Encyclopedia/All topics/Gravity

Gravity

Articles 1,621–1,680 of 1,755. Alphabetical by title.

• Gravity Seven Gaps Weighted Hypersurface Bracket Pderiv Q Ham W

  A machine-checked theorem says how a weighted Hamiltonian changes when you nudge the field values, and it is careful about what it does not prove.

• Gravity Seven Gaps Weighted Hypersurface Bracket Weighted Structure Sum Tendsto

  A machine-checked theorem shows that certain weighted sums on a lattice converge to a continuous integral, a step toward linking discrete and continuous gravity.

• Gravity Seven Gaps Wick Action Complex First Lorentzian Endpoint Sign Factor

  A single minus sign in a complex continuation, proved by hand, that fixes the value of a geometric cosine at the Lorentzian end of a path.

• Gravity Seven Gaps Wick Action Complex First Real Lorentzian Product Cos Eq

  A machine-checked theorem pins down the sign of a complex gravity formula at its starting point, settling a convention question that could have silently flipped the result.

• Gravity Seven Gaps Wick Action Complex First Wick Boundary Continuation Four One

  A machine-checked proof shows a specific geometric quantity can be smoothly carried from a Lorentzian to a Euclidean setting, with exact endpoint values.

• Gravity Seven Gaps Wick Four One All Hinges

  A machine-checked proof that every one of the ten triangular joints in a five-vertex spacetime building block behaves regularly as the geometry rotates from Lorentzian to Euclidean

• Gravity Seven Gaps Wick Four One All Hinges Boundary Four One Spacelike Pair

  In a quantum gravity calculation, a machine-checked proof shows that a specific class of geometric building blocks, the spacelike hinges of a causal 4-simplex, have a well-defined,

• Gravity Seven Gaps Wick Four One All Hinges Boundary Four One Timelike Pair

  A machine-checked proof shows that a specific quantum gravity path integral, the (4,1) causal 4-simplex, can be smoothly continued from Lorentzian to Euclidean geometry without hit

• Gravity Seven Gaps Wick Four One All Hinges Branch Regular Four One All Hinges

  A machine-checked proof that all ten triangular hinges of a specific four-dimensional simplex stay on the correct mathematical sheet during a complex rotation, and a clear statemen

• Gravity Seven Gaps Wick Four One All Hinges Branch Regular Four One Spacelike Pa

  A machine-checked proof shows that a specific geometric piece of a four-dimensional spacetime model behaves smoothly, but it does not yet connect that piece to a full theory of gra

• Gravity Seven Gaps Wick Four One All Hinges Branch Regular Four One Timelike Pai

  A machine-checked proof verifies that a specific four-dimensional spacetime geometry stays mathematically well-behaved across every one of its ten triangular faces when rotated int

• Gravity Seven Gaps Wick Four One All Hinges Four One Area Sq Interior Off Cut

  A machine-checked proof that the area-squared formulas for a curved spacetime building block stay on the safe side of a complex square-root cut, with the boundary case left open.

• Gravity Seven Gaps Wick Four One All Hinges Wick Boundary Continuation Four One

  A machine-checked proof shows that all ten hinges of a special curved spacetime building block connect smoothly to its Euclidean counterpart, with no gaps at the boundary.

• Gravity Seven Gaps Wick Hinge Data Complete

  A machine-checked proof certifies that the geometric data of every triangular hinge in a causal 4-simplex continues smoothly from Euclidean to Lorentzian signature, a complete but

• Gravity Seven Gaps Wick Hinge Data Complete Action Level Closed By V2 Elsewhere

  A tiny declaration in a machine-checked library records that one open problem in quantum gravity was closed elsewhere, without claiming to close it itself.

• Gravity Seven Gaps Wick Hinge Data Complete Wick Hinge Area Sq Closed Forms Comp

  For a single causal 4-simplex, the squared areas of all twenty triangular hinges follow exactly two closed forms under the complex Wick continuation.

• Gravity Seven Gaps Wick Hinge Data Complete Wick Hinge Data Continuation Complet

  A machine-checked theorem certifies that the geometry of a single quantum simplex continues smoothly from Lorentzian to Euclidean signature, while leaving the full action-level con

• Gravity Seven Gaps Wick Hinge Data Complete Wick Product Form Kills Memorialized

  A machine-checked theorem records two exact numerical failures in a proposed transcription of a Wick rotation, preserving them as permanent warnings rather than erasing them.

