Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- He generalised the binomial theorem to Anglesey any real number, introduced the Puiseux series, was the 12th President of the Royal Society first to state Bézout's theorem, classified most of the In office cubic plane curves, contributed to the study of Cremona 1703–1727 transformations, developed a method for approximating Preceded by John Somers the roots of a function, originated the Newton–Cotes formulas used for numerical integration, and further Succeeded by Hans Sloane produced the earliest explicit enunciation of the general Master of the Mint Taylor series.
- In addition to his Preceded by Anthony Hammond creation of calculus, Newton's work on mathematics Succeeded by Arthur Annesley, 5th Earl of was extensive.
- He also formulated an Serving with Henry Boyle empirical law of cooling, which was the first heat Preceded by Robert Brady transfer formulation and serves as the formal basis of Succeeded by Edward Finch convective heat transfer,[11] made the first theoretical calculation of the speed of sound, and introduced the In office 1701–1702 notions of a Newtonian fluid and a black body.
- Moreover, he Serving with Henry Boyle was the first to analyse Couette flow.
- He originated prisms as beam expanders and multipleMember of Parliament prism arrays, which would later become integral to the for the University of Cambridge development of tunable lasers.[10] He anticipated the In office wave–particle duality of light and was first to theorise 1689–1690 the Goos–Hänchen effect.

He generalised the binomial theorem to Anglesey any real number, introduced the Puiseux series, was the 12th President of the Royal Society first to state Bézout's theorem, classified most of the In office cubic plane curves, contributed to the study of Cremona 1703–1727 transformations, developed a method for approximating Preceded by John Somers the roots of a function, originated the Newton–Cotes formulas used for numerical integration, and further Succeeded by Hans Sloane produced the earliest explicit enunciation of the general Master of the Mint Taylor series.

In addition to his Preceded by Anthony Hammond creation of calculus, Newton's work on mathematics Succeeded by Arthur Annesley, 5th Earl of was extensive.

He also formulated an Serving with Henry Boyle empirical law of cooling, which was the first heat Preceded by Robert Brady transfer formulation and serves as the formal basis of Succeeded by Edward Finch convective heat transfer,[11] made the first theoretical calculation of the speed of sound, and introduced the In office 1701–1702 notions of a Newtonian fluid and a black body.

Moreover, he Serving with Henry Boyle was the first to analyse Couette flow.

He originated prisms as beam expanders and multipleMember of Parliament prism arrays, which would later become integral to the for the University of Cambridge development of tunable lasers.[10] He anticipated the In office wave–particle duality of light and was first to theorise 1689–1690 the Goos–Hänchen effect.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- 854 Non-equilibrium processes in the FLRW background the Sobolev escape probability P , S ∫ ∞ ∫ ∞ ( ∫ ∞ ) P S ≡ e−τλφ λ dlnλ= exp −τ S φ λ′ dlnλ′ φ λ dlnλ 0 0 λ 1−e−τS = , (31.100) τ S whichisevidentlyindependentoftheshapeofthelineprofile(justsolongasthelineisnarrow).TheSobolev escape probability P varies from 0 as τ →∞ to 1 as τ →0.
- S S S For large Sobolev optical depth τ , the Sobolev escape probability approximates the reciprocal of the S Sobolev optical depth (31.98), P = (τ ≫1) .
- (31.101) S τ S S The rate per unit time and volume at which photons are emitted and escape is then n g 8πH n A P = 2 1 .

Chosen based on domain + required checks.

Produce bounded conclusion + next actions

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.

Apply expert-specific checks; do not introduce new facts beyond evidence.

854 Non-equilibrium processes in the FLRW background the Sobolev escape probability P , S ∫ ∞ ∫ ∞ ( ∫ ∞ ) P S ≡ e−τλφ λ dlnλ= exp −τ S φ λ′ dlnλ′ φ λ dlnλ 0 0 λ 1−e−τS = , (31.100) τ S whichisevidentlyindependentoftheshapeofthelineprofile(justsolongasthelineisnarrow).TheSobolev escape probability P varies from 0 as τ →∞ to 1 as τ →0.

