Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- — Moments after, sweaty and shaky, we lie intertwined and gazing out at the lights of our city.
- The streets as quiet and subdued as they get with the exception of snowstorm nights.
- The air creeping through the crack in the window is the coldest of the season.
- “I need to get back to my house,” I say.

— Moments after, sweaty and shaky, we lie intertwined and gazing out at the lights of our city.

The streets as quiet and subdued as they get with the exception of snowstorm nights.

The air creeping through the crack in the window is the coldest of the season.

“I need to get back to my house,” I say.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- but in the 1840s several additional asteroids were discovered (Astraea in 1845; Hebe, Iris, and Flora in 1847; Metis in 1848; and Hygiea in 1849).
- New "planets" were discovered every year; as a result, astronomers began tabulating the asteroids (minor planets) separately from the major planets and assigning them numbers instead of abstract planetary symbols,[153] although they continued to be considered as small planets.[184] Neptune was discovered in 1846, its position having been predicted thanks to its gravitational influence upon Uranus.
- Because the orbit of Mercury appeared to be affected in a similar way, it was believed in the late 19th century that there might be another planet even closer to the Sun.

Locate highest-signal evidence sentences from chunks for the question.

Check consistency, units, conservation constraints, and whether evidence supports claims.

Compose bounded answer and (if applicable) a proposal/hypothesis clearly labeled.

Generate falsification tests and identify unknowns or missing evidence.

Merge outputs, remove speculation, keep only evidence-backed facts.

but in the 1840s several additional asteroids were discovered (Astraea in 1845; Hebe, Iris, and Flora in 1847; Metis in 1848; and Hygiea in 1849).

New "planets" were discovered every year; as a result, astronomers began tabulating the asteroids (minor planets) separately from the major planets and assigning them numbers instead of abstract planetary symbols,[153] although they continued to be considered as small planets.[184] Neptune was discovered in 1846, its position having been predicted thanks to its gravitational influence upon Uranus.

Because the orbit of Mercury appeared to be affected in a similar way, it was believed in the late 19th century that there might be another planet even closer to the Sun.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Evolution in this regime is nonlinear, m and must usually be followed with large computer simulations.
- 30.21 Nonlinear evolution of the matter power spectrum 825 )3cpM3−h( )k(P Ω Λ=0.69 Ω =0.31 m b=1.05 Ω =1 m b=1.05 1.2 1.0 .001 .01 .1 1 k (hMpc −1) slaudiseR N S Figure30.15 Modelmatterpowerspectracomputedinthesimpleapproximation,comparedtoobservationsfromthe North (N) and South (S) Galactic Caps of the the Sloan Digital Sky Survey IV (Gil-Marín et al., 2020).
- The ΛCDM power spectrum calculated here in the simple approximation may be compared to the corresponding power spectra in the hydrodynamicapproximation,Figure32.4,andfromaBoltzmanncomputation,Figure33.5.
- The data comprise377,458luminousredgalaxiescoveringapproximately18%oftheskyoverredshiftsz=0.6–1.Twomodels are shown, a flat ΛCDM model with concordance parameters ΩΛ = 0.69 and Ωm = 0.31, and a flat matter-only CDMmodel,Ωm=1.Thedashedlinesonthemodelsshowpowercalculatedfrom|δ k 2|,whichincludesunmeasurable superhorizon power; the solid lines are calculated from |(δ k −δ0)2|, which excludes the unmeasurable superhorizon powerbysubtractingaconstantδ0 fromtheoverdensity.TheΛCDMmodelisnormalizedtotheamplitude(30.138) measured by Planck (Aghanim et al., 2018), multiplied by a bias squared factor of b2 = 1.052.

Evolution in this regime is nonlinear, m and must usually be followed with large computer simulations.

30.21 Nonlinear evolution of the matter power spectrum 825 )3cpM3−h( )k(P Ω Λ=0.69 Ω =0.31 m b=1.05 Ω =1 m b=1.05 1.2 1.0 .001 .01 .1 1 k (hMpc −1) slaudiseR N S Figure30.15 Modelmatterpowerspectracomputedinthesimpleapproximation,comparedtoobservationsfromthe North (N) and South (S) Galactic Caps of the the Sloan Digital Sky Survey IV (Gil-Marín et al., 2020).

The ΛCDM power spectrum calculated here in the simple approximation may be compared to the corresponding power spectra in the hydrodynamicapproximation,Figure32.4,andfromaBoltzmanncomputation,Figure33.5.

The data comprise377,458luminousredgalaxiescoveringapproximately18%oftheskyoverredshiftsz=0.6–1.Twomodels are shown, a flat ΛCDM model with concordance parameters ΩΛ = 0.69 and Ωm = 0.31, and a flat matter-only CDMmodel,Ωm=1.Thedashedlinesonthemodelsshowpowercalculatedfrom|δ k 2|,whichincludesunmeasurable superhorizon power; the solid lines are calculated from |(δ k −δ0)2|, which excludes the unmeasurable superhorizon powerbysubtractingaconstantδ0 fromtheoverdensity.TheΛCDMmodelisnormalizedtotheamplitude(30.138) measured by Planck (Aghanim et al., 2018), multiplied by a bias squared factor of b2 = 1.052.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- They begin the set-up with an eternal BTZ black hole (Ban ̃ados, Teitelboim and Zanelli) - a black hole solution for (2 + 1)-dimensional topological gravity with a negative cosmological constant [41], which contains a non-traversable Einstein-Rosen bridge.
- The future event horizon is 1 2
- Due to the possible large charge of the black holes, a very big number of 2dimensional equivalent fermions could be obtained, which in turn would produce a large amount of negative energy.
- 5.2 Other recent papers In the previous section, a possible wormhole solution was presented in detail, startingwithitsgeometricconstruction,themechanismemployedtoviolatetheaveraged null energy condition and possible methods used to stabilize the wormhole.

They begin the set-up with an eternal BTZ black hole (Ban ̃ados, Teitelboim and Zanelli) - a black hole solution for (2 + 1)-dimensional topological gravity with a negative cosmological constant [41], which contains a non-traversable Einstein-Rosen bridge.

Due to the possible large charge of the black holes, a very big number of 2dimensional equivalent fermions could be obtained, which in turn would produce a large amount of negative energy.

5.2 Other recent papers In the previous section, a possible wormhole solution was presented in detail, startingwithitsgeometricconstruction,themechanismemployedtoviolatetheaveraged null energy condition and possible methods used to stabilize the wormhole.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- — Nordsieck, Lamb, and Uhlenbeck, "On the theory of cosmic-ray showers I: The Furry model and the fluctuation problem" (1940) Introduction A master equation is a phenomenological set of first-order differential equations describing the time evolution of (usually) the probability of a system to occupy each one of a discrete set of states with regard to a continuous time variable t.
- Master equation In physics, chemistry, and related fields, master equations are used to describe the time evolution of a system that can be modeled as being in a probabilistic combination of states at any given time, and the switching between states is determined by a transition rate matrix.
- When the connections are time-independent rate constants, the master equation represents a kinetic scheme, and the process is Markovian (any jumping time probability density function for state i is an exponential, with a rate equal to the value of the connection).
- The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states.

— Nordsieck, Lamb, and Uhlenbeck, "On the theory of cosmic-ray showers I: The Furry model and the fluctuation problem" (1940) Introduction A master equation is a phenomenological set of first-order differential equations describing the time evolution of (usually) the probability of a system to occupy each one of a discrete set of states with regard to a continuous time variable t.

Master equation In physics, chemistry, and related fields, master equations are used to describe the time evolution of a system that can be modeled as being in a probabilistic combination of states at any given time, and the switching between states is determined by a transition rate matrix.

When the connections are time-independent rate constants, the master equation represents a kinetic scheme, and the process is Markovian (any jumping time probability density function for state i is an exponential, with a rate equal to the value of the connection).

The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Corey, the planet Ilus has indigenous life with partially-mirrored chirality.
- Sample, Ian (12 December 2024).
- The two have even been mixed using genetic [22] engineering, producing viable modified E.
- In the 2014 science fiction novel Cibola Burn by James S.

Corey, the planet Ilus has indigenous life with partially-mirrored chirality.

The two have even been mixed using genetic [22] engineering, producing viable modified E.

In the 2014 science fiction novel Cibola Burn by James S.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- On the left, the collapse is to thefutureofanobserveratthecentreofthediagram;ontheright,thecollapseistothepastofanobserveratthe centreofthediagram.Thediagramsareattimes−16,−4,0,4,and16Schwarzschildtimeunits(c=rs=1)relative to the middle diagram.
- In particular, as long as the singularity is chosen to be horizontal, it is impossible to arrange that the left edge of the diagram, defined by the centre of the collapsing star at r =0, be vertical.
- 7.27 Illusory horizon 167 centres.InFigure7.20,thePenrosediagramlookslikeMinkowskiwellbeforecollapse,andlikeSchwarzschild well after collapse.
- On the left the Penrose diagram resembles that of Minkowski space, while on the right the diagramresemblesthatoftheSchwarzschildgeometry.ThesePenrosediagramsarespacetimediagramscalculatedin thePenrosecoordinatesdefinedbyequations(7.87)and(7.88).

On the left, the collapse is to thefutureofanobserveratthecentreofthediagram;ontheright,thecollapseistothepastofanobserveratthe centreofthediagram.Thediagramsareattimes−16,−4,0,4,and16Schwarzschildtimeunits(c=rs=1)relative to the middle diagram.

In particular, as long as the singularity is chosen to be horizontal, it is impossible to arrange that the left edge of the diagram, defined by the centre of the collapsing star at r =0, be vertical.

7.27 Illusory horizon 167 centres.InFigure7.20,thePenrosediagramlookslikeMinkowskiwellbeforecollapse,andlikeSchwarzschild well after collapse.

On the left the Penrose diagram resembles that of Minkowski space, while on the right the diagramresemblesthatoftheSchwarzschildgeometry.ThesePenrosediagramsarespacetimediagramscalculatedin thePenrosecoordinatesdefinedbyequations(7.87)and(7.88).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Type III: The M-dimension can be 0 or ∞.
- Any two non-zero modules are isomorphic, and all nonzero modules are standard.
- Amenable von Neumann algebras Connes (1976) and others proved that the following conditions on a von Neumann algebra M on a separable Hilbert space H are all equivalent: M is hyperfinite or AFD or approximately finite dimensional or approximately finite: this means the algebra contains an ascending sequence of finite dimensional subalgebras with dense union.
- (Warning: some authors use "hyperfinite" to mean "AFD and finite".) M is amenable: this means that the derivations of M with values in a normal dual Banach bimodule are all inner.[2] M has Schwartz's property P: for any bounded operator T on H the weak operator closed convex hull of the elements uTu* contains an element commuting with M.

