560 field photographs of five durian disease categories, collected from commercial orchards across Peninsular Malaysia between July 2025 and June 2026, with per-image capture-session identifiers. The session identifiers are the point of this release. The 560 images come from only 73 independent capture sessions. A symptomatic leaf is normally photographed several times in a few seconds from slightly different angles, and those frames are not independent observations. Split this data at image level and near-identical views of one specimen land on both sides of the train/test boundary. In our own initial partition, 79.6% of images fell in sessions that straddled a split. Re-running the identical experiment with sessions kept whole lowered macro F1 by 12.2 points on average across nine architectures, positive in all nine and as much as 18.4 in one. Group your partitions by the session column in sessions.csv. Contents. images_fullres/ — the 560 originals as captured, in class folders. images_512/ — the same images at 512 px maximum edge, which is what the models were trained and evaluated on. sessions.csv — class, filename and session for every image. splits/session_level/ — the partition reported in the paper (446/58/56). splits/image_level/ — the control partition used to measure leakage (446/54/60). Evaluate at the resolution you train at. Every figure in the paper is computed on images_512. Running the same checkpoint over images_fullres through an identical Resize(256) and CenterCrop(224) pipeline gives 77.6% instead of 72.0% on the held-out set, because the two resampling paths to 224 px are not the same. The originals are included so the collection is complete, not because they are the working copy. Classes. Algal Leaf Spot (Cephaleuros virescens), Leaf Rot (Colletotrichum spp.), Phomopsis Fruit and Stem Blight (Phomopsis durionis), Pink Disease (Erythricium salmonicolor), Root Disease (Phytophthora spp.). Pink_disease is represented by three capture sessions in the entire collection; its per-class metrics are not interpretable at that support, and it is what bounds grouped cross-validation at k = 3. Annotation. Labels were assigned by the author under the guidance of growers and extension staff with field experience in these orchards. There was no second independent rater, so no inter-rater agreement statistic is available. Consent. Images were collected on site with the orchard owner's permission, or contributed by growers who were told at the time that the images would be released publicly for research. No images contain identifiable persons. A small number show a hand holding a leaf; that framing is part of the field condition being modelled. No location is published at finer resolution than district.
Lin Ding Shan· Zenodo (CERN European Organi...· 0 citations
Computer vision---making machines interpret images---traveled from blocks-world edge finders to deep convolutional networks matching human benchmarks, and its history is AI's most complete case of representation learning's triumph. This article presents a narrative review of the field's canonical line: Roberts's 1963 machine perception of solids, Marr's 1982 computational vision, Viola and Jones's 2001 face detection, Lowe's 2004 SIFT features, Dalal and Triggs's 2005 HOG descriptors, Felzenszwalb and colleagues' 2010 deformable part models, Szeliski's 2010 synthesis, Girshick's 2015 Fast R-CNN, Long, Shelhamer, and Darrell's 2015 fully convolutional nets, Simonyan and Zisserman's 2015 VGG, He and colleagues' 2016 ResNet, and Redmon and colleagues' 2016 YOLO. The synthesis is organized around three themes: representation, in which hand-engineered features gave way to learned hierarchies; architecture, in which convolution, regions, and residual depth solved recognition's geometry; and tasks, in which classification widened into detection, segmentation, and real-time video. It is concluded that vision's deep learning settlement reorganized the field around data and compute---and that its open problems, robustness and embodiment, define the current frontier.
Zen Revista, 10 IA· Zenodo (CERN European Organi...· 0 citations
Abstract: The growing combination of geospatial technologies, Artificial Intelligence (AI), and edge computing is changing the field of spatial analysis, environmental monitoring, and infrastructural design. This article gives a thorough summary of the way modern computer science approaches—namely machine learning (ML), deep learning (DL), container orchestration using Kubernetes, and ultra-reliable low-latency communications (URLLC)—are being incorporated into geospatial geoinformatics. Instead of carrying out processing in centralised cloud systems, geospatial systems can now handle high-resolution Earth Observation (EO) data, LiDAR point clouds, and Internet of Things (IoT) spatial streams in near real-time by moving the processing tasks to the network edge. We look systematically at the basic methods involved in spatial intelligence, containerized orchestration, multi-sensor data fusion, and edge deployment architectures. Moreover, we combine the more recent literature from a range of disciplines to show the way in which spatial technologies directly contribute to the UN Sustainable Development Goals (SDGs), help reduce regional environmental degradation, and improve university-based entrepreneurial ecosystems. Lastly, the main research gaps—such as the problem of bandwidth limitations in remote areas, model drift in changing environments, and governance constraints—are identified, together with specific future directions for next-generation spatial computing.
