Journal of the Institute of Mathematics of Jussieu

Papers
(The median citation count of Journal of the Institute of Mathematics of Jussieu is 0. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-05-01 to 2025-05-01.)
ArticleCitations
ON GROUPS OF UNITS OF SPECIAL AND ONE-RELATOR INVERSE MONOIDS12
ZETA INVARIANTS OF MORSE FORMS11
JMJ volume 21 Issue 1 Cover and Back matter10
PETERZIL–STEINHORN SUBGROUPS AND -STABILIZERS IN ACF10
GALOIS REPRESENTATIONS FOR EVEN GENERAL SPECIAL ORTHOGONAL GROUPS8
ON RESIDUES AND CONJUGACIES FOR GERMS OF 1-D PARABOLIC DIFFEOMORPHISMS IN FINITE REGULARITY8
GEOMETRIC QUADRATIC CHABAUTY7
COMPARISON OF KUMMER LOGARITHMIC TOPOLOGIES WITH CLASSICAL TOPOLOGIES7
JMJ volume 21 issue 6 Cover and Back matter7
THE EISENSTEIN IDEAL OF WEIGHT k AND RANKS OF HECKE ALGEBRAS6
ISOMETRIES AND HERMITIAN OPERATORS ON SPACES OF VECTOR-VALUED LIPSCHITZ MAPS6
JMJ volume 24 issue 3 Cover and Front matter6
JMJ volume 22 issue 6 Cover and Front matter6
ON SOME CONSEQUENCES OF A THEOREM OF J. LUDWIG6
SUFFICIENT CONDITIONS FOR A GROUP OF HOMEOMORPHISMS OF THE CANTOR SET TO BE TWO-GENERATED6
VARIANTS OF A MULTIPLIER THEOREM OF KISLYAKOV5
TEMPERED HOMOGENEOUS SPACES IV5
REDUCTIONS OF -DIMENSIONAL SEMISTABLE REPRESENTATIONS WITH LARGE -INVARIANT5
p-ADIC L-FUNCTIONS AND RATIONAL POINTS ON CM ELLIPTIC CURVES AT INERT PRIMES5
RIGIDITY FOR VON NEUMANN ALGEBRAS OF GRAPH PRODUCT GROUPS II. SUPERRIGIDITY RESULTS5
COHOMOLOGICAL MACKEY 2-FUNCTORS5
THE p-ZASSENHAUS FILTRATION OF A FREE PROFINITE GROUP AND SHUFFLE RELATIONS4
THE SIMPLE SEPARATING SYSTOLE FOR HYPERBOLIC SURFACES OF LARGE GENUS4
JMJ volume 22 issue 1 Cover and Back matter4
THERMODYNAMIC FORMALISM FOR AMENABLE GROUPS AND COUNTABLE STATE SPACES4
LINEAR GROWTH OF TRANSLATION LENGTHS OF RANDOM ISOMETRIES ON GROMOV HYPERBOLIC SPACES AND TEICHMÜLLER SPACES4
SHUFFLE ALGEBRAS FOR QUIVERS AND R-MATRICES4
CHARACTERIZATION OF THE REDUCED PERIPHERAL SYSTEM OF LINKS4
THE LOCAL-ORBIFOLD CORRESPONDENCE FOR SIMPLE NORMAL CROSSING PAIRS4
ON THE TEMPERED FUNDAMENTAL GROUPS OF HYPERBOLIC CURVES OF GENUS OVER3
ORDERS OF GROWTH AND GENERALIZED ENTROPY3
JMJ volume 23 issue 2 Cover and Front matter3
THE p-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES3
GEOMETRICAL AND MEASURE-THEORETIC STRUCTURES OF MAPS WITH A MOSTLY EXPANDING CENTER3
LELONG NUMBERS OF m-SUBHARMONIC FUNCTIONS ALONG SUBMANIFOLDS3
K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES3
