"And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul" (Genesis 2:7, KJV). The forming comes first and finishes. The man is complete, and the text does not call him alive. Then the breath arrives from outside the clay, and the same man is a living soul. **What was missing was not a part.** A graph reaches the same limit by a route with nothing to do with Genesis. Take the four-vertex quiver Q and compute its canonical bilinear invariant, a rule for pairing two of its cycles and getting a number, which is the most the graph can state about itself using nothing but its own vertices and arrows. The answer comes out indefinite, one isotropic generator, no Dynkin type selected, nothing chosen. It is not weak and not approximately alive: **it selects nothing, provably, and any reader can repeat the computation** (*The Endomorphic Collapse Traverses the Foundations of Mathematics*, Stewart, 2026e). Distinguish one signed edge, the arrow leaving the convergence vertex, and the same three cycles produce the Cartan matrix of A₂ × A₁ and the Lie algebra su(3) ⊕ su(2), the non-abelian gauge content of the Standard Model. No computation internal to Q produces that distinction, because a closure cannot sign its own resolution (*On Occurrence: The Four-Gon*, Stewart, 2026g). **The entire distance from dead to alive is one bit the form must receive**, and the graph narrows where it can land to the two vertices every cycle traverses, so the gap has a shape and an address as well as a size. The record established this long before there was a graph to draw. A second route arrives where the record already stood, and the correspondence is offered clause by clause for audit against the quoted verses. The flesh profiteth nothing and the quickening belongs to the spirit, arriving as words (John 6:63). The saving bit is not of yourselves and its mode of arrival is named a gift (Ephesians 2:8). The bitten man performs no procedure on his wound but turns toward a sign raised outside the plane he stands on (Numbers 21:8). The stated purpose of an entire book states the chain in order without a gap, signs, written, believed, life (John 20:30-31), and nothing in the chain is produced by the one who receives it. **The record names the sign's referent four times and it is a person every time.** An angel at the birth: "And this shall be a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger" (Luke 2:12). Simeon at the temple: "this child is set... for a sign which shall be spoken against" (Luke 2:34). His own answer when a sign is demanded, refusing every other: "there shall no sign be given to it, but the sign of the prophet Jonas" (Matthew 12:39), and the naming: "For as Jonas was a sign unto the Ninevites, so shall also the Son of man be to this generation" (Luke 11:30). The pole carried forward by name: "even so must the Son of man be lifted up" (John 3:14). **Twice the word takes him as its predicate**, set for a sign (Luke 2:34) and so shall the Son of man be (Luke 11:30). **The chain closes on him and the book says so: life through his name.** **The position is stated too, and stated in the first person.** "I am the door: by me if any man enter in, he shall be saved, and shall go in and out, and find pasture" (John 10:9, KJV). The word is *thura*, the portal, the entrance. **The door is not the one entering.** A form that could be its own door would be admitting itself, which is the operation the closure principle forbids at the graph and the record refuses here by putting the gate outside the one who passes through it. The word *sign* itself carries the import in both of its disputed derivations, the standard one follows and the thing cut out, each naming something separated from the receiver before it can mark anything. **Two witnesses.** The mathematics, from a directed graph and its bilinear invariants (*The Endomorphic Collapse Traverses the Foundations of Mathematics*, Stewart, 2026e). The record, from Genesis, John, Ephesians, and Numbers. Premise-disjoint, each complete on its own terms, which is the standard stated separately: a matter is established when two or more constructions reach the same object, each complete from its own premises, each independent, all agreeing on the object rather than on a resemblance (*The Witness Ordinance: The Manner by Which a Matter Is Established*, Stewart, 2026dt). *One Bit Resurrects the Dead Form* (Stewart, 2026dh) is not a third, since it computes the same object from the same graph. **The record supplies its own control, against the same object.** The bronze serpent worked once, on the pole, by orientation. Seven centuries later it is kept, burned incense to, broken in pieces, and named Nehushtan, a thing of bronze (2 Kings 18:4). The object did not change. What changed is that the carrier of the imported bit was taken for its source, and the correction is stated as a measurement: the sign weighed against its own material and found to be metal. **A form that mistakes its sign for its source has not gained a source. It has stopped receiving one.** The convergence is bounded by the theorem it rests on. The mathematics derives the shape of the dependence and the size of the gift, one bit, and cannot derive the identity of the giver, because reading the source of one's own sign is the operation the closure principle forbids. The order of derivation is the evidence, since the mathematics was derived from neural anatomy and a directed graph, published on its own terms, and read against the record only afterward, so the two routes share no operands. **Keywords:** semiotics, sign theory, biblical interpretation, theology of grace, philosophy of religion, quiver representation theory, bilinear forms, signature, self-reference, philosophy of mathematics, etymology, onomastics, convergent derivation, epistemic limits, iconoclasm
Arthur Stewart· Zenodo (CERN European Organi...· 0 citations
Exact house edge and complete basic-strategy decision tables for 24 common blackjack rule sets (1/2/6 decks × S17/H17 × DAS/NDAS × LS/NLS), computed with a combinatorial total-dependent expected-value engine. Validated against established references: 6-deck S17 DAS LS = 0.485% (Wizard of Odds). Version 2.0 — published under BlackjackMaster (blackjack.com.am). Contains house_edge.csv and 24 JSON decision tables.