Type III: The M-dimension can be 0 or ∞.

Any two non-zero modules are isomorphic, and all nonzero modules are standard.

Amenable von Neumann algebras Connes (1976) and others proved that the following conditions on a von Neumann algebra M on a separable Hilbert space H are all equivalent: M is hyperfinite or AFD or approximately finite dimensional or approximately finite: this means the algebra contains an ascending sequence of finite dimensional subalgebras with dense union.

(Warning: some authors use "hyperfinite" to mean "AFD and finite".) M is amenable: this means that the derivations of M with values in a normal dual Banach bimodule are all inner.[2] M has Schwartz's property P: for any bounded operator T on H the weak operator closed convex hull of the elements uTu* contains an element commuting with M.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- As will be shown momentarily, the extrinsic curvature ab K is a spatial tetrad tensor.
- a0β A reminder: do not confuse the Lorentz connections Γ (of which there are 24) with the coordinate mnλ connectionsΓ (ofwhichthereare40,forvanishingtorsion).TheLorentzconnectionsΓ withfinalindex μνλ mnλ acoordinateindexλarerelatedtotheLorentzconnectionsΓ withalltetradindicesby,equation(15.20), mnl Γ ≡el Γ .
- As remarked before equation (16.116), the same equations of motion are obtained whether the action is varied withrespectto either π or Γ ,so onecanchoose either π or Γ asthe momentumvariables a0β a0β a0β a0β conjugate to the coordinates eaα.
- The original choice of Arnowitt, Deser, and Misner (1963) was π , but a0β equations using Γ were proposed by Smarr and York (1978) and York (1979).

As will be shown momentarily, the extrinsic curvature ab K is a spatial tetrad tensor.

a0β A reminder: do not confuse the Lorentz connections Γ (of which there are 24) with the coordinate mnλ connectionsΓ (ofwhichthereare40,forvanishingtorsion).TheLorentzconnectionsΓ withfinalindex μνλ mnλ acoordinateindexλarerelatedtotheLorentzconnectionsΓ withalltetradindicesby,equation(15.20), mnl Γ ≡el Γ .

As remarked before equation (16.116), the same equations of motion are obtained whether the action is varied withrespectto either π or Γ ,so onecanchoose either π or Γ asthe momentumvariables a0β a0β a0β a0β conjugate to the coordinates eaα.

The original choice of Arnowitt, Deser, and Misner (1963) was π , but a0β equations using Γ were proposed by Smarr and York (1978) and York (1979).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Specifically, the President must provide a written finding that justifies covert action and submit it to the House and Senate Intelligence Committees.
- The first article of the United States Constitution specifies this responsibility.
- There is, however, a growing body of evidence that the government is not being transparent about what it knows about unidentified anomalous phenomena (UAP), formerly called UFOs, and that elements within the military and IC are in violation of their Constitutional duty to notify Congress of their operations.
- 10 USC Sec 119 and 50 USC Sec 3093 are applicable here.

Specifically, the President must provide a written finding that justifies covert action and submit it to the House and Senate Intelligence Committees.

The first article of the United States Constitution specifies this responsibility.

There is, however, a growing body of evidence that the government is not being transparent about what it knows about unidentified anomalous phenomena (UAP), formerly called UFOs, and that elements within the military and IC are in violation of their Constitutional duty to notify Congress of their operations.

10 USC Sec 119 and 50 USC Sec 3093 are applicable here.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- doi:10.1103/PhysRevA.56.4405 (https://doi.org/10.110 3%2FPhysRevA.56.4405).
- harvard.edu/abs/1997PhRvA..56.4405W).
- Journal articles Alvager, T.; Farley, F.
- Bibcode:1997PhRvA..56.4405W (https://ui.adsabs.

Journal articles Alvager, T.; Farley, F.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- not explicitly defined by the IAU due to the large relative uncertainty (10−4 ) of ☉ the Newtonian constant of gravitation G.
- Since the product of the Newtonian constant of gravitation and solar mass together (GM ) has been determined to much greater precision, the IAU defined the ☉ nominal solar mass parameter to be: nominal solar mass parameter: GM = 1.327 1244 ×1020 m3 /s2[56] ☉ The nominal solar mass parameter can be combined with the most recent (2014) CODATA estimate of the Newtonian constant of gravitation G to derive the solar mass to be approximately 1.9885 ×1030 kg.
- Although the exact values for the luminosity, radius, mass parameter, and mass may

not explicitly defined by the IAU due to the large relative uncertainty (10−4 ) of ☉ the Newtonian constant of gravitation G.

Since the product of the Newtonian constant of gravitation and solar mass together (GM ) has been determined to much greater precision, the IAU defined the ☉ nominal solar mass parameter to be: nominal solar mass parameter: GM = 1.327 1244 ×1020 m3 /s2[56] ☉ The nominal solar mass parameter can be combined with the most recent (2014) CODATA estimate of the Newtonian constant of gravitation G to derive the solar mass to be approximately 1.9885 ×1030 kg.

Although the exact values for the luminosity, radius, mass parameter, and mass may

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- New York: Gestalt Journal Press.
- Totowa, NJ: Littlefield, Adams.
- Adverse life-events and risk of breast cancer: A meta-analysis.
- Ingram (Eds.), Handbook of psychological change (pp.

Adverse life-events and risk of breast cancer: A meta-analysis.

Ingram (Eds.), Handbook of psychological change (pp.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Using FC, the argument goes, largely or entirely mute autistic individuals can type out words and sentences on a keyboard with the aid of a “facilitator,” who guides their hands and thereby compensates for their presumed motor impairment.
- In the early 1990s, shortly after FC was introduced to the United States, scores of ecstatic facilitators reported astonishing s uccess stories of previously uncommunicative autistic individuals typing out eloquent sentences, at times speaking of their sense of liberation upon at last being able to express their imprisoned feelings.
- Regrettably, FC has raised false hopes among thousands of desperate parents of autistic individuals.
- Yet numerous controlled studies soon showed that FC was entirely a product of unintentional facilitator control over autistic children’s hand movements.

Using FC, the argument goes, largely or entirely mute autistic individuals can type out words and sentences on a keyboard with the aid of a “facilitator,” who guides their hands and thereby compensates for their presumed motor impairment.

In the early 1990s, shortly after FC was introduced to the United States, scores of ecstatic facilitators reported astonishing s uccess stories of previously uncommunicative autistic individuals typing out eloquent sentences, at times speaking of their sense of liberation upon at last being able to express their imprisoned feelings.

Regrettably, FC has raised false hopes among thousands of desperate parents of autistic individuals.

Yet numerous controlled studies soon showed that FC was entirely a product of unintentional facilitator control over autistic children’s hand movements.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- This property nearly characterizes symmetric spaces; Élie Cartan proved in the 1920s that a locally symmetric Riemannian manifold which is geodesically complete and simply-connected must in fact be symmetric.[45] Many of the fundamental examples of Riemannian manifolds are symmetric.
- Riemannian manifolds with this curvature property, which could loosely be phrased as "constant Riemann curvature tensor" (not to be confused with constant curvature), are said to be locally symmetric.
- The complex projective space, quaternionic projective space, and Cayley plane are analogues of the real
- g) is said to be symmetric if for every point p of M there exists some isometry of the manifold with p as a fixed point and for which the negation of the differential at p is the identity map.

This property nearly characterizes symmetric spaces; Élie Cartan proved in the 1920s that a locally symmetric Riemannian manifold which is geodesically complete and simply-connected must in fact be symmetric.[45] Many of the fundamental examples of Riemannian manifolds are symmetric.

Riemannian manifolds with this curvature property, which could loosely be phrased as "constant Riemann curvature tensor" (not to be confused with constant curvature), are said to be locally symmetric.

The complex projective space, quaternionic projective space, and Cayley plane are analogues of the real

g) is said to be symmetric if for every point p of M there exists some isometry of the manifold with p as a fixed point and for which the negation of the differential at p is the identity map.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Separating each of equations (22.46) according to the pattern of 0 1 2 3 equation (22.47) leads to the homogeneous solutions (f +f ω )(h +h ω ) (f +f ω )(h +h ω ) Y = 0 1 x 0 1 x , Y = 1 0 y 1 0 y .
- (22.48) x dω /dx y dω /dy x y Solutions including the energy-momentum of a static electromagnetic field fall out with little extra work.
- 652 Ideal rotating black holes In terms of Y and Y , the Einstein components G −G and G +G are x y 00 11 22 33 ρ2(G −G ) (22.46a) 00 11 ( ) ( ) [ ] 1 dlnω dlnω d f +f ω ∂Y d ω (f +f ω ) = Y x −Y y +Y ln 0 1 x − y +Y ln y 1 0 y , 1−ω ω x dx y dy xdx ω ∂y ydy dω /dy x y x y ρ2(G +G ) (22.46b) 22 33 ( ) ( ) [ ] 1 dlnω dlnω d f +f ω ∂Y d ω (f +f ω ) = Y x −Y y −Y ln 1 0 y + x −Y ln x 0 1 x .
- Solutions with G = −G = 00 11 G = G , as is true for a static radial electromagnetic field, are found by taking the difference of equa22 33 tions (22.46) and separating that difference in the pattern of equation (22.47).

Separating each of equations (22.46) according to the pattern of 0 1 2 3 equation (22.47) leads to the homogeneous solutions (f +f ω )(h +h ω ) (f +f ω )(h +h ω ) Y = 0 1 x 0 1 x , Y = 1 0 y 1 0 y .

(22.48) x dω /dx y dω /dy x y Solutions including the energy-momentum of a static electromagnetic field fall out with little extra work.

652 Ideal rotating black holes In terms of Y and Y , the Einstein components G −G and G +G are x y 00 11 22 33 ρ2(G −G ) (22.46a) 00 11 ( ) ( ) [ ] 1 dlnω dlnω d f +f ω ∂Y d ω (f +f ω ) = Y x −Y y +Y ln 0 1 x − y +Y ln y 1 0 y , 1−ω ω x dx y dy xdx ω ∂y ydy dω /dy x y x y ρ2(G +G ) (22.46b) 22 33 ( ) ( ) [ ] 1 dlnω dlnω d f +f ω ∂Y d ω (f +f ω ) = Y x −Y y −Y ln 1 0 y + x −Y ln x 0 1 x .

