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

EVIDENCE:
- A variety of water models exist with increasing levels of complexity, representing water as a simple hard sphere (a united-atom
- The most accurate way to solvate a system is to place explicit water molecules in the simulation box with the molecules of interest and treat the water molecules as interacting particles like those in the other molecule(s).
- A system can be simulated in vacuum (termed a gas-phase simulation) with no surrounding environment, but this is usually undesirable because it introduces artifacts in the molecular geometry, especially in charged molecules.
- In molecular mechanics, several ways exist to define the environment surrounding a molecule or molecules of interest.

A variety of water models exist with increasing levels of complexity, representing water as a simple hard sphere (a united-atom

The most accurate way to solvate a system is to place explicit water molecules in the simulation box with the molecules of interest and treat the water molecules as interacting particles like those in the other molecule(s).

A system can be simulated in vacuum (termed a gas-phase simulation) with no surrounding environment, but this is usually undesirable because it introduces artifacts in the molecular geometry, especially in charged molecules.

In molecular mechanics, several ways exist to define the environment surrounding a molecule or molecules of interest.

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:
- drink and becoming a vegetarian later in life.
- He has been described as an "incredible polymath" who was "immensely versatile", with some of his earliest investigations involving a phonetic alphabet and a universal language.[215] Newton's diverse range of interests is seen in his library, which contained 1,752 books that could be identified.
- His note to the latter included the charge that Locke had endeavoured to "embroil" him with "woemen & by other means".[222] Newton appeared to be relatively modest about his achievements, writing in a later memoir, "I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."[223] Nonetheless, he could be fiercely competitive and did on occasion hold grudges against his intellectual rivals, not abstaining from personal attacks when it suited him—a common trait found in many of his contemporaries.[215] In a letter to Robert Hooke in February 1675, for instance, he confessed "If I have seen further it is by standing on the shoulders of giants."[224] Some historians argued that this, written at a time when Newton and Hooke were disputing over optical discoveries, was an oblique attack on Hooke who
- Ultimately, books related to his famous scientific work made up slightly less than 12% of the total collection.[216] Although it was claimed that he was once engaged,[b] Newton never married.

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.

drink and becoming a vegetarian later in life.

He has been described as an "incredible polymath" who was "immensely versatile", with some of his earliest investigations involving a phonetic alphabet and a universal language.[215] Newton's diverse range of interests is seen in his library, which contained 1,752 books that could be identified.

His note to the latter included the charge that Locke had endeavoured to "embroil" him with "woemen & by other means".[222] Newton appeared to be relatively modest about his achievements, writing in a later memoir, "I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."[223] Nonetheless, he could be fiercely competitive and did on occasion hold grudges against his intellectual rivals, not abstaining from personal attacks when it suited him—a common trait found in many of his contemporaries.[215] In a letter to Robert Hooke in February 1675, for instance, he confessed "If I have seen further it is by standing on the shoulders of giants."[224] Some historians argued that this, written at a time when Newton and Hooke were disputing over optical discoveries, was an oblique attack on Hooke who

Ultimately, books related to his famous scientific work made up slightly less than 12% of the total collection.[216] Although it was claimed that he was once engaged,[b] Newton never married.

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:
- TheUSAFwritesthatitisattempting toguidetheSubcommitteetoissueastatementcertifyingtheAirForceisproperlyconductingitsUAP investigationandnotwithholdinginformationfromthepublic.
- RawOTSreportsdiscoveredbyCook,though,showafacilityinBrunswickwasworkingon radio-controlledcraftanddiscoveredbyUSofficials;anotherfacilityinViennaexperimented withdirectenergyweapons;anotherinStuttgartusedEMtointerferewithvehiclemotors.
- ● https://archive.org/details/huntforzeropoint0000cook/page/70/mode/1up(p70,p71) Note:ItalianauthorRenatoVesco,citingItaliansourcesafterWWII,claimssaucertechnology wasdevelopeddifferentlythanLusarclaims.
- Allpartiesagree“itwouldbe unwisetogivethesubjectunduepublicity,inanopenorclosedformalCongressionalhearing.” ● https://files.afu.se/Downloads/Documents/USA%20-%20Congress/1958%20-%20Congressman %20Henderson%20briefing.pdf

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:
- advisor, Paul Gordan, was known as the "king of invariant theory", and his chief contribution to mathematics was his 1870 solution of the finite basis problem for invariants of homogeneous polynomials in two variables.[181][182] He proved this by giving a constructive method for finding all of the invariants and their generators, but was not able to carry out this constructive approach for invariants in three or more variables.
- In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables.[183][184] Furthermore, his method worked, not only for the special linear group, but also for some of its subgroups such as the special orthogonal group.[185] Noether followed Gordan's lead, writing her doctoral dissertation and several other publications on invariant theory.
- She extended Gordan's results and also built upon Hilbert's research.
- Later, she would disparage this work, finding it of little interest and admitting to forgetting the details of it.[186] Hermann Weyl wrote,

advisor, Paul Gordan, was known as the "king of invariant theory", and his chief contribution to mathematics was his 1870 solution of the finite basis problem for invariants of homogeneous polynomials in two variables.[181][182] He proved this by giving a constructive method for finding all of the invariants and their generators, but was not able to carry out this constructive approach for invariants in three or more variables.

In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables.[183][184] Furthermore, his method worked, not only for the special linear group, but also for some of its subgroups such as the special orthogonal group.[185] Noether followed Gordan's lead, writing her doctoral dissertation and several other publications on invariant theory.

She extended Gordan's results and also built upon Hilbert's research.

Later, she would disparage this work, finding it of little interest and admitting to forgetting the details of it.[186] Hermann Weyl wrote,

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:
- of activity that some might say constitutes a different form of life.”2 Said Avril Haines, the Biden Administration’s Director of National Intelligence, “There’s always the question of ‘is there something else that we simply do not understand, that might come extraterrestrially?’”3 Senate Intelligence Committee vice chairman Marco Rubio, former Congressman Mike Gallagher, and long-time congressional staffer Kirk McConnell have said that multiple individuals with firsthand knowledge of UAP programs have spoken to Congress and/or one of the inspectors general.
- And, in 2023, a high-ranking former intelligence officer named David Grusch testified to Congress that individuals told him the US government had retrieved craft and biological material of nonhuman origin.4 Shellenberger Testimony 2

of activity that some might say constitutes a different form of life.”2 Said Avril Haines, the Biden Administration’s Director of National Intelligence, “There’s always the question of ‘is there something else that we simply do not understand, that might come extraterrestrially?’”3 Senate Intelligence Committee vice chairman Marco Rubio, former Congressman Mike Gallagher, and long-time congressional staffer Kirk McConnell have said that multiple individuals with firsthand knowledge of UAP programs have spoken to Congress and/or one of the inspectors general.

And, in 2023, a high-ranking former intelligence officer named David Grusch testified to Congress that individuals told him the US government had retrieved craft and biological material of nonhuman origin.4 Shellenberger Testimony 2

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:
- Introduce a Cartesiancoordinatesystemxμ ≡{t ,xα}≡{t ,x,y,z}.TheGullstrand-PainlevémetricintheseCartesian ff ff coordinates is ds2 =−dt2 +δ (dxα−βαdt )(dxβ −ββdt ) , (19.22) ff αβ ff ff with implicit summation over spatial indices α,β =x,y,z.
- In other words, the black hole behaves as if it were a river of space that flows radially inward through Galilean space and time at the Newtonian escape velocity.
- nm0 Remarkably, the transformation (19.25) from coordinate to tetrad axes is just a Galilean transformation of space and time, which shifts the time axis by velocity β along the direction of motion, but which leaves unchanged both the time component of the time axis and all the spatial axes.
- 558 Black hole waterfalls 19.2.2 Gullstrand-Painlevé-Cartesian tetrad The manner in which the Gullstrand-Painlevé line-element depicts a flow of space into a black hole is elucidated further if the line-element is written in Cartesian rather than spherical polar coordinates.

Introduce a Cartesiancoordinatesystemxμ ≡{t ,xα}≡{t ,x,y,z}.TheGullstrand-PainlevémetricintheseCartesian ff ff coordinates is ds2 =−dt2 +δ (dxα−βαdt )(dxβ −ββdt ) , (19.22) ff αβ ff ff with implicit summation over spatial indices α,β =x,y,z.

In other words, the black hole behaves as if it were a river of space that flows radially inward through Galilean space and time at the Newtonian escape velocity.

nm0 Remarkably, the transformation (19.25) from coordinate to tetrad axes is just a Galilean transformation of space and time, which shifts the time axis by velocity β along the direction of motion, but which leaves unchanged both the time component of the time axis and all the spatial axes.

558 Black hole waterfalls 19.2.2 Gullstrand-Painlevé-Cartesian tetrad The manner in which the Gullstrand-Painlevé line-element depicts a flow of space into a black hole is elucidated further if the line-element is written in Cartesian rather than spherical polar coordinates.

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:
- parallel universes.[15] Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with Joseph Polchinski's proposal of an Everett phone[62] (named after Hugh Everett) in Steven Weinberg's formulation of nonlinear quantum mechanics.[63] The possibility of communication between parallel universes has been dubbed interuniversal travel.[64] Wormholes can also be depicted in a Penrose diagram of a Schwarzschild black hole.
- In the Penrose diagram, an object traveling faster than light will cross the black hole and will emerge from another end into a different space, time or universe.
- This will be an inter-universal wormhole.

parallel universes.[15] Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with Joseph Polchinski's proposal of an Everett phone[62] (named after Hugh Everett) in Steven Weinberg's formulation of nonlinear quantum mechanics.[63] The possibility of communication between parallel universes has been dubbed interuniversal travel.[64] Wormholes can also be depicted in a Penrose diagram of a Schwarzschild black hole.

In the Penrose diagram, an object traveling faster than light will cross the black hole and will emerge from another end into a different space, time or universe.

This will be an inter-universal wormhole.

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:
- Inourexperiments, each qubit is respresented by a superposition of the S (m = −1/2) ≡ |Si ground 1/2 j stateandtheD (m =−1/2)≡|Dimetastablestateofa40Ca+ ion.
- Inaddition,ourexperimentshowthatthelifetimesofBell √ statesofthetype(|DSi+eiφ|SDi/ 2approachthefundamentallimitgivenby thespontaneousdecayrateofthemetastableD -levelof1.2s.
- Allthreeions 5/2 j are stored together in a linear Paul trap and arrange themselves as a string with an inter-iondistanceof5μm.
- [8]demonstratedunconditionalteleportationofcontinuousvariables.