S S S For large Sobolev optical depth τ , the Sobolev escape probability approximates the reciprocal of the S Sobolev optical depth (31.98), P = (τ ≫1) .

(31.101) S τ S S The rate per unit time and volume at which photons are emitted and escape is then n g 8πH n A P = 2 1 .

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- 16.9 Trading coordinates and momenta In the Hamiltonian approach, the coordinates and momenta appear on an equal footing.
- (16.110) mnl mnl l[mn] [lmn] The expression for the Ricci scalar in the Hilbert Lagrangian (16.88) is valid with or without torsion, but extremization of the action in vacuo has yielded the torsion-free connection.
- Consider integrating the first term of the gravitational Lagrangian (16.91) by parts (this is essentially the same integration by parts as (16.99), but with the connection Γ itself instead of the varied connection mnλ δΓ ), mnλ ∂Γ e−1∂(eemnκλΓ ) e−1∂(eemnκλ) emnκλ mnλ = mnλ − Γ .
- (16.108) lmn l[mn] lm [kn] ln [km] Inverting equation (16.106) yields the tetrad-frame connections Γ in terms of f , mnl lmn Γ =2f −3f +2γ fp .
- Hamilton’s equations follow from extremizing the mnλ remaining integral.

16.9 Trading coordinates and momenta In the Hamiltonian approach, the coordinates and momenta appear on an equal footing.

(16.110) mnl mnl l[mn] [lmn] The expression for the Ricci scalar in the Hilbert Lagrangian (16.88) is valid with or without torsion, but extremization of the action in vacuo has yielded the torsion-free connection.

Consider integrating the first term of the gravitational Lagrangian (16.91) by parts (this is essentially the same integration by parts as (16.99), but with the connection Γ itself instead of the varied connection mnλ δΓ ), mnλ ∂Γ e−1∂(eemnκλΓ ) e−1∂(eemnκλ) emnκλ mnλ = mnλ − Γ .

(16.108) lmn l[mn] lm [kn] ln [km] Inverting equation (16.106) yields the tetrad-frame connections Γ in terms of f , mnl lmn Γ =2f −3f +2γ fp .

Hamilton’s equations follow from extremizing the mnλ remaining integral.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Since the name mass inflation can be misleading, I prefer to call it the inflationary instability.
- In the Reissner-Nordström geometry, outgoing and ingoing streams resolve their differences by exceeding the speed of light relative to each other, and passing into causally separated regions.
- It was not until a seminal paper by Poisson & Israel (1990) that the nonlinear nature of the instability at the inner horizon was clarified.
- The interior mass is not the only thing that increases exponentially during mass inflation.
- 8.13 The inflationary instability 203 densitydiverges.TheperturbationtheorycalculationswerewidelyconstruedasindicatingthattheReissnerNordström geometry was “unstable,” although the precise nature of this instability remained obscure.

Since the name mass inflation can be misleading, I prefer to call it the inflationary instability.

In the Reissner-Nordström geometry, outgoing and ingoing streams resolve their differences by exceeding the speed of light relative to each other, and passing into causally separated regions.

It was not until a seminal paper by Poisson & Israel (1990) that the nonlinear nature of the instability at the inner horizon was clarified.

The interior mass is not the only thing that increases exponentially during mass inflation.

8.13 The inflationary instability 203 densitydiverges.TheperturbationtheorycalculationswerewidelyconstruedasindicatingthattheReissnerNordström geometry was “unstable,” although the precise nature of this instability remained obscure.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- In order to make this example as general as possible we will not specify a representation until the final step.
- The Dirac matrices are typically written as where runs from 0 to 3.
- This is a closed loop in SO(3,1), i.e.
- rotations ranging from 0 to 2π around the z-axis under the exponential mapping, but it is only "half" a loop in GL(U), ending at −I.
- Construction with a given spin direction and charge First we choose a spin

In order to make this example as general as possible we will not specify a representation until the final step.

