that textual invariance is independent of the formal sequence applied, making it possible to alter structural architecture (...) without compromising the lexical, syntactic, or punctuation integrity of the work. For empirical verification, two complete versions of the same previously published short story are presented, organized in distinct sequences yet composed of exactly the same textual units. The formal analysis includes descriptive logical modeling, objective criteria of verifiability, and full demonstration in the annexes. It is concluded that ANIT constitutes a verifiable structural model in which order functions as an ontological operator capable of producing distinct narrative realities without any rewriting, suppression, insertion, or modification of content. (shrink)

In the social sciences, within the explanatory paradigm of structural individualism, a theory of action—like rational choice theory—models how individuals behave and interact at the micro level in order to explain macro-observations as the aggregation of these individuals’ actions. A central epistemological issue is that such theoretical models are stuck in a dilemma between falsity of their basic assumptions and triviality of their explanation. On the one hand, models which have had great empirical success often rest on unrealistic or (...) even knowingly false assumptions; on the other hand, more complex models, with additional more realistic hypotheses, can (trivially) adapt to a wide range of situations and thus lose their explanatory power. My purpose here is epistemological and consists in wondering to what extent demanding realistic assumptions in such cases is a relevant criterion with respect to the acceptance of a given explanatory model. Via analogical reasoning with physics, I argue that this criterion seems too strong, and it is also irrelevant. General physical principles are not just idealised or unrealistic. They can also be formulated in many different yet equivalent ways that do not imply the same fundamental unobservable entities or phenomena. However, the classification of phenomena that such principles allow us to highlight does not depend, at the end, on any particular formulation of these basic assumptions. This suggests that some hypotheses in theoretical models are not genuine empirical statements that could be independently tested but only substrates of modelling embodying a classification principle. Thus, I develop a structural invariance criterion that I then apply to rational choice models in the social sciences. I argue that this criterion allows us to escape from the epistemological dilemma without condemning formal approaches like rational choice theory for their lack of realisticness or for being stuck to a merely anti-realist viewpoint. (shrink)

The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization that there are infinitely many gravitational energy-momenta. Initially use is made of a flat background metric (or rather, all of them) or connection, because the desired gauge invariance properties are obvious. Partial gauge-fixing then yields an appropriate covariant quantity without any background metric or connection; one version is the collection of (...) pseudotensors of a given type, such as the Einstein pseudotensor, in _every_ coordinate system. This solution to the gauge covariance problem is easily adapted to any pseudotensorial expression (Landau-Lifshitz, Goldberg, Papapetrou or the like) or to any tensorial expression built with a background metric or connection. Thus the specific functional form can be chosen on technical grounds such as relating to Noether's theorem and yielding expected values of conserved quantities in certain contexts and then rendered covariant using the procedure described here. The application to angular momentum localization is straightforward. Traditional objections to pseudotensors are based largely on the false assumption that there is only one gravitational energy rather than infinitely many. (shrink)