Inourexperiments, each qubit is respresented by a superposition of the S (m = −1/2) ≡ |Si ground 1/2 j stateandtheD (m =−1/2)≡|Dimetastablestateofa40Ca+ ion.

Inaddition,ourexperimentshowthatthelifetimesofBell √ statesofthetype(|DSi+eiφ|SDi/ 2approachthefundamentallimitgivenby thespontaneousdecayrateofthemetastableD -levelof1.2s.

Allthreeions 5/2 j are stored together in a linear Paul trap and arrange themselves as a string with an inter-iondistanceof5μm.

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

List tests or derivations implied by the evidence.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper


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

EVIDENCE:
- “Gravitational field of a spinning mass as an example of algebraically special metrics”.
- “Supermassive Black Holes in Nuclei of Galaxies”.
- “Discovering the Kerr and Kerr-Schild metrics”.
- Metaphysics Research Lab, Stanford University.

“Gravitational field of a spinning mass as an example of algebraically special metrics”.

“Supermassive Black Holes in Nuclei of Galaxies”.

“Discovering the Kerr and Kerr-Schild metrics”.

Metaphysics Research Lab, Stanford University.

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:
- FrawleywasaknightoftheSovereignMilitaryOrderofMalta(SMOM),aRomanCatholicorder withtiestotheCIAandformerCIAdirectorswhoservedasknightsincludingWilliamCaseyandJohn McCone.
- SunnalsoproducedInSearchofNoah’sArkin1976atatimewhentheCIAwasinvestigating Mt.AraratasalocationoftheArk(andmentionAraratinthefilm),TheAmazingWorldofPsychic PhenomenaaboutpsiandTKduringthepredecessorprogramsofProjectStarGateandTheOuter SpaceConnection,afilmabouttheancientalienhypothesis.
- (PUBLICDOMAIN) -July1980—SunnClassicPicturesreleasesthefilmHangar18aboutacover-up followingacrashedUAPinArizona;thecraftinthestoryistakentothefictional“WolfAFB”inTexas whereitisanalyzed.
- SepulvedaBoulevardinElSegundo,CAoperatedbyHughesAircraft.

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:
- Index | 827 356,711,751,782;positive,633;inquantum failurefor,342;andobjectscarryingvectorial world,forbiddingremovalof,361;andscalefactor arrow,109;inparalleltransport,543–544;of ofuniverse,496f;scalingof,753–754;universe’s vectors,340 equationofstate,497 covariantdifferentiation,320–333;andChristoffel cosmologicalconstantparadox,745–759;algebraic symbol,321;alongcurves,327 solutionof,754–755;analogiesof,786;anthropic covariantdivergence,326;oftensors,332 principle,751–752,757;breakingfreeoflocalfield covariantindices,72,315 theory,756;aschallengeforphysics,712;cosmic covariantvectors,183 coincidenceproblem,751;deeperunderstanding CP(chargeconjugationfollowedbyparity)violation, ofphysics,753;deletionofFeynmandiagrams, 528;inhigherdimensionaltheories,683 756–757;effectiveactionforgravity,711;and “crazy”coordinates,94 effectivefieldtheory,782;extremeultrainfrared creationofspace,498 regime,750–751;inflation,751;largestand creationoperator,447–448 smallestmasses,747–748;linkagebetween criticaldensity,497–498;andHubblelength,514; infraredandultravioletregime,752;naturalness ratioofenergydensityto,505 doctrine,749–750;omniscienceofgravity,745; criticalphenomena,theoryof,621 Planckmass,746–747;potentialsolutionof, Crommelin,Andrew,andRoyalSocietyexpedition, 778;quantumfluctuations,745–746;question 367 forexplanationofvacuumenergy,752–753; cross-productnotation,angularmomentum unimodulargravity,755–756;vacuumenergy conservation,48n density,749 crosssectionscattering,715 cosmologicaldistances,750;scalingat,753–754 cube,topologyof,725 cosmologicalequation,501;appropriateunits,633; cubeofphysics,12–13 andhistoryofuniverse,503–504 cubicvertex,739 cosmologicalprinciple,289,491–492;Einstein’sfield curl:covariant,325; exteriorderivative,599; equations,494;Newtonianmechanicalanalogies relativistic,252 from,507,513 curledupspace,673–674 cosmologicalredshift,295 current:conservationof,225,253;inrelativistic cosmologicaltime,inoutgoingbranewavemodel, physics,223;instringtheory,235 706 curvature,667;5-dimensionalscalar,684–685;and cosmology:curvatureofuniverse,490;gasesfor, acceleration,554;angulardeficitsas“measure” 230;goldenageof,491;inflationary,530–536; of,727;calculatedonbasisofgivenmetric, nonlocal,712;observational,505;physicalhistory 66;calculatedwithCartanformalism,602, ofearlyuniverse,515–529;properdistances,296– 605;calculatedwithdifferentialforms,607; 297;trans-Planckian,518;useofscalarfieldsin, connectionwithfieldstrengthbydifferential 759n forms,602n;constantofscalars,589;ofcurve, couchpotatoproblem:actionprinciple,143;particles 89,97;fromcurvestosurfaces,106;ofcylinders atrest,142 andspheres,6;ofearth,airlineexamplefor Coulombpotential,dilationinvariance,620 proving,66;expressingfailureofNewton-Leibniz counting:forcharacterizingintrinsiccurvature,110; rulecovariantderivatives,342;extrinsic(see andgrouptheory,56–57;ofmatrixelements, extrinsiccurvature);of“fixedlatitude”circle, 87–90 80e;intrinsic(seeintrinsiccurvature);invariant coupledEinsteinandMaxwellequations,static orcovariantdescriptionof,339;andleastpath solutions,482–483 principle,5–6;measurementof,89,547,548e; coupledordinarydifferentialequations,relativistic negative,definitionof,85;Riemann(seeRiemann stellarinteriors,452 curvature);scalar(seescalarcurvature);ofspace, coupledpartialdifferentialequations,transferof 65–66;ofspacetime(seecurvedspacetime);spatial, spacetimes,664 effectonCMBfluctuations,525–526;ofsurface covariance:differencefrominvariance,47;general, andcurves,104–105;ofuniverse,490–491,495, 285 748;vanishing,85 covariantcurl,325;derivationofenergymomentum curvature2-form,600 tensor,381 curvaturedensity,504,512;andflatnessproblem, covariantcurvature,339 531 covariantderivatives:alonggeodesic,553;inCartan curvaturetensor:alternativederivationof,547–548; formalism,605;conceptof,anddifferential antideSitterspacetime,651;computationof,with geometry,100–101;constructedbyparallel symbolicmanipulationsoftware,607;constraints transportofvectors,103;Newton-Leibnizrule, on,591;fordeSitterspacetime,626;directly

Index | 827 356,711,751,782;positive,633;inquantum failurefor,342;andobjectscarryingvectorial world,forbiddingremovalof,361;andscalefactor arrow,109;inparalleltransport,543–544;of ofuniverse,496f;scalingof,753–754;universe’s vectors,340 equationofstate,497 covariantdifferentiation,320–333;andChristoffel cosmologicalconstantparadox,745–759;algebraic symbol,321;alongcurves,327 solutionof,754–755;analogiesof,786;anthropic covariantdivergence,326;oftensors,332 principle,751–752,757;breakingfreeoflocalfield covariantindices,72,315 theory,756;aschallengeforphysics,712;cosmic covariantvectors,183 coincidenceproblem,751;deeperunderstanding CP(chargeconjugationfollowedbyparity)violation, ofphysics,753;deletionofFeynmandiagrams, 528;inhigherdimensionaltheories,683 756–757;effectiveactionforgravity,711;and “crazy”coordinates,94 effectivefieldtheory,782;extremeultrainfrared creationofspace,498 regime,750–751;inflation,751;largestand creationoperator,447–448 smallestmasses,747–748;linkagebetween criticaldensity,497–498;andHubblelength,514; infraredandultravioletregime,752;naturalness ratioofenergydensityto,505 doctrine,749–750;omniscienceofgravity,745; criticalphenomena,theoryof,621 Planckmass,746–747;potentialsolutionof, Crommelin,Andrew,andRoyalSocietyexpedition, 778;quantumfluctuations,745–746;question 367 forexplanationofvacuumenergy,752–753; cross-productnotation,angularmomentum unimodulargravity,755–756;vacuumenergy conservation,48n density,749 crosssectionscattering,715 cosmologicaldistances,750;scalingat,753–754 cube,topologyof,725 cosmologicalequation,501;appropriateunits,633; cubeofphysics,12–13 andhistoryofuniverse,503–504 cubicvertex,739 cosmologicalprinciple,289,491–492;Einstein’sfield curl:covariant,325; exteriorderivative,599; equations,494;Newtonianmechanicalanalogies relativistic,252 from,507,513 curledupspace,673–674 cosmologicalredshift,295 current:conservationof,225,253;inrelativistic cosmologicaltime,inoutgoingbranewavemodel, physics,223;instringtheory,235 706 curvature,667;5-dimensionalscalar,684–685;and cosmology:curvatureofuniverse,490;gasesfor, acceleration,554;angulardeficitsas“measure” 230;goldenageof,491;inflationary,530–536; of,727;calculatedonbasisofgivenmetric, nonlocal,712;observational,505;physicalhistory 66;calculatedwithCartanformalism,602, ofearlyuniverse,515–529;properdistances,296– 605;calculatedwithdifferentialforms,607; 297;trans-Planckian,518;useofscalarfieldsin, connectionwithfieldstrengthbydifferential 759n forms,602n;constantofscalars,589;ofcurve, couchpotatoproblem:actionprinciple,143;particles 89,97;fromcurvestosurfaces,106;ofcylinders atrest,142 andspheres,6;ofearth,airlineexamplefor Coulombpotential,dilationinvariance,620 proving,66;expressingfailureofNewton-Leibniz counting:forcharacterizingintrinsiccurvature,110; rulecovariantderivatives,342;extrinsic(see andgrouptheory,56–57;ofmatrixelements, extrinsiccurvature);of“fixedlatitude”circle, 87–90 80e;intrinsic(seeintrinsiccurvature);invariant coupledEinsteinandMaxwellequations,static orcovariantdescriptionof,339;andleastpath solutions,482–483 principle,5–6;measurementof,89,547,548e; coupledordinarydifferentialequations,relativistic negative,definitionof,85;Riemann(seeRiemann stellarinteriors,452 curvature);scalar(seescalarcurvature);ofspace, coupledpartialdifferentialequations,transferof 65–66;ofspacetime(seecurvedspacetime);spatial, spacetimes,664 effectonCMBfluctuations,525–526;ofsurface covariance:differencefrominvariance,47;general, andcurves,104–105;ofuniverse,490–491,495, 285 748;vanishing,85 covariantcurl,325;derivationofenergymomentum curvature2-form,600 tensor,381 curvaturedensity,504,512;andflatnessproblem, covariantcurvature,339 531 covariantderivatives:alonggeodesic,553;inCartan curvaturetensor:alternativederivationof,547–548; formalism,605;conceptof,anddifferential antideSitterspacetime,651;computationof,with geometry,100–101;constructedbyparallel symbolicmanipulationsoftware,607;constraints transportofvectors,103;Newton-Leibnizrule, on,591;fordeSitterspacetime,626;directly

