Encyclopedia/All topics/Gravity

Gravity

Articles 1,381–1,440 of 1,755. Alphabetical by title.

• Gravity Seven Gaps Causal Simplex Wick Dihedral Angle3 Physical Mem Ioo

  In a discrete model of quantum gravity, a machine-checked theorem fixes the angle between two faces of a spacetime tetrahedron at the physical point, and states plainly what remain

• Gravity Seven Gaps Causal Simplex Wick Dihedral Cos3 Sq Alpha One Mem Ioo

  A machine-checked proof that the angles of a regular tetrahedron are real and well-defined, a small but certified step in a larger program to build a Lorentzian quantum gravity fro

• Gravity Seven Gaps Causal Simplex Wick Is Timelike Three One Eq Cross Slice

  In a three-dimensional causal triangulation, an edge is timelike exactly when it connects two different layers of space, a fact the framework's machine-checked library proves

• Gravity Seven Gaps Causal Simplex Wick Is Timelike Two Two Eq Cross Slice

  In a discrete model of spacetime, one theorem certifies which edges of a building block are timelike: exactly those that cross from one time slice to the next.

• Gravity Seven Gaps Causal Simplex Wick Lorentzian Cm3 Neg Three One

  A machine-checked proof shows that the basic building blocks of a causal spacetime cannot exist as ordinary Euclidean shapes, and must be reached by a mathematical rotation.

• Gravity Seven Gaps Causal Simplex Wick Lorentzian Sector Status Flags

  A small table of four Boolean flags records what a machine-checked library has proved about a discrete model of spacetime, and what it has left for later.

• Gravity Seven Gaps Causal Simplex4 D

  A machine-checked module certifies the exact geometry of the two building blocks of four-dimensional causal spacetime, and proves when each one is real.

• Gravity Seven Gaps Causal Simplex4 D Causal Simplex4 Dstatus Flags

  A machine-checked status record for four-dimensional causal simplices, and the honest line between what is proved and what remains open.

• Gravity Seven Gaps Causal Simplex4 D Cm Matrix N Euclidean Three Two

  In causal dynamical triangulations, a 4-simplex with three vertices on one time slice and two on the next has a squared-volume formula whose positivity threshold is exactly 7/12.

• Gravity Seven Gaps Causal Simplex4 D Cm Matrix N Lorentzian Four One

  A machine-checked proof shows that a standard 4D spacetime building block has a negative volume-squared, and explains why physics needs a Wick rotation.

• Gravity Seven Gaps Causal Simplex4 D Cm Matrix N Lorentzian Three Two

  A machine-checked proof shows that one of the two building blocks of 4D causal triangulations has a negative Cayley-Menger determinant, meaning it cannot be embedded in flat Euclid

• Gravity Seven Gaps Causal Simplex4 D Cm4 Euclidean Degenerate At Min

  A machine-checked theorem in the Recognition Science library fixes the exact point where a four-dimensional spacetime building block collapses to zero volume.

• Gravity Seven Gaps Causal Simplex4 D Is Timelike Four One Eq Cross Slice

  In a four-dimensional building block of spacetime, a machine-checked proof counts exactly which edges point across time, not just across space.

• Gravity Seven Gaps Causal Simplex4 D Is Timelike Three Two Eq Cross Slice

  A four-dimensional simplex with three vertices on one time slice and two on the next has exactly six timelike edges, a fact the framework verifies by exhaustive checking.

• Gravity Seven Gaps Causal Simplex4 D Wick Lorentzian Nondegenerate

  A machine-checked proof shows that rotating time into space in a four-dimensional simplex is its own inverse, and that the Lorentzian version can never be a Euclidean shape.

• Gravity Seven Gaps Class Pushforward

  Gravity's path sum can be reorganized by symmetry classes, and the framework proves exactly how the weights must be counted.

• Gravity Seven Gaps Class Pushforward Class Mass Eq Fiber Card Mul Mu

  A simple bookkeeping identity says that when you group objects into classes, the total weight of a class equals the number of objects in it times the weight of a representative.

• Gravity Seven Gaps Class Pushforward Class Pushforward Status Flags

  A machine-checked status board records which parts of a path-sum decomposition are proved theorems and which remain open targets.

• Gravity Seven Gaps Class Pushforward Exists Non Singleton Fiber

  A machine-checked proof shows that two distinct labeled complexes can be equivalent under relabeling, a fact that changes how sums over physical states must be counted.