• Gravity Seven Gaps Wick Three Two Hinges

  A machine-checked proof verifies the analytic continuation of a quantum gravity model across all ten hinges of a causal 4-simplex, and kills two simpler candidate formulas along th

• Gravity Seven Gaps Wick Three Two Hinges Branch Regular Three Two Mixed Pair

  In a discrete model of quantum gravity, a proposed shortcut for computing angles fails at two exact points, and a machine-checked proof says why.

• Gravity Seven Gaps Wick Three Two Hinges Branch Regular Three Two Spacelike

  A machine-checked proof shows that a particular angle in a four-dimensional simplex can be followed smoothly through time, and that a naive shortcut fails.

• Gravity Seven Gaps Wick Three Two Hinges Branch Regular Three Two Upper Pair

  A machine-checked certificate that a specific quantum gravity path avoids a mathematical branch cut, and the exact limits of that certificate.

• Gravity Seven Gaps Wick Three Two Hinges Product Form Crossing Three Two Mixed

  A machine-checked proof shows a certain simplified formula for quantum gravity angles fails at a precise point; here is what that failure means and what it does not prove.

• Gravity Seven Gaps Wick Three Two Hinges Product Form Crossing Three Two Upper

  A machine-checked proof shows a proposed shortcut for computing quantum gravity angles fails at an exact point, ruling out a simpler formula.

• Gravity Seven Gaps Wick Three Two Hinges Product Form Crossing Value Mixed

  A machine-checked proof shows a proposed simplification of a quantum gravity calculation fails at a specific point, turning a suspicion into a precise number.

• Gravity Seven Gaps Wick Three Two Hinges Product Form Crossing Value Upper

  A machine-checked theorem shows a proposed simplification of a quantum gravity calculation fails at an exact, simple point, and the failure is itself a precise result.

• Gravity Seven Gaps Wick Three Two Hinges Wick Continuation Three Two Hinges

  A machine-checked proof that all ten triangular hinges of a (3,2) causal 4-simplex can be continued from Lorentzian to Euclidean signature without branch cuts, and the two places w

• Gravity Seven Gaps Zq Continuum Blocker

  A formal module that pinpoints the exact missing step between a finite approximation and a complete theory of gravity.

• Gravity Seven Gaps Zq Continuum Blocker Cauchy Seq Zcap Iff Oscillatory Tail

  A machine-checked theorem gives a plain test for when an infinite sum of quantum gravity pieces settles to a finite value, and shows the default choice fails it.

• Gravity Seven Gaps Zq Continuum Blocker Has Exact Complexity Cutoff Limit Iff Ta

  A machine-checked theorem pins down exactly when removing a computational cutoff in a gravity path sum yields a stable answer: the late terms must cancel.

• Gravity Seven Gaps Zq Continuum Blocker Has Phased Zq Complexity Limit Iff Cauch

  A machine-checked theorem gives an exact test for when a sequence of finite path sums in a gravity model has a limit, and it names the one bridge still missing.

• Gravity Seven Gaps Zq Continuum Blocker Has Phased Zq Limit Iff Exact Shell Tail

  A formal bridge shows that two different ways of summing a gravity path model converge or fail together, provided they agree at every finite cutoff.

• Gravity Seven Gaps Zq Continuum Blocker Not Has Exact Complexity Cutoff Limit Ze

  A machine-checked theorem shows that the simplest possible phase assignment makes a certain gravity sum diverge, blocking one route to removing a computational cutoff.

• Gravity Seven Gaps Zq Continuum Blocker Zero Phase Compatibility And Limit Impos

  A machine-checked proof shows that a particular way of removing an approximation from a quantum-gravity calculation cannot work: the zero-phase case is a dead end, not a gap to be

• Gravity Seven Gaps Zq Continuum Blocker Zero Phase Fails Both Removal Routes

  A machine-checked theorem shows that a path sum with no phase adjustments cannot be made to converge by any of two standard cutoff-removal methods.

• Gravity Seven Gaps Zq Continuum Blocker Zero Phase Not Exact Shell Tail Cancella

  A machine-checked theorem shows that the simplest possible phase assignment makes a gravity path sum diverge, blocking a proposed route to remove an artificial complexity cutoff.

• Gravity Seven Gaps Zq Phase Structure

  A finite sum over triangulations can be made smaller by pairing terms whose phases cancel, a step toward taming an infinite sum that remains open.

• Gravity Seven Gaps Zq Phase Structure Opposite Phase Pair Cancels

  A simple identity about waves that are half a cycle apart is the engine behind a proposed mechanism for taming an infinite sum in a theory of quantum gravity.

