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Only two independent amplitudes exist for elastic spin‑zero–spin‑1/2 scattering in the five‑dimensional DKP algebraResearchers prove a new ‘K‑property’ criterion for dynamic systems with hidden directionsGeometry of curves at infinity and a regular connection together determine the elementary formal blocks of one-variable differential operatorsAn asymptotic Γ‑BMT inequality holds on every smooth polarized complex threefoldAsymptotic count of d‑anticodes: almost all anticodes come from subsets of a maximum anticode (for fixed q and 4≤d≤n−1, except the binary endpoint)Map EΓ → ĒΓ is rationally injective on equivariant KK-theory for every countable discrete group Γ and every Γ–C*-algebra ANew “convex-like” submanifolds in Lorentz–Minkowski space come with roofs, caps and a volume comparison: inner boundaries are no larger than outer onesCyclic number fields: integral trace lattices match exactly when degree, signature and signed discriminant agreeAuthor: recent AI math triumphs stoke fears but do not show machines can invent new concepts or self‑improveProof of Nagata’s conjecture for r ≥ 10: degree must exceed m·√r for very general point setsOnly two independent amplitudes exist for elastic spin‑zero–spin‑1/2 scattering in the five‑dimensional DKP algebraResearchers prove a new ‘K‑property’ criterion for dynamic systems with hidden directionsGeometry of curves at infinity and a regular connection together determine the elementary formal blocks of one-variable differential operatorsAn asymptotic Γ‑BMT inequality holds on every smooth polarized complex threefoldAsymptotic count of d‑anticodes: almost all anticodes come from subsets of a maximum anticode (for fixed q and 4≤d≤n−1, except the binary endpoint)Map EΓ → ĒΓ is rationally injective on equivariant KK-theory for every countable discrete group Γ and every Γ–C*-algebra ANew “convex-like” submanifolds in Lorentz–Minkowski space come with roofs, caps and a volume comparison: inner boundaries are no larger than outer onesCyclic number fields: integral trace lattices match exactly when degree, signature and signed discriminant agreeAuthor: recent AI math triumphs stoke fears but do not show machines can invent new concepts or self‑improveProof of Nagata’s conjecture for r ≥ 10: degree must exceed m·√r for very general point sets

Today's Briefing

Thursday, October 29, 2026
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MathematicsFeatured briefing

Only two independent amplitudes exist for elastic spin‑zero–spin‑1/2 scattering in the five‑dimensional DKP algebra

A recent analysis shows that the rich set of Lorentz covariants of the five‑dimensional Duffin‑Kemmer‑Petiau (DKP) algebra collapses to just

October 29, 2026EN2 min read
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Latest Research

Mathematics
October 29, 2026

Researchers prove a new ‘K‑property’ criterion for dynamic systems with hidden directions

A team of mathematicians has shown that the unique equilibrium state of many complex systems—such as the flow of a fluid around an object or

EN
2 min read
Mathematics
October 28, 2026

Geometry of curves at infinity and a regular connection together determine the elementary formal blocks of one-variable differential operators

Main discovery The authors give a geometric description of the formal local data of holonomic modules over the first Weyl algebra. Restricte

EN
2 min read
Mathematics
October 26, 2026

An asymptotic Γ‑BMT inequality holds on every smooth polarized complex threefold

Main result. The paper proves an asymptotic Γ‑Bayer–Macrì–Toda (Γ‑BMT) inequality on every smooth polarized complex threefold. Set D = 1/2·K

EN
2 min read
Mathematics
October 24, 2026

Asymptotic count of d‑anticodes: almost all anticodes come from subsets of a maximum anticode (for fixed q and 4≤d≤n−1, except the binary endpoint)

Main discovery. For fixed finite field size q, and for diameters 4 ≤ d ≤ n−1 (excluding the binary endpoint q=2, d=n−1), the total number of

EN
2 min read
Mathematics
October 24, 2026

Map EΓ → ĒΓ is rationally injective on equivariant KK-theory for every countable discrete group Γ and every Γ–C*-algebra A

Main discovery. For every countable discrete group Γ and every Γ–C*-algebra A, the map π_* induced by the natural Γ‑equivariant map π: EΓ →

EN
2 min read
Mathematics
October 24, 2026

New “convex-like” submanifolds in Lorentz–Minkowski space come with roofs, caps and a volume comparison: inner boundaries are no larger than outer ones

Main discovery The authors introduce a broad class of shapes called convex-like submanifolds in Lorentz–Minkowski space. They attach three g

EN
2 min read
Mathematics
October 23, 2026

Cyclic number fields: integral trace lattices match exactly when degree, signature and signed discriminant agree

Main discovery Two cyclic number fields have isometric integral trace lattices exactly when they share three arithmetic invariants: degree,

EN
2 min read
Mathematics
October 23, 2026

Author: recent AI math triumphs stoke fears but do not show machines can invent new concepts or self‑improve

Main finding: The author argues that recent AI achievements in mathematics have intensified predictions of human intellectual obsolescence.

EN
2 min read
Mathematics
October 23, 2026

Proof of Nagata’s conjecture for r ≥ 10: degree must exceed m·√r for very general point sets

Main discovery A proof shows that for r ≥ 10 and very general points p1,…,pr in the complex projective plane P2, any nonzero homogeneous pol

EN
2 min read
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