The Dirac matrices are typically written as where runs from 0 to 3.

rotations ranging from 0 to 2π around the z-axis under the exponential mapping, but it is only "half" a loop in GL(U), ending at −I.

Construction with a given spin direction and charge First we choose a spin

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Equation (22.62) separates with 4 separation constants t φ q as i (1−ω ω ) ( −q 0 +q 3 ω x ) + q 0 −2q 1 ω x −q 2 ω x 2 +(1−ω ω ) ( −q 2 −q 3 ω y ) + q 2 +2q 1 ω y −q 0 ω y 2 =0 , x y ω ω x y ω ω x x y y (22.64) and equation (22.62) separates in a similar fashion, the vanishing of the second term inside braces in either of equations (22.62) or (22.63) requiring that q =q .
- 22.6 Λ-Kerr-Newman boundary conditions 655 If one provisionally supposes that A =0, then the Maxwell equation for the angular current j is φ 3 A √ Δ { dω [ dln(A /ω ) dlnω ] dω [ d ( dlnω ) dlnω ]} t y x (1−ω ω ) t x + x + y (1−ω ω ) ln y + y ρ3(1−ω ω )2 dx x y dx dx dy x y dy dy dy x y =4πj .
- (22.66b) dy 2 1 y 0 y These are consistent with the separated solution (22.44) found for Einstein’s equations provided that q =f g , 2q =f g −f g , q =f g .
- (22.63) The homogeneous solutions of equations (22.62) and (22.63) prove to be the homogeneous solutions of the full equations without any restriction on A or A .
- (22.65) 3 1 The separated solutions for ω and ω are x y dω x =2 √ q −2q ω −q ω2 , (22.66a) dx 0 1 x 2 x dω √ y =2 q +2q ω −q ω2 .

Equation (22.62) separates with 4 separation constants t φ q as i (1−ω ω ) ( −q 0 +q 3 ω x ) + q 0 −2q 1 ω x −q 2 ω x 2 +(1−ω ω ) ( −q 2 −q 3 ω y ) + q 2 +2q 1 ω y −q 0 ω y 2 =0 , x y ω ω x y ω ω x x y y (22.64) and equation (22.62) separates in a similar fashion, the vanishing of the second term inside braces in either of equations (22.62) or (22.63) requiring that q =q .

22.6 Λ-Kerr-Newman boundary conditions 655 If one provisionally supposes that A =0, then the Maxwell equation for the angular current j is φ 3 A √ Δ { dω [ dln(A /ω ) dlnω ] dω [ d ( dlnω ) dlnω ]} t y x (1−ω ω ) t x + x + y (1−ω ω ) ln y + y ρ3(1−ω ω )2 dx x y dx dx dy x y dy dy dy x y =4πj .

(22.66b) dy 2 1 y 0 y These are consistent with the separated solution (22.44) found for Einstein’s equations provided that q =f g , 2q =f g −f g , q =f g .

(22.63) The homogeneous solutions of equations (22.62) and (22.63) prove to be the homogeneous solutions of the full equations without any restriction on A or A .

(22.65) 3 1 The separated solutions for ω and ω are x y dω x =2 √ q −2q ω −q ω2 , (22.66a) dx 0 1 x 2 x dω √ y =2 q +2q ω −q ω2 .

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

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

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

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

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

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Thus the dot productofa1-formεwithap-forma≡a dpxΛ is,mirroringthemultivectordotproduct(13.35)(theform Λ .
- 462 Action principle for electromagnetism and gravity not transform like equation (16.277).
- (16.280) InvarianceoftheactionunderlocalLorentztransformationsrequiresthatthevariation(16.280)mustvanish for arbitrary choices of the bivector ε vanishing on the initial and final hypersurfaces.
- The Lie derivative ε of a form is written most elegantly in terms of a dot product of forms.
- (16.279) Inserting the variations (16.278) and (16.279) of the line interval e and Lorentz connection Γ into the variation (16.248) of the matter action yields the variation of the matter action under an infinitesimal Lorentz transformation generated by the bivector ε, ∫ δS =I −Σ ** ∧ ( dε+ 1[Γ,ε] ) + 1[ε,e]∧T ** m 2 2 ∮ ∫ =I Σ ** ∧ε−I ( dΣ ** + 1[Γ,Σ ** ]−e·T **) ∧ε .