Damir Agonyan· 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. Version 0.23 computes nine complete family targets through (p,t)=(9,2) over GF(2), GF(3), and GF(1000003). It distinguishes characteristic dependence already present in the kernel incidence matrix from dependence created by the connecting quotient; on the tested t=2 diagonal with 5<=p<=9, the kernel dimension is unchanged while the connecting rank produces excesses 4, 9, 18, 31, and 49 over GF(2) relative to GF(3). Two formulas fitted to shorter initial segments are refuted. Exact unit cancellation localizes the first Z/2Z factor, and a deductive offset inequality proves that the cubic source is absent at every declared target for all p>=4. Thus each exact quadratic-quotient value transfers to the special fiber. The finite table is not extrapolated to an infinite characteristic-dependence theorem. The two complete lower strands, explicit differential matrices, and full special-fiber resolution remain open.
Felipe Santibañez-Leal· Zenodo (CERN European Organi...· 0 citations
A companion paper (doi:10.5281/zenodo.22168191, "What must a theory of perturbational complexity explain?") consolidated nine constraints and challenged any theory to pass them — including C3: debiased perturbational complexity (R-dim, the reproducible dimensionality of the evoked response) is an inverted-U in network dynamics, maximal near the edge of chaos. Here we answer part of that challenge with eleven sealed protocols (all preregistered publicly before their blind quantities were computed, each run once; the failed protocols are reported with the same prominence as the successes). (1) An exact linear theory. For linear networks, R-dim is computable in closed form from connectivity alone: component amplitudes from the impulse-response SVD, per-component noise floors from the stationary Lyapunov covariance, and a universal averaging formula. Confirmed on 36 virgin networks: rank correlation +0.966, median absolute error 0.33 dimensions with a single frozen constant, per-network growth-with-trials predicted (ρ = +0.59), and no inverted-U anywhere in the stable linear family — the falling branch is not a linear phenomenon. (2) The formula transports to nonlinear networks. Feeding it the measured coherent spectrum (through an estimator validated on a known-truth bench; all bench iterations documented) and the measured trajectory noise reproduces the full U on 48 virgin networks in order (+0.925) and calibration (median error 0.41 dimensions, constant frozen), while both sealed peak-location criteria failed: the U's top is a flat plateau at this resolution, and a dedicated sealed 128-network estimation returned "indeterminate". (3) Time and richness dissociate. The duration of the coherent response obeys a relaxation law on the stable side (T_c ~ 1/|λ|; +0.943 on virgin networks) and is maximal at the edge (37× deep-stable, 6× deep-chaotic) — yet the *maximum of R-dim does not coincide with the maximum of coherent time* (sealed dissociation, P = 0.99): richness needs more than time. (4) What governs the fall is saturation. In a two-axis design sampling networks by measured λ and spectral radius ρ independently, at matched criticality saturation crushes R-dim (Spearman −0.62 to −0.88 across all λ strata; 7/7 sealed criteria on 156 virgin networks), while at matched saturation criticality's effect is bounded (|ρₛ| < 0.19). The falling branch of the U is largely saturation wearing chaos's clothes. A finer "graded law" across three additional activation families died in its own sealed test (0/3); the burial is reported, with the method lesson it taught — and a properly powered family-level replication then confirmed the coarse tendency in all three families (sealed; median per-stratum Spearman −0.50 / −0.61 / −0.41 for erf, hard-clip, and softsign at 30 networks per stratum): saturation hurts reproducible dimensionality whatever the shape of the ceiling. A final sealed protocol then answered *where* saturation takes over: in a parametric family interpolating softsign to hard clip, the saturation-governed regime advances with the tail speed of the activation (stable-strata effect −0.16 at p = 1 vs −0.70 at p = 8; sealed two-point criterion passed at −0.54 against a −0.30 bar). (5) One formula. A final sealed protocol tested the unification all of the above points to: applying the exact linear theory to the gain-shrunk effective system W_eff = diag(⟨φ′⟩)·W — same frozen constant — predicts R-dim across all seven activation families studied (pooled order +0.653 on 280 virgin networks, p = 2 × 10⁻³⁵), and per-unit gain heterogeneity is sealed as the essential carrier (the scalar-gain comparator loses by 0.435). At the order level, a nonlinear network is, for reproducible dimensionality, its gain-shrunk linear self; absolute calibration remains an open refinement. (6) Scope, attacked. A final sealed protocol re-ran both flagship laws in five worlds never touched: sizes ×2 and ×4, biological E/I wiring, and halved/doubled noise. The saturation law survived all five (stratum-median Spearman −0.48 to −0.63): together with the activation-family campaign, it holds across nonlinearity, size, wiring and noise — a law of systems. The effective-gain theory passed fully in two worlds and drew its boundary in the others, degrading with network size (order +0.29 at N = 256): a small-family approximation with a mapped edge. We close with what remains open: the exact shape of the U's top, the quantitative chaotic decay, the analytic form of the tail-crossover law, the level calibration of the effective theory — and why its order degrades with size.