MUKAI’S PROGRAM FOR NONPRIMITIVE CURVES ON K3 SURFACES2
ON ODA’S PROBLEM AND SPECIAL LOCI2
NATURAL MAPS FOR MEASURABLE COCYCLES OF COMPACT HYPERBOLIC MANIFOLDS2
GENERALISED AUTOMORPHIC SHEAVES AND THE PROPORTIONALITY PRINCIPLE OF HIRZEBRUCH-MUMFORD2
EXTENSION BETWEEN SIMPLE MODULES OF PRO-p-IWAHORI HECKE ALGEBRAS2
$ \epsilon $ -ISOMORPHISMS FOR RANK ONE $( \varphi , \Gamma )$ -MODULES OVER LUBIN-TATE ROBBA RINGS2
A $dd^c$ -TYPE CONDITION BEYOND THE KÄHLER REALM2
ZERO-CYCLES ON NORMAL PROJECTIVE VARIETIES2
JMJ volume 22 issue 5 Cover and Back matter2
GEOMETRIC LOCAL -FACTORS IN HIGHER DIMENSIONS2
HORN PROBLEM FOR QUASI-HERMITIAN LIE GROUPS2
BERNOULLI ACTIONS OF TYPE III WITH PRESCRIBED ASSOCIATED FLOW2
MODEL THEORY OF GALOIS ACTIONS OF TORSION ABELIAN GROUPS2
JMJ volume 22 issue 3 Cover and Front matter2
MILNOR K-THEORY, F-ISOCRYSTALS AND SYNTOMIC REGULATORS2
GAGA FOR HENSELIAN SCHEMES2
JMJ volume 21 issue 6 Cover and Front matter2
ON NONCRITICAL GALOIS REPRESENTATIONS2
AUTOMORPHIC LEFSCHETZ PROPERTIES FOR NONCOMPACT ARITHMETIC MANIFOLDS2
THE DIAGONAL CYCLE EULER SYSTEM FOR2
ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS2
CODIMENSION ONE FOLIATIONS IN POSITIVE CHARACTERISTIC1
JMJ volume 22 issue 4 Cover and Back matter1
QUASI-ISOMETRIC EMBEDDINGS INAPPROXIMABLE BY ANOSOV REPRESENTATIONS1
KOBAYASHI-OCHIAI’S FINITENESS THEOREM FOR ORBIFOLD PAIRS OF GENERAL TYPE1
UNIFORM LOCAL CONSTANCY OF ÉTALE COHOMOLOGY OF RIGID ANALYTIC VARIETIES1
TWISTED DOUBLING INTEGRALS FOR BRYLINSKI–DELIGNE EXTENSIONS OF CLASSICAL GROUPS1
TWISTED GAN–GROSS–PRASAD CONJECTURE FOR CERTAIN TEMPERED L-PACKETS1
PERFECTING GROUP SCHEMES1
JMJ volume 23 issue 6 Cover and Back matter1
ON THE CHOW THEORY OF PROJECTIVIZATIONS1
MOCK PLECTIC POINTS1
PRESCRIBED VIRTUAL HOMOLOGICAL TORSION OF 3-MANIFOLDS1
JMJ volume 20 Issue 6 Cover and Back matter1
RANK 2 $\ell $ -ADIC LOCAL SYSTEMS AND HIGGS BUNDLES OVER A CURVE1
NORMAL REFLECTION SUBGROUPS OF COMPLEX REFLECTION GROUPS1
FUNCTIONAL CALCULI FOR SECTORIAL OPERATORS AND RELATED FUNCTION THEORY1
ARCHIMEDEAN NEWFORM THEORY FOR $\operatorname {\mathrm {GL}}_n$1
GEOMETRIC WEIGHT-SHIFTING OPERATORS ON HILBERT MODULAR FORMS IN CHARACTERISTIC p1
GENERALISED QUADRATIC FORMS OVER TOTALLY REAL NUMBER FIELDS1
TEICHMÜLLER CURVES IN HYPERELLIPTIC COMPONENTS OF MEROMORPHIC STRATA1
JMJ volume 23 issue 3 Cover and Front matter1
INDIVISIBILITY OF HEEGNER CYCLES OVER SHIMURA CURVES AND SELMER GROUPS1
SIMPLE TYPE THEORY FOR METAPLECTIC COVERS OF $\operatorname {GL}(r)$ OVER A NON-ARCHIMEDEAN LOCAL FIELD1