Dr. Ambrose Ndubuisi Ekebuike*, Abdulaziz Ahmad, Yusuf Aliyu Adamu· Zenodo (CERN European Organi...· 0 citations
Archived source release of BioMCP-TS v0.8.0 (npm package biomcp): 41 core tools across 15 registration modules federating 33 verified upstream data hosts, plus optional plugin sets for read-only SQL analytics and in-process WebAssembly compute (Bioconductor DESeq2/edgeR/limma under webR; samtools/bedtools/bcftools under biowasm). Zero-config stdio MCP server for Node >= 22.13, single runtime dependency. Repository: https://github.com/yeyuan98/biomcp-ts (live development continues there; this record archives the exact tag evaluated in the Technical Report).
Ye Yuan· Zenodo (CERN European Organi...· 0 citations
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This technical data package establishes the engineering blueprints, economic integration thesis, and provisional utility patent specifications for the Lawrence Aero Brick Solid-State Transformer (LAB-SST). The LAB-SST is a zero-silicon, plasma-state power transformation architecture that replaces physical Silicon Carbide (SiC) semiconductor lattices and copper electromagnetic windings with a dynamically generated atmospheric Universal Dielectric Barrier Discharge (U-DBD) plasma gateway. By driving a non-linear Townsend avalanche at an electric field threshold of E ≥ 56 kV/mm, the system acts as an asymmetric electrical valve, rectifying alternating current (AC) grid power directly into ±400V or 800V High-Voltage Direct Current (HVDC) for hyperscale computing and AI infrastructure. To eliminate the severe thermal degradation and parasitic cooling loads associated with multi-megawatt solid-state switching, the LAB-SST utilizes Electrohydrodynamic (EHD) momentum transfer to generate a solid-state convective vacuum (Δm = 0). System stability is maintained by Phase-Shifted Agentic Swarm (PSAS) logic running on edge NPU hardware, which truncates pulse widths (< 10 ns) whenever space-charge growth approaches Meek's criterion (α·d ≥ 14) to prevent thermal arc transitions. Economic Integration: Across a 100 MW hyperscale deployment, the LAB-SST obsoletes a USD 22,000,000 SiC SST installation with a USD 10,000,000 plasma-state alternative, while eliminating 10 MW in parasitic cooling load to retain USD 8,760,000 in annual cooling OpEx. This repository includes the complete USD 67,500 Bill of Materials (BOM) required for TRL-4 benchtop prototype validation. Note: Accompanying system schematics are conceptual AI-assisted architectural renderings; refer to the technical specifications and patent claims for precise operational mathematics and material parameters.
Charles Clark Lawrence· Zenodo (CERN European Organi...· 0 citations
Artificial intelligence (AI), digital phenotyping, passive sensing, and edge computing are increasingly being explored to extend psychiatric assessment beyond intermittent clinical encounters. This review evaluates the evidence relevant to a privacy-preserving, closed-loop architecture in which environmental and wearable signals are processed locally, converted into abstract behavioral biomarkers, and used to support longitudinal diagnostic reasoning. The literature indicates that digital phenotyping can capture clinically relevant changes in sleep, activity, mobility, communication, speech, and social behavior, with the most consistent evidence observed for bipolar disorder and depressive symptoms. However, external validation is uncommon, study samples are often small, missingness is frequently ignored, labels are temporally misaligned with sensor streams, and reported discrimination can therefore overestimate real-world performance. Edge AI offers lower latency, reduced network exposure, and bandwidth savings, but it introduces device constraints and does not by itself guarantee privacy. Privacy-preserving strategies should therefore combine data minimization, local feature extraction, strict retention limits, cryptographic separation of identity, access control, and auditable governance. Recent work on evidence conflict further shows that diagnostic AI may be sensitive to the order and presence of contradictory information, supporting the need for explicit contradiction detection, uncertainty calibration, abstention, and clinician escalation rather than probability accumulation alone. The central translational finding is that the components of the proposed Psychiatric Diagnostic Assistant Device (PDAD) are individually supported by adjacent evidence, but the specific combination of continuous behavioral biomarker extraction, privacy-preserving edge processing, contradiction-aware inference, and information-gain-driven adaptive sensor control has not yet been clinically validated as an integrated psychiatric diagnostic system. The most defensible next step is a staged prospective programme using independent reference standards, external validation, safety monitoring, privacy verification, and a clinical utility design aligned with current AI reporting and evaluation guidance.