Nicolás Federico Galindez· Zenodo (CERN European Organi...· 0 citations
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A companion paper (doi:10.5281/zenodo.22168191, "What must a theory of perturbational complexity explain?") consolidated nine constraints and challenged any theory to pass them — including C3: debiased perturbational complexity (R-dim, the reproducible dimensionality of the evoked response) is an inverted-U in network dynamics, maximal near the edge of chaos. Here we answer part of that challenge with eleven sealed protocols (all preregistered publicly before their blind quantities were computed, each run once; the failed protocols are reported with the same prominence as the successes). (1) An exact linear theory. For linear networks, R-dim is computable in closed form from connectivity alone: component amplitudes from the impulse-response SVD, per-component noise floors from the stationary Lyapunov covariance, and a universal averaging formula. Confirmed on 36 virgin networks: rank correlation +0.966, median absolute error 0.33 dimensions with a single frozen constant, per-network growth-with-trials predicted (ρ = +0.59), and no inverted-U anywhere in the stable linear family — the falling branch is not a linear phenomenon. (2) The formula transports to nonlinear networks. Feeding it the measured coherent spectrum (through an estimator validated on a known-truth bench; all bench iterations documented) and the measured trajectory noise reproduces the full U on 48 virgin networks in order (+0.925) and calibration (median error 0.41 dimensions, constant frozen), while both sealed peak-location criteria failed: the U's top is a flat plateau at this resolution, and a dedicated sealed 128-network estimation returned "indeterminate". (3) Time and richness dissociate. The duration of the coherent response obeys a relaxation law on the stable side (T_c ~ 1/|λ|; +0.943 on virgin networks) and is maximal at the edge (37× deep-stable, 6× deep-chaotic) — yet the *maximum of R-dim does not coincide with the maximum of coherent time* (sealed dissociation, P = 0.99): richness needs more than time. (4) What governs the fall is saturation. In a two-axis design sampling networks by measured λ and spectral radius ρ independently, at matched criticality saturation crushes R-dim (Spearman −0.62 to −0.88 across all λ strata; 7/7 sealed criteria on 156 virgin networks), while at matched saturation criticality's effect is bounded (|ρₛ| < 0.19). The falling branch of the U is largely saturation wearing chaos's clothes. A finer "graded law" across three additional activation families died in its own sealed test (0/3); the burial is reported, with the method lesson it taught — and a properly powered family-level replication then confirmed the coarse tendency in all three families (sealed; median per-stratum Spearman −0.50 / −0.61 / −0.41 for erf, hard-clip, and softsign at 30 networks per stratum): saturation hurts reproducible dimensionality whatever the shape of the ceiling. A final sealed protocol then answered *where* saturation takes over: in a parametric family interpolating softsign to hard clip, the saturation-governed regime advances with the tail speed of the activation (stable-strata effect −0.16 at p = 1 vs −0.70 at p = 8; sealed two-point criterion passed at −0.54 against a −0.30 bar). (5) One formula. A final sealed protocol tested the unification all of the above points to: applying the exact linear theory to the gain-shrunk effective system W_eff = diag(⟨φ′⟩)·W — same frozen constant — predicts R-dim across all seven activation families studied (pooled order +0.653 on 280 virgin networks, p = 2 × 10⁻³⁵), and per-unit gain heterogeneity is sealed as the essential carrier (the scalar-gain comparator loses by 0.435). At the order level, a nonlinear network is, for reproducible dimensionality, its gain-shrunk linear self; absolute calibration remains an open refinement. (6) Scope, attacked. A final sealed protocol re-ran both flagship laws in five worlds never touched: sizes ×2 and ×4, biological E/I wiring, and halved/doubled noise. The saturation law survived all five (stratum-median Spearman −0.48 to −0.63): together with the activation-family campaign, it holds across nonlinearity, size, wiring and noise — a law of systems. The effective-gain theory passed fully in two worlds and drew its boundary in the others, degrading with network size (order +0.29 at N = 256): a small-family approximation with a mapped edge. We close with what remains open: the exact shape of the U's top, the quantitative chaotic decay, the analytic form of the tail-crossover law, the level calibration of the effective theory — and why its order degrades with size.