Solutions with G = −G = 00 11 G = G , as is true for a static radial electromagnetic field, are found by taking the difference of equa22 33 tions (22.46) and separating that difference in the pattern of equation (22.47).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Three gauges considered later are harmonic gauge (§27.7), Newtonian gauge (§27.8), and synchronous gauge (§27.9).
- Solution.InN spacetimedimensions,thereareN−2transversedirections.InN spacetimedimensions,the vierbein perturbations φ , equations (27.6), decompose into: 5 scalars ψ, w, w ̃, Φ, h; 4 vectors w , w ̃ , h , mn a a b h ̃ ; 1 transverse antisymmetric tensor h ̃ (which for N = 4 reduces to a scalar ε ∇ h ̃ ); and 1 transverse a ab abc c traceless symmetric tensor h ; for a total of 5+4(N−2)+ 1(N−2)(N−3)+ 1N(N−3) = N2 degrees of ab 2 2 freedom.Coordinatetransformations,equation(27.8),decomposeinto2scalarsε ,ε,and1vectorε ,atotal 0 a of 2+(N−2)=N degrees of freedom, leaving 3 scalars, 3 vectors, 1 antisymmetric tensor, and 1 symmetric
- (27.11d) a a a a a ab ab Eliminating the coordinate shift ε from the transformations (27.11) yields 12 coordinate gauge-invariant m combinations of the potentials ψ−w ̃ ̇ , w−h ̇ , w −h ̇ , w ̃ , Φ , h ̃ , h ̃ , h .
- These 6 coordinate and tetrad gauge-invariant perturbations comprise 2 scalars, 1 vector, and 1 tensor Ψ ≡ ψ−w ̇ −w ̃ ̇ +h ̈ , (27.13a) scalar Φ , (27.13b) scalar W ≡ w +w ̃ −h ̇ −h ̃ ̇ , (27.13c) a a a a a vector h .

Three gauges considered later are harmonic gauge (§27.7), Newtonian gauge (§27.8), and synchronous gauge (§27.9).

Solution.InN spacetimedimensions,thereareN−2transversedirections.InN spacetimedimensions,the vierbein perturbations φ , equations (27.6), decompose into: 5 scalars ψ, w, w ̃, Φ, h; 4 vectors w , w ̃ , h , mn a a b h ̃ ; 1 transverse antisymmetric tensor h ̃ (which for N = 4 reduces to a scalar ε ∇ h ̃ ); and 1 transverse a ab abc c traceless symmetric tensor h ; for a total of 5+4(N−2)+ 1(N−2)(N−3)+ 1N(N−3) = N2 degrees of ab 2 2 freedom.Coordinatetransformations,equation(27.8),decomposeinto2scalarsε ,ε,and1vectorε ,atotal 0 a of 2+(N−2)=N degrees of freedom, leaving 3 scalars, 3 vectors, 1 antisymmetric tensor, and 1 symmetric

(27.11d) a a a a a ab ab Eliminating the coordinate shift ε from the transformations (27.11) yields 12 coordinate gauge-invariant m combinations of the potentials ψ−w ̃ ̇ , w−h ̇ , w −h ̇ , w ̃ , Φ , h ̃ , h ̃ , h .

These 6 coordinate and tetrad gauge-invariant perturbations comprise 2 scalars, 1 vector, and 1 tensor Ψ ≡ ψ−w ̇ −w ̃ ̇ +h ̈ , (27.13a) scalar Φ , (27.13b) scalar W ≡ w +w ̃ −h ̇ −h ̃ ̇ , (27.13c) a a a a a vector h .

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Reheating It is not known exactly when the inflationary epoch ended, but it is thought to have been between 10−33 and 10−32 seconds after the Big Bang.
- All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 ×10−29 m, then grew to a sphere with a radius around 0.09m by the end of inflation.[14]: 202 This phase of the cosmic expansion history is known as inflation [16]: 3 or sometimes as the inflationary epoch.[17] Inflation explains how today's universe has concentrations of matter, like galaxies and clusters of galaxies, rather than having matter spatially uniform through the universe.[4]: 324 Tiny quantum fluctuations in the universe, amplified by inflation, are believed to be the basis of large-scale structures that formed much later.[18]: 2 The mechanism that drove inflation remains unknown, although many models have been put forward.
- One of the theoretical products of this phase transition was a scalar field called the inflaton field.[19] As this field settled into its lowest-energy state throughout the universe, it generated an enormous repulsive force that led to a rapid expansion of the universe.
- After inflation ended, the universe continued to expand.

Chronology of the universe - Wikipedia.pdf

Reheating It is not known exactly when the inflationary epoch ended, but it is thought to have been between 10−33 and 10−32 seconds after the Big Bang.

All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 ×10−29 m, then grew to a sphere with a radius around 0.09m by the end of inflation.[14]: 202 This phase of the cosmic expansion history is known as inflation [16]: 3 or sometimes as the inflationary epoch.[17] Inflation explains how today's universe has concentrations of matter, like galaxies and clusters of galaxies, rather than having matter spatially uniform through the universe.[4]: 324 Tiny quantum fluctuations in the universe, amplified by inflation, are believed to be the basis of large-scale structures that formed much later.[18]: 2 The mechanism that drove inflation remains unknown, although many models have been put forward.

One of the theoretical products of this phase transition was a scalar field called the inflaton field.[19] As this field settled into its lowest-energy state throughout the universe, it generated an enormous repulsive force that led to a rapid expansion of the universe.

After inflation ended, the universe continued to expand.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Specifically, an observer inside a horizon patch can perform a global transformation (29.18) of the cosmic scale factor a (and time coordinate η) so as to set the large-scale Φ (and Ψ) to zero in their patch.
- The constancy of ζ is a generalization of this law to superhorizon perturbations of a FLRW universe.
- (30.25) It is conventional to define a quantity ζ by ζ ≡ 1δ−Φ , (30.26) which has the property that it is constant at large scales in any fluid component that does not exchange energy with other components, ζ =constant if kη ≪1 .
- Assume that the proper pressure p(ρ) is a definite function of proper density ρ.

Specifically, an observer inside a horizon patch can perform a global transformation (29.18) of the cosmic scale factor a (and time coordinate η) so as to set the large-scale Φ (and Ψ) to zero in their patch.

The constancy of ζ is a generalization of this law to superhorizon perturbations of a FLRW universe.

(30.25) It is conventional to define a quantity ζ by ζ ≡ 1δ−Φ , (30.26) which has the property that it is constant at large scales in any fluid component that does not exchange energy with other components, ζ =constant if kη ≪1 .

Assume that the proper pressure p(ρ) is a definite function of proper density ρ.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Organizations Antiquarian Horological Society – AHS (United Kingdom) Chronometrophilia (Switzerland) Deutsche Gesellschaft für Chronometrie – DGC (Germany) National Association of Watch and Clock Collectors – NAWCC (United States) Miscellaneous arts and sciences Miscellaneous units Date and time representation by country Fiscal year – One-year term for government List of cycles and business financial reporting Nonlinear narrative – Narrative technique Half-life – Time for exponential decay to remove half of a quantity Philosophy of physics – Truths and principles of the study of matter, space, time and energy Hexadecimal time – Base 16 time format proposed in 1863 Rate (mathematics) – Ratio between two related quantities in different units Tithi – Lunar day in the Hindu calendar Unix epoch References 1.
- "Time" (https://web.archive.org/web/20120704084938/http://oxforddictionaries.com/definition/tim e).
- Archived from the original (http://oxforddictionarie s.com/definition/time) on 4 July 2012.
- "The indefinite continued progress of existence and events in the past, present, and future regarded as a whole"

Organizations Antiquarian Horological Society – AHS (United Kingdom) Chronometrophilia (Switzerland) Deutsche Gesellschaft für Chronometrie – DGC (Germany) National Association of Watch and Clock Collectors – NAWCC (United States) Miscellaneous arts and sciences Miscellaneous units Date and time representation by country Fiscal year – One-year term for government List of cycles and business financial reporting Nonlinear narrative – Narrative technique Half-life – Time for exponential decay to remove half of a quantity Philosophy of physics – Truths and principles of the study of matter, space, time and energy Hexadecimal time – Base 16 time format proposed in 1863 Rate (mathematics) – Ratio between two related quantities in different units Tithi – Lunar day in the Hindu calendar Unix epoch References 1.

Archived from the original (http://oxforddictionarie s.com/definition/time) on 4 July 2012.

"The indefinite continued progress of existence and events in the past, present, and future regarded as a whole"

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- A mathematically oriented article describes that the Reissner–Nordström metric for a charged, nonrotating black hole.[1] A similarly technical article on the Kerr–Newman black hole gives an overview of the most general known solution for a black hole, which has both angular momentum and charge (all the other solutions are simplified special cases of the Kerr–Newman black hole).
- See also Reissner–Nordström metric References 1.
- "Journey into and through a Reissner-Nordström black hole" (https://jila.colorado.edu/~ajsh/inside bh/rn.html#:~:text=The%20big%20difference%20between%20a,to%20another%20space%20an d%20time.).
- External links COSMOS - The SAO Encyclopedia of Astronomy - Black Hole (https://astronomy.swin.edu.au/cos mos/B/Black+Hole) Retrieved from "https://en.wikipedia.org/w/index.php?title=Charged_black_hole&oldid=1266681900"

A mathematically oriented article describes that the Reissner–Nordström metric for a charged, nonrotating black hole.[1] A similarly technical article on the Kerr–Newman black hole gives an overview of the most general known solution for a black hole, which has both angular momentum and charge (all the other solutions are simplified special cases of the Kerr–Newman black hole).

See also Reissner–Nordström metric References 1.

"Journey into and through a Reissner-Nordström black hole" (https://jila.colorado.edu/~ajsh/inside bh/rn.html#:~:text=The%20big%20difference%20between%20a,to%20another%20space%20an d%20time.).

External links COSMOS - The SAO Encyclopedia of Astronomy - Black Hole (https://astronomy.swin.edu.au/cos mos/B/Black+Hole) Retrieved from "https://en.wikipedia.org/w/index.php?title=Charged_black_hole&oldid=1266681900"

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- In other words, participants could literally “see” their bodies at a second location, separate from their physical selves.
- Ehrsson touched participants in the chest with a rod while he used cameras to make it appear that the visual image in the display was being touched at the same time.
- | 112 Chapter 5 Altered States
- Participants reported the eerie sensation that their video double was also being touched, thus sensing they were at a location outside their physical bodies.