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:
- μνλ νμλ νλμ 2 [λμν] The contortion K is antisymmetric in its first two indices, λμν K =−K , (2.66) λμν μλν and thus like the torsion tensor S has 6×4 = 24 degrees of freedom.
- The torsion tensor S can be λμν λμν expressed in terms of the contortion tensor K , λμν S =K −K =−K +3K a coordinate tensor .
- (2.67) λμν λμν λνμ μνλ [λμν] The torsion-full covariant derivative D differs from the torsion-free covariant derivative D ̊ by the conν ν tortion, D Aκ ≡D ̊ Aκ+Kκ Aμ a coordinate tensor .

μνλ νμλ νλμ 2 [λμν] The contortion K is antisymmetric in its first two indices, λμν K =−K , (2.66) λμν μλν and thus like the torsion tensor S has 6×4 = 24 degrees of freedom.

The torsion tensor S can be λμν λμν expressed in terms of the contortion tensor K , λμν S =K −K =−K +3K a coordinate tensor .

(2.67) λμν λμν λνμ μνλ [λμν] The torsion-full covariant derivative D differs from the torsion-free covariant derivative D ̊ by the conν ν tortion, D Aκ ≡D ̊ Aκ+Kκ Aμ a coordinate tensor .

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:
- Wedefinearotationasamatrixthatisbothorthogonalandspecial,thatis,amatrixthat satisfies both (3) and (5).
- FromNewtontoRiemann:CoordinatestoCurvature To focus on rotations, let us exclude reflections by imposing the condition (since detP=−1) detR=1 (5) Matriceswithunitdeterminantarecalledspecial.
- Since by assumption, A2 can be neglected relative to A, RTR(cid:16) (I +AT)(I +A)(cid:16)(I +AT +A)=I.WethusobtainAT =−A,namelythatAmustbe antisymmetric.Butthereisbasicallyonlyone2-by-2antisymmetricmatrix: (cid:15) (cid:16) 0 1 J = (7) −1 0 In other words, the solution of AT =−A is A=θJ for some r(cid:12)eal nu(cid:14)mber θ.
- In particular, a reflection in the x-axis −1 0 ,whichistheproductofP andarotationthrough90 ◦ ,isalsoexcluded.

Wedefinearotationasamatrixthatisbothorthogonalandspecial,thatis,amatrixthat satisfies both (3) and (5).

FromNewtontoRiemann:CoordinatestoCurvature To focus on rotations, let us exclude reflections by imposing the condition (since detP=−1) detR=1 (5) Matriceswithunitdeterminantarecalledspecial.

Since by assumption, A2 can be neglected relative to A, RTR(cid:16) (I +AT)(I +A)(cid:16)(I +AT +A)=I.WethusobtainAT =−A,namelythatAmustbe antisymmetric.Butthereisbasicallyonlyone2-by-2antisymmetricmatrix: (cid:15) (cid:16) 0 1 J = (7) −1 0 In other words, the solution of AT =−A is A=θJ for some r(cid:12)eal nu(cid:14)mber θ.

In particular, a reflection in the x-axis −1 0 ,whichistheproductofP andarotationthrough90 ◦ ,isalsoexcluded.

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:
- Wormholes might allow effective superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time.
- Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance.
- For both these methods, time dilation causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; time connects differently through the wormhole than outside it, however, so that synchronized clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around.[38]: 502 This means that an observer entering the "younger" end would exit the "older" end at a time when it was the same age as the "younger" end, effectively going back in time as seen by an observer from the outside.
- If two points are connected by a wormhole whose length is shorter than the distance between them outside the wormhole, the time taken to traverse it could be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole.

Wormholes might allow effective superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time.

Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance.

For both these methods, time dilation causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; time connects differently through the wormhole than outside it, however, so that synchronized clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around.[38]: 502 This means that an observer entering the "younger" end would exit the "older" end at a time when it was the same age as the "younger" end, effectively going back in time as seen by an observer from the outside.

If two points are connected by a wormhole whose length is shorter than the distance between them outside the wormhole, the time taken to traverse it could be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole.

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

EVIDENCE:
- It’s hardly a surprise that we glom on to techniques that offer foolproof promises of rapid and painless behavior changes.
- 9781405131117_4_000int.qxd 30/6/09 11:44 AM Page 10 claims in your everyday life.
- Furthermore, research shows that hearing one person express an opinion (“Joe Smith is the best qualified person to be President!”) 10 times can lead us to assume that this opinion is as widely held as hearing 10 people express this opinion once (Weaver, Garcia, Schwarz, & Miller, 2007).
- For example, because the phrase “opposites attract” is catchy and easily remembered, people tend to pass it on to others.

It’s hardly a surprise that we glom on to techniques that offer foolproof promises of rapid and painless behavior changes.

9781405131117_4_000int.qxd 30/6/09 11:44 AM Page 10 claims in your everyday life.

Furthermore, research shows that hearing one person express an opinion (“Joe Smith is the best qualified person to be President!”) 10 times can lead us to assume that this opinion is as widely held as hearing 10 people express this opinion once (Weaver, Garcia, Schwarz, & Miller, 2007).

For example, because the phrase “opposites attract” is catchy and easily remembered, people tend to pass it on to others.

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 locations of circular orbits are bounded by the two conditions (23.80).
- Asdiscussedfurtherin§23.13,theboundaryofthesecondofthetwoconditions(23.80),F =0,corresponds ± to null circular orbits.
- 23.13 Null circular orbits Nullcircularorbitsdefinethephoton sphere,markedbysolidvioletlinesinFigures23.4and23.5.Circular orbits for massless particles, m = 0, or null circular orbits, follow from the solutions for massive particles in the case where the energy and angular momentum on the circular orbit become infinite, which occurs when P → ±∞.
- The boundaries corresponding tothetwoconditions(23.80)aremarkedrespectivelybysolidamberandvioletlinesinFigures23.4and23.5.

The locations of circular orbits are bounded by the two conditions (23.80).

Asdiscussedfurtherin§23.13,theboundaryofthesecondofthetwoconditions(23.80),F =0,corresponds ± to null circular orbits.

23.13 Null circular orbits Nullcircularorbitsdefinethephoton sphere,markedbysolidvioletlinesinFigures23.4and23.5.Circular orbits for massless particles, m = 0, or null circular orbits, follow from the solutions for massive particles in the case where the energy and angular momentum on the circular orbit become infinite, which occurs when P → ±∞.

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

EVIDENCE:
- Brown opened a box, took out lamps, then they went into a much larger room.
- Like Daniel, they weren't hurt.
- At 05:45, the scientist began to move the white stone signs.
- He seemed to fly for thousands of years, until ...

Brown opened a box, took out lamps, then they went into a much larger room.

At 05:45, the scientist began to move the white stone signs.

He seemed to fly for thousands of years, until ...

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

EVIDENCE:
- The equation is generally covariant.
- For vanishing torsion, the Bianchi identities (2.128) guarantee covariant conservation of the Einstein tensor, equation (2.130), which in turn guarantees covariant conservation of energy-momentum, DκT =0 .
- It is worth remarking that the derivation of the contracted Bianchi identities (3.7) holds in arbitrarily many spacetime dimensions, so the factor of 1 multiplying the Ricci scalar R in the definition (2.124) of the Einstein tensor holds in arbitrarily many spacetime dimensions, not just 4.
- (2.131) κμ κμ What motivates the form of Einstein’s equations?

For vanishing torsion, the Bianchi identities (2.128) guarantee covariant conservation of the Einstein tensor, equation (2.130), which in turn guarantees covariant conservation of energy-momentum, DκT =0 .

It is worth remarking that the derivation of the contracted Bianchi identities (3.7) holds in arbitrarily many spacetime dimensions, so the factor of 1 multiplying the Ricci scalar R in the definition (2.124) of the Einstein tensor holds in arbitrarily many spacetime dimensions, not just 4.

(2.131) κμ κμ What motivates the form of Einstein’s equations?

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

EVIDENCE:
- Some readers skeptical of psychic abilities might assume that callers, who ended up paying an average of $60 for each call, were simply suckers.
- Yet this judgment doesn’t consider the fact that belief in psychic abilities and extrasensory perception (ESP) is firmly entrenched in modern society.
- Coined in 1870 by Sir Richard Burton, the term ESP has come to mean knowledge or perception without the use of any of the senses.
- adults surveyed believe in ESP, 31% in the existence of “telepathy/communication between minds without using traditional senses,” and 26% in “clairvoyance/the power of the mind to know the past and predict the future.” Among 92 introductory psychology students, 73% said they believed that the existence of ESP was well documented (Taylor & Kowalski, 2003).

Some readers skeptical of psychic abilities might assume that callers, who ended up paying an average of $60 for each call, were simply suckers.

Yet this judgment doesn’t consider the fact that belief in psychic abilities and extrasensory perception (ESP) is firmly entrenched in modern society.