POLYNOMIALS REPRESENTED BY NORM FORMS VIA THE BETA SIEVE1
COMBINED COUNT OF REAL RATIONAL CURVES OF CANONICAL DEGREE 2 ON REAL DEL PEZZO SURFACES WITH1
REDUCED QUIVER QUANTUM TOROIDAL ALGEBRAS1
JMJ volume 23 issue 6 Cover and Front matter1
JMJ volume 22 issue 2 Cover and Back matter1
WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY1
A GENERALISATION OF WITTEN’S CONJECTURE FOR THE PIXTON CLASS AND THE NONCOMMUTATIVE KDV HIERARCHY1
GENUS MINIMAL k-NOIDS AND SADDLE TOWERS IN1
KHOVANOV SPECTRA FOR TANGLES1
JMJ volume 20 Issue 3 Cover and Front matter1
QUASI-ERGODICITY OF COMPACT STRONG FELLER SEMIGROUPS ON $L^2$1
OBSERVABILITY OF BAOUENDI–GRUSHIN-TYPE EQUATIONS THROUGH RESOLVENT ESTIMATES1
JMJ volume 21 Issue 1 Cover and Front matter1
EULER CHARACTERISTIC AND SIGNATURE OF REAL SEMI-STABLE DEGENERATIONS1
ON K-STABILITY OF CALABI-YAU FIBRATIONS1
DYNAMICAL MCDUFF-TYPE PROPERTIES FOR GROUP ACTIONS ON VON NEUMANN ALGEBRAS1
THE QUANTUM ISOMERIC SUPERCATEGORY0
THE BOREL CHARACTER0
ON THE EXISTENCE OF NON-NORM-ATTAINING OPERATORS0
THE p-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES – CORRIGENDUM0
A FOURIER-TYPE CHARACTERISATION FOR GEVREY VECTORS ON HYPO-ANALYTIC STRUCTURES AND PROPAGATION OF GEVREY SINGULARITIES0
JMJ volume 23 issue 5 Cover and Front matter0
JMJ volume 21 issue 2 Cover and Front matter0
JMJ volume 22 issue 3 Cover and Back matter0
INTRINSIC STABILIZER REDUCTION AND GENERALIZED DONALDSON–THOMAS INVARIANTS0
JMJ volume 21 issue 2 Cover and Back matter0
GOOD REDUCTION AND CYCLIC COVERS0
REPRESENTATION VARIETIES OF ALGEBRAS WITH NODES0
JMJ volume 22 issue 5 Cover and Front matter0
EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS0
JMJ volume 23 issue 1 Cover and Front matter0
EQUILIBRIUM STATES FOR CENTER ISOMETRIES0
COMPACTNESS AND STRUCTURE OF ZERO-STATES FOR UNORIENTED AVILES–GIGA FUNCTIONALS0
A HECKE ACTION ON -MODULES0
TRILINEAR FOURIER MULTIPLIERS ON HARDY SPACES0
JMJ volume 21 issue 5 Cover and Front matter0
THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY0
TWISTED RUELLE ZETA FUNCTION ON HYPERBOLIC MANIFOLDS AND COMPLEX-VALUED ANALYTIC TORSION0
WILES DEFECT OF HECKE ALGEBRAS VIA LOCAL-GLOBAL ARGUMENTS0
JMJ volume 23 issue 2 Cover and Back matter0
PROJECTIVELY FLAT FOLIATIONS0
ABELIAN CYCLES IN THE HOMOLOGY OF THE TORELLI GROUP0
FORMALLY REGULAR RINGS AND DESCENT OF REGULARITY0
HYPERBOLIC MANIFOLDS THAT FIBRE ALGEBRAICALLY UP TO DIMENSION 80