In other words, participants could literally “see” their bodies at a second location, separate from their physical selves.

Ehrsson touched participants in the chest with a rod while he used cameras to make it appear that the visual image in the display was being touched at the same time.

Participants reported the eerie sensation that their video double was also being touched, thus sensing they were at a location outside their physical bodies.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Many of the greats of quantumphysicswerealsoskepticalofthezeropointenergy.Atthe1913SolvayCongress, Einsteindeclaredthathedidnotbelieveinthezeropointenergy,writingtoEhrenfestthat theconceptwasdeadasadoornail.However,theexperimentγ +H →H +H convinced Pauliandothers.Forenergytobeconserved, 1(cid:2)ωhastobeincludedintheenergyofthe H nucleus.
- GravityPast,Present,andFuture whichisofcoursejustthestatementthatthedarkenergyalmostsinglehandedlyclosesthe universe.Well,M isthelargestmassconsideredinfundamentalphysics,andsurely,M P U isthesmallest, andsointerestingly, M isthegeometricmeanbetweenthelargestand (cid:27) thesmallest,asalreadyremarkedoninchapterX.3butintermsoflengthscales.(Bythe way,betweenusfriends,whenIsay“largest”and“smallest,”youknowwhatIamtalking about.Tothenitpickers:yes,Iknowabout∞and0.) (cid:8) √ Idefine(cid:27)asanenergydensitybywritingtheEinstein-Hilbertactionas d4x −g((cid:27)+ 1R).
- G λ Again,observationally,weknowthatthetwotermsintheactionhavecomparableweight, and hence the length scale associated with the cosmological constant is on the order of the size of the universe.
- In other words, the radius of curvature associated with the cosmologicalconstantisgivenbyL =M /M2 ∼1/M ∼L .

Many of the greats of quantumphysicswerealsoskepticalofthezeropointenergy.Atthe1913SolvayCongress, Einsteindeclaredthathedidnotbelieveinthezeropointenergy,writingtoEhrenfestthat theconceptwasdeadasadoornail.However,theexperimentγ +H →H +H convinced Pauliandothers.Forenergytobeconserved, 1(cid:2)ωhastobeincludedintheenergyofthe H nucleus.

GravityPast,Present,andFuture whichisofcoursejustthestatementthatthedarkenergyalmostsinglehandedlyclosesthe universe.Well,M isthelargestmassconsideredinfundamentalphysics,andsurely,M P U isthesmallest, andsointerestingly, M isthegeometricmeanbetweenthelargestand (cid:27) thesmallest,asalreadyremarkedoninchapterX.3butintermsoflengthscales.(Bythe way,betweenusfriends,whenIsay“largest”and“smallest,”youknowwhatIamtalking about.Tothenitpickers:yes,Iknowabout∞and0.) (cid:8) √ Idefine(cid:27)asanenergydensitybywritingtheEinstein-Hilbertactionas d4x −g((cid:27)+ 1R).

G λ Again,observationally,weknowthatthetwotermsintheactionhavecomparableweight, and hence the length scale associated with the cosmological constant is on the order of the size of the universe.

In other words, the radius of curvature associated with the cosmologicalconstantisgivenbyL =M /M2 ∼1/M ∼L .

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- • There is no event horizon at the wormhole throat.
- - [(1/2) gir.· R] = -(8nG/c4)T,,,, where Gill" is the Einstein curvature tensor, R pl' is the Ricci curvature tensor, R = R)'l' (the trace of R}".) is the Ricci scalar curvature, Till'is the stress-energy momentum tensor (a matrix quantity that encodes the density and flux of a matter source's energy and momentum), G is Newton's universal gravitation constant (6.673 x 10-11 Nm}/kgi'), and c is the speed of light.
- ) induced by a source of matter (T JH.).
- 3) denote spacetime coordinates, Xa.

• There is no event horizon at the wormhole throat.

- [(1/2) gir.· R] = -(8nG/c4)T,,,, where Gill" is the Einstein curvature tensor, R pl' is the Ricci curvature tensor, R = R)'l' (the trace of R}".) is the Ricci scalar curvature, Till'is the stress-energy momentum tensor (a matrix quantity that encodes the density and flux of a matter source's energy and momentum), G is Newton's universal gravitation constant (6.673 x 10-11 Nm}/kgi'), and c is the speed of light.

) induced by a source of matter (T JH.).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Completionandpromotion Considerthe3-velocityv(cid:3) ≡ dx(cid:3) .Whatanawkwardquantity,a3-vectordx(cid:3)dividedbya3N dt scalardt thathappenstobethe“timecomponent”ofa4-vector.Ugh!A3-vectordivided bya3-scalar,withneithertransformingnicelyundertheLorentzgroup.Gimmeabreak, nowaytheresultingobjectv(cid:3) isgoingtotransformnicely!
- Inthischapter,wewillstudyhowvariousquantitiesinnonrelativisticphysicsaretobe “completedandpromoted.”Doingthis,wewillalsodiscoverthenatureofthegravitational fieldandbeonestepclosertothemainsubjectofthisbook.
- III.6 Completion, Promotion, and the Nature of the Gravitational Field Naturalandunnaturalquantities Wenowknowthatnonrelativisticphysicsisbutanapproximationtoadeepertruth.Since physics is Lorentz invariant, all physical quantities have to transform in a well-defined fashion under the Lorentz group, namely according to some definite representation of the group.
- If you insist, as some authors do, on writing relativistic quantities in terms of “nonrelativistic quantities,” you can do it (it’s a free country), but it’s best not to do so.

Completionandpromotion Considerthe3-velocityv(cid:3) ≡ dx(cid:3) .Whatanawkwardquantity,a3-vectordx(cid:3)dividedbya3N dt scalardt thathappenstobethe“timecomponent”ofa4-vector.Ugh!A3-vectordivided bya3-scalar,withneithertransformingnicelyundertheLorentzgroup.Gimmeabreak, nowaytheresultingobjectv(cid:3) isgoingtotransformnicely!

III.6 Completion, Promotion, and the Nature of the Gravitational Field Naturalandunnaturalquantities Wenowknowthatnonrelativisticphysicsisbutanapproximationtoadeepertruth.Since physics is Lorentz invariant, all physical quantities have to transform in a well-defined fashion under the Lorentz group, namely according to some definite representation of the group.

If you insist, as some authors do, on writing relativistic quantities in terms of “nonrelativistic quantities,” you can do it (it’s a free country), but it’s best not to do so.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Because the mirror keeps rotating while the light 5.
- On the way from the source to the mirror, the beam passes through a rotating cogwheel.
- The setup as used by Fizeau consists of a beam of light directed at a mirror 8 kilometres (5 mi) away.
- At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam Diagram of the Fizeau apparatus: strikes a tooth and does not pass through the wheel.

Because the mirror keeps rotating while the light 5.

On the way from the source to the mirror, the beam passes through a rotating cogwheel.

The setup as used by Fizeau consists of a beam of light directed at a mirror 8 kilometres (5 mi) away.

At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam Diagram of the Fizeau apparatus: strikes a tooth and does not pass through the wheel.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- More accurately, the vacuum energy caused by the virtual particle pairs is pushing the plates together, and the vacuum energy between the plates is too small to negate this effect since fewer virtual particles can exist per unit volume between the plates than can exist outside them.[5] Squeezed light It is possible to arrange multiple beams of laser light such that destructive quantum interference suppresses the vacuum fluctuations.
- Since this restriction does not exist or is much less significant on the opposite sides of the plates, the forces outside the plates are greater than those between the plates.
- This theory was developed to explain the anomaly of negative-energy quantum states predicted by the Dirac equation.
- A year later, after work by Weyl, the negative energy concept was abandoned and replaced by a theory of antimatter.[6]: 9 The following year, 1932, saw the discovery of the positron by Carl Anderson.

More accurately, the vacuum energy caused by the virtual particle pairs is pushing the plates together, and the vacuum energy between the plates is too small to negate this effect since fewer virtual particles can exist per unit volume between the plates than can exist outside them.[5] Squeezed light It is possible to arrange multiple beams of laser light such that destructive quantum interference suppresses the vacuum fluctuations.

Since this restriction does not exist or is much less significant on the opposite sides of the plates, the forces outside the plates are greater than those between the plates.

This theory was developed to explain the anomaly of negative-energy quantum states predicted by the Dirac equation.

A year later, after work by Weyl, the negative energy concept was abandoned and replaced by a theory of antimatter.[6]: 9 The following year, 1932, saw the discovery of the positron by Carl Anderson.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- It is sometimes referred as speakable information.[62] Applications to other fields Network Physiology Information theory concepts, methods and approaches have broad applications in Network Physiology[63][64][65], a field which provides a quantitative framework, based on adaptive networks of dynamical systems, to investigate how physiological systems exchange, process, and integrate information as a network to (i) coordinate their functions across levels and scales (from sub-cellular to organs and organism level) and (ii) generate distinct physiological states in health and disease.
- Namely, at time the channel is given by the conditional probability .
- Through measures such as mutual information, transfer entropy, and co-information, information theory enables the detection of coupling strength, directionality, synergy/redundancy and higherorder interactions among physiological systems and sub-systems, revealing how network crosscommunication and regulation occur within the organism.
- Fungible information Fungible information is the information for which the means of encoding is not important.[61] Classical information theorists and computer scientists are mainly concerned with information of this sort.

It is sometimes referred as speakable information.[62] Applications to other fields Network Physiology Information theory concepts, methods and approaches have broad applications in Network Physiology[63][64][65], a field which provides a quantitative framework, based on adaptive networks of dynamical systems, to investigate how physiological systems exchange, process, and integrate information as a network to (i) coordinate their functions across levels and scales (from sub-cellular to organs and organism level) and (ii) generate distinct physiological states in health and disease.

Namely, at time the channel is given by the conditional probability .

Through measures such as mutual information, transfer entropy, and co-information, information theory enables the detection of coupling strength, directionality, synergy/redundancy and higherorder interactions among physiological systems and sub-systems, revealing how network crosscommunication and regulation occur within the organism.