• Gravity Seven Gaps Zq Phase Structure Opposite Phase Pair Strict

  Two equal contributions with opposite phases cancel exactly, and the triangle inequality is strict there; the result is a finite sum, not a continuum limit.

• Gravity Seven Gaps Zq Phase Structure Phased Zq Beats Triangle Witness

  A machine-checked proof shows that adding oscillatory phases to a sum over triangulations can make the sum strictly smaller than the naive bound, a first concrete step toward tamin

• Gravity Seven Gaps Zq Phase Structure Phased Zq Pairing Witness

  A formal proof shows that certain oscillatory weights can make a gravitational path sum smaller than its worst-case bound, but only for a fixed, finite approximation.

• Gravity Seven Gaps Zq Phase Structure Two Le Total Class Mass Two

  A small inequality in a formal library guarantees that a certain total mass is at least 2, a fact that makes a more interesting cancellation result meaningful.

• Gravity Seven Gaps Zq Phase Structure Zq Norm Le Total Class Mass

  A machine-checked theorem puts a hard upper limit on a quantum gravity path sum, and it does so without touching the continuum limit.

• Gravity Seven Gaps Zq Phase Structure Zq Pairing Beats Triangle

  A theorem about a discrete sum shows when cancellation beats a crude bound, and it names exactly what it does not prove.

• Gravity Seven Gaps Zq Phase Structure Zq Phase Structure Status Grounded

  A machine-checked status report records what a quantum gravity path sum can and cannot do with oscillatory phases at a fixed complexity cap.

• Gravity Seven Gaps Zq Shell Balance Blocker

  A machine-checked result pins down exactly what is missing for a complete theory of gravity's seven gaps: a precise condition on how phases must balance inside late shells.

• Gravity Seven Gaps Zq Shell Balance Blocker Eventually Zero Phase Not Oscillator

  A phase that goes quiet forever cannot be the oscillatory tail a gravity proof needs, no matter how it behaves early on.

• Gravity Seven Gaps Zq Shell Balance Blocker Exact Shell Amplitude Shell Constant

  A phase pattern that is constant inside each shell cannot satisfy the uniform tail condition, and the framework proves why.

• Gravity Seven Gaps Zq Shell Balance Blocker Norm Exact Shell Amplitude Shell Con

  A theorem about a phase that never changes inside a shell pins its total amplitude to a mass that grows without bound, ruling out a whole class of candidate solutions.

• Gravity Seven Gaps Zq Shell Balance Blocker Oscillatory Tail Implies Shell Ampli

  A machine-checked theorem shows that a certain kind of oscillatory behavior forces each individual shell's amplitude to shrink to zero, and it names exactly what it does not p

• Gravity Seven Gaps Zq Shell Balance Blocker Oscillatory Tail Of Eventually Agree

  A theorem about when two phase assignments share the same long-range behavior, and the precise limits of that agreement.

• Gravity Seven Gaps Zq Shell Balance Blocker P24 Shell Balance Blocker Certificat

  A machine-checked theorem isolates the exact missing condition that prevents the Seven Gaps program from completing its phase-balance obligation.

• Gravity Seven Gaps Zq Shell Balance Blocker Shell Constant Not Shell Amplitude V

  A machine-checked proof shows that a phase which is constant inside each shell cannot satisfy the oscillatory tail condition, isolating the exact missing ingredient in a program to

• Gravity Seven Gaps Zq Shell Balance Blocker Supported Below Not Oscillatory Tail

  A phase that goes silent beyond a fixed complexity cutoff can never satisfy the oscillatory tail condition, no matter how it behaves early on.

• Gravity Sparcfalsifier

  A machine-checked protocol that states exactly when the framework's gravity prediction is wrong, and what would count as proof.

• Gravity Sparcfalsifier Falsification Decidable

  A machine-checked theorem says a galaxy rotation prediction can be cleanly ruled out by data.

• Gravity Sparcfalsifier Parameters From Phi

  A machine-checked theorem fixes three galaxy-model parameters to powers of the golden ratio, and defines the test that could falsify the model.

• Gravity Sparcfalsifier Sparc Falsifier Cert

  A machine-checked certificate that the ILG gravity model can be tested against 175 galaxies with zero free parameters, and what that test does and does not prove.

• Gravity Stress Energy Tensor

  The stress-energy tensor is the object that tells spacetime how much energy and momentum live at each point, and general relativity says that curvature and this tensor are two side

• Gravity Stress Energy Tensor Conservation From Efe And Bianchi

  In general relativity, the local conservation of energy and momentum is not an extra assumption: it follows from the field equations themselves.