MODEL CATEGORIES AND PRO-p IWAHORI–HECKE MODULES0
JMJ volume 20 Issue 3 Cover and Back matter0
THE ZEROTH -STABLE HOMOTOPY SHEAF OF A MOTIVIC SPACE0
STRUCTURAL STABILITY OF MEANDERING-HYPERBOLIC GROUP ACTIONS0
A NONCOMMUTATIVE ANALOGUE OF CLAUSEN’S VIEW ON THE IDÈLE CLASS GROUP0
JMJ volume 24 issue 2 Cover and Back matter0
JMJ volume 22 issue 6 Cover and Back matter0
DISTRIBUTION OF FROBENIUS ELEMENTS IN FAMILIES OF GALOIS EXTENSIONS0
JMJ volume 20 Issue 4 Cover and Back matter0
A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES0
OPTIMAL GEVREY STABILITY OF HYDROSTATIC APPROXIMATION FOR THE NAVIER-STOKES EQUATIONS IN A THIN DOMAIN0
JMJ volume 21 issue 3 Cover and Back matter0
RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE $K3^{[n]}$0
INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS0
JMJ volume 22 issue 1 Cover and Front matter0
SPECIAL VALUES OF ZETA-FUNCTIONS OF REGULAR SCHEMES0
ON DEFORMATION THEORY IN HIGHER LOGARITHMIC GEOMETRY0
GYSIN TRIANGLES IN THE CATEGORY OF MOTIFS WITH MODULUS0
REAL TOPOLOGICAL HOCHSCHILD HOMOLOGY OF SCHEMES0
ON THE DISTINCTION OF IWAHORI-SPHERICAL DISCRETE SERIES REPRESENTATIONS0
DT INVARIANTS FROM VERTEX ALGEBRAS0
JMJ volume 23 issue 1 Cover and Back matter0
GENERALISATIONS OF LODAY’S ASSEMBLY MAPS FOR LAWVERE’S ALGEBRAIC THEORIES0
JMJ volume 21 issue 4 Cover and Front matter0
ON THE GEOMETRY OF THE PAPPAS–RAPOPORT MODELS FOR PEL SHIMURA VARIETIES0
JMJ volume 24 issue 3 Cover and Back matter0
A NOTE ON CHARACTER SUMS OVER SHORT MOVING INTERVALS0
GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS0
INTEGRAL POINTS ON SINGULAR DEL PEZZO SURFACES0
ODD RANK VECTOR BUNDLES IN ETA-PERIODIC MOTIVIC HOMOTOPY THEORY0
FINITE-DIMENSIONAL DIFFERENTIAL-ALGEBRAIC PERMUTATION GROUPS0
ACTIONS OF MONOIDAL CATEGORIES AND REPRESENTATIONS OF CARTAN TYPE LIE ALGEBRAS0
THE COHOMOLOGY OF p-ADIC DELIGNE-LUSZTIG SCHEMES OF COXETER TYPE0
JMJ volume 22 issue 4 Cover and Front matter0
SPECTRAL INEQUALITIES FOR COMBINATIONS OF HERMITE FUNCTIONS AND NULL-CONTROLLABILITY FOR EVOLUTION EQUATIONS ENJOYING GELFAND–SHILOV SMOOTHING EFFECTS0
AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES0
PONTRYAGIN DUALITY FOR VARIETIES OVER p-ADIC FIELDS0
ON BOUNDEDNESS OF DIVISORS COMPUTING MINIMAL LOG DISCREPANCIES FOR SURFACES0
COVERING INTEGERS BY $x^2 + dy^2$0
MOMENTS AND HYBRID SUBCONVEXITY FOR SYMMETRIC-SQUARE L-FUNCTIONS0
ALGEBRAIC CLASSES IN MIXED CHARACTERISTIC AND ANDRÉ’S p-ADIC PERIODS0