Fungible information Fungible information is the information for which the means of encoding is not important.[61] Classical information theorists and computer scientists are mainly concerned with information of this sort.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Research shows that we can boost the probability of subjects choosing “guide” by priming them subliminally with words like “direct,” “lead,” and “escort,” whereas we can boost the probability of their choosing “guile” by priming them subliminally with words like “deceit,” “treachery,” and “duplicity.” “Subliminal” means “under the limen.” The limen, better known as the “sensory threshold,” is the narrow range in which a diminishing stimulus goes from being just barely detectable to being just barely undetectable.
- 9781405131117_4_001.qxd 30/6/09 11:48 AM Page 37 relieve constipation, improve one’s sex life, or cure deafness (although the mechanism by which a deaf person could detect subliminal sounds remains truly mysterious).
- Interestingly, there’s evidence that under tightly controlled laboratory conditions, psychologists can demonstrate short-lived and modest subliminal effects.
- Investigators can similarly influence verbal behaviors, as when a shared theme in a series of subliminally flashed priming words increases the odds that a person will choose a related word from a list of alternatives (Merikle, 1992).

Research shows that we can boost the probability of subjects choosing “guide” by priming them subliminally with words like “direct,” “lead,” and “escort,” whereas we can boost the probability of their choosing “guile” by priming them subliminally with words like “deceit,” “treachery,” and “duplicity.” “Subliminal” means “under the limen.” The limen, better known as the “sensory threshold,” is the narrow range in which a diminishing stimulus goes from being just barely detectable to being just barely undetectable.

9781405131117_4_001.qxd 30/6/09 11:48 AM Page 37 relieve constipation, improve one’s sex life, or cure deafness (although the mechanism by which a deaf person could detect subliminal sounds remains truly mysterious).

Interestingly, there’s evidence that under tightly controlled laboratory conditions, psychologists can demonstrate short-lived and modest subliminal effects.

Investigators can similarly influence verbal behaviors, as when a shared theme in a series of subliminally flashed priming words increases the odds that a person will choose a related word from a list of alternatives (Merikle, 1992).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- JohnL.Petersen,ChairmanoftheTAIboard,deniedFitts’ allegationsandJoeFirmage,anotherBoardmember,didnotrecallthemeetingdescribedinthe minutes.
- (PUBLICDOMAIN) -3December1999—TheArlingtonInstitute(TAI),adefenseindustry non-profit,holdsaboardmeetingwithmembersincludingformerCIAdirectorR.JamesWoolsey,former AssistantSecretaryofHousingandUrbanDevelopmentCatherineAustinFitts,andseveralmediaand financialindustryexecutives.
- ● https://medium.com/@throwmasterjohn/jacques-vallees-details-interactions-with-joe-fir mage-in-the-late-1990s-a87ecc3c20ca Note:In2017,CatherineAustinFittspublishedapaperwithaMichiganStateUniversity economistthatfound$21trillioninunauthorizedspendinginthedepartmentsofDefenseand HousingandUrbanDevelopmentbetween1998and2015.
- (DoolittleislinkedtotheUAPsubjectbyhisinvestigationof“ghost rockets”inSwedeninthe1940s).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Participants then took part in a simulated “competition” allowing them to retaliate against their essay evaluator with a loud and annoying blast of noise.
- Narcissistic participants responded to negative evaluations by bombarding their opponents with significantly louder noises than other participants.
- Positive essay evaluations produced no such effect (Bushman & Baumeister, 1998).

Participants then took part in a simulated “competition” allowing them to retaliate against their essay evaluator with a loud and annoying blast of noise.

Narcissistic participants responded to negative evaluations by bombarding their opponents with significantly louder noises than other participants.

Positive essay evaluations produced no such effect (Bushman & Baumeister, 1998).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- The study of materials with The study of the physics both solid and fluid of continuous materials Non-Newtonian fluid characteristics.
- Fluid mechanics is the branch of Major areas physics concerned with the mechanics of fluids and the forces on them.
- The region corresponding to the body's configuration at time is labeled .
- The elastomer is a true continuum, but a homogeneous distribution of voids gives it unusual properties.[2] Formulation of models Continuum mechanics models begin by assigning a region in threedimensional Euclidean space to the material body being modeled.

The study of materials with The study of the physics both solid and fluid of continuous materials Non-Newtonian fluid characteristics.

Fluid mechanics is the branch of Major areas physics concerned with the mechanics of fluids and the forces on them.

The region corresponding to the body's configuration at time is labeled .

The elastomer is a true continuum, but a homogeneous distribution of voids gives it unusual properties.[2] Formulation of models Continuum mechanics models begin by assigning a region in threedimensional Euclidean space to the material body being modeled.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- RP3 is (diffeomorphic to) SO(3), hence admits a group structure; the covering map S3 → RP3 is a map of groups Spin(3) → SO(3), where Spin(3) is a Lie group that is the universal cover of SO(3).
- 3-torus The 3-dimensional torus is the product of 3 circles.
- 3-sphere A 3-sphere is a higher-dimensional analogue of a sphere.
- Real projective 3-space Real projective 3-space, or RP3, is the topological space of lines passing through the origin 0 in R4.

RP3 is (diffeomorphic to) SO(3), hence admits a group structure; the covering map S3 → RP3 is a map of groups Spin(3) → SO(3), where Spin(3) is a Lie group that is the universal cover of SO(3).

3-torus The 3-dimensional torus is the product of 3 circles.

3-sphere A 3-sphere is a higher-dimensional analogue of a sphere.

Real projective 3-space Real projective 3-space, or RP3, is the topological space of lines passing through the origin 0 in R4.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- doi:10.1063/1.1664769 (https://doi.org/10.
- International Journal of Modern Physics D.
- See page 325 (https://books.google.
- Especially see equations (7.10), (7.11) and 29.

International Journal of Modern Physics D.

Especially see equations (7.10), (7.11) and 29.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- The commutator [Γ,Γ] of the bivector1-formΓissymmetric,theanticommutationofmultivectorscancellingagainsttheanticommutation of 1-forms, equation (16.196).
- (16.208) Equation (16.208) is Cartan’s second equation of structure.
- It constitutes the definition of Riemann curvature R in terms of the Lorentz connection Γ.
- The exterior derivative of the Lorentz connection 1-form is, equation (15.70), the 2-form ( ) ( ) ∂Γ ∂Γ ∂Γ ∂Γ dΓ= λ − κ d2xκλ = mnλ − mnκ γγm∧γγnd2xκλ , (16.206) ∂xκ ∂xλ ∂xκ ∂xλ implicitly summed over distinct antisymmetric indices mn and κλ.

The commutator [Γ,Γ] of the bivector1-formΓissymmetric,theanticommutationofmultivectorscancellingagainsttheanticommutation of 1-forms, equation (16.196).

(16.208) Equation (16.208) is Cartan’s second equation of structure.

It constitutes the definition of Riemann curvature R in terms of the Lorentz connection Γ.

The exterior derivative of the Lorentz connection 1-form is, equation (15.70), the 2-form ( ) ( ) ∂Γ ∂Γ ∂Γ ∂Γ dΓ= λ − κ d2xκλ = mnλ − mnκ γγm∧γγnd2xκλ , (16.206) ∂xκ ∂xλ ∂xκ ∂xλ implicitly summed over distinct antisymmetric indices mn and κλ.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- "Ivan The Honourable" (http://iang.org/rants/ivan_the_honourabl e.html).
- Cattaneoa, Giuseppe; De Santisa, Alfredo; Ferraro Petrillo, Umberto (April 2008).
- "Security's inseparable couple: Alice & Bob" (https://www.network world.com/article/2318241/lan-wan-security-s-inseparable-couple.html).
- Bennett, Charles H.; Brassard, Gilles; Robert, Jean-Marc (1988).

"Ivan The Honourable" (http://iang.org/rants/ivan_the_honourabl e.html).

Cattaneoa, Giuseppe; De Santisa, Alfredo; Ferraro Petrillo, Umberto (April 2008).

"Security's inseparable couple: Alice & Bob" (https://www.network world.com/article/2318241/lan-wan-security-s-inseparable-couple.html).

Bennett, Charles H.; Brassard, Gilles; Robert, Jean-Marc (1988).

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List tests or derivations implied by the evidence.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- ,ψ ψ ,andψ ψ =ψ ψ R I ⇑ ⇑ ⇓ ⇓ ⇑ ⇓ ⇓ ⇑ are Lorentz-invariant scalars.
- If ψ ≡ λε is a Dirac spinor corresponding to a ⇑↑ complex quaternion λ=λ +Iλ with no quaternionic part (so λ=λ), should it not be that R I ψψ =ε⊤ λλε =ε⊤ λ2ε =λ2 , (14.145) ⇑↑ ⇑↑ ⇑↑ ⇑↑ which is a complex number, not a real number?
- Do not confuse the quantum-mechanical

,ψ ψ ,andψ ψ =ψ ψ R I ⇑ ⇑ ⇓ ⇓ ⇑ ⇓ ⇓ ⇑ are Lorentz-invariant scalars.

If ψ ≡ λε is a Dirac spinor corresponding to a ⇑↑ complex quaternion λ=λ +Iλ with no quaternionic part (so λ=λ), should it not be that R I ψψ =ε⊤ λλε =ε⊤ λ2ε =λ2 , (14.145) ⇑↑ ⇑↑ ⇑↑ ⇑↑ which is a complex number, not a real number?

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- of a cube is lit from above, the resulting shadow on a flat twodimensional surface is a square within a square with the corresponding corners connected.
- Similarly, if the wireframe of a tesseract were lit from "above" (in the fourth dimension), its shadow would be that of a threedimensional cube within another three-dimensional cube suspended in midair (a "flat" surface from a four-dimensional perspective).
- (Note that, technically, the visual representation shown here is a two-dimensional image of the three-dimensional shadow of the four-dimensional wireframe figure.) Bounding regions The dimensional analogy also helps in inferring basic properties of objects in higher dimensions, such as the bounding region.
- Three-dimensional objects are bounded by two-dimensional surfaces: a cube is bounded by

of a cube is lit from above, the resulting shadow on a flat twodimensional surface is a square within a square with the corresponding corners connected.

Similarly, if the wireframe of a tesseract were lit from "above" (in the fourth dimension), its shadow would be that of a threedimensional cube within another three-dimensional cube suspended in midair (a "flat" surface from a four-dimensional perspective).

(Note that, technically, the visual representation shown here is a two-dimensional image of the three-dimensional shadow of the four-dimensional wireframe figure.) Bounding regions The dimensional analogy also helps in inferring basic properties of objects in higher dimensions, such as the bounding region.