Coined in 1870 by Sir Richard Burton, the term ESP has come to mean knowledge or perception without the use of any of the senses.

adults surveyed believe in ESP, 31% in the existence of “telepathy/communication between minds without using traditional senses,” and 26% in “clairvoyance/the power of the mind to know the past and predict the future.” Among 92 introductory psychology students, 73% said they believed that the existence of ESP was well documented (Taylor & Kowalski, 2003).

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

EVIDENCE:
- arch.worldcat.org/issn/1476-4687).
- See Guth (1997) for a popular description of S2CID 55539246 (https://api.semanticscholar.
- bs.harvard.edu/abs/1974Natur.248...30H).
- s://books.google.com/books?id=f3_rnRVxGIs Bibcode:1975CMaPh..43..199H (https://ui.ads C&pg=PT9) from the original on 18 January abs.harvard.edu/abs/1975CMaPh..43..199H).

See Guth (1997) for a popular description of S2CID 55539246 (https://api.semanticscholar.

s://books.google.com/books?id=f3_rnRVxGIs Bibcode:1975CMaPh..43..199H (https://ui.ads C&pg=PT9) from the original on 18 January abs.harvard.edu/abs/1975CMaPh..43..199H).

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

EVIDENCE:
- time the variations in the first observable, say the energy, are reduced below the ZPF such that the energy becomes "negative." "Squeezing" is thus the control of quantum fluctuations and corresponding uncertainties, whereby one can squeeze/reduce the variance of one (physically important) observable quantity provided the variance in the (physically unimportant) conjugate variable is stretched/increased.
- The squeezed quantity possesses an unusually low variance meaning less variance l than would be expected on the basis of the equipartition theorem.
- One can in principle G Electron mass, m~ = 9.11 x 10-31 kg; electron charge, e = 1.602 x lO-11l C.

time the variations in the first observable, say the energy, are reduced below the ZPF such that the energy becomes "negative." "Squeezing" is thus the control of quantum fluctuations and corresponding uncertainties, whereby one can squeeze/reduce the variance of one (physically important) observable quantity provided the variance in the (physically unimportant) conjugate variable is stretched/increased.

The squeezed quantity possesses an unusually low variance meaning less variance l than would be expected on the basis of the equipartition theorem.

One can in principle G Electron mass, m~ = 9.11 x 10-31 kg; electron charge, e = 1.602 x lO-11l C.

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

EVIDENCE:
- 9781405131117_6_ind.qxd 30/6/09 11:49 AM Page 321 Bushman, Brad 150, 165 clinical method of decision-making Buston, Peter 138 228, 229 Butterfly Effect 74 clinical neurology 22–3 Byrne, Donn 137 clinician’s illusion 15 Byrne, Rhonda 129–30 Clinton, Bill 193 bystander nonintervention 140–2 Clinton, Hillary 61, 153 Cloud Picture Test 173 Campbell, Donald 45–6, 124 codependent personality traits, Campbell, Jennifer 164 ACOAs and 194 Canadian Broadcasting Corporation Coffield, Frank 94, 96 (CBC) 39 cognitive-behavioral therapists 238 cancer, staved off by positive attitude cognitive behavioral therapy, 129–32 hypnosis and 73 scientific evidence 131 cognitive illusions 7–8 Cape Fear 209 Cohen, Jacob 15, 145 Carnegie, Dale 24 Cohen, Patricia 15 Carrie 30 Cohen’s d 145–6 catharsis 147–51 coincidences 31 causation 13–14, 46, 204, 252 Columbine High School 162 “Central Park Five” 223 comas 78, 79, 80 Chandler, Jordan 121 command hallucinations 211 Chaplin, Charlie 232 common sense 5–8, 16, 139, 247 character reading 175 see also hunches; intuitions Charlie’s Drunken Daze 232 communication, gender differences “Chicken Soup” books 55 143–6 child abuse Comparison Question Test 118–19, personality disturbance and 120 166–9 complementarity 136 repressed memories and 75 Comprehensive System (CS) of childhood memories 236–9 Rorschach 173, 175 childhood resilience 169 –70 confessions, false 220–4 childhood sexual abuse and characteristics that increase personality disorders 166–71 likelihood of 224 children, diagnostic labels and police bias 222 185–6 reasons for 222 Cho, Seung-Hui 210 Confessions of Crime 221 “Choker Chicken” 148 confirmation bias 119 “Choking Strangler Boss” 148 consciousness 100–15 Chopra, Deepak 130 controlled drinking 234–6 Chowchilla kidnapping 170 Cook, Steven 70 City Slickers 53 Copycat 213 clairvoyance 29–30 corpus callosum 25, 27 classical music 45–9 correlation 12–14, 46, 88, 156, clinical decision-making 227–31 164, 167–9, 174, 202, 203–4, clinical depression 186–9 252 | Index 321

9781405131117_6_ind.qxd 30/6/09 11:49 AM Page 321 Bushman, Brad 150, 165 clinical method of decision-making Buston, Peter 138 228, 229 Butterfly Effect 74 clinical neurology 22–3 Byrne, Donn 137 clinician’s illusion 15 Byrne, Rhonda 129–30 Clinton, Bill 193 bystander nonintervention 140–2 Clinton, Hillary 61, 153 Cloud Picture Test 173 Campbell, Donald 45–6, 124 codependent personality traits, Campbell, Jennifer 164 ACOAs and 194 Canadian Broadcasting Corporation Coffield, Frank 94, 96 (CBC) 39 cognitive-behavioral therapists 238 cancer, staved off by positive attitude cognitive behavioral therapy, 129–32 hypnosis and 73 scientific evidence 131 cognitive illusions 7–8 Cape Fear 209 Cohen, Jacob 15, 145 Carnegie, Dale 24 Cohen, Patricia 15 Carrie 30 Cohen’s d 145–6 catharsis 147–51 coincidences 31 causation 13–14, 46, 204, 252 Columbine High School 162 “Central Park Five” 223 comas 78, 79, 80 Chandler, Jordan 121 command hallucinations 211 Chaplin, Charlie 232 common sense 5–8, 16, 139, 247 character reading 175 see also hunches; intuitions Charlie’s Drunken Daze 232 communication, gender differences “Chicken Soup” books 55 143–6 child abuse Comparison Question Test 118–19, personality disturbance and 120 166–9 complementarity 136 repressed memories and 75 Comprehensive System (CS) of childhood memories 236–9 Rorschach 173, 175 childhood resilience 169 –70 confessions, false 220–4 childhood sexual abuse and characteristics that increase personality disorders 166–71 likelihood of 224 children, diagnostic labels and police bias 222 185–6 reasons for 222 Cho, Seung-Hui 210 Confessions of Crime 221 “Choker Chicken” 148 confirmation bias 119 “Choking Strangler Boss” 148 consciousness 100–15 Chopra, Deepak 130 controlled drinking 234–6 Chowchilla kidnapping 170 Cook, Steven 70 City Slickers 53 Copycat 213 clairvoyance 29–30 corpus callosum 25, 27 classical music 45–9 correlation 12–14, 46, 88, 156, clinical decision-making 227–31 164, 167–9, 174, 202, 203–4, clinical depression 186–9 252 | Index 321

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

EVIDENCE:
- (cid:190) D-Brane and 3-Brane Theories/Parallel Spaces (Rubakov and Shaposhnikov, 1983a, b; Polchinski, 1995; Antoniadis et al., 1998; Randall and Sundrum, 1999a, b; Weiss, 2000; Pease, 2001; Arkani-Hamed et al., 1998, 2000, 2002): D-brane theory is a recent incarnation of the original superstring theories in which open strings, corresponding to the fundamental particles of the standard model (quarks, leptons, gauge bosons), have their free ends stuck on a (hypersurface) Approved for public release; distribution unlimited.
- There are different versions of these theories that require ten, eleven or twenty-six extra space dimensions to unify and quantise gravity, whereby the extra dimensions are curled up (i.e., compactified) into balls of space with a radius < 10 −35 m.
- The mathematics behind this class of theories is very ugly, and it is difficult for even the best superstring theorists to make simple or sophisticated calculations and predictions.
- The superstrings are ≈ 10 −35 m (i.e., the Planck length) in size.

(cid:190) D-Brane and 3-Brane Theories/Parallel Spaces (Rubakov and Shaposhnikov, 1983a, b; Polchinski, 1995; Antoniadis et al., 1998; Randall and Sundrum, 1999a, b; Weiss, 2000; Pease, 2001; Arkani-Hamed et al., 1998, 2000, 2002): D-brane theory is a recent incarnation of the original superstring theories in which open strings, corresponding to the fundamental particles of the standard model (quarks, leptons, gauge bosons), have their free ends stuck on a (hypersurface) Approved for public release; distribution unlimited.

There are different versions of these theories that require ten, eleven or twenty-six extra space dimensions to unify and quantise gravity, whereby the extra dimensions are curled up (i.e., compactified) into balls of space with a radius < 10 −35 m.

The mathematics behind this class of theories is very ugly, and it is difficult for even the best superstring theorists to make simple or sophisticated calculations and predictions.

The superstrings are ≈ 10 −35 m (i.e., the Planck length) in size.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Planck spacecraft.[74] This analysis shows that the Universe is flat to within percent, and that it is homogeneous and isotropic to one part in 100,000.
- In addition, it accounts for the observed flatness and absence of magnetic monopoles.
- Magnetic monopoles were one example of a stable topological defect predicted by grand unified theories of the early universe.
- The idea was that as the very early universe cools from an initial hot, dense state it triggered a series of phase transitions much like what happens in condensed-matter systems such as vortices in liquid helium.

Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Planck spacecraft.[74] This analysis shows that the Universe is flat to within percent, and that it is homogeneous and isotropic to one part in 100,000.

In addition, it accounts for the observed flatness and absence of magnetic monopoles.

Magnetic monopoles were one example of a stable topological defect predicted by grand unified theories of the early universe.

The idea was that as the very early universe cools from an initial hot, dense state it triggered a series of phase transitions much like what happens in condensed-matter systems such as vortices in liquid helium.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- In this formalism, distances in space can be measured by how long light takes to travel that distance, e.g., a light-year is a measure of distance, and a meter is now defined in terms of how far light travels in a
- Einstein, in his special theory of relativity,[90] postulated the constancy and finiteness of the speed of light for all observers.
- He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.
- The theory of special relativity finds a convenient formulation in Minkowski spacetime, a mathematical structure that combines three dimensions of space with a single dimension of time.