M. A. N. Makeen· Zenodo (CERN European Organi...· 0 citations
The Selection-Stitch Model derives quark charges in thirds from the geometry of a trapped lattice defect. The integer unit that lifts -1/3 to the up-type +2/3 has resisted every mechanism tried: it is not a Cartan charge of the vacuum-matter algebra under the lattice's geometric C and P, and a circuit-ordering geometric phase was excluded by computation. This paper derives the unit from the one place those exclusions left open: the topology of the gauge sector. The framework's electromagnetic channels live on the <100> square faces; the lattice nodes and octahedral voids together form a simple cubic grid, and a compact U(1) on that grid carries monopole defects as a matter of compactness. The chiral defect worldline of the companion paper - directed hopping with point-gap winding W = +1, derived from the verification front - couples to this gauge field, and the pre-registered calculation is a spectral flow: thread one flux quantum through the worldline and count the charge pumped. The answer, computed as a determinant winding and therefore an integer identically, is exactly W: +1 in the physical configuration, 0 in a static crystal, -1 with the frontier inverted, robust across system sizes and every reference inside the point gap. By anomaly matching this boundary flow is the edge of a bulk theta = 2*pi*W, and by the Witten effect flux-bound matter shifts its electric charge by e*theta/2pi = e*W: the charge ladder is q = -1/3 + W, and the up-type +2/3 is derived. Because a determinant winding cannot be fractional, the mechanism cannot touch the thirds: the geometric and topological charges live in different places and add. Two further results follow. The companion matter paper's empirical restriction of the winding to w >= 0 is now derived - negative winding requires an inverted frontier, which the physical configuration forbids - matching the non-observation of charge -4/3; and the framework now requires monopole-type defects of the photon grid, a falsifier-shaped commitment whose microscopic construction is stated as open. Every claim carries a status tag, and the pre-registration rides in the verification archive.
Raghu Kulkarni· Zenodo (CERN European Organi...· 0 citations
Son Pham publicly identified the first counterexample to the Huneke-Wiegand conjecture in the class of two-generated monomial ideals over symmetric numerical semigroup rings, subsequently verified independently by Professor Craig Huneke. This preprint preserves that discovery priority and develops separate extensions: Frobenius minimality, classification of the minimum layer, an explicit infinite family, and the family's uniform endomorphism, type, trace, conductor, stability, reduction, tangent-cone, fiber-cone, and homological anatomy. Proof-carrying exact computation shows that the least Frobenius number is 181, attained by Pham's example at shift 14. Complete theorem-tree enumeration and 1,156 independently checked fixed-pair DRAT proofs reproduce the published range F<69. A selector CNF gives accepted DRAT proofs for every odd F from 69 through 179 and recovers the exact public semigroup at F=181. Projected enumeration then proves that shift 14 and the public membership vector are unique at the minimum. For every integer p>=4, we give a deductive construction of a symmetric numerical semigroup with multiplicity 24p, Frobenius number 78p-1, conductor 78p, and embedding dimension 11p, carrying the nonprincipal rigid ideal (t^(24p),t^(30p)). Seven exact interval-sum identities prove closure, symmetry, generation, and rigidity. For every family member, the endomorphism value semigroup is determined exactly: it has multiplicity 24p, Frobenius number 54p-1, conductor 54p, genus 38p-1, embedding dimension 12p, and Cohen-Macaulay type and reduced type 10p. It has maximal reduced type, is not almost symmetric, and its completed semigroup ring is not almost Gorenstein. The rigid ideal is not reflexive over its endomorphism ring; adjacent Ext and Tor obstruction groups are nonzero. The trace of the ideal, the trace of its endomorphism ring, and the conductor of the finite birational extension are equal. Their common value ideal is computed exactly, with length(R/(R:E))=length(E/R)=p+1. Version 0.06 identifies the equality of these two lengths as general one-dimensional Gorenstein local duality and restricts the family-specific claim to the exact common ideal and the value p+1. It further proves that the conductor