This paper derives the spectral coupling invariant ξ² ≡ (μα)² in closed form from the axiom system {A1 non-commutativity, A2 Π_d-saturation, A4 redundancy exclusion} of Operatiology, completing the Level 2 Class I certification mandated by the companion paper (DOI: 10.5281/zenodo.20577184). The derivation proceeds through the field Q(D₀), where D₀=(δ−1)δγ satisfies 16D₀²−24D₀+3=0, making Q(D₀) two-dimensional over Q. Since μ and α⁻¹ are each elements of L(M₃(ℂ)) with coefficients in Q(D₀), their ratio ξ=μ/α⁻¹ belongs to this field, and ξ²=(ξ_a+ξ_b·D₀)² reduces exactly to (...) A+B·D₀ — the unique mandatory representation forced by the two-dimensionality of Q(D₀), itself the algebraic expression of Axiom A4. No other value of ξ² is algebraically possible. The result is ξ² = A + B·D₀ = 179.534632529506…, with A = −1202.60331893592…, B = 10042.5954528296…, zero free parameters, and no reference to individually derived values of μ or α⁻¹. Agreement with benchmark (μ_CODATA2022/α⁻¹_Morel2020)² at +1.085σ. The Morel–Parker 5.5σ discrepancy is identified as structural evidence that α is a Tier-3 projection of ξ², not an independent fundamental constant. The complete derivation runs from the spectrum {1,1,−2} alone. ◆◆◆ [PYTHON VERIFICATION CODE — note: × denotes * and ^ denotes **] ◆◆◆ from mpmath import mp, mpf, pi, sqrt, exp, euler import math mp.dps = 50 h = [mpf(1), mpf(1), mpf(-2)] dim = 3 e1 = sum(h) e2 = h[0]×h[1] + h[0]×h[2] + h[1]×h[2] e3 = h[0]×h[1]×h[2] delta = sqrt(mpf(3)/2) gamma = mpf(1)/(dim-1) D0 = (delta-1)×delta×gamma gamma_E = euler Phi1 = mpf(2); Phi3 = mpf(13); Phi6 = mpf(7) ch2 = (e1^2 - 2×e2)/2 ch3 = (e1^3 - 3×e1×e2 + 3×e3)/6 N2 = mpf(10)/4 N3 = mpf(7)/2 C2 = sqrt(ch2/N2)×gamma L6 = abs(ch3)/N3 L0 = 6×pi^5 L2 = Phi3/Phi6 L4 = -delta^2/gamma × exp(-gamma_E) L5 = -Phi1/Phi3 mu_a = L0 + L2×(-3)/16 + L4×(-99)/256 + L5×(-135)/256 mu_b = L2×3/2 + L4×45/16 + L5×981/256 ainv_a = 48×pi + L6×(-2943)/4096 ainv_b = -32×pi + C2 + L6×2673/512 N = ainv_a^2 + ainv_a×ainv_b×mpf(3)/2 + ainv_b^2×mpf(3)/16 inv_a = (ainv_a + ainv_b×mpf(3)/2) / N inv_b = -ainv_b / N xi_a = mu_a×inv_a - 3×mu_b×inv_b/16 xi_b = mu_a×inv_b + mu_b×inv_a + 3×mu_b×inv_b/2 A = xi_a^2 - 3×xi_b^2/16 B = 2×xi_a×xi_b + 3×xi_b^2/2 print("A =", A) print("B =", B) print("xi^2 =", A + B×D0) ◆◆◆ [END] ◆◆◆ Published on June 7, 2026 DOI 10.5281/zenodo.20581357. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found (...) already in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

The paper outlines a novel version of mathematical structuralism related to invariants. The main objective here is twofold: first, to present a formal theory of structures based on the structuralist methodology underlying work with invariants. Second, to show that the resulting framework allows one to model several typical operations in modern mathematical practice: the comparison of invariants in terms of their distinctive power, the bundling of incomparable invariants to increase their collective strength, as well as a heuristic principle related to (...) the search for new invariants. (shrink)

A recent article of Chernikov, Hrushovski, Kruckman, Krupinski, Moconja, Pillay, and Ramsey finds the first examples of simple structures with formulas which do not fork over the empty set but are universally measure zero. In this article we give the first known simple $\omega $ -categorical counterexamples. These happen to be various $\omega $ -categorical Hrushovski constructions. Using a probabilistic independence theorem from Jahel and Tsankov, we show how simple $\omega $ -categorical structures where a formula forks over $\emptyset $ (...) if and only if it is universally measure zero must satisfy a stronger version of the independence theorem. (shrink)

The paper discusses the invariance view of reality: a view inspired by the relativity and quantum theory. It is an attempt to show that both versions of Structural Realism (epistemological and ontological) are already embedded in the invariance view but in each case the invariance view introduces important modifications. From the invariance view we naturally arrive at a consideration of symmetries and structures. It is often claimed that there is a strong connection between invariance (...) and reality, established by symmetries. The invariance view seems to render frame-invariant properties real, while frame-specific properties are illusory. But on a perspectival, yet observer-free view of frame-specific realities they too must be regarded as real although supervenient on frame-invariant realities. Invariance and perspectivalism are thus two faces of symmetries. Symmetries also elucidate structures. Because of this recognition, the invariance view is more comprehensive than Structural Realism. Referring to broken symmetries and coherence considerations, the paper concludes that at least some symmetries are ontological, not just epistemological constraints. (shrink)