Three-dimensional objects are bounded by two-dimensional surfaces: a cube is bounded by

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Bibcode:1993PhRvA..48...34C (https://ui.adsabs.harvard.edu/abs/1993PhRvA..48...34C).
- Buchanan, Mark (11 February 2015).
- "Day 4: Lunar Orbits 7, 8 and 9" (https://web.archive.org/web/20110104032114/http://history.nasa.
- 10th International Conference, PaCT 2009, Novosibirsk, Russia, 31 August – 4 September 2009.

"Day 4: Lunar Orbits 7, 8 and 9" (https://web.archive.org/web/20110104032114/http://history.nasa.

10th International Conference, PaCT 2009, Novosibirsk, Russia, 31 August – 4 September 2009.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Instead, the collapsing matter on the other side of the event horizon reaches an enormous but finite density and rebounds, forming a regular Einstein–Rosen bridge.[17] The other side of the bridge becomes a new, growing baby universe.
- antisymmetric part, the torsion tensor, as a dynamical variable.
- Such an interaction prevents the formation of a gravitational singularity.
- According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole.

Instead, the collapsing matter on the other side of the event horizon reaches an enormous but finite density and rebounds, forming a regular Einstein–Rosen bridge.[17] The other side of the bridge becomes a new, growing baby universe.

antisymmetric part, the torsion tensor, as a dynamical variable.

Such an interaction prevents the formation of a gravitational singularity.

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics," Studies in History and Philosophy of Science, 4 (1973): 165–72.
- Lindberg, Beginnings of Western Science, p.
- "The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle Metaphysics 1072b4.
- Van Helden, Measuring the Universe, pp.

Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics," Studies in History and Philosophy of Science, 4 (1973): 165–72.

Lindberg, Beginnings of Western Science, p.

"The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle Metaphysics 1072b4.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- The God Particle: If the Universe Is the Answer, What Is the Question?
- Speakable and Unspeakable in Quantum Mechanics.
- Quantum Mechanics Versus Local Realism: The Einstein–Podolsky–Rosen Paradox.
- External links Stanford Encyclopedia of Philosophy: The Einstein–Podolsky–Rosen Argument in Quantum Theory; 1.2 The argument in the text (http://plato.stanford.edu/entries/qt-epr/#1.2) Internet Encyclopedia of Philosophy: "The Einstein-Podolsky-Rosen Argument and the Bell Inequalities (http://www.iep.utm.edu/epr/)" Stanford Encyclopedia of Philosophy: Abner Shimony (2019) "Bell's Theorem (http://plato.stanfor d.edu/entries/bell-theorem/)" EPR, Bell & Aspect: The Original References (http://www.drchinese.com/David/EPR_Bell_Aspect.

Einstein–Podolsky–Rosen paradox - Wikipedia.pdf

The God Particle: If the Universe Is the Answer, What Is the Question?

Speakable and Unspeakable in Quantum Mechanics.

Quantum Mechanics Versus Local Realism: The Einstein–Podolsky–Rosen Paradox.

External links Stanford Encyclopedia of Philosophy: The Einstein–Podolsky–Rosen Argument in Quantum Theory; 1.2 The argument in the text (http://plato.stanford.edu/entries/qt-epr/#1.2) Internet Encyclopedia of Philosophy: "The Einstein-Podolsky-Rosen Argument and the Bell Inequalities (http://www.iep.utm.edu/epr/)" Stanford Encyclopedia of Philosophy: Abner Shimony (2019) "Bell's Theorem (http://plato.stanfor d.edu/entries/bell-theorem/)" EPR, Bell & Aspect: The Original References (http://www.drchinese.com/David/EPR_Bell_Aspect.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Cheeger & Ebin 2008, Proposition 3.18.
- Cheeger & Ebin 2008, Corollary 3.19; Petersen 2016, Section 4.4.
- Petersen 2016, Section 4.4.3 and p.

Cheeger & Ebin 2008, Corollary 3.19; Petersen 2016, Section 4.4.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- If the same thing were done in connection with Earth, Earth's gravitational field would also be only one fourth as intense at the new position as at the old.
- The intensity of the gravitational field of each planet (or of any body) decreases as the square of the distance, which means that the relative intensity of the gravitational field of two bodies of different mass remains the same at any distance.
- THE PLANETS 37 TABLE 5-Mass and Density of the Planets Mass Density (Earth = 1) (g/cm3) Mercury 0.055 5.4 Venus 0.815 5.2 Earth 1 5.52 Moon 0.0123 3.3 Mars 0.108 3.96 Jupiter 317.9 1.34 Saturn 95.2 0.71 Uranus 14.6 1.27 Neptune 17.2 1.7 Pluto 0.1 4 times as massive as the other eight planets put together.
- For instance, a spaceship a million kilometers from Jupiter's center would feel Jupiter's gravitational pull to be 317.9 times as strong as it would feel Earth's gravitational pull to be if it were a million kilometers from Earth's center.

If the same thing were done in connection with Earth, Earth's gravitational field would also be only one fourth as intense at the new position as at the old.

The intensity of the gravitational field of each planet (or of any body) decreases as the square of the distance, which means that the relative intensity of the gravitational field of two bodies of different mass remains the same at any distance.

THE PLANETS 37 TABLE 5-Mass and Density of the Planets Mass Density (Earth = 1) (g/cm3) Mercury 0.055 5.4 Venus 0.815 5.2 Earth 1 5.52 Moon 0.0123 3.3 Mars 0.108 3.96 Jupiter 317.9 1.34 Saturn 95.2 0.71 Uranus 14.6 1.27 Neptune 17.2 1.7 Pluto 0.1 4 times as massive as the other eight planets put together.

For instance, a spaceship a million kilometers from Jupiter's center would feel Jupiter's gravitational pull to be 317.9 times as strong as it would feel Earth's gravitational pull to be if it were a million kilometers from Earth's center.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Energy condition In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically phrased mathematical formulation.
- Motivation In general relativity and allied theories, the distribution of the mass, momentum, and stress due to matter and to any non-gravitational fields is described by the energy–momentum tensor (or matter tensor) .
- Energy conditions are not physical constraints per se, but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive".[1] Many energy conditions are known to not correspond to physical reality—for example, the observable effects of dark energy are well known to violate the strong energy condition.[2][3] In general relativity, energy conditions are often used (and required) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics.
- There are multiple possible alternative ways to express such a condition such that can be applied to the matter content of the theory.

Energy condition In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically phrased mathematical formulation.

Motivation In general relativity and allied theories, the distribution of the mass, momentum, and stress due to matter and to any non-gravitational fields is described by the energy–momentum tensor (or matter tensor) .

Energy conditions are not physical constraints per se, but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive".[1] Many energy conditions are known to not correspond to physical reality—for example, the observable effects of dark energy are well known to violate the strong energy condition.[2][3] In general relativity, energy conditions are often used (and required) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics.

There are multiple possible alternative ways to express such a condition such that can be applied to the matter content of the theory.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- People may confess voluntarily to crimes they didn’t commit for a myriad of other reasons, including a need for self-punishment to “pay for” real or imagined past transgressions; a desire to protect the real perpetrator, such as a spouse or child; or because they find it difficult to distinguish fantasy from reality (Gudjonsson, 2003; Kassin & Gudjonsson, 2004).
- In one study (Kassin et al., 2005), police were more confident in their ability to detect false confessions than were college students, although the police were no more accurate.
- Clearly, these sorts of motivations may be at play in confessions regarding many wellpublicized murders like the JonBenet Ramsey and Black Dahlia crimes.
- Moreover, laboratory studies reveal that neither college students nor police officers are good at detecting when people falsely confess to prohibited or criminal activities (Kassin, Meissner, & Norwick, 2005; Lassiter, Clark, Daniels, & Soinski, 2004).

People may confess voluntarily to crimes they didn’t commit for a myriad of other reasons, including a need for self-punishment to “pay for” real or imagined past transgressions; a desire to protect the real perpetrator, such as a spouse or child; or because they find it difficult to distinguish fantasy from reality (Gudjonsson, 2003; Kassin & Gudjonsson, 2004).

In one study (Kassin et al., 2005), police were more confident in their ability to detect false confessions than were college students, although the police were no more accurate.

Clearly, these sorts of motivations may be at play in confessions regarding many wellpublicized murders like the JonBenet Ramsey and Black Dahlia crimes.

Moreover, laboratory studies reveal that neither college students nor police officers are good at detecting when people falsely confess to prohibited or criminal activities (Kassin, Meissner, & Norwick, 2005; Lassiter, Clark, Daniels, & Soinski, 2004).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Completion,Promotion,andtheNatureoftheGravitationalField | 219 ⎛ ⎞ (cid:3) (cid:4) dxμ dt dx(cid:3) dt ⎜ 1 v(cid:3) ⎟ vμ= = , =⎝(cid:6) , (cid:6) N ⎠ dτ dτ dt dτ 1−v2 1−v2 N N (with v2 =v(cid:3) .v(cid:3) ) and other awkward looking relations such as v(cid:3)=v0v(cid:3) .
- Correspondingly, the laws of physics have to be promotedalso.TowardtheendofchapterI.3onrotation,Iexplainedwhyphysicistsinsist that physical quantities must transform “nicely.” (The reader new to this might want to rereadwhatIsaidthere.)Thenicenessisnotsomuchanaestheticnicetybutratherthe fundamentalrequirementthatphysicallawsshouldnotdependontheobserver.Physics mustbeindependentofphysicists!
- dτ The conservation of nonrelativistic 3-momentum p(cid:3) =mv(cid:3) in nonrelativistic physics N N strongly suggests that the 4-momentum pμ=mdxμ is also conserved.
- Intheoreticalphysics,youarefreetodefineanyquantityyouwant,buttwocriteriaare ofprimeconcern:(1)whetherthequantityyoudefineisusefulintheparticularsituation youareconsidering,and(2)whetherthequantityyoudefineisconceptuallynaturaland thusservestodeepen,ratherthanconfound,yourunderstanding.

Completion,Promotion,andtheNatureoftheGravitationalField | 219 ⎛ ⎞ (cid:3) (cid:4) dxμ dt dx(cid:3) dt ⎜ 1 v(cid:3) ⎟ vμ= = , =⎝(cid:6) , (cid:6) N ⎠ dτ dτ dt dτ 1−v2 1−v2 N N (with v2 =v(cid:3) .v(cid:3) ) and other awkward looking relations such as v(cid:3)=v0v(cid:3) .