is nonstable and computes length(T^2/t^(4s)T)=14p. Version 0.07 determines the entire conductor reduction sequence: t^(4s)R is a minimal reduction of exact reduction number four, the successive quotient lengths are 23p-1, 14p, 2p, 1, 0, and the Hilbert-Samuel coefficients are e0=24p and e1=39p. Version 0.08 proves that the conductor tangent cone has depth zero: the complete Valabrega-Valla module is concentrated in one degree with length p. Its Hilbert series is computed exactly, and its numerator has only positive coefficients despite failure of Cohen-Macaulayness. Version 0.09 proves that the complete zeroth local cohomology is k^p in degree zero and is annihilated by the full homogeneous maximal ideal. Thus the tangent cones are Buchsbaum but not Cohen-Macaulay with unbounded Buchsbaum invariant p; their quotients by finite-length torsion are Cohen-Macaulay with an exact Hilbert series. Version 0.10 determines the complete graded module over the polynomial Noether normalization induced by the minimal reduction: a rank-24p free part with explicit shifts plus p exponent-one torsion summands. It gives the complete minimal resolution, projective dimension one, regularity four, top-local-cohomology a-invariant three, and length(G/xG)=25p=e0+I. Version 0.11 proves T^2=mT and identifies the conductor special fiber canonically with the tangent cone modulo its complete zeroth local cohomology. The fiber cone is Cohen-Macaulay of type 10p+1, but its Artinian socle occurs in degrees two and four, so it is neither level nor Gorenstein. Version 0.12 determines the complete defining ideal of this special fiber: 50p^2-17p minimal quadrics and the single additional cubic X_0^2 X_(3p)-X_p^3. Thus its relation type is three and it is not Koszul. The all-parameter component calculation is exact Presburger verification with a separately encoded graph audit and an explicitly disclosed solver trust boundary. Version 0.13 determines exact edges of the minimal resolution over the full 10p-variable presentation ring: projective dimension 10p-1, regularity four, beta_(2,3)=2p(500p^2-330p+31)/3, the complete last row, beta_(10p-2,10p+2)=8p, and canonical-module generators in degrees -1 and -3. Version 0.14 determines the first interior strand: beta_(2,4)=8p with complete multiplicity-free multigraded support, and beta_(3,4)=p(5p-1)(500p^2-440p+47)/2. Relative squarefree-divisor complexes, an integral unit matching, an exact colon computation, and a minimal mapping cone prove the result in every characteristic. The remaining interior Betti table remains open. Failed overbroad predictions and budget-only attempts remain preserved. Exact campaigns and independent audits support, but do not replace, the symbolic reductions. The results remain confined to numerical semigroup rings and two-generated monomial ideals. They do not classify arbitrary modules or arbitrary one-dimensional Gorenstein domains. Code, compact artifacts, verdicts, symbolic proofs, and verification instructions: https://github.com/fsantibanezleal/CAOS_RESEARCH. Version 0.15 completes the second graded Betti row of the conductor special fiber for every p>=4 and over every field: beta_(2,5)=p(2p-3), beta_(2,6)=0, with the complete three-block multigraded support and multiplicity profile. Integral lexicographic matching and unit Smith normal forms prove characteristic independence. Version 0.16 determines the complete degree-five third-syzygy profile from the exact high cubic colon: beta_(3,(5,b)) counts unordered pairs of distinct high-colon variables with shifted sum b-3p, beta_(3,5)=4p(8p-1), and the support is [15p+1,39p-3] minus {33p-1}. The primitive integral pair basis proves characteristic independence. Together with the complete second row and Hilbert numerator, beta_(4,5)=2p(5p-1)(10p-3)(100p^2-110p+13)/3, completing internal degree five. Version 0.17 identifies the complete cubic-colon quotient as the canonical idealization of the p-th Veronese rational normal curve ring, with Hilbert series (1+(2p-2)z+z^2)/(1-z)^2. Its multigraded Hilbert numerator and an integral relative normal form prove beta_(3,6)=8p(7p^2-12p+2)/3 over every field, with exact support [3p+4,29p-5] minus ([6p-3,6p+1] union [9p-3,9p]). Version 0.18 proves beta_(3,7)=0 over every field by an integral zero-vertex matching and signed unit tetrahedral filler block. Together with the earlier degree-four, degree-five, and degree-six strands, this completes the third homological row. Its total rank is