With increasing attention on the role of parenting stress on family functioning and children’s development, one area that has been neglected is how such relations differ across cultures. Although sometimes viewed as homogeneous, Asian countries often have markedly different belief systems. Cross-cultural studies require instruments that have been validated in different socio-cultural contexts. The widely used parenting stress index-short form has been used in several locations. However, results regarding its factorial structure have been mixed. Furthermore, there are only a few (...) cross-cultural comparison studies. This study examined the factorial structure of an abridged version of the PSI-SF with data from Hong Kong and Thailand. The results from confirmatory factor analyses indicated that, in both cultures, a three-factorial structure provides the best model fit. Furthermore, we found evidence for partial metric invariance, suggesting that the test scores can be compared directly. Tests for convergent and discriminant validity revealed that the three factors were correlated with parent general distress, authoritative, authoritarian, and permissive parenting behaviors, in both cultures. These findings suggest that the abridged PSI-SF can provide a meaningful comparison of parenting stress between Hong Kong and Thailand. (shrink)

This study aimed to investigate the factor structure and measurement invariance of the Brief Symptom Inventory-18 among Chinese adults. A sample comprising 1,839 adults from four cities in Shaanxi province completed the BSI-18 and background information. The best-fitting factor structure model of the BSI-18 was verified by confirmatory factor analyses, and multigroup confirmatory factor analyses were performed to test the measurement invariance. The results indicated that the three-factor bi-factor model fitted the current data best. The configural, metric, scalar, (...) and strict invariance models all had acceptable model fit indexes across genders, and the configural, metric, scalar invariance models with different living areas and educational levels were all acceptable. Overall, the three-factor bi-factor model of the BSI-18 shows a good fit for use with Chinese adults, making it a viable tool for effectively measuring the mental health of Chinese adults. (shrink)

This paper establishes the structural foundation of the spectral coupling constant ξ = μα, the product of the proton-to-electron mass ratio μ and the fine-structure constant α, within the Operatiology and Cognitional Mechanics framework. A two-stage proof is presented. The first stage demonstrates that μ and α share a common algebraic origin in the matrix algebra M₃(ℂ): the product ξ = μα forces the cancellation of the common Casimir invariant Tr(H²) = 6 appearing in the leading terms of both (...) independent derivations, making algebraically manifest the shared Cartan generator H = diag(1,1,-2) underlying both constants. This addresses a question that the Standard Model of particle physics has no framework to pose. The second stage identifies the common origin algebraically: Axiom A1 of Operatiology forces the su(3)-type minimal non-commutative closure, whose tracelessness implies p₁ = Tr(Hλ) = 0. This constraint forces the invariant algebra to satisfy Inv(O) ~ R[λ²], making λ² the unique minimal coordinate of the algebra's self-description. Since ξ is proportional to λ, ξ lies outside the invariant algebra; since ξ² is proportional to λ², ξ² is the minimal generator of the invariant algebra. The asymmetry between ξ and ξ² is therefore a necessary consequence of A1, not an external imposition. Conditional on prior spectral completeness results, ξ² functions as the generator of all physical constants within the framework. The paper is the first of a two-part work; the companion paper derives ξ² independently with zero free parameters. Published on June 7, 2026 DOI: 10.5281/zenodo.20577184. (shrink)

This study addresses the problem of Arrovian preference aggregation. Social rationality plays a crucial role in the standard Arrovian framework. However, no assumptions on social rationality are imposed here. Social preferences are allowed to be any binary relation (possibly incomplete and intransitive). We introduce the axiom of hybrid invariance, which requires that if social preferences under two preference profiles make the same judgment, then a social preference under a “hybrid” of the two profiles must extend the original judgment in (...) a certain way. Then, we characterize the structure of decisive coalitions under hybrid invariance. (shrink)

We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of $\operatorname{Aut}(M)$ . This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ 0 -categorical structures without the independence property including those which are stable.