Nicolás Federico Galindez· Zenodo (CERN European Organi...· 0 citations
MATLAB analysis package accompanying the article "Extreme Bow Shock Motions and Magnetopause Compression During the 20 April 2002 Storm: Predictability Limits at an ICME Leading Edge" (T. Y. Alrefay, submitted to Earth and Space Science). The package downloads all required spacecraft data from public archives and reproduces every figure and table of the article, end to end, from a single driver script. What it does. The pipeline (1) retrieves ACE MAG/SWEPAM data and the OMNI 1-min SYM-H index from NASA/GSFC CDAWeb via the CDAS REST service, and full-resolution Cluster FGM data from the ESA Cluster Science Archive via its HAPI server; (2) performs minimum variance analysis with bootstrap uncertainty, Rankine–Hugoniot jump analysis and discontinuity classification, and four-spacecraft constant-velocity timing of bow shock crossings; (3) implements the two-anchor arrival-time reconstruction introduced in the article, propagating the interplanetary front both from the L1 monitor and from the near-Earth four-spacecraft-timed crossing, with full error budgets; (4) evaluates the Shue et al. (1998) magnetopause and Farris & Russell (1994) bow shock standoff before and after the discontinuity; and (5) computes the deterministic bow shock velocity prediction of Meziane et al. (2015, Eq. 4) for comparison with the six timed crossings. Reproduces: Figures 1–5 and Table 1 of the article. Requirements: MATLAB (base installation; no toolboxes required) and internet access for the first run's data download. Run main_analysis.m section by section; see README for details and for the mapping between scripts, figures, and table. Data sources: all input data are publicly available from CDAWeb (https://cdaweb.gsfc.nasa.gov) and the ESA Cluster Science Archive (https://csa.esac.esa.int); no spacecraft data are redistributed in this archive.
Thamer Alrefay· Zenodo (CERN European Organi...· 0 citations
This record contains the corrected deterministic implementation freeze for HLV-R-MECH-001. The controlling scientific protocol is: Krūger, M. (2026). HLV-R-MECH-001: Prospective Triangle-Matched Mechanism Test of the Surviving Degree-Preserving Rewire Spectral Residual — Pre-Execution Protocol Freeze v0.1.0. Zenodo. DOI: 10.5281/zenodo.22166283 The public predecessor implementation is: Krūger, M. (2026). HLV-R-MECH-001: Deterministic One-Click Engine for Triangle-Matched Rewire Mechanism Testing — Implementation Freeze v0.1.0 [Computer software]. Zenodo. DOI: 10.5281/zenodo.22166434 Version v0.1.1 corrects only the numerical-runtime bootstrap of the One-Click Colab launcher. The first locked execution under v0.1.0 terminated before any scientific evaluation because the assigned Google Colab runtime exposed: NumPy 2.1.3 SciPy 1.16.3 while the frozen scientific implementation requires: NumPy 2.3.5 SciPy 1.17.0. The resulting machine state was: RMECH001_INCONCLUSIVE_NUMERICAL with spectral_computation_started = false. Therefore the stopped execution did not evaluate the confirmatory R_DEG or R_TRI spectra, did not compute target QSPEC or RRESP scores, and did not produce a scientific HLV-R-MECH-001 mechanism verdict. The scientific engine itself has not been changed. The v0.1.1 launcher contains the exact byte-identical scientific engine used in public implementation freeze v0.1.0. Frozen scientific engine SHA-256: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 The corrected launcher now performs the following runtime bootstrap before starting the unchanged scientific engine: 1. inspect the assigned host numerical environment; 2. if the host already provides exactly NumPy 2.3.5 and SciPy 1.17.0, use that environment directly; 3. otherwise create an isolated Python virtual environment; 