beta_3=p(7500p^3-7988p^2+2025p-133)/6. Version 0.19 determines the complete ordinary graded Betti polynomial of the cubic-colon quotient. For c=2p-2 and m=8p, the low canonical idealization has Betti polynomial 1+sum_(a=1)^(c-1) lambda_(c,a)x^a z^(a+1)+x^c z^(c+2), where lambda_(c,a)=c binom(c,a)-binom(c,a+1)-binom(c,a-1); the full presentation-ring polynomial is its product with (1+xz)^m. Thus every free-module rank and shift is known over every field, with projective dimension 10p-2 and regularity two. Version 0.20 proves that the quadratic quotient has depth one, projective dimension 10p-1, and regularity two. The strict grading gap makes the cubic mapping cone minimal, so the complete special-fiber Betti polynomial is the sum of the quadratic-quotient polynomial and x z^3 times the known colon polynomial. This determines both upper regularity strands over every field and removes every comparison-rank ambiguity. Version 0.21 reduces the high-variable kernel modulo the common regular element to a two-layer incidence module. For tau_p=8p-1+p(p+1)/2, a unique primitive cokernel cell and a separate integral unit pivot prove beta_(p,(p+2,tau_p))=1 in the kernel, quadratic quotient, and special fiber over every field. Thus beta_(p,p+2) of the quadratic quotient is at least one and the corresponding special-fiber entry is at least binom(8p,p-1)+1. This is one exact point in a lower strand. Version 0.22 classifies every primitive zero row of the two-layer incidence cokernel by the exact criterion R_b subset F and obtains consecutive kernel classes in homological degrees p+1 through 2p-3. The first new connecting cell has an integral source cycle, refuting the naive coordinatewise survival mechanism. Its complete target quotient instead proves characteristic dependence: beta_(5,(7,87)) of both the quadratic quotient and special fiber is 4 over GF(2) and 3 over GF(3). The integral kernel cokernel is Z^4 direct-sum Z/2Z. The two complete lower strands, explicit differential matrices, and full special-fiber resolution remain open.
Felipe Santibañez-Leal· Zenodo (CERN European Organi...· 0 citations
The quarter in the Bekenstein–Hawking entropy is one of the most quoted numbers in physics, and one that no closed framework derives from first principles. This paper reports what happens to that number inside a framework whose gravity is induced rather than fundamental — manufactured at one loop by an underlying E8 field content, with the compactification scale locked to the same ultraviolet scale. In that setting the quarter changes epistemic status: it is shown to arise as a fixed geometric ratio between two faces of one and the same computation, so the framework inherits the area law by construction, species by species, with the known subtleties of the gauge sector incorporated rather than hidden, and the result stable under compactification with the internal volume computed exactly. Three sharp uniqueness statements about ten dimensions follow within the declared frame, including a new internal selection argument for the dimensionality of spacetime — of the four dimensions in which super-Yang–Mills theories can exist, only one allows the multiplet to generate its own gravity — and an exact split of the horizon's entropy budget into a bulk share and a dimension-blind boundary share identified with horizon edge modes, which take exactly half of the gross budget only in ten dimensions. The entanglement spectrum of the horizon is computed from the internal geometry by three independent methods that agree to a part in a hundred thousand, one new spectral coefficient is measured, and a sober accounting shows that in induced gravity almost all of a black hole's entropy is paid by ultraviolet physics rather than by the known light fields. One pre-registered counting hypothesis fails its own statistical null and is published as a negative result. The paper closes with an honest map of observability for the framework's logarithmic fingerprint: astrophysical channels are quantitatively dead; the only physical window is the final stage of an evaporating primordial black hole, stated with its conditions; and laboratory realizations of E8 in condensed matter are carefully distinguished from gravitational measurements. Every claim is classified by its epistemic status; scheme dependence and the framework's premises are declared; internal replications are disclosed as such. All numerical statements are script-verified; materials are available from the author on reasonable request.