JMJ volume 22 issue 2 Cover and Front matter0
GAUSSIAN HOLOMORPHIC SECTIONS ON NONCOMPACT COMPLEX MANIFOLDS0
JMJ volume 23 issue 4 Cover and Front matter0
POLISH SPACES OF BANACH SPACES: COMPLEXITY OF ISOMETRY AND ISOMORPHISM CLASSES0
TWISTED BLANCHFIELD PAIRINGS AND TWISTED SIGNATURES II: RELATION TO CASSON-GORDON INVARIANTS0
OVERCONVERGENT DE RHAM EICHLER–SHIMURA MORPHISMS0
TRUNCATED AFFINE SPRINGER FIBERS AND ARTHUR’S WEIGHTED ORBITAL INTEGRALS0
ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 20
A FREENESS CRITERION WITHOUT PATCHING FOR MODULES OVER LOCAL RINGS0
STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS0
CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES0
COUNTING DISCRETE, LEVEL- $1$ , QUATERNIONIC AUTOMORPHIC REPRESENTATIONS ON $G_2$0
A CATEGORICAL APPROACH TO THE BAUM–CONNES CONJECTURE FOR ÉTALE GROUPOIDS0
ADDENDUM: REAL TOPOLOGICAL HOCHSCHILD HOMOLOGY OF SCHEMES0
INTRINSIC STABILIZER REDUCTION AND GENERALIZED DONALDSON–THOMAS INVARIANTS – ERRATUM0
NORMALISED TANGENT BUNDLE, VARIETIES WITH SMALL CODEGREE AND PSEUDOEFFECTIVE THRESHOLD0
EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS $\mathfrak {f}_4$ AND $\mathfrak {e}_6$ VIA CONTACTIFICATIONS0
STATED SKEIN MODULES OF 3-MANIFOLDS AND TQFT0
FANO FOURFOLDS WITH LARGE ANTICANONICAL BASE LOCUS0
ARBITRARILY LARGE p-TORSION IN TATE-SHAFAREVICH GROUPS0
NOMBRE DE PETITS POINTS SUR UNE VARIÉTÉ ABÉLIENNE0
JMJ volume 20 Issue 5 Cover and Front matter0
JMJ volume 24 issue 1 Cover and Back matter0
JMJ volume 23 issue 3 Cover and Back matter0
RATIONALITY OVER NONCLOSED FIELDS OF FANO THREEFOLDS WITH HIGHER GEOMETRIC PICARD RANK0
INTERSECTION COHOMOLOGY OF THE MODULI SPACE OF HIGGS BUNDLES ON A GENUS 2 CURVE0
HIGHER MOMENT FORMULAE AND LIMITING DISTRIBUTIONS OF LATTICE POINTS0
THE SLICE-BENNEQUIN INEQUALITY FOR THE FRACTIONAL DEHN TWIST COEFFICIENT0
JMJ volume 21 issue 3 Cover and Front matter0
THE STABLE LIMIT DAHA AND THE DOUBLE DYCK PATH ALGEBRA0
LOG-TRANSFORM AND THE WEAK HARNACK INEQUALITY FOR KINETIC FOKKER-PLANCK EQUATIONS0
BERRY–ESSEEN BOUND AND LOCAL LIMIT THEOREM FOR THE COEFFICIENTS OF PRODUCTS OF RANDOM MATRICES0
RANKS OF SOFT OPERATORS IN NOWHERE SCATTERED $\mathrm {C}^*$ -ALGEBRAS0
ERRATUM TO: CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES0
CATEGORICAL AND K-THEORETIC HALL ALGEBRAS FOR QUIVERS WITH POTENTIAL0
VALUES OF ZETA FUNCTIONS OF ARITHMETIC SURFACES AT0
THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC0