• Gravity Seven Gaps Class Pushforward First Endpoint Val Edge Ab

  A single line in a machine-checked proof library records which vertex of a two-vertex edge is listed first, and that choice turns out to matter for how the framework counts its sum

• Gravity Seven Gaps Class Pushforward Mu Lt Class Mass Edge Class

  In a discrete ledger, swapping two labels can change a counted mass, and a kernel-checked theorem shows exactly where the difference first appears.

• Gravity Seven Gaps Class Pushforward One Lt Fiber Card Edge Class

  A machine-checked proof shows that two differently labeled triangles belong to the same symmetry class, a fact that changes how a certain sum over geometries is counted.

• Gravity Seven Gaps Class Pushforward Sum Eq Quotient Sum Class Mass

  A theorem about summing over equivalence classes shows how a labeled sum can be rewritten as a sum over classes, with a weight that counts how many labels collapse into each class.

• Gravity Seven Gaps Curved Operator Underdetermination

  A flat spectrum cannot tell you how gravity couples to curvature, and a machine-checked proof now shows exactly why.

• Gravity Seven Gaps Curved Operator Underdetermination Curvature Correction Consi

  A machine-checked proof shows that a simple rate bound certifies whether a curved lattice operator's spectrum converges to its continuum limit.

• Gravity Seven Gaps Curved Operator Underdetermination Curved Continuum Eigenvalu

  A machine-checked theorem shows why the flat spectrum of a lattice operator cannot reveal how curvature couples to it, a core obstacle in the framework's gravity program.

• Gravity Seven Gaps Curved Operator Underdetermination Curved Spectrum Converges

  A machine-checked theorem shows that a curved operator's spectrum converges exactly when its correction to the flat case does, turning a technical check into a precise criteri

• Gravity Seven Gaps Curved Operator Underdetermination Extensions Agree On Entire

  A machine-checked theorem shows two different curved versions of a gravitational operator become identical when space is flat, exposing a gap in what flat measurements can tell us.

• Gravity Seven Gaps Curved Operator Underdetermination Extensions Distinct At Non

  On a curved lattice, two candidate gravity operators that look identical in flat space are provably different, exposing a gap in what flat measurements can tell us.

• Gravity Seven Gaps Curved Operator Underdetermination Flat Spectrum Underdetermi

  A machine-checked theorem shows why a flat geometry's vibration pattern cannot uniquely determine how curvature couples to matter.

• Gravity Seven Gaps Discrete Lichnerowicz

  A machine-checked proof that lattice vibrations on a flat 3-torus converge to the continuum gravity operator, with an honest scope limit.

• Gravity Seven Gaps Discrete Lichnerowicz Continuum Profile Second Deriv

  A machine-checked proof that the simplest continuous wave has exactly the second derivative expected of it, and nothing more.

• Gravity Seven Gaps Discrete Lichnerowicz Discrete Eigenvalue Tendsto

  A machine-checked proof shows that a certain discrete eigenvalue on a lattice converges to the continuum value as the lattice is refined, but only along one axis.

• Gravity Seven Gaps Discrete Lichnerowicz Discrete Eigenvalue Tendsto Raw

  A discrete eigenvalue on a lattice of points approaches a continuum value as the lattice is refined, but only along one direction.

• Gravity Seven Gaps Discrete Lichnerowicz Discrete Tt Spectrum Converges To Flat

  On a flat three-torus, the vibration frequencies of a lattice of points approach the continuous gravitational-wave frequencies as the lattice gets finer, in one direction only.

• Gravity Seven Gaps Discrete Lichnerowicz Polarizations Linear Independent

  A machine-checked proof that the two standard gravitational wave polarizations are distinct, and why that is only a small piece of the story.

• Gravity Seven Gaps Discrete Lichnerowicz Status Curved Background Open

  A machine-checked flag in the framework's gravity library records that curved spacetimes remain unproved, marking a precise boundary of current knowledge.

• Gravity Seven Gaps Dynamic Structure Function Blocker

  A machine-checked proof shows why a fixed background weight cannot represent the dynamic inverse metric that full gravity requires.

• Gravity Seven Gaps Dynamic Structure Function Blocker Background Weighted Contin

  A machine-checked theorem shows a fixed background weight can reach the continuum limit, but cannot represent a metric that changes with the phase-space point.

• Gravity Seven Gaps Dynamic Structure Function Blocker Concrete Dynamic Inverse M

  A simple two-point example shows why a fixed background cannot capture the full dynamics of general relativity.

• Gravity Seven Gaps Dynamic Structure Function Blocker Exists Fixed Background If

  A machine-checked theorem pins down exactly when a fixed background can stand in for a dynamic one in a lattice gravity model: only when the dynamic object does not actually vary.