In this formalism, distances in space can be measured by how long light takes to travel that distance, e.g., a light-year is a measure of distance, and a meter is now defined in terms of how far light travels in a

Einstein, in his special theory of relativity,[90] postulated the constancy and finiteness of the speed of light for all observers.

He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.

The theory of special relativity finds a convenient formulation in Minkowski spacetime, a mathematical structure that combines three dimensions of space with a single dimension of time.

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

EVIDENCE:
- 1, the functions have the limiting solution, R = r+a and φ = (cid:25)=2 (r > 0).
- (2) we write the perturbed functions as f(t;r) = f (r)+"f (r)ei!t; (13) 0 1 (cid:14)(t;r) = (cid:14) (r)+"(cid:14) (r)ei!t; (14) 0 1 R(t;r) = R (r)+"R (r)ei!t; (15) 0 1 φ(t;r) = φ (r)+"φ (r)ei!t; (16) 0 1 where " is an in(cid:12)nitesimal parameter, and the variables with subscript 0 denote the static solution.
- IC-MSQUARE2014 IOPPublishing JournalofPhysics: ConferenceSeries574(2015)012056 doi:10.1088/1742-6596/574/1/012056 Figure 2.
- Stability analysis In this subsection, we investigate the linear stability of the higher-dimensional wormhole.

1, the functions have the limiting solution, R = r+a and φ = (cid:25)=2 (r > 0).

(2) we write the perturbed functions as f(t;r) = f (r)+"f (r)ei!t; (13) 0 1 (cid:14)(t;r) = (cid:14) (r)+"(cid:14) (r)ei!t; (14) 0 1 R(t;r) = R (r)+"R (r)ei!t; (15) 0 1 φ(t;r) = φ (r)+"φ (r)ei!t; (16) 0 1 where " is an in(cid:12)nitesimal parameter, and the variables with subscript 0 denote the static solution.

IC-MSQUARE2014 IOPPublishing JournalofPhysics: ConferenceSeries574(2015)012056 doi:10.1088/1742-6596/574/1/012056 Figure 2.

Stability analysis In this subsection, we investigate the linear stability of the higher-dimensional wormhole.

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

EVIDENCE:
- Conversely, an oriented atlas determines such a generator as compatible local orientations can be glued together to give a generator for the homology group .[4] Orientation and cohomology A manifold is orientable if and only if the first Stiefel–Whitney class vanishes.
- generator therefore corresponds to a decision of whether, in the given chart, a sphere around is positive or negative.
- This generator determines an oriented atlas by fixing a generator of the infinite cyclic group and taking the oriented charts to be those for which pushes forward to the fixed generator.
- Moreover, if is orientable and vanishes, then parametrizes the choices of orientations.[5] This characterization of orientability extends to orientability of general vector bundles over , not just the tangent bundle.

Conversely, an oriented atlas determines such a generator as compatible local orientations can be glued together to give a generator for the homology group .[4] Orientation and cohomology A manifold is orientable if and only if the first Stiefel–Whitney class vanishes.

generator therefore corresponds to a decision of whether, in the given chart, a sphere around is positive or negative.

This generator determines an oriented atlas by fixing a generator of the infinite cyclic group and taking the oriented charts to be those for which pushes forward to the fixed generator.

Moreover, if is orientable and vanishes, then parametrizes the choices of orientations.[5] This characterization of orientability extends to orientability of general vector bundles over , not just the tangent bundle.

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

EVIDENCE:
- By adding Robertson[1] and Ozawa relations we obtain The four terms can be written as: Defining: as the inaccuracy in the measured values of the variable A and as the resulting fluctuation in the conjugate variable B, Kazuo Fujikawa[74] established an uncertainty relation similar to the Heisenberg original one, but valid both for systematic and statistical errors: Quantum entropic uncertainty principle For many distributions, the standard deviation is not a particularly natural way of quantifying the structure.
- The two simultaneous measurements on A and B are necessarily[73] unsharp or weak.
- It is also possible to derive an uncertainty relation that, as the Ozawa's one, combines both the statistical and systematic error components, but keeps a form very close to the Heisenberg original inequality.
- Beckner[80] and by Iwo Bialynicki-Birula and Jerzy Mycielski[81] is that, for two normalized, dimensionless Fourier transform pairs f(a) and g(b) where and

By adding Robertson[1] and Ozawa relations we obtain The four terms can be written as: Defining: as the inaccuracy in the measured values of the variable A and as the resulting fluctuation in the conjugate variable B, Kazuo Fujikawa[74] established an uncertainty relation similar to the Heisenberg original one, but valid both for systematic and statistical errors: Quantum entropic uncertainty principle For many distributions, the standard deviation is not a particularly natural way of quantifying the structure.

The two simultaneous measurements on A and B are necessarily[73] unsharp or weak.

It is also possible to derive an uncertainty relation that, as the Ozawa's one, combines both the statistical and systematic error components, but keeps a form very close to the Heisenberg original inequality.

Beckner[80] and by Iwo Bialynicki-Birula and Jerzy Mycielski[81] is that, for two normalized, dimensionless Fourier transform pairs f(a) and g(b) where and

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

EVIDENCE:
- Even here, though, these reductions aren’t especially long-lasting—they’ve largely dissipated by 3 to 5 months—suggesting that a one-shot exposure to a refutational message may not do the trick.
- Nevertheless, there may be a “ray” of hope, if we can be forgiven for the pun.
- Psychologists still don’t understand why so many of us hold extramission beliefs, but they have a few tantalizing leads.
- Many of us have seen the gleaming light generated by this layer, sometimes called “eyeshine,” in cats or raccoons at night (Ollivier et al., 2004).

Even here, though, these reductions aren’t especially long-lasting—they’ve largely dissipated by 3 to 5 months—suggesting that a one-shot exposure to a refutational message may not do the trick.

Nevertheless, there may be a “ray” of hope, if we can be forgiven for the pun.

Psychologists still don’t understand why so many of us hold extramission beliefs, but they have a few tantalizing leads.

Many of us have seen the gleaming light generated by this layer, sometimes called “eyeshine,” in cats or raccoons at night (Ollivier et al., 2004).

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

EVIDENCE:
- The conjugation operator C is by construction Lorentz invariant, so the conjugate spinor ψ ̄ Lorentz transforms as R: ψ ̄≡Cψ* →CR*ψ* =RCψ* =Rψ ̄ , (39.92) that is, the conjugate spinor ψ ̄ Lorentz transforms in the same way as the spinor ψ.
- (39.86) In both Dirac and chiral representations, commuting the conjugation operator C through the orthonormal basis vectors γγ converts them to their complex (with respect to i) conjugates, m Cγγ =γγ*C .
- (39.87) m m In both Dirac and chiral representations, commuting C through the spinor metric ε converts the former to minus its complex conjugate, Cε=−εC* .
- The middle expression of equation (39.92) is CR*ψ* =C(Rψ)* =Rψ, so Rψ =Rψ ̄ , (39.93) that is, the operations of conjugation and Lorentz transformation commute.

The conjugation operator C is by construction Lorentz invariant, so the conjugate spinor ψ ̄ Lorentz transforms as R: ψ ̄≡Cψ* →CR*ψ* =RCψ* =Rψ ̄ , (39.92) that is, the conjugate spinor ψ ̄ Lorentz transforms in the same way as the spinor ψ.

(39.86) In both Dirac and chiral representations, commuting the conjugation operator C through the orthonormal basis vectors γγ converts them to their complex (with respect to i) conjugates, m Cγγ =γγ*C .

(39.87) m m In both Dirac and chiral representations, commuting C through the spinor metric ε converts the former to minus its complex conjugate, Cε=−εC* .

The middle expression of equation (39.92) is CR*ψ* =C(Rψ)* =Rψ, so Rψ =Rψ ̄ , (39.93) that is, the operations of conjugation and Lorentz transformation commute.

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

EVIDENCE:
- that he is Ra, and he stays (b) Ra keeps all the white stone that the miners on their world as their king.
- 3 Who are Sha’uri’s people really?
- wants to go to Earth and make everyone happy.
- 5 Who were the people who hid the StarGate on Earth 2 Did you enjoy the book?

that he is Ra, and he stays (b) Ra keeps all the white stone that the miners on their world as their king.

wants to go to Earth and make everyone happy.

5 Who were the people who hid the StarGate on Earth 2 Did you enjoy the book?

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

EVIDENCE:
- Philosophical Transactions of the Royal Society of London.
- United States National Institute for Occupational Safety and Health.
- 3, §§ "Force", "Matter", and "The Higgs Field".
- Further reading Griffiths, David J.

Philosophical Transactions of the Royal Society of London.

United States National Institute for Occupational Safety and Health.

3, §§ "Force", "Matter", and "The Higgs Field".

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

EVIDENCE:
- Notably, Imre Lakatos and Paul Feyerabend, Karl Popper's colleague and student, respectively, have produced novel attempts at such a synthesis.
- According to Schick and Vaughn,[15] researchers weighing up alternative hypotheses may take into consideration: Testability (compare falsifiability as discussed above) Parsimony (as in the application of "Occam's razor", discouraging the postulation of excessive numbers of entities) Scope – the apparent applicability of the hypothesis to multiple known phenomena Fruitfulness – the prospect that the hypothesis may explain further phenomena in the future Conservatism – the degree of "fit" with existing recognized knowledge-systems.
- Frequently the interpreted hypothesis will be derivative hypotheses of the theory; but their confirmation or disconfirmation by empirical data will then immediately strengthen or weaken also the primitive hypotheses from which they were derived.[21]: 36 Hempel provides a useful metaphor that describes the relationship between a conceptual framework and the framework as it is observed and perhaps tested (interpreted framework).
- When a set of hypotheses are grouped together, they become a type of conceptual framework.

Notably, Imre Lakatos and Paul Feyerabend, Karl Popper's colleague and student, respectively, have produced novel attempts at such a synthesis.