E.U.O.· Zenodo (CERN European Organi...· 0 citations
The Selection-Stitch Model derives quark charges in thirds from the geometry of a trapped lattice defect. The integer unit that lifts -1/3 to the up-type +2/3 has resisted every mechanism tried: it is not a Cartan charge of the vacuum-matter algebra under the lattice's geometric C and P, and a circuit-ordering geometric phase was excluded by computation. This paper derives the unit from the one place those exclusions left open: the topology of the gauge sector. The framework's electromagnetic channels live on the <100> square faces; the lattice nodes and octahedral voids together form a simple cubic grid, and a compact U(1) on that grid carries monopole defects as a matter of compactness. The chiral defect worldline of the companion paper - directed hopping with point-gap winding W = +1, derived from the verification front - couples to this gauge field, and the pre-registered calculation is a spectral flow: thread one flux quantum through the worldline and count the charge pumped. The answer, computed as a determinant winding and therefore an integer identically, is exactly W: +1 in the physical configuration, 0 in a static crystal, -1 with the frontier inverted, robust across system sizes and every reference inside the point gap. By anomaly matching this boundary flow is the edge of a bulk theta = 2*pi*W, and by the Witten effect flux-bound matter shifts its electric charge by e*theta/2pi = e*W: the charge ladder is q = -1/3 + W, and the up-type +2/3 is derived. Because a determinant winding cannot be fractional, the mechanism cannot touch the thirds: the geometric and topological charges live in different places and add. Two further results follow. The companion matter paper's empirical restriction of the winding to w >= 0 is now derived - negative winding requires an inverted frontier, which the physical configuration forbids - matching the non-observation of charge -4/3; and the framework now requires monopole-type defects of the photon grid, a falsifier-shaped commitment whose microscopic construction is stated as open. Every claim carries a status tag, and the pre-registration rides in the verification archive.
Raghu Kulkarni· Zenodo (CERN European Organi...· 0 citations
Abstract: The growing combination of geospatial technologies, Artificial Intelligence (AI), and edge computing is changing the field of spatial analysis, environmental monitoring, and infrastructural design. This article gives a thorough summary of the way modern computer science approaches—namely machine learning (ML), deep learning (DL), container orchestration using Kubernetes, and ultra-reliable low-latency communications (URLLC)—are being incorporated into geospatial geoinformatics. Instead of carrying out processing in centralised cloud systems, geospatial systems can now handle high-resolution Earth Observation (EO) data, LiDAR point clouds, and Internet of Things (IoT) spatial streams in near real-time by moving the processing tasks to the network edge. We look systematically at the basic methods involved in spatial intelligence, containerized orchestration, multi-sensor data fusion, and edge deployment architectures. Moreover, we combine the more recent literature from a range of disciplines to show the way in which spatial technologies directly contribute to the UN Sustainable Development Goals (SDGs), help reduce regional environmental degradation, and improve university-based entrepreneurial ecosystems. Lastly, the main research gaps—such as the problem of bandwidth limitations in remote areas, model drift in changing environments, and governance constraints—are identified, together with specific future directions for next-generation spatial computing.