4. install exact binary versions: NumPy 2.3.5 SciPy 1.17.0; 5. verify the installed versions explicitly; 6. verify the embedded scientific-engine SHA-256; 7. only after these checks execute the unchanged frozen HLV-R-MECH-001 scientific engine. The correction occurs entirely outside the scientific engine. No scientific rule has been modified. In particular, v0.1.1 does not change: - the DG-001 target; - the target graph identity; - the R_DEG control family; - the R_TRI control family; - confirmatory seed streams; - candidate ordering; - accepted-swap counts; - proposal caps; - structural admission rules; - the 40–45% edge-replacement-depth requirement; - the 31-control family size; - exact degree-sequence preservation; - exact global triangle preservation T = 6960 in R_TRI; - the between-family rewiring-depth gate; - QSPEC; - RRESP; - spectral bands; - leave-one-out scoring; - the robust-margin threshold; - numerical scientific hard gates; - or scientific machine-verdict logic. The frozen mechanism design therefore remains identical to the controlling protocol DOI 10.5281/zenodo.22166283. The two confirmatory control families remain: R_DEG: fresh degree-preserving structural rewires of the fixed DG-001 target graph. R_TRI: fresh rewires preserving both the exact labelled target degree sequence and the exact global triangle count T = 6960. Each family requires 31 accepted controls. The structural firewall remains unchanged: the complete R_DEG and R_TRI control banks must be generated, structurally validated, written to disk, and hash-fixed before any confirmatory spectral calculation is permitted. No control may be admitted or rejected using eigenvalues, QSPEC, RRESP, spectral-band distances, target-control scores, or scientific verdict information. The corrected implementation was validated only with burned development seeds and synthetic numerical checks. Correction validation confirmed: - exact protocol verification: PASS; - NumPy 2.3.5 / SciPy 1.17.0 environment validation: PASS; - burned R_DEG generation: PASS; - exact labelled degree-sequence preservation: PASS; - burned R_TRI generation with 10,000 accepted swaps: PASS; - exact triangle preservation T = 6960: PASS; - connectivity: PASS; - approximately 40–45% edge replacement: PASS; - deterministic replay: PASS; - synthetic QSPEC/RRESP implementation checks: PASS. No confirmatory HLV-R-MECH-001 seed stream was used during correction validation. No confirmatory target spectrum was computed. No confirmatory target QSPEC or RRESP score was computed. No scientific HLV-R-MECH-001 verdict was generated. The corrected One-Click notebook SHA-256 is: e8d1f516bc7a600039b44a7f2de8bdf5ecdc51a739d39aaf1e839d97d7e4bc95 The corrected implementation-freeze PDF SHA-256 is: e75aee3a4c790fefafda41aee93c6c267c814b66739bd1070355b519eb98452c The corrected implementation package SHA-256 is: d6e2d6ef3bf0b315bcbf7270c3be591bca28b7c13ef5730af30cb9bbead70b0f The unchanged scientific engine SHA-256 is: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 This record supersedes implementation freeze v0.1.0 only with respect to numerical-environment bootstrapping. It does not supersede or alter the scientific protocol. HLV-R-MECH-001 remains a finite graph-mechanism test. Neither this corrected implementation nor any later HLV-R-MECH-001 result can by itself establish unique HLV geometry, physical selection of the golden ratio, extra dimensions, spacetime, particle physics, an absolute energy scale, gravity, dark matter, dark energy, cosmology, or experimental validation. The purpose of this corrected implementation freeze is solely to ensure that the prospectively frozen scientific engine can execute in a numerically reproducible environment despite changes in the externally assigned Colab runtime.