According to Schick and Vaughn,[15] researchers weighing up alternative hypotheses may take into consideration: Testability (compare falsifiability as discussed above) Parsimony (as in the application of "Occam's razor", discouraging the postulation of excessive numbers of entities) Scope – the apparent applicability of the hypothesis to multiple known phenomena Fruitfulness – the prospect that the hypothesis may explain further phenomena in the future Conservatism – the degree of "fit" with existing recognized knowledge-systems.

Frequently the interpreted hypothesis will be derivative hypotheses of the theory; but their confirmation or disconfirmation by empirical data will then immediately strengthen or weaken also the primitive hypotheses from which they were derived.[21]: 36 Hempel provides a useful metaphor that describes the relationship between a conceptual framework and the framework as it is observed and perhaps tested (interpreted framework).

When a set of hypotheses are grouped together, they become a type of conceptual framework.

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:
- Such skewed media coverage may fuel the erroneous impression that most individuals with schizophrenia, bipolar disorder (once called manic depression), and other serious mental illnesses are physically dangerous.
- If we’re walking down the street and | Introduction 15
- (6) Exposure to a Biased Sample In the media and many aspects of daily life, we’re often exposed to a nonrandom—or what psychologists called a “biased”—sample of people from the general population.
- A “heuristic,” by the way, is a mental shortcut or rule of thumb.

Such skewed media coverage may fuel the erroneous impression that most individuals with schizophrenia, bipolar disorder (once called manic depression), and other serious mental illnesses are physically dangerous.

If we’re walking down the street and | Introduction 15

(6) Exposure to a Biased Sample In the media and many aspects of daily life, we’re often exposed to a nonrandom—or what psychologists called a “biased”—sample of people from the general population.

A “heuristic,” by the way, is a mental shortcut or rule of thumb.

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:
- There were moments, early on, when I considered running from Daniela.
- It played a critical part in why he never married, never had kids.
- What a strange thing to consider imagining a world into being with nothing but words, intention, and desire.
- I think maybe I can help you get home.” — I lean back against the trunk of a pine tree, a notebook resting on my knees, my thoughts teeming.

There were moments, early on, when I considered running from Daniela.

It played a critical part in why he never married, never had kids.

What a strange thing to consider imagining a world into being with nothing but words, intention, and desire.

I think maybe I can help you get home.” — I lean back against the trunk of a pine tree, a notebook resting on my knees, my thoughts teeming.

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:
- Proceedings (https://books.google.com/books?id=XmwiCwAAQBAJ).
- 4090, arXiv:gr-qc/0204090 (https://arxiv.org/abs/gr-qc/020 4090), Bibcode:2002gr.qc.....4090C (https://ui.adsabs.harvard.edu/abs/2002gr.qc.....4090C), ISBN 978-981-238-171-2 Dalal, Neal; Holz, Daniel E.; Hughes, Scott A.; Jain, Bhuvnesh (2006), "Short GRB and binary black hole standard sirens as a probe of dark energy", Phys.
- (2002), "An overview of gravitational wave sources", in Bishop, Nigel; Maharaj, Sunil D.
- Theory and Practice of Natural Computing: Fourth International Conference, TPNC 2015, Mieres, Spain, December 15– 16, 2015.

4090, arXiv:gr-qc/0204090 (https://arxiv.org/abs/gr-qc/020 4090), Bibcode:2002gr.qc.....4090C (https://ui.adsabs.harvard.edu/abs/2002gr.qc.....4090C), ISBN 978-981-238-171-2 Dalal, Neal; Holz, Daniel E.; Hughes, Scott A.; Jain, Bhuvnesh (2006), "Short GRB and binary black hole standard sirens as a probe of dark energy", Phys.

(2002), "An overview of gravitational wave sources", in Bishop, Nigel; Maharaj, Sunil D.

Theory and Practice of Natural Computing: Fourth International Conference, TPNC 2015, Mieres, Spain, December 15– 16, 2015.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- Walencik-Łata, A.; Kozłowska, B.; Dorda, J.; Przylibski, T.A.
- Bibcode:2020Chmsp.24225171G (http s://ui.adsabs.harvard.edu/abs/2020Chmsp.24225171G).
- Sainz, Carlos; Rábago, Daniel; Fuente, Ismael; Celaya, Santiago; Quindós, Luis Santiago (February 2016).
- doi:10.1080/10256016.2016.1116986 (https://doi.org/10.1080%2F10256016.2016.1116986).

Walencik-Łata, A.; Kozłowska, B.; Dorda, J.; Przylibski, T.A.

Sainz, Carlos; Rábago, Daniel; Fuente, Ismael; Celaya, Santiago; Quindós, Luis Santiago (February 2016).

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

EVIDENCE:
- The spinor representation of SU(N) given by equation (42.172a) is that for spinor grade p = 1, which is the only non-trivial spinor grade for the groups SU(2) and SU(3) considered here.
- The Dynkin index S , equation (42.39), of a multiplet equals the trace of the square of an orthonormal generator, suitably normalized.
- Y The Dynkin index of U (1) that enters equation (42.171) equals the hypercharge squared summed over Y the particles of the SM, suitably normalized.
- Spin(N) has a unique spin representation, but SU(N) has spinor representations of spinor grades p≤N/2.

The spinor representation of SU(N) given by equation (42.172a) is that for spinor grade p = 1, which is the only non-trivial spinor grade for the groups SU(2) and SU(3) considered here.

The Dynkin index S , equation (42.39), of a multiplet equals the trace of the square of an orthonormal generator, suitably normalized.

Y The Dynkin index of U (1) that enters equation (42.171) equals the hypercharge squared summed over Y the particles of the SM, suitably normalized.

Spin(N) has a unique spin representation, but SU(N) has spinor representations of spinor grades p≤N/2.

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

EVIDENCE:
- • The ones with Standard Model matter can only be microscopic.
- Randall Sundrum II model (1999) • We can then get a traversable wormhole similar to the one we discussed that is big enough for us to travel through it.
- • We postulate an extra ``dark sector’’.
- Involving an an extra dimension, a 5th dimension.

• The ones with Standard Model matter can only be microscopic.

Randall Sundrum II model (1999) • We can then get a traversable wormhole similar to the one we discussed that is big enough for us to travel through it.

• We postulate an extra ``dark sector’’.

Involving an an extra dimension, a 5th dimension.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- Constant linear acceleration in any direction The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical form.
- Using equation [4] in the set above, we have:
- At the highest point, the ball will be at rest: therefore v = 0.
- While these quantities appear to be scalars, the direction of displacement, speed and acceleration is important.

Constant linear acceleration in any direction The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical form.

Using equation [4] in the set above, we have:

At the highest point, the ball will be at rest: therefore v = 0.

While these quantities appear to be scalars, the direction of displacement, speed and acceleration is important.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- The standard representation is the one with M-dimension ∞.
- Type III: The M-dimension can be 0 or ∞.
- The standard representation of B(H) is ∞ H⊗H; its M-dimension is ∞.
- The possible M-dimensions of modules are given as follows: Type I (n finite): The M-dimension can be any of 0/n, 1/n, 2/n, 3/n, ..., ∞.

The standard representation is the one with M-dimension ∞.

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

The standard representation of B(H) is ∞ H⊗H; its M-dimension is ∞.

The possible M-dimensions of modules are given as follows: Type I (n finite): The M-dimension can be any of 0/n, 1/n, 2/n, 3/n, ..., ∞.

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

EVIDENCE:
- As he approaches, I catch a whiff of cologne, and then alcohol on his breath.
- I just...I hate everything that’s happened.
- “I’m sure you have some things you want to say, Jason, but I hope you’ll let me go first.
- Leighton eases down onto the edge of the paper-thin mattress.

As he approaches, I catch a whiff of cologne, and then alcohol on his breath.

I just...I hate everything that’s happened.

“I’m sure you have some things you want to say, Jason, but I hope you’ll let me go first.

Leighton eases down onto the edge of the paper-thin mattress.

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

EVIDENCE:
- insight into natural systems or be inspired by them.
- In the general sense, a mathematical theory is a branch of mathematics devoted to some specific topics or methods, such as set theory, number theory, group theory, probability theory, game theory, control theory, perturbation theory, etc., such as might be appropriate for a single textbook.
- In mathematical logic, a theory has a related but different sense: it is the collection of the theorems that can be deduced from a given set of axioms and a given set of inference rules.

insight into natural systems or be inspired by them.

In the general sense, a mathematical theory is a branch of mathematics devoted to some specific topics or methods, such as set theory, number theory, group theory, probability theory, game theory, control theory, perturbation theory, etc., such as might be appropriate for a single textbook.

In mathematical logic, a theory has a related but different sense: it is the collection of the theorems that can be deduced from a given set of axioms and a given set of inference rules.

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

EVIDENCE:
- A covariant exterior derivative D, distinguished like the coordinate exterior derivative d by latin font, can be defined that is covariant not only with respect to coordinate transformations but also with respect to Lorentz transformations.
- The Bianchi identities are identities in the sense that if the torsion and Riemann tensors are expressed in terms of the line interval e and Lorentz connection Γ in accordance with Cartan’s equations (16.212) and (16.208), then the Bianchi identities are satisfied automatically.
- In this context, covariance meansthatDcommuteswithbothcoordinateandLorentztransformations.Thereisatorsion-freecovariant exterior derivative D ̊ , and a torsion-full covariant exterior derivative D.
- The contracted Bianchi identities (16.406) enforce conservation laws on the total spin angular-momentum Σ and matter energy-momentum T.

A covariant exterior derivative D, distinguished like the coordinate exterior derivative d by latin font, can be defined that is covariant not only with respect to coordinate transformations but also with respect to Lorentz transformations.

The Bianchi identities are identities in the sense that if the torsion and Riemann tensors are expressed in terms of the line interval e and Lorentz connection Γ in accordance with Cartan’s equations (16.212) and (16.208), then the Bianchi identities are satisfied automatically.

In this context, covariance meansthatDcommuteswithbothcoordinateandLorentztransformations.Thereisatorsion-freecovariant exterior derivative D ̊ , and a torsion-full covariant exterior derivative D.

The contracted Bianchi identities (16.406) enforce conservation laws on the total spin angular-momentum Σ and matter energy-momentum T.