Dr. Ambrose Ndubuisi Ekebuike*, Abdulaziz Ahmad, Yusuf Aliyu Adamu· Zenodo (CERN European Organi...· 0 citations
Between the plates of a charging capacitor, not one charge crosses. And still a magnetic field stands there. This paper asks what, then, a current is──the answer is not the motion of charge. What closes Ampere's law is what has been called a current. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──the Ampere-Maxwell law, the displacement current, and the field of a parallel-plate capacitor are all standard. No electromagnetism is built──what is used is one line integral and the comparison of two expressions. Maxwell's equations are not derived──Paper 93 treats the discovery of the field and Paper 116 the exponent of c. This paper receives the equations as a premise and asks only after the standing of one term. No physical medium is posited for the displacement current──neither an ether nor a polarisation of the vacuum is invoked. Only the behaviour of a term in an equation is treated. The relativistic treatment is not entered──that displacement and conduction currents exchange with the observer is mentioned but not formalised. Edge effects are not treated──the plates are taken as large with no fringing, and the numbers are values inside that idealisation. The standing of epsilon_0 is not discussed──since the SI revision of 2019, epsilon_0 is a measured quantity. This paper uses it as a conversion constant and does not make its standing a subject. The 4pi in mu_0 is not called a discovery──mu_0=4pix10^-7 comes from the choice of units. Paper 116 treated the non-uniqueness of 4pi, and this paper follows it in writing that this one is a choice of units. Relation to earlier papers: Paper 02 showed that a pure solid angle 4pi appears in an inverse-square field──Section 6 here looks at the 4pi in mu_0 and writes that its standing is not the same. Paper 116 treated the non-uniqueness of 4pi──this paper follows that and claims no credit for the 4pi here. Paper 258 wrote the condition for 4pi to appear as three items──this paper stands on the side where the condition is not met. Paper 240 counted “mass” as seven things──this paper writes that “current” does not have one meaning. Paper 201 counted “complete” as four different claims──the same shape of division. What is added is stating explicitly that the crossing charge is 0 A, computing the field between the plates at each distance, confirming that the inside and outside expressions agree at 4.0000 muT on the rim, and treating the 4pi of mu_0 as a choice of units and writing that its standing differs from the 4pi of Paper 02. First, count the charge that crosses. The conduction current in the wire is 1 A, and the charge crossing between the plates is 0 A (Section 2). Second, this is the core of the paper. The charge is zero and a field stands anyway. With plates of radius 5 cm and I=1 A, the field 1 cm from the axis is 0.8000 muT (Section 3). Third, the field grows in proportion to the distance from the axis. At 1,2,3,4,5 cm it is 0.8000,1.6000,2.4000,3.2000,4.0000 muT──the same form as inside a current-carrying wire (Section 3). Fourth, the two meet exactly at the rim. At r=5 cm, the inside expression and the outside expression both give 4.0000 muT──the side where no charge crosses and the side where it does return the same value (Section 4). Fifth, epsilon_0 dPhi_E/dt equals the