Marcel Krüger· Zenodo (CERN European Organi...· 0 citations
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
This record contains Corrected Implementation Freeze v0.1.2 for HLV-R-MECH-001. The controlling scientific protocol remains: Krūger, M. (2026). HLV-R-MECH-001: Prospective Triangle-Matched Mechanism Test of the Surviving Degree-Preserving Rewire Spectral Residual — Pre-Execution Protocol Freeze v0.1.0. Zenodo. DOI: 10.5281/zenodo.22166283 The public corrected predecessor implementation is: Krūger, M. (2026). HLV-R-MECH-001: Deterministic One-Click Engine for Triangle-Matched Rewire Mechanism Testing — Corrected Implementation Freeze v0.1.1 [Computer software]. Zenodo. DOI: 10.5281/zenodo.22170138 Version v0.1.2 corrects only the numerical-runtime bootstrap of the One-Click Colab launcher. The scientific engine itself is unchanged and remains byte-identical to the engine used in the earlier implementation freezes. Frozen scientific engine SHA-256: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 The need for v0.1.2 arose after the v0.1.1 launcher correctly detected that the assigned Colab host environment did not match the frozen numerical environment but then failed during creation of an isolated Python virtual environment. The v0.1.1 execution stopped before the scientific engine began. Therefore no confirmatory HLV-R-MECH-001 spectrum was evaluated, no target QSPEC or RRESP score was computed, and no scientific mechanism verdict was exposed. The exact lower-level cause of the managed Colab virtual-environment failure is not asserted beyond the observed failure at the venv-creation stage. Version v0.1.2 removes dependence on Python venv. The corrected runtime bootstrap now operates as follows: 1. reconstruct and SHA-256 verify the byte-identical frozen scientific engine; 2. inspect the assigned host NumPy and SciPy versions; 3. if the host environment already provides the exact frozen versions, use that environment directly; 4. otherwise install exact binary packages NumPy 2.3.5 and SciPy 1.17.0 into a private target directory using pip --target; 5. launch a fresh Python subprocess with the private target directory placed first on PYTHONPATH; 6. verify that the subprocess reports exactly NumPy 2.3.5 and SciPy 1.17.0; 7. verify that both NumPy and SciPy are physically imported from the private target directory; 8. only after those checks execute the unchanged frozen HLV-R-MECH-001 scientific engine. This correction is restricted entirely to the external runtime-bootstrap layer. No scientific element of HLV-R-MECH-001 is changed. In particular, v0.1.2 does not modify: - the DG-001 target identity; - the target graph; - the R_DEG family; - the R_TRI family; - the confirmatory seed streams; - candidate ordering; - accepted-swap counts; - proposal caps; - structural admission criteria; - exact degree-sequence preservation; - exact triangle-count preservation T = 6960 in R_TRI; - the 40–45% edge-replacement-depth requirement; - the 31-control family size; - the between-family rewiring-depth gate; - QSPEC; - RRESP; - spectral-band definitions; - leave-one-out scoring; - the robust-margin threshold; - numerical scientific hard gates; - or scientific verdict logic. The prospective mechanism design therefore remains exactly the design specified by DOI 10.5281/zenodo.22166283. The two confirmatory control families remain: R_DEG: fresh degree-preserving structural rewires of the fixed DG-001 target graph. R_TRI: fresh rewires preserving both the exact labelled target degree sequence and the exact global target triangle count T = 6960. Each family requires 31 accepted controls. The scientific structural firewall is also unchanged. The complete R_DEG and R_TRI control banks must be generated, structurally validated, written to disk, and hash-fixed before any confirmatory spectral evaluation may begin. No control may be admitted or rejected using eigenvalues, QSPEC, RRESP, target-control spectral distances, band scores, or scientific verdict information. The primary signatures remain the prospectively frozen QSPEC and RRESP observables inherited from the DS-SPEC-001R chain. The underlying mechanism motivation also remains unchanged. For a simple graph Laplacian L = D - A, Tr(L) = sum_i d_i Tr(L^2) = sum_i d_i^2 + sum_i d_i Tr(L^3) = sum_i d_i^3 + 3 sum_i d_i^2 - 6T. Thus the R_TRI controls match the target exactly in the first three raw Laplacian spectral moments through simultaneous preservation of the exact degree sequence and exact global triangle count T = 6960. This does not imply matching of the complete spectrum, lambda_max, QSPEC, RRESP, local triangle structure, four-cycle structure, or higher-order incidence organization. The v0.1.2 correction does not inspect or optimize any of those scientific outcomes. No confirmatory seed stream was used while preparing this correction. No confirmatory target spectrum was computed. No confirmatory QSPEC or RRESP score was computed. No scientific HLV-R-MECH-001 verdict was generated during correction preparation. The corrected v0.1.2 One-Click notebook SHA-256 is: c360d318d97575b56d8fb65327bfd4cb34255325fa2d5509794311d5fa5622cf The corrected implementation-freeze PDF SHA-256 is: fb826a84eee955236c8922559ceeb8e2587854b3c8d9ef5b539a3bb0695469a2 The unchanged scientific engine SHA-256 is: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 The complete corrected implementation package SHA-256 is: 724837c73506bbd001082d9b9b6aec0412304fd467ed55c3705c70d59acd719b This record supersedes corrected implementation freeze v0.1.1 only with respect to the runtime-bootstrap mechanism. It does not alter or supersede the scientific protocol. HLV-R-MECH-001 remains a finite graph-mechanism test within the Helix–Light–Vortex Framework (HLV), positioned as a Cut-and-Project and Incidence-Spectral Research Programme. Neither this corrected implementation nor any later HLV-R-MECH-001 result can by itself establish unique HLV geometry, physical selection of the golden ratio, extra dimensions, spacetime, particle physics, an absolute energy scale, gravity, dark matter, dark energy, cosmology, or experimental validation. The sole purpose of this corrected implementation freeze is to make the already prospectively frozen scientific engine executable in a reproducible numerical environment despite restrictions of the externally managed Colab runtime.