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:
- For entanglement in a single qubit variable, only three distinct classes out of four Bell states are distinguishable using such linear optical techniques.
- Linear evolution means that the detection apparatus acts on each particle independent of the state or evolution of the other, and local measurement means that each particle is localized at a particular detector registering a "click" to indicate that a particle has been detected.
- If an experimenter chose to measure both qubits in a Bell state using the same basis, the qubits would appear positively correlated when measuring in the basis, anti-correlated in the basis[a], and partially (probabilistically) correlated in other bases.
- For the state, this means selecting the same basis for both qubits.

For entanglement in a single qubit variable, only three distinct classes out of four Bell states are distinguishable using such linear optical techniques.

Linear evolution means that the detection apparatus acts on each particle independent of the state or evolution of the other, and local measurement means that each particle is localized at a particular detector registering a "click" to indicate that a particle has been detected.

If an experimenter chose to measure both qubits in a Bell state using the same basis, the qubits would appear positively correlated when measuring in the basis, anti-correlated in the basis[a], and partially (probabilistically) correlated in other bases.

For the state, this means selecting the same basis for both qubits.

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:
- †Forexample,bycomparingsimilartrianglesinthefigure,weobtainx(cid:5)=(x/cosθ)+(y−xtanθ)sinθ.
- ∗Ifyoudon’tknowrotationsintheplaneextremelywell,thenperhapsyouarenotreadyforthisbook.A noddingfamiliaritywithmatricesandlinearalgebraisamongtheprerequisites.
- I.3 Rotation: Invariance and Infinitesimal Transformation Rotationintheplane ∗ Mypedagogicalstrategyforthischapteristotakesomethingyouknowextremely well, namelyrotationsintheplane,presentitinawaypossiblyunfamiliartoyou,andgothrough itslowlyingreatdetail,“beatingthesubjecttodeath,”sotospeak.
- According to Pythagoras, this requires x(cid:5)2+y(cid:5)2= x2+y2, which you can check using(1).

I.3 Rotation: Invariance and Infinitesimal Transformation Rotationintheplane ∗ Mypedagogicalstrategyforthischapteristotakesomethingyouknowextremely well, namelyrotationsintheplane,presentitinawaypossiblyunfamiliartoyou,andgothrough itslowlyingreatdetail,“beatingthesubjecttodeath,”sotospeak.

According to Pythagoras, this requires x(cid:5)2+y(cid:5)2= x2+y2, which you can check using(1).

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

EVIDENCE:
- The members of τ are called open sets in X.
- A subset of X is said to be closed if its complement is in τ (that is, its complement is open).
- The notation X may be used τ to denote a set X endowed with the particular topology τ.
- For further developments, see point-set topology and algebraic topology.

The members of τ are called open sets in X.

A subset of X is said to be closed if its complement is in τ (that is, its complement is open).

The notation X may be used τ to denote a set X endowed with the particular topology τ.

For further developments, see point-set topology and algebraic topology.

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

EVIDENCE:
- , and, denoting the angular momentum of the electron as L, introduces the equation: Eq.
- (4) stems from the virial theorem, and from the classical mechanics relationships between the angular momentum, the kinetic energy and the frequency of revolution.
- (1a, 1b, 2), it descends: He further assumes that the orbit is circular, i.e.
- Then Bohr assumes that is an integer multiple of the energy of a quantum of light with half the frequency of the electron's revolution frequency,[11]: 4 i.e.: From eq.

, and, denoting the angular momentum of the electron as L, introduces the equation: Eq.

(4) stems from the virial theorem, and from the classical mechanics relationships between the angular momentum, the kinetic energy and the frequency of revolution.

(1a, 1b, 2), it descends: He further assumes that the orbit is circular, i.e.

Then Bohr assumes that is an integer multiple of the energy of a quantum of light with half the frequency of the electron's revolution frequency,[11]: 4 i.e.: From eq.

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

EVIDENCE:
- Атомная Стратегия (in Russian).
- "Occurrence of the (4n + 1) series in nature" (htt ps://digital.library.unt.edu/ark:/67531/metadc172698/m2/1/high_res_d/metadc172698.pdf) (PDF).
- Archived from the original (http://npc.sarov.ru/issues/sarovbook/section3p11.ht ml) on 1 May 2007.
- "Q&A: Polonium-210" (http://www.rsc.org/chemistryworld/News/2006/November/27110601.asp).

Атомная Стратегия (in Russian).

"Occurrence of the (4n + 1) series in nature" (htt ps://digital.library.unt.edu/ark:/67531/metadc172698/m2/1/high_res_d/metadc172698.pdf) (PDF).

Archived from the original (http://npc.sarov.ru/issues/sarovbook/section3p11.ht ml) on 1 May 2007.

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:
- I put it on speaker and mouth, “Say something.” She says, “Hey.
- It was so perfect.” Her voice breaks on the last word, and I think she’s right on the verge of losing her composure, but she somehow manages to hold the scaffolding together.
- I want to prove to you he’s not the man you think he is.” My doppelgänger says, “Daniela?
- How’s your day going so far?” “Great.

I put it on speaker and mouth, “Say something.” She says, “Hey.

It was so perfect.” Her voice breaks on the last word, and I think she’s right on the verge of losing her composure, but she somehow manages to hold the scaffolding together.

I want to prove to you he’s not the man you think he is.” My doppelgänger says, “Daniela?

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:
- ww.theguardian.com/science/2013/may/08/ha 277.
- awking-donald-trump-paris-climate-change-ag 261.
- e.com/books?id=NU9SoEwgdskC&pg=PT20) html).
- Retrieved server/2004/apr/04/features.review17).

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

EVIDENCE:
- (III.18) Each direct product | (cid:105)| (cid:105) in (III.18) can be written in the Bell operator basis (II.43), |Ψ ±(cid:105) 1 2 12 and|Φ ±(cid:105),whichyields (cid:179) (cid:180) (cid:161) (cid:162) (cid:161) (cid:162) |Ψ (cid:105) = 1 |Ψ −(cid:105) − a|↑ (cid:105) − b|↓ (cid:105) + |Ψ +(cid:105) − a|↑ (cid:105) + b|↓ (cid:105) 123 2 12 3 3 12 3 3 (cid:179) (cid:180) (cid:161) (cid:162) (cid:161) (cid:162) + 1 |Φ −(cid:105) a|↓ (cid:105) + b|↑ (cid:105) + |Φ +(cid:105) a|↓ (cid:105) − b|↑ (cid:105) .
- To perform the teleportation of the unknown state of particle1, thenonclassicalpartistransmittedfirstusingthetwoancillaryspin1/2particlesinthesingletstate √ (cid:161) (cid:162) |Ψ 23 −(cid:105) = 1 2 2 |↑ 2 (cid:105)|↓ 3 (cid:105) − |↓ 2 (cid:105)|↑ 3 (cid:105) .
- (III.16) The entire system, which consists of Alice’s unknown particle 1 and the ancillary EPR pair, is inapureproductstate|φ (cid:105)|Ψ −(cid:105), involvingneitherclassicalcorrelationnorquantumentanglement 1 23 between the unknown state |φ 1 (cid:105) and the EPR pair.
- (III.19) 2 12 3 3 12 3 3 Regardless of the unknown state |φ (cid:105), each of the four measurement outcomes are equally probable.

To perform the teleportation of the unknown state of particle1, thenonclassicalpartistransmittedfirstusingthetwoancillaryspin1/2particlesinthesingletstate √ (cid:161) (cid:162) |Ψ 23 −(cid:105) = 1 2 2 |↑ 2 (cid:105)|↓ 3 (cid:105) − |↓ 2 (cid:105)|↑ 3 (cid:105) .

(III.16) The entire system, which consists of Alice’s unknown particle 1 and the ancillary EPR pair, is inapureproductstate|φ (cid:105)|Ψ −(cid:105), involvingneitherclassicalcorrelationnorquantumentanglement 1 23 between the unknown state |φ 1 (cid:105) and the EPR pair.

(III.19) 2 12 3 3 12 3 3 Regardless of the unknown state |φ (cid:105), each of the four measurement outcomes are equally probable.

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

EVIDENCE:
- Thequestionnaturallyarises,ifaneternalblackholeexistssomewhere,whetheronecouldgetthroughthe wormholetoanotherasymptoticallyflatuniverse.InspectionofthePenrosediagraminfigure8showsthatitis notpossibletogetfromItoIIIevenifyouweretotravelatthespeedoflight.However,anobserverstartingin I,afterfallingthroughthehorizonintoII,couldreceivesignalsoriginatingfromwithinIII.Inotherwords,our intrepidobserver,whileunabletogettoIII,canlookatpartofIII.
- †Thisclassicalanalysis,liketherestofthischapter,completelyignorestheincreasinglylargefluctuations duetoquantumgravityasweapproachthephysicalsingularity.
- (RecallthatV isthetimelikevariable.)From(7), wehaveU=± V 2− 1− r r S er/rS.Substitutingthisand V =V into(13),wefind ds2= (cid:29) (cid:30)dr2+r2d(cid:24)2 (15) 1−r r S 1−V 2e−r/rS Weseethatthethroatofthewormhole,determinedbythevalueofrwhereg rr →∞,decreasesfromr S atV =0, approaching0asV →1,andreaches0whenwehitthephysicalsingularityatV =1.Thewormholeclosesup 0 0 atthephysicalsingularity.Bydimensionalanalysis,sincer istheonlydimensionfulparameteraround,wesee S thatthewormholeclosesup†onatimescaleoftheorderofr .
- Incontrast, mathematiciansandspeculatorscancertainlyinvitethemselves(freecountry, remember?)to studythespacetimedescribedmathematicallyby(13).Lookingat(13),weseethat,sincequadrantIIIisrelated toIbyU→−U,thetwoquadrantsarethesame:IIIalsodescribestheoutsideofablackhole,app√roaching anasymptoticallyflatspacetime.QuadrantIVismorepeculiar,withaphysicalsingularityatV =− U2+1.

(RecallthatV isthetimelikevariable.)From(7), wehaveU=± V 2− 1− r r S er/rS.Substitutingthisand V =V into(13),wefind ds2= (cid:29) (cid:30)dr2+r2d(cid:24)2 (15) 1−r r S 1−V 2e−r/rS Weseethatthethroatofthewormhole,determinedbythevalueofrwhereg rr →∞,decreasesfromr S atV =0, approaching0asV →1,andreaches0whenwehitthephysicalsingularityatV =1.Thewormholeclosesup 0 0 atthephysicalsingularity.Bydimensionalanalysis,sincer istheonlydimensionfulparameteraround,wesee S thatthewormholeclosesup†onatimescaleoftheorderofr .