Correspondingly, the laws of physics have to be promotedalso.TowardtheendofchapterI.3onrotation,Iexplainedwhyphysicistsinsist that physical quantities must transform “nicely.” (The reader new to this might want to rereadwhatIsaidthere.)Thenicenessisnotsomuchanaestheticnicetybutratherthe fundamentalrequirementthatphysicallawsshouldnotdependontheobserver.Physics mustbeindependentofphysicists!

dτ The conservation of nonrelativistic 3-momentum p(cid:3) =mv(cid:3) in nonrelativistic physics N N strongly suggests that the 4-momentum pμ=mdxμ is also conserved.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Butnowsupposethattheshelloflightcontainssufficientenergytoformablackhole.
- BlackHoles (a) (b) J ⇒ H (c) Figure8 Athinsphericalshellofphotons,representedbya doubleline,(a)inaMinkowskispacetime,and(b)inaneternal Schwarzschild spacetime.
- So,wecutoffthepartsoffigure8aandfigure8bthatareirrelevant.Letusthen“sew together”thetwophysicallyrelevantregionsleftinthesetwofigurestoformonesingle spacetime,asshowninfigure8c.Beforetheshellarrives,wehaveflatspacetime,andafterward,aSchwarzschildspacetimecontainingablackhole.Thus,thiscuttingandsewing construction provides us with a spacetime description of an idealized black hole formationprocess.TheresultingPenrosediagramshowsablackholeforminginaninitiallyflat spacetime,causingahorizon(indicatedbythesolidlineintheSchwarzschildportionof thecompositespacetime,continuedasadottedlineintotheMinkowskispacetimebefore
- (c) After excising the physically irrelevantregionsfromthespacetimeinpanelsaandb,wesew togetherthetwophysicallyrelevantregionstoformonesingle spacetime.BeforereachingpointH,youcouldstillreachthe futuretimelikeinfinity.ButafterpointH,yourfateeventually istomeetthesingularityrepresentedbythejaggedline.

BlackHoles (a) (b) J ⇒ H (c) Figure8 Athinsphericalshellofphotons,representedbya doubleline,(a)inaMinkowskispacetime,and(b)inaneternal Schwarzschild spacetime.

So,wecutoffthepartsoffigure8aandfigure8bthatareirrelevant.Letusthen“sew together”thetwophysicallyrelevantregionsleftinthesetwofigurestoformonesingle spacetime,asshowninfigure8c.Beforetheshellarrives,wehaveflatspacetime,andafterward,aSchwarzschildspacetimecontainingablackhole.Thus,thiscuttingandsewing construction provides us with a spacetime description of an idealized black hole formationprocess.TheresultingPenrosediagramshowsablackholeforminginaninitiallyflat spacetime,causingahorizon(indicatedbythesolidlineintheSchwarzschildportionof thecompositespacetime,continuedasadottedlineintotheMinkowskispacetimebefore

(c) After excising the physically irrelevantregionsfromthespacetimeinpanelsaandb,wesew togetherthetwophysicallyrelevantregionstoformonesingle spacetime.BeforereachingpointH,youcouldstillreachthe futuretimelikeinfinity.ButafterpointH,yourfateeventually istomeetthesingularityrepresentedbythejaggedline.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- It’s the beautiful thing about youth.
- I love my life, but I haven’t felt that lightness of being in ages.
- I pass beneath the rusting ironwork of the railway.
- I smell ripening apples, and the sour reek of beer from keg parties in the cornfields.

I love my life, but I haven’t felt that lightness of being in ages.

I pass beneath the rusting ironwork of the railway.

I smell ripening apples, and the sour reek of beer from keg parties in the cornfields.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- The first thing I notice in the new light are four fingers at the foot of the door, severed at the second knuckle.
- Amanda is struggling, so I throw my weight into the door alongside her.
- Kind of like a built-in safeguard.” “Safeguard against what?” “I don’t know.
- Amanda is kneeling over an open backpack, her arm thrust in to her shoulder, and considering how everything just exploded in her face, she seems remarkably composed, calmly triaging the situation.

The first thing I notice in the new light are four fingers at the foot of the door, severed at the second knuckle.

Amanda is struggling, so I throw my weight into the door alongside her.

Kind of like a built-in safeguard.” “Safeguard against what?” “I don’t know.

Amanda is kneeling over an open backpack, her arm thrust in to her shoulder, and considering how everything just exploded in her face, she seems remarkably composed, calmly triaging the situation.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- Thesetofallcommutationrelationsoftheform(21)issaidtodefineaLiealgebra,withc ijkreferredtoasthe
- forasetofreal(convinceyourselfofthis!)numbersc ijk.Thesummationoverkisimpliedbytherepeatedindex summationconvention.
- Byexplicitcomputationusing(14),wefind [J x,J y]=iJ z (22) Youshouldworkouttheothercommutatorsorarguebycyclicsubstitutionx→y→z→x.Thethreecommutationrelationsmaybesummarizedby [J i,J j]=i(cid:8) ijk J k (23) Wedefinethetotallyantisymmetricsymbol(cid:8) ijkbysayingthatitchangessignupontheinterchangeofanypair ofindices(andhenceitvanisheswhenanytwoindicesareequal)andbyspecifyingthat(cid:8) =1.Inotherwords, wefoundthatc ijk =(cid:8) ijk.
- Lie’sgreatinsightisthattheprecedingdiscussionholdsforanygroupwhoseelementsarelabeledbyasetof continuousparameters(suchasθ i,i=1,2,3inthecaseofSO(3)),groupsnowknownasLiegroups.Expanding thegroupelementsaroundtheorigin,wearriveat(20)andhencethestructure(21)foranycontinuousgroup.

Byexplicitcomputationusing(14),wefind [J x,J y]=iJ z (22) Youshouldworkouttheothercommutatorsorarguebycyclicsubstitutionx→y→z→x.Thethreecommutationrelationsmaybesummarizedby [J i,J j]=i(cid:8) ijk J k (23) Wedefinethetotallyantisymmetricsymbol(cid:8) ijkbysayingthatitchangessignupontheinterchangeofanypair ofindices(andhenceitvanisheswhenanytwoindicesareequal)andbyspecifyingthat(cid:8) =1.Inotherwords, wefoundthatc ijk =(cid:8) ijk.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- 2 ShowthattheEinsteintensorE μνvanishesidenticallyin2-dimensionalspacetime.
- Nowcomesthekeypoint:(29)and(30)arestructurallythesamewithf “corresponding”toF.Hence,an actionthatdoesnotdistinguishbetweendifferentcoordinatechoicesisinvariantunderactivediffeomorphisms.
- A map f of a manifold M onto itself that is smooth, differentiable, and invertible is called a diffeomorphism.(ThinkofasphereS2beingmappedontoitself.)LetapointP onthemanifoldbemapped toapointQ=f(P).SupposethatassociatedwitheachpointP isanumberT(P).Inotherwords,thefunction T isdefinedonthemanifold.SupposealsothatthediffeomorphismmovesthenumberT(P)tothepointQ.
- Exercises 1 CheckthatvaryingthePalatiniactionwithrespectto(cid:25)ρ givestheusualrelationbetweentheChristoffel μν symbolandthemetric.

A map f of a manifold M onto itself that is smooth, differentiable, and invertible is called a diffeomorphism.(ThinkofasphereS2beingmappedontoitself.)LetapointP onthemanifoldbemapped toapointQ=f(P).SupposethatassociatedwitheachpointP isanumberT(P).Inotherwords,thefunction T isdefinedonthemanifold.SupposealsothatthediffeomorphismmovesthenumberT(P)tothepointQ.

Exercises 1 CheckthatvaryingthePalatiniactionwithrespectto(cid:25)ρ givestheusualrelationbetweentheChristoffel μν symbolandthemetric.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- Thermo-electric Currents" (https://archive.org/details/transactionsofro21royal/page/125).
- Cambridge, MA: Harvard–Smithsonian Center for Astrophysics.
- Regnault's Observations on Steam" (https:// archive.org/details/londonedinburghp04maga/page/8).
- Archived (https://web.archive.org/web/2019050915 0726/https://onceuponauniverse.com/) from the original on 9 May 2019.

Cambridge, MA: Harvard–Smithsonian Center for Astrophysics.

Regnault's Observations on Steam" (https:// archive.org/details/londonedinburghp04maga/page/8).

Archived (https://web.archive.org/web/2019050915 0726/https://onceuponauniverse.com/) from the original on 9 May 2019.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- Heclaimsheheardrumorsofautopsiesof“midgetpeople”atLosAlamos,experimentsat HollomanAFBandKirtlandAFB,metal-likewoodtestedinBerkleyhewasnotinvolvedwith,and flyingdisclandingsonmilitarybasesinCaliforniaandNewMexico.
- Itislaterclaimedtheentirestorywasdisinformationplantedbythe CIAOfficeofPolicyCoordinationPoliticalandPsychologicalWarfareStaffheadedbyJosephBryanIII toconfusetheAmericanpublic.
- ● https://majesticdocuments.com/pdf/cia_oscurapeak.pdf (PUBLICDOMAIN) -17August1949—GreatFallsAFBtoAMCatWrightPattersonAFBwriteson 17August1949thataninformant,pronetoexaggerationbuttrustworthy,sees7flyingdiscsandtwo crasheddiscs.
- ● https://www.earthfiles.com/2004/05/16/part-8-ufo-crashretrievals-the-inner-sanctum-status-report -vi-july-1991-by-leonard-h-stringfield/ (PUBLICDOMAIN) -17August1949—AnallegedCIAOSIinformationreportontheanalysisof UAPstatesaspecialstudiesprojectwithintheDODknownasUnidentifiedLenticularAerodyne TechnologyTransfer(ULATT)ExploitationProgramhousessixundisclosedprojects.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Design a retrieval plan to answer a missing detail without guessing.