conduction current exactly. What makes them agree is the conversion constant epsilon_0=8.8541878x10^-12 (Section 5). Sixth, a 4pi sits here too. mu_0=4pix10^-7=1.2566371x10^-6──a solid angle sits inside the constant that fixes the size of the field (Section 6). the displacement current was not a current. The charge crossing between the plates is 0 A, and there is nothing to carry it. Still the field stands, rising in proportion to r and reaching 4.0000 muT at the rim──and computing with the outside expression, where charge does cross, returns the same 4.0000 muT. The epsilon_0 cancels and dQ/dt remains, so the two agree exactly and not approximately. So the word “current” carries two definitions──the motion of charge and what closes Ampere's law. And the 4pi inside mu_0 likewise differs in standing from the 4pi that came out of geometry──this one is embedded in the definition of a unit. One thing separates them──writing down which of the two definitions the word is being used in. Write it down, and the occasions for looking for charge separate from those for counting terms in an equation. Do not write it down, and one goes on searching for something crossing a place where nothing does. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 充電中のコンデンサの板のあいだには、電荷が一つも渡っていない。それでも、そこには磁場が立っている。本稿が問うのは、では「電流」とは何なのかである──答は、電荷の移動ではない。アンペール則を閉じるものが電流と呼ばれている。新しい数学定理も新しい法則も主張しない。 本稿の射程(射程注記):新しい数学定理も新しい法則も主張しない──アンペール=マクスウェル則、変位電流、平行平板コンデンサの磁場は、いずれも標準的である。電磁気学を作らない──使うのは一つの周回積分と、二つの式の突き合わせだけである。マクスウェル方程式を導かない──論文93 が場という発見を、論文116 が c の冪を扱う。本稿は方程式を前提として受け取り、その一項の身分だけを問う。変位電流に物理的な媒質を仮定しない──エーテルも、真空の分極も持ち出さない。扱うのは式の項としての振る舞いだけである。相対論的な扱いに立ち入らない──変位電流と伝導電流が観測者によって入れ替わることには触れるが、定式化しない。端の効果を扱わない──板は十分大きく、縁の漏れは無視している。数値は理想化の内側の値である。 epsilon_0 の身分を論じない──2019 年のSI改定以降 epsilon_0 は測定量である。本稿は換算係数として使うだけで、その身分を主題にしない。 mu_0 の 4pi を発見だと言わない──mu_0=4pix10^-7 は単位系の取り方から来る。論文116 が 4pi の非一意性を扱っており、本稿もそれを踏まえて「単位の選択である」と書く。既刊との関係:論文02 は逆二乗場に純粋立体角 4pi が現れることを示した──本稿の第6節は mu_0 の中の 4pi を見るが、そちらは単位の選択であって同じ身分ではないと書く。論文116 は 4pi の非一意性を扱った──本稿はその指摘に従い、mu_0 の 4pi を手柄にしない。論文258 は 4pi が出る条件を三つに書き出した──本稿は条件を満たさない例の側に立つ。論文240 は「質量」が七つあることを数えた──本稿は「電流」が一つの意味ではないことを書く。論文201 は「完備」が四つの別の主張であることを数えた──同じ形の分け方である。加えたのは渡る電荷が 0 A であることを明示したこと、板の中の磁場を距離ごとに計算したこと、縁で内外の式が 4.0000 muT で一致することを確かめたこと、mu_0 の 4pi を単位の選択として扱い、論文02 の 4pi と身分が違うと書いたことである。 第一に、渡っている電荷を数える。導線を流れる伝導電流は 1 A、板のあいだを渡る電荷は 0 A である(第2節)。 第二に、これが本稿の芯である。電荷が 0 なのに磁場が立つ。板半径 5 cm、I=1 A で、中心から 1 cm の点の磁場は 0.8000 muT である(第3節)。 第三に、磁場は中心からの距離に比例して増える。1,2,3,4,5 cm で 0.8000,1.6000,2.4000,3.2000,4.0000 muT──導線の中の磁場と同じ形である(第3節)。 第四に、縁でぴたりと繋がる。板の縁 r=5 cm を、中の式で計算しても外の式で計算しても 4.0000 muT になる──電荷が渡っていない側と、渡っている側が、同じ値を返す(第4節)。 第五に、epsilon_0 dPhi_E/dt が伝導電流と厳密に一致する。一致させているのは epsilon_0=8.8541878x10^-12 という換算係数である(第5節)。 第六に、ここにも 4pi が座っている。 mu_0=4pix10^-7=1.2566371x10^-6──磁場の大きさを決めている定数の中に、球の立体角が入っている(第6節)。 変位電流は、電流ではなかった。板のあいだを渡る電荷は 0 A であり、運ぶものが何も無い。それでも磁場は立ち、r に比例して増え、縁で 4.0000 muT になる──そして電荷が渡っている外側の式で計算しても、同じ 4.0000 muT が返る。 epsilon_0 が約分されて dQ/dt が残るので、二つは近似ではなく厳密に一致している。つまり「電流」という語には二つの定義がある──電荷の移動と、アンペール則を閉じるものである。そして mu_0 の中の 4pi もまた、幾何から出た 4pi とは身分が違う──こちらは単位の定義に埋め込まれている。分けるものは一つ──その語をどちらの定義で使っているのかを書き出すこと。書き出せば、電荷を探すべき場面と、式の項を数えるべき場面が分かれる。書き出さなければ、何も渡っていない場所に、渡っているものを探し続けることになる。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
Yuuki Yamagishi· Zenodo (CERN European Organi...· 0 citations
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