This paper deals with some results of various simulations with Forrester's World Dynamics. These simulations concern the temporal and quantitative fixing of limits in relation to initial values and deal with the effects of specific table functions in this model. In addition, they also treat the behavior of the curves in approaching the limits.

A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of bel...

We consider successor-invariant first-order logic (FO + succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (.

This paper establishes two related structural results within the Cognitional Mechanics (CM) framework. Part I proves that the spectral coupling constant ξ² = (μα)² is a complete statistic for the observational content of M₃(ℂ). The state space S is defined generatively as the union of O-orbits of the one-parameter family H_λ = diag(λ, λ, −2λ), where O is the operation algebra derived from axioms A1–A4. Normality of all elements of S holds by construction, eliminating Jordan structure entirely. The residual (...) degree of freedom is λ ∈ ℝ⁺, uniquely recoverable from any state s via λ(s) = √(Tr(s²)/6). The map f(s) = Tr(s²)·(αμ₀)² satisfies f ∝ λ² and induces a bijection S/∼_f ≅ Im(f) of dimension exactly 1: all observational distinctions within M₃(ℂ) collapse to a single scalar. Part II classifies the 19 Standard Model parameters as eigenvalue-type (12), orbit-invariant (4), and basis-mixing (3) projections of Spec(D), and bounds the independent degrees of freedom to at most 11. The connecting corollary establishes that every Standard Model projection map πᵢ is a rational function of ξ² alone, so that the Standard Model parameter structure is a representation layer of the invariant algebra, not an independent ontological structure. Anomaly cancellation and asymptotic freedom are shown to be algebraic necessities of M₃(ℂ) at n = 3. A falsifiable prediction is derived: the ratio αₛ/α_em at the Planck scale equals Φ₃/Φ₆ = 13/7 ≈ 1.857, deviating from the Standard Model perturbative result by approximately 0.24. No free parameters are introduced at any stage. All logical gaps are closed within the CM axiom system. -/- Published on April 26, 2026 doi: 10.5281/zenodo.19784769 . (shrink)

We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms.

Being building block of data sciences, link prediction plays a vital role in revealing the hidden mechanisms that lead the networking dynamics. Since many techniques depending in vertex similarity and edge features were put forward to rule out many well-known link prediction challenges, many problems are still there just because of unique formulation characteristics of sparse networks. In this study, we applied some graph transformations and several inequalities to determine the greatest value of first and second Zagreb invariant, S K (...) and S K 1 invariants, for acyclic connected structures of given order, diameter, and pendant vertices. Also, we determined the corresponding extremal acyclic connected structures for these topological indices and provide an ordering giving a sequence of acyclic connected structures having these indices from greatest in decreasing order. (shrink)

Introduction: The Binge Eating Scale (BES) is a widely-used self-report questionnaire to identify compulsive eaters. However, research on the dimensions and psychometric properties of the BES is limited. Objective: The aim of this study was to examine the properties of the Spanish version of the BES. Method: Confirmatory Factor Analyses (CFAs) were carried out to verify the BES factor structure in a sample of Spanish college students (N = 428, 75.7% women; age range = 18–30). An invariance measurement routine (...) was carried out across sexes, the latent means were compared, and estimates of reliability and convergent and discriminant validity were presented. Results: A one-factor model fit the data best and was also equivalent between sexes. The scalar invariance model showed statistically significant differences across sexes, with a higher prevalence in women. Regarding reliability, the results were excellent. Finally, high statistically significant correlations were obtained with other measures of binge eating (BE), food addiction, impulsivity, binge drinking, and body mass index (BMI). Conclusions: The Spanish 16-item BES is a valid and reliable scale to evaluate BE in the youth population. (shrink)