EVIDENCE:
- 1.8 The spacetime wheel 29 t x Figure1.15 Therightquadrantofthespacetimewheelrepresentstheworldlinesandlinesofsimultaneityofpersons whoaccelerateinthexdirectionwithuniformaccelerationintheirownframes.
- In the case where the acceleration is one Earth gravity, g =9.80665ms−2, the unit of time is c 299,792,458ms−1 = =0.97yr , (1.25) g 9.80665ms−2 Table 1.1: Trip across the Universe.
- Time elapsed Time elapsed on spaceship on Earth Distance travelled To in years in years in lightyears α sinhα coshα−1 0 0 0 Earth (starting point) 1 1.175 .5431 2 3.627 2.762 2.34 5.12 4.22 Proxima Cen 3.962 26.3 25.3 Vega 6.60 368 367 Pleiades 10.9 2.7×104 2.7×104 Centre of Milky Way 15.4 2.44×106 2.44×106 Andromeda galaxy 18.4 4.9×107 4.9×107 Virgo cluster 19.2 1.1×108 1.1×108 Coma cluster 25.3 5×1010 5×1010 Edge of observable Universe

1.8 The spacetime wheel 29 t x Figure1.15 Therightquadrantofthespacetimewheelrepresentstheworldlinesandlinesofsimultaneityofpersons whoaccelerateinthexdirectionwithuniformaccelerationintheirownframes.

In the case where the acceleration is one Earth gravity, g =9.80665ms−2, the unit of time is c 299,792,458ms−1 = =0.97yr , (1.25) g 9.80665ms−2 Table 1.1: Trip across the Universe.

Time elapsed Time elapsed on spaceship on Earth Distance travelled To in years in years in lightyears α sinhα coshα−1 0 0 0 Earth (starting point) 1 1.175 .5431 2 3.627 2.762 2.34 5.12 4.22 Proxima Cen 3.962 26.3 25.3 Vega 6.60 368 367 Pleiades 10.9 2.7×104 2.7×104 Centre of Milky Way 15.4 2.44×106 2.44×106 Andromeda galaxy 18.4 4.9×107 4.9×107 Virgo cluster 19.2 1.1×108 1.1×108 Coma cluster 25.3 5×1010 5×1010 Edge of observable Universe

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- "Isaac Newton and Heat Transfer".
- Isaac Newton: A Biography (https://archive.org/details/isaacnewton biogr0000loui/page/327).
- org/sandbox/lhl/dsb/page.50.a.php).
- Archived (https://w eb.archive.org/web/20150217223512/http://www.tunablelasers.com/F.J.DuarteOPN%282000%29.

Isaac Newton: A Biography (https://archive.org/details/isaacnewton biogr0000loui/page/327).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- The Hermitian conjugate matrix is q† = −γγ qγγ , and 0 0 ε⊤ γγ =iε⊤ , so ψ† ≡ε⊤ q† =−iε⊤ qγγ .
- 14.9 Dirac spinors as complex quaternions 377 Exercise 14.15.
- (14.133c) −q† q† I R Conclude that the Dirac spinor ψ ≡qε corresponding to the complex quaternion q is ⇑↑ ( ) ψ ψ ≡qε = R , (14.134) ⇑↑ ψ I where ψ and ψ are the Pauli spinors corresponding to the real quaternions q and q , equation (13.131).
- Show that ψ and ψ† are related by ψ =−iψ†γγ , ψ† =−iψγγ , (14.130) 0 0 by showing from equations (14.123) and (14.124) that ψ† =−iε⊤ qγγ .

The Hermitian conjugate matrix is q† = −γγ qγγ , and 0 0 ε⊤ γγ =iε⊤ , so ψ† ≡ε⊤ q† =−iε⊤ qγγ .

14.9 Dirac spinors as complex quaternions 377 Exercise 14.15.

(14.133c) −q† q† I R Conclude that the Dirac spinor ψ ≡qε corresponding to the complex quaternion q is ⇑↑ ( ) ψ ψ ≡qε = R , (14.134) ⇑↑ ψ I where ψ and ψ are the Pauli spinors corresponding to the real quaternions q and q , equation (13.131).

Show that ψ and ψ† are related by ψ =−iψ†γγ , ψ† =−iψγγ , (14.130) 0 0 by showing from equations (14.123) and (14.124) that ψ† =−iε⊤ qγγ .

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- Microcomets, due to the stresses of solar heating, shatter and burn up much more quickly because the forces are more concentrated within their small masses.
- For one, the hypothesis did not explain how an antimatter meteor could have managed to survive that low into the Earth's atmosphere, without being annihilated as soon as it encountered terrene matter at the upper levels.[12][13] Ball lightning In 1971, fragments of antimatter comets or meteoroids were hypothesized, by David E.
- They monitored the sky with gamma-ray detection apparatus, and reported unusually high numbers at 511 keV (kilo-electron volts) which is the characteristic gamma ray frequency of a collision between an electron and a positron.
- They instead presented the hypothesis of antimatter meteors as an interesting one that did explain all of what their observations had recorded, and suggested that it merited further investigation.[14][15] Gamma-ray bursts Antimatter comets thought to exist in the Oort cloud were in the 1990s hypothesized as one possible explanation for gamma-ray bursts.[16] These bursts can be explained by the annihilation of matter and antimatter microcomets.

Microcomets, due to the stresses of solar heating, shatter and burn up much more quickly because the forces are more concentrated within their small masses.

For one, the hypothesis did not explain how an antimatter meteor could have managed to survive that low into the Earth's atmosphere, without being annihilated as soon as it encountered terrene matter at the upper levels.[12][13] Ball lightning In 1971, fragments of antimatter comets or meteoroids were hypothesized, by David E.

They monitored the sky with gamma-ray detection apparatus, and reported unusually high numbers at 511 keV (kilo-electron volts) which is the characteristic gamma ray frequency of a collision between an electron and a positron.

They instead presented the hypothesis of antimatter meteors as an interesting one that did explain all of what their observations had recorded, and suggested that it merited further investigation.[14][15] Gamma-ray bursts Antimatter comets thought to exist in the Oort cloud were in the 1990s hypothesized as one possible explanation for gamma-ray bursts.[16] These bursts can be explained by the annihilation of matter and antimatter microcomets.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- In all these formulae (h , k) are the center coordinates of the hyperbola, a is the length of the semimajor axis, and b is the length of the semi-minor axis.
- Note that in the rational forms of these formulae, the points (−a , 0) and (0 , −a), respectively, are not represented by a real value of t, but are the limit of x and y as t tends to infinity.
- Hypotrochoid A hypotrochoid is a curve traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is at a distance d from the center of the interior circle.
- A hypotrochoid for A hypotrochoid for which r = d which R = 5, r = 3, d = 5 The parametric equations for the hypotrochoids are: Some examples:

In all these formulae (h , k) are the center coordinates of the hyperbola, a is the length of the semimajor axis, and b is the length of the semi-minor axis.

Note that in the rational forms of these formulae, the points (−a , 0) and (0 , −a), respectively, are not represented by a real value of t, but are the limit of x and y as t tends to infinity.

Hypotrochoid A hypotrochoid is a curve traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is at a distance d from the center of the interior circle.

A hypotrochoid for A hypotrochoid for which r = d which R = 5, r = 3, d = 5 The parametric equations for the hypotrochoids are: Some examples:

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Summarize the most important claims and how to verify them.

EVIDENCE:
- "Results for object MESSIER 031 (Andromeda Galaxy)" (https://ned.ipac.caltech.edu/byname?obj name=Andromeda+Galaxy&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1).
- NASA/IPAC Extragalactic Database.
- doi:10.1051/0004-6361:20010107 (https://doi.org/10.1051%2F0004-6361%3A20010107).
- "Surface Brightness and Evolution of Galaxies" (https://doi.org/10.1086% 2F182301).

"Results for object MESSIER 031 (Andromeda Galaxy)" (https://ned.ipac.caltech.edu/byname?obj name=Andromeda+Galaxy&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1).

"Surface Brightness and Evolution of Galaxies" (https://doi.org/10.1086% 2F182301).

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
Which parts are established vs speculative, and what evidence supports each?

EVIDENCE:
- A decade later, Gail Sheehy’s (1976) bestselling book, Passages: Predictable Crises of Adult Life, cemented the idea of a midlife crisis in the public imagination.
- In Bull Durham (1988), Kevin Costner portrays baseball player “Crash” Davis, exiled to the minor leagues to coach a talented young player.
- By 1994, 86% of young adults surveyed believed in the reality of a “midlife crisis” (Lachman, Lewkowicz, Marcus, & Peng, 1994).
- No movie captures the supposed rut of middle age better than Groundhog Day (1993), in which comedian Bill Murray portrays Phil Connors, a heavy drinking, self-absorbed weatherman, who’s fated to repeat the same day, every day, until he finally “gets” that his life can have meaning when he becomes a better person.

A decade later, Gail Sheehy’s (1976) bestselling book, Passages: Predictable Crises of Adult Life, cemented the idea of a midlife crisis in the public imagination.

In Bull Durham (1988), Kevin Costner portrays baseball player “Crash” Davis, exiled to the minor leagues to coach a talented young player.

By 1994, 86% of young adults surveyed believed in the reality of a “midlife crisis” (Lachman, Lewkowicz, Marcus, & Peng, 1994).

No movie captures the supposed rut of middle age better than Groundhog Day (1993), in which comedian Bill Murray portrays Phil Connors, a heavy drinking, self-absorbed weatherman, who’s fated to repeat the same day, every day, until he finally “gets” that his life can have meaning when he becomes a better person.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- that behaves similarly to what is expected from the Higgs boson.[9] The Standard Model, as currently formulated, has 61 elementary particles.[10] Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s.
- The Standard Model has been found to agree with almost all the experimental tests conducted to date.
- However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery (See Theory of Everything).
- In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model, since neutrinos do not have mass in the Standard Model.[11]

that behaves similarly to what is expected from the Higgs boson.[9] The Standard Model, as currently formulated, has 61 elementary particles.[10] Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s.

The Standard Model has been found to agree with almost all the experimental tests conducted to date.

However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery (See Theory of Everything).

In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model, since neutrinos do not have mass in the Standard Model.[11]

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.


Prompt:
What does the evidence say about necessary conditions and constraints?

EVIDENCE:
- This led him, in collaboration with Luis ÁlvarezGaumé, to study violations of the conservation laws in gravity theories with anomalies, concluding that type I string theories were inconsistent.
- Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaumé had missed, which restricted the gauge group of the type I string theory to be SO(32).
- Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution.
- In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate.

This led him, in collaboration with Luis ÁlvarezGaumé, to study violations of the conservation laws in gravity theories with anomalies, concluding that type I string theories were inconsistent.

Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaumé had missed, which restricted the gauge group of the type I string theory to be SO(32).

Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution.

In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate.

If evidence lacks a detail, retrieve more chunks rather than guessing.

List tests or derivations implied by the evidence.