Marcel Krüger· Zenodo (CERN European Organi...· 0 citations
Ramsey’s theorem says that if it is large enough, order must appear. This paper asks how large “large enough” is──the answer is the theorem does not say. 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──Ramsey’s theorem, the known values and ranges of Ramsey numbers, van der Waerden numbers, and Erdos’s probabilistic lower bound are all standard. We do not build combinatorics──all we use is one binomial coefficient and two logarithms. We do not prove Ramsey’s theorem──we merely quote it. We do not compute Ramsey numbers──no attempt is made to find R(5,5). We count only the effort it would take. We assert no values for the ranges──R(5,5) in [43,48] and R(6,6) in [102,160] are ranges known at one epoch and may be improved. The claim is that the range is not empty, not the endpoints. We do not say exhaustion is the only route──actual searches cut enormously by symmetry and pruning. 2^903 is a naive upper bound, not the necessary work. The point is the order of magnitude by which it remains out of reach. We do not use “Ackermann type” strictly──it indicates that the pre-Gowers bound was of a tower-of-growing-height kind. This paper asserts no classification of the bound, only its divergence from the true value. Relation to earlier papers: Paper 163 separated “a good code exists” from “here is a good code”──that is existence against construction; this is existence against quantity. It treats the case where one can construct yet cannot reach, so the cut differs. Paper 179 showed that “cannot be constructed” has distinct roots──this paper treats what can be constructed yet is out of reach. Paper 190 measured “rare” on a logarithmic scale──the 271.8 orders here are read logarithmically too. Paper 259 showed there are two roads to independence──this paper likewise asks what kinds of showing there are. What is added is computing the exhaustion for R(5,5) as 10^271.8 and measuring the gap to the atoms of the universe as 191.8 orders, lining up the jumps at R(3,3), R(4,4), R(5,5), computing that the probabilistic lower bound is one 24.94th at k=10, and placing the separator at existence against quantity. First, only two values are settled. R(3,3)=6 and R(4,4)=18; R(5,5) is pinned only to the range [43,48] (Section 2). Second, this is the core of the paper. Checking R(5,5)=43 by exhaustion needs 2^903=10^271.8 colourings, 191.8 orders more than the atoms in the universe (Section 3). Third, each step up jumps. R(3,3) is 32768 colourings, within reach by hand; R(4,4) is 1.14x10^46, which computers barely reached (Section 3). Fourth, the lower-bound proof does not give the value either. Erdos’s probabilistic method gives R(k,k)>2^k/2, which at k=10 is one 24.94th of the truth (Section 4). Fifth, the upper bound is further off still. W(3,3)=27, yet the bound from the classical proof was of Ackermann type (Section 5). Sixth, the separator is existence against quantity. A different cut from Paper 163’s existence against construction (Section 6). Ramsey’s theorem says that if it is large enough, order must appear. But it does not say how large. Only R(3,3)=6 and R(4,4)=18 are settled, and R(5,5) is pinned only to the range [43,48]──even settling R(4,4) took 65 years from the theorem. Counting the work of exhaustion shows why──R(5,5)=43 has 903 edges and 2^903=10^271.8 colourings, 191.8 