Let M be a big o-minimal structure and G a type-definable group in Mⁿ. We show that G is a type-definable subset of a definable manifold in Mⁿ that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the wider class of so-called invariant (...) groups: each invariant group G in Mⁿ has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as Mⁿ. (shrink)

Students’ perceptions of instructional quality are among the most important criteria for evaluating teaching effectiveness. The present study evaluates different latent variable modeling approaches (confirmatory factor analysis, exploratory structural equation modeling, and bifactor modeling), which are used to describe these individual perceptions with respect to their factor structure, measurement invariance, and the relations to selected educational outcomes (achievement, self-concept, and motivation in mathematics). On the basis of the Programme for International Student Assessment (PISA) 2012 large-scale data sets of (...) Australia, Canada, and the USA (N = 26,746 students), we find support for the distinction between three factors of individual students’ perceptions and full measurement invariance across countries for all modeling approaches. In this regard, bifactor exploratory structural equation modeling outperformed alternative approaches with respect to model fit. Our findings reveal significant relations to the educational outcomes. This study synthesizes different modeling approaches of individual students’ perceptions of instructional quality and provides insights into the nature of these perceptions from an individual differences perspective. Implications for the measurement and modeling of individually perceived instructional quality are discussed. (shrink)

Symmetry carries the connotation of beautyBeauty. Mathematized, it is a deep and reoccurring theme in the Book of Nature. Many unexpected properties of reality are uncovered by it. A key concept related to symmetry is invarianceInvariance, the simple property of a system to remaining unchanged under manipulations. Invariance has the power to unlock fundamental knowledge.Level of mathematical formality: high (however, the mathematicallyMathematical involved parts are encapsulated and demarcated by the tags, hence easily bypassed).

Informational Renormalization of the Invariant Speed: A Causal–Symmetric Framework for Dynamical Light Propagation -/- In a causal-symmetric informational framework, where both time and space emerge from an underlying dynamics of information, the usual status of the speed of light as a primitive constant is reconsidered. The paper extends a previously developed “kappa framework”, in which an informational conductivity between initial and final boundary conditions generates microscopic irreversibility, emergent time and spacetime geometry, to the electromagnetic sector. Instead of treating the speed (...) of light as a fixed input, the theory introduces an informational renormalization factor that depends on scalar informational quantities such as the deviation from a preferred reference state, the cosmological expansion, and informational potentials. In this setting, the invariant speed is defined operationally as the signal speed of electromagnetic disturbances measured by rods and clocks whose behaviour is themselves governed by the same informational law. The numerically measured “invariant speed” thus becomes an emergent quantity determined by the informational state of the universe, rather than a built-in constant. -/- In its minimal version, the modified Maxwell dynamics remain covariant and gauge invariant, preserve well-behaved wave propagation, and share the same causal structure as the unmodified theory; informational renormalization changes the calibration of spacetime units but not the underlying light cones. The paper argues that this effect cannot be removed by local redefinitions of fields without simultaneously altering the matter sector and the informational action, so the modification is physically meaningful. In homogeneous cosmology, the effective invariant speed reduces to a function of the scale-dependent informational conductivity, linking its numerical value directly to the same law that also governs time flow and curvature. As an optional extension, the same informational structure allows an effective metric with a wider “informational” light cone and a superluminal sector, while a global time function defined by kappa prevents causal paradoxes. The result is a unified informational picture in which the invariant speed emerges from the global informational state of the universe. (shrink)

This commentary focuses on the nature of combinatorial properties for speech and the locus equation. The presence of some overlap in locus equation space suggests that this higher order property may not be strictly invariant and may require other cues or properties for the perception of place of articulation. Moreover, combinatorial analysis in two-dimensional space and the resultant linearity appear to have a “special” status in the development of this theoretical framework. However, place of articulation is only one of many (...) phonetic dimensions in language. It is suggested that a multidimensional space including patterns derived in the frequency, amplitude, and time domains will be needed to characterize the phonetic categories of speech, and that although the derived properties ultimately may not meet the conditions of linearity, they will reflect a higher order acoustic invariance. (shrink)