• Gravity Seven Gaps Dynamic Structure Function Blocker Fixed Background Represent

  In general relativity, the gravitational field itself carries energy, so its equations must respond to the field's own state; a simplified model that keeps the field's in

• Gravity Seven Gaps Dynamic Structure Function Blocker Ham W Has Background Struc

  A machine-checked theorem certifies that a certain Hamiltonian bracket works, and then shows exactly why that success is not enough for full gravity.

• Gravity Seven Gaps Dynamic Structure Function Blocker No Fixed Background Repres

  A machine-checked theorem shows why a fixed background cannot encode the full dynamics of general relativity, and what that leaves open.

• Gravity Seven Gaps Edge Tensor Sector

  A machine-checked proof that the simplest way to describe gravity's geometry on a lattice leaves out most of the possible distortions, and an explicit example of what it misse

• Gravity Seven Gaps Edge Tensor Sector Periodic Conformal Log Subspace5 Iff Encod

  A machine-checked theorem shows that two different ways of describing a special class of edge strains on a 5x5x5 grid are exactly the same class.

• Gravity Seven Gaps Edge Tensor Sector Periodic Edge Inner Product5 Rectangle She

  A simple rectangle-shaped strain on a 5x5x5 grid of points is proved to be invisible to a whole family of smoother strains, and that fact is exactly what the declaration records.

• Gravity Seven Gaps Edge Tensor Sector Periodic Torus5 Conformal Range Finrank Lt

  A proved theorem on a 5×5×5 periodic grid shows that a simple, vertex-based approximation to gravity's edge distortions misses most of the possible motions.

• Gravity Seven Gaps Edge Tensor Sector Periodic Torus5 Edge Tensor Sector Beyond

  On a small periodic grid, the simplest edge distortions form a tiny slice of all possible ones, and a concrete example proves the rest exists.

• Gravity Seven Gaps Edge Tensor Sector Periodic Torus5 Exists Nonconformal Constr

  On a periodic 5x5x5 grid, most edge distortions cannot be reduced to vertex scalings; this theorem exhibits one explicitly.

• Gravity Seven Gaps Edge Tensor Sector Periodic Torus5 Exists Not Mem Conformal R

  On a small periodic grid, a machine-checked proof shows that most possible edge strains cannot arise from a simple vertex-based rule.

• Gravity Seven Gaps Edge Tensor Sector Rectangle Shear Face5 Nonzero In Orthogona

  A concrete deformation pattern on a periodic grid proves that a simple class of edge strains does not cover all possibilities, leaving a measurable gap.

• Gravity Seven Gaps Edge Tensor Sector X Uniform Strain5 Nonzero Orthogonal Compo

  A simple uniform strain on a 5×5×5 grid is proved to lie outside the conformal slice, with a concrete witness showing why.

• Gravity Seven Gaps Exact Shell Gauge Preflight

  A machine-checked derivation shows that the standard symmetry-factor weight in discrete gravity follows from a simple counting principle, not from a postulate.

• Gravity Seven Gaps Exact Shell Gauge Preflight Gauge Counting Mass Unique

  A machine-checked proof shows that one natural way of counting discrete geometries forces a specific symmetry factor, the same one physicists have long used by convention.

• Gravity Seven Gaps Exact Shell Gauge Preflight Gauge Orbit Mass Mul Pair Count

  A theorem about counting symmetries shows why a standard weight in discrete gravity is forced, not chosen.

• Gravity Seven Gaps Exact Shell Gauge Preflight Gauge Preflight Grounded

  A machine-checked theorem shows that a standard symmetry factor in discrete gravity, the 1/|Aut| measure, follows from a simple counting principle, but the principle itself remains

• Gravity Seven Gaps Exact Shell Gauge Preflight Labeled Z Eq Orbit Weighted Class

  A machine-checked theorem shows that a sum over every labeled triangulation equals a sum over classes of equivalent ones, with each class weighted by its symmetry count.

• Gravity Seven Gaps Exact Shell Gauge Preflight Pair Count Eq Orbit Card Mul Aut

  A simple counting identity, derived from a symmetry principle, explains why each distinct configuration in a discrete gravity model carries a specific statistical weight.

• Gravity Seven Gaps Exact Shell Gauge Preflight Relabeling Count Eq Aut Card

  A theorem about counting the ways to relabel a discrete geometric object pins down a standard symmetry factor in quantum gravity, without assuming it.