orders more than the atoms in the observable universe. What is lacking is not the speed of computers but the quantity of matter. The lower bound is no better──the probabilistic method gives R(k,k)>2^k/2, one 24.94th of the truth at k=10, and the ratio widens with k. The upper bound is further off still──W(3,3) is truly 27, yet the classical bound could not be written down. A theorem’s upper bound measures the power of the proof’s tools, not the size of the object. One thing separates them──whether it exists, how large it is, and which one it is, are three different questions. The first may be “yes” while the other two stay open. The single word “proved” points at only one of the three. 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. ----- ラムゼーの定理は「十分大きければ必ず秩序が現れる」と言う。本稿が問うのは、「十分大きい」がどれだけかである──答は、定理は教えないである。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──ラムゼーの定理、ラムゼー数の既知の値と範囲、ファン・デル・ヴェルデン数、エルデシュの確率論的下限は、いずれも標準的である。組合せ論を作らない──使うのは一つの二項係数と、二つの対数だけである。ラムゼーの定理を証明しない──引くだけである。ラムゼー数を計算しない──R(5,5) の値を求めようとはしていない。求めるのに要る手間だけを数える。範囲の値を主張しない──R(5,5) in [43,48]、R(6,6) in [102,160] はある時点で知られている範囲であり、改善されうる。本稿の主張は範囲が空でないことであって、端の値ではない。総当たりが唯一の道だと言わない──実際の探索は対称性と枝刈りで大幅に減らす。2^903 は素朴な上界であって、必要な計算量ではない。それでも到底届かない、という桁の話である。アッカーマン級という語を厳密に使わない──ガワーズ以前の上界が塔の高さが増える型だったことを指す。本稿は上界の形を主張せず、真の値との乖離だけを言う。既刊との関係:論文163 は「良い符号が在る」と「これが良い符号だ」を分けた──あちらは存在と構成、本稿は存在と定量である。構成できても大きさが分からない場合を扱うので、切り口が違う。論文179 は「構成できない」に別根があると示した──本稿は構成できるのに手が届かない場合である。論文190 は「稀」を対数の目盛りで測った──本稿の 271.8 桁も対数で読む。論文259 は独立性を示す道が二つあると示した──本稿も示し方の種類を問う。加えたのはR(5,5) の総当たりを 10^271.8 通りと計算し、宇宙の原子との差を 191.8 桁と測ったこと、R(3,3)・R(4,4)・R(5,5) で手間が跳ぶ段を並べたこと、確率論的下限が k=10 で 24.94 分の一だと計算したこと、分離子を「存在と定量」に置いたことである。 第一に、確定している値は二つだけである。 R(3,3)=6 と R(4,4)=18 で、R(5,5) は[43,48] の範囲にしか収まっていない(第2節)。 第二に、これが本稿の芯である。 R(5,5)=43 を総当たりで確かめるには 2^903=10^271.8 通りが要り、宇宙の原子より 191.8 桁多い(第3節)。 第三に、一段上がるごとに跳ぶ。 R(3,3) は 32768 通りで手が届き、R(4,4) は 1.14x10^46 通りで計算機がようやく届いた(第3節)。 第四に、下限の証明も値を教えない。エルデシュの確率論的方法は R(k,k)>2^k/2 を与えるが、k=10 で実際の 24.94 分の一である(第4節)。 第五に、上界はもっと外れる。 W(3,3)=27 なのに、古典的証明が与えた上界はアッカーマン級だった(第5節)。 第六に、分離子は「存在と定量」である。論文163 の「存在と構成」とは別の切り口である(第6節)。 ラムゼーの定理は「十分大きければ必ず秩序が現れる」と言う。だが「十分大きい」を教えない。確定している値は R(3,3)=6 と R(4,4)=18 の二つだけで、R(5,5) は[43,48] の範囲にしか収まっていない──R(4,4) の確定でさえ、定理から 65 年かかった。総当たりの手間を数えれば理由が分かる──R(5,5)=43 は辺が 903 本、塗り分けが 2^903=10^271.8 通りで、観測可能な宇宙の原子より 191.8 桁多い。足りないのは計算機の速さではなく、物質の量である。下限の側も同じである──確率論的方法は R(k,k)>2^k/2 を与えるが、k=10 で実際の 24.94 分の一であり、比は k とともに開いていく。上界はもっと外れる──W(3,3) の真の値は 27 なのに、古典的証明の上界は書き下せない大きさだった。定理の上界は、証明の道具の性能を測っているのであって、対象の大きさを測っていない。分けるものは一つ──存在するかと、いくつかと、どれかは、三つの別の問いである。一つ目が「はい」でも、残り二つは開いたままでありうる。「証明された」という一語が、三つのうち一つしか指していない。 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
What if pathology foundation models could do more with less? GigaPath-Flash and GigaTIME-Flash cut computational demands while maintaining strong performance, opening the door to larger studies and broader exploration. The post GigaPath-Flash and GigaTIME-Flash: Toward population-scale discovery with efficient pathology foundation models appeared first on Microsoft Research.
MIT News · Artificial Intelligence· news.mit.eduAug 31, 2026
With millions of users across the world, Julia has been used to conduct cutting-edge research and to design new drugs, jet engines, heat pumps, and more.
MIT News · Artificial Intelligence· news.mit.eduAug 27, 2026
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