JMJ volume 23 issue 5 Cover and Back matter0
ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS0
GENERAL HYPERPLANE SECTIONS OF LOG CANONICAL THREEFOLDS IN POSITIVE CHARACTERISTIC0
COHOMOLOGIE DE DE RHAM DU REVÊTEMENT MODÉRÉ DE L’ESPACE DE DRINFELD0
PROPER $\mathrm {CAT(0)}$ ACTIONS OF UNIPOTENT-FREE LINEAR GROUPS0
LOGARITHMIC DE RHAM–WITT COMPLEXES VIA THE DÉCALAGE OPERATOR0
BANACH SPACES IN WHICH LARGE SUBSETS OF SPHERES CONCENTRATE0
ON GROUPS AND FIELDS DEFINABLE IN $1$ -H-MINIMAL FIELDS0
JMJ volume 21 issue 4 Cover and Back matter0
LIMIT SETS OF UNFOLDING PATHS IN OUTER SPACE0
QUANTUM ERGODICITY FOR COMPACT QUOTIENTS OF IN THE BENJAMINI–SCHRAMM LIMIT0
ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON SPACES OF JACOBI DIAGRAMS. II0
THE HITCHIN CONNECTION IN ARBITRARY CHARACTERISTIC0
PARITY OF CONJUGATE SELF-DUAL REPRESENTATIONS OF INNER FORMS OF $\operatorname { {GL}}_n$ OVER p-ADIC FIELDS0
A DERIVED LAGRANGIAN FIBRATION ON THE DERIVED CRITICAL LOCUS0
BNS INVARIANTS AND ALGEBRAIC FIBRATIONS OF GROUP EXTENSIONS0
THE OPTIMAL MALLIAVIN-TYPE REMAINDER FOR BEURLING GENERALIZED INTEGERS0
JMJ volume 20 Issue 5 Cover and Back matter0
BIG MAPPING CLASS GROUPS WITH HYPERBOLIC ACTIONS: CLASSIFICATION AND APPLICATIONS0
JMJ volume 20 Issue 6 Cover and Front matter0
JMJ volume 21 issue 5 Cover and Back matter0
ON LARGE EXTERNALLY DEFINABLE SETS IN NIP0
UNIFORM BOUNDS FOR $\operatorname {GL}(3)\times \operatorname {GL}(2)$ L-FUNCTIONS0
ON THE DEGREE OF IRRATIONALITY OF LOW GENUS $K3$ SURFACES0
JMJ volume 23 issue 4 Cover and Back matter0
ON MORPHISMS KILLING WEIGHTS AND STABLE HUREWICZ-TYPE THEOREMS0
JMJ volume 20 Issue 4 Cover and Front matter0
TOROIDAL q-OPERS0
TRANSITION DENSITIES OF SUBORDINATORS OF POSITIVE ORDER0
THE GENERIC FIBRE OF MODULI SPACES OF BOUNDED LOCAL G-SHTUKAS0
AN EFFECTIVE UPPER BOUND FOR ANTI-CANONICAL VOLUMES OF SINGULAR FANO THREEFOLDS0
ERRATUM TO THE PAPER ‘BREUIL–KISIN–FARGUES MODULES WITH COMPLEX MULTIPLICATION’0
-CONNECTEDNESS OF MODULI OF VECTOR BUNDLES ON A CURVE0
CARLSON–GRIFFITHS THEORY FOR COMPLETE KÄHLER MANIFOLDS0
JMJ volume 24 issue 1 Cover and Front matter0
UNITARY REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS AT ROOTS OF UNITY: COMBINATORIAL CLASSIFICATION AND BGG RESOLUTIONS0
JMJ volume 24 issue 2 Cover and Front matter0
LINEAR SERIES ON GENERAL CURVES WITH PRESCRIBED INCIDENCE CONDITIONS0
MORAVA K-THEORY AND FILTRATIONS BY POWERS0
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