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

EVIDENCE:
- In contrast, non-magnetized planets have only small magnetospheres induced by interaction of the ionosphere with the solar wind, which cannot effectively protect the planet.[137]
- In other words, magnetized planets have flows of electrically conducting material in their interiors, which generate their magnetic fields.
- A magnetized planet creates a cavity in the solar wind around itself called the magnetosphere, which the wind cannot penetrate.
- been shown to be losing their atmospheres into space due to stellar radiation, much like the tails of comets.[132][133] These planets may have vast differences in temperature between their day and night sides that produce supersonic winds,[134] although multiple factors are involved and the details of the atmospheric dynamics that affect the day-night temperature difference are complex.[135][136] Magnetosphere One important characteristic of the planets is their intrinsic magnetic moments, which in turn give rise to magnetospheres.

In contrast, non-magnetized planets have only small magnetospheres induced by interaction of the ionosphere with the solar wind, which cannot effectively protect the planet.[137]

In other words, magnetized planets have flows of electrically conducting material in their interiors, which generate their magnetic fields.

A magnetized planet creates a cavity in the solar wind around itself called the magnetosphere, which the wind cannot penetrate.

been shown to be losing their atmospheres into space due to stellar radiation, much like the tails of comets.[132][133] These planets may have vast differences in temperature between their day and night sides that produce supersonic winds,[134] although multiple factors are involved and the details of the atmospheric dynamics that affect the day-night temperature difference are complex.[135][136] Magnetosphere One important characteristic of the planets is their intrinsic magnetic moments, which in turn give rise to magnetospheres.

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List tests or derivations implied by the evidence.


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

EVIDENCE:
- In fact, I haven’t been in this store in probably four years.” She locks the cabinet and returns the key ring to her pocket.
- I have a really nice Smith and Wesson .357 if you were thinking more along the lines of a revolver.” “No, this would do fine.
- I need to figure out my money situation.
- Charlie never accesses that account.

In fact, I haven’t been in this store in probably four years.” She locks the cabinet and returns the key ring to her pocket.

I have a really nice Smith and Wesson .357 if you were thinking more along the lines of a revolver.” “No, this would do fine.

I need to figure out my money situation.

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:
- RawOTSreportsdiscoveredbyCook,though,showafacilityinBrunswickwasworkingon radio-controlledcraftanddiscoveredbyUSofficials;anotherfacilityinViennaexperimented withdirectenergyweapons;anotherinStuttgartusedEMtointerferewithvehiclemotors.
- VescoclaimsheobtainedthisinformationfromBritishIntelligenceObjectivesSubcommittee (BIOS)andUS-UKadministeredCombinedIntelligenceObjectivesSubcommittee(CIOS); otherswhohaveaccesstoBIOS/CIOSsaynoevidenceoftheKugelblitzorFeuerballexistin therecords.
- Theseconclusionsarereachedasaresult ofinformalmeetingsandzeroinvestigationisperformed.
- ● https://files.afu.se/Downloads/Documents/USA%20-%20Congress/1958%20-%20McClelland%2 0congressional%20sub-committee.pdf (PUBLICDOMAIN) -20June1958—TheAirForcebriefsReps.Henderson,Cramer,Magnuson, WalkerandtheirstaffstoassistthemindealingwithconstituentinquiriesrelatedtoUAP.

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

EVIDENCE:
- The radial pressure p and energy flux f generated by the counter-streaming outgoing and ingoing streams increase the gravitational force.
- Inflation produces an exponential growth in the streaming energy, and along with it the interior mass, and the Weyl curvature.
- 21.6.3 Collapse phase Itmightseemthatinflationislockedintoanexponentialgrowthfromwhichthereisnoexit.ButtheEinstein equations (20.62) have one more trick up their sleave.
- This follows from the fact that for mass inflation to begin,thegravitationalforceproducedbythecounter-streamingpressurepmustbecomecomparabletothat produced by the mass M, which for streams of low proper density requires a hyper-relativistic streaming velocity.Foracoldstreamofproperdensityρmovingat4-velocityum ≡{u0,u1,0,0},thestreamingenergy flux would be f ∼ ρu0u1, while the streaming pressure would be p ∼ ρ(u1)2.

The radial pressure p and energy flux f generated by the counter-streaming outgoing and ingoing streams increase the gravitational force.

Inflation produces an exponential growth in the streaming energy, and along with it the interior mass, and the Weyl curvature.

21.6.3 Collapse phase Itmightseemthatinflationislockedintoanexponentialgrowthfromwhichthereisnoexit.ButtheEinstein equations (20.62) have one more trick up their sleave.

This follows from the fact that for mass inflation to begin,thegravitationalforceproducedbythecounter-streamingpressurepmustbecomecomparabletothat produced by the mass M, which for streams of low proper density requires a hyper-relativistic streaming velocity.Foracoldstreamofproperdensityρmovingat4-velocityum ≡{u0,u1,0,0},thestreamingenergy flux would be f ∼ ρu0u1, while the streaming pressure would be p ∼ ρ(u1)2.

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:
- We use that freedom to avoid paradoxes."[24] Einstein was likewise dissatisfied with the indeterminism of quantum theory.
- Steven Weinberg writes that the traditional presentation gives "no way to locate the boundary between the realms in which [...] quantum mechanics does or does not apply."[86] The problem of thinking in terms of classical measurements of a quantum system becomes particularly acute in the field of quantum cosmology, where the quantum system is the universe.[87][88] How does an observer stand outside the universe in order to measure it, and who was there to observe the universe in its earliest stages?
- As typically portrayed, Copenhagen-type interpretations involve two different kinds of time evolution for wave functions, the deterministic flow according to the Schrödinger equation and the probabilistic jump during measurement, without a clear criterion for when each kind applies.
- Regarding the possibility of randomness in nature, Einstein said that he was "convinced that He [God] does not throw dice."[84] Bohr, in response, reputedly said that "it cannot be for us to tell God, how he is to run the world".[note 7] The Heisenberg cut Much criticism of Copenhagen-type interpretations has focused on the need for a classical domain where observers or measuring devices can reside, and the imprecision of how the boundary between quantum and classical might be defined.

Copenhagen interpretation - Wikipedia.pdf

We use that freedom to avoid paradoxes."[24] Einstein was likewise dissatisfied with the indeterminism of quantum theory.

Steven Weinberg writes that the traditional presentation gives "no way to locate the boundary between the realms in which [...] quantum mechanics does or does not apply."[86] The problem of thinking in terms of classical measurements of a quantum system becomes particularly acute in the field of quantum cosmology, where the quantum system is the universe.[87][88] How does an observer stand outside the universe in order to measure it, and who was there to observe the universe in its earliest stages?

As typically portrayed, Copenhagen-type interpretations involve two different kinds of time evolution for wave functions, the deterministic flow according to the Schrödinger equation and the probabilistic jump during measurement, without a clear criterion for when each kind applies.

Regarding the possibility of randomness in nature, Einstein said that he was "convinced that He [God] does not throw dice."[84] Bohr, in response, reputedly said that "it cannot be for us to tell God, how he is to run the world".[note 7] The Heisenberg cut Much criticism of Copenhagen-type interpretations has focused on the need for a classical domain where observers or measuring devices can reside, and the imprecision of how the boundary between quantum and classical might be defined.

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:
- After retroflexion, upon passing the crystal for the second time, the pulse creates another pair of photons, where one of the two is prepared to be photon 1 of which the initial state is to be teleported, while the other, photon 4, upon detection by detector p, serves as a trigger indicating that photon 1 is underway.
- If the photons do not arrive within the region of temporal overlap, and do not entangle, they will endupinthedetectors f1and f2independently, leadingtoacoincidenceprobabilityof50%, which istwiceashighaswhentheyhadbeenentangled.
- Thiscould be seeninfigureIV.3byareduceddip.
- A pulse of ultraviolet radiation passing through a nonlinear crystal creates the ancillary pair of EPR photons 2 and 3.

After retroflexion, upon passing the crystal for the second time, the pulse creates another pair of photons, where one of the two is prepared to be photon 1 of which the initial state is to be teleported, while the other, photon 4, upon detection by detector p, serves as a trigger indicating that photon 1 is underway.

If the photons do not arrive within the region of temporal overlap, and do not entangle, they will endupinthedetectors f1and f2independently, leadingtoacoincidenceprobabilityof50%, which istwiceashighaswhentheyhadbeenentangled.

A pulse of ultraviolet radiation passing through a nonlinear crystal creates the ancillary pair of EPR photons 2 and 3.

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:
- Consistent with Piaget’s observations, 57% of elementary school children say that something comes out of the eye when people see (Cottrell & Winer, 1994; Winer & Cottrell, 1996a).
- and causes the sensation we call seeing” (Gross, 1999).
- This “extramission theory” of vision dates back at least as far as Greek philosopher Plato (427–347 b.c.), who spoke of a “fire” that emanated from the eye during vision, which “coalesces with the daylight...
- Biologist Rupert Sheldrake (2003) even created a stir in the scientific community by conducting research purporting to show that many people can tell they’re being stared at by people they can’t see, but a number of researchers have identified serious flaws in his studies, including the fact that Sheldrake’s subjects may have subtly influenced people to stare back at them (Marks & Colwell, 2000; Shermer, 2005).

Consistent with Piaget’s observations, 57% of elementary school children say that something comes out of the eye when people see (Cottrell & Winer, 1994; Winer & Cottrell, 1996a).

and causes the sensation we call seeing” (Gross, 1999).

This “extramission theory” of vision dates back at least as far as Greek philosopher Plato (427–347 b.c.), who spoke of a “fire” that emanated from the eye during vision, which “coalesces with the daylight...

Biologist Rupert Sheldrake (2003) even created a stir in the scientific community by conducting research purporting to show that many people can tell they’re being stared at by people they can’t see, but a number of researchers have identified serious flaws in his studies, including the fact that Sheldrake’s subjects may have subtly influenced people to stare back at them (Marks & Colwell, 2000; Shermer, 2005).

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

List tests or derivations implied by the evidence.