Thus the dot productofa1-formεwithap-forma≡a dpxΛ is,mirroringthemultivectordotproduct(13.35)(theform Λ .

462 Action principle for electromagnetism and gravity not transform like equation (16.277).

(16.280) InvarianceoftheactionunderlocalLorentztransformationsrequiresthatthevariation(16.280)mustvanish for arbitrary choices of the bivector ε vanishing on the initial and final hypersurfaces.

The Lie derivative ε of a form is written most elegantly in terms of a dot product of forms.

(16.279) Inserting the variations (16.278) and (16.279) of the line interval e and Lorentz connection Γ into the variation (16.248) of the matter action yields the variation of the matter action under an infinitesimal Lorentz transformation generated by the bivector ε, ∫ δS =I −Σ ** ∧ ( dε+ 1[Γ,ε] ) + 1[ε,e]∧T ** m 2 2 ∮ ∫ =I Σ ** ∧ε−I ( dΣ ** + 1[Γ,Σ ** ]−e·T **) ∧ε .

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Strings, Conformal Fields, and Topology: An Introduction (https://books.googl e.com/books?id=pM8FCAAAQBAJ&pg=PA151).
- Springer Science & Business Media.
- Archived (https://web.archive.org/web/20191229224624/https://books.g oogle.com/books?id=RGz1BQAAQBAJ&pg=PA132) from the original on 29 December 2019.
- World Scientific Publishing Company.
- Archived (https://web.archive.org/web/20191226063925/https://books.google.com/book s?id=zpGZwmTJZIUC&pg=PA272) from the original on 26 December 2019.

Strings, Conformal Fields, and Topology: An Introduction (https://books.googl e.com/books?id=pM8FCAAAQBAJ&pg=PA151).

Archived (https://web.archive.org/web/20191229224624/https://books.g oogle.com/books?id=RGz1BQAAQBAJ&pg=PA132) from the original on 29 December 2019.

Archived (https://web.archive.org/web/20191226063925/https://books.google.com/book s?id=zpGZwmTJZIUC&pg=PA272) from the original on 26 December 2019.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Discoveries revealed that black holes could possess mass, spin, and electric charge, with their properties predictable from these three parameters.
- Subrahmanyan Chandrasekhar's Journey After years of research, Chandrasekhar returned to black hole studies in 1975, driven by a desire to explore their intricate properties.
- Although he was part of a younger generation of researchers, his return was met with skepticism regarding the details that remained to be understood.
- Mentorship in Black Hole Research The chapter pays homage to the contributions of notable mentors in the field: John Archibald Wheeler, Yakov Borisovich Zel’dovich, and Dennis Sciama.
- Each uniquely influenced the development of black hole research through different mentoring styles—Wheeler's inspirational vision, Zel’dovich's energetic drive, and Sciama's supportive guidance.

Discoveries revealed that black holes could possess mass, spin, and electric charge, with their properties predictable from these three parameters.

Subrahmanyan Chandrasekhar's Journey After years of research, Chandrasekhar returned to black hole studies in 1975, driven by a desire to explore their intricate properties.

Although he was part of a younger generation of researchers, his return was met with skepticism regarding the details that remained to be understood.

Mentorship in Black Hole Research The chapter pays homage to the contributions of notable mentors in the field: John Archibald Wheeler, Yakov Borisovich Zel’dovich, and Dennis Sciama.

Each uniquely influenced the development of black hole research through different mentoring styles—Wheeler's inspirational vision, Zel’dovich's energetic drive, and Sciama's supportive guidance.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Let us demand that the Einstein tensor match a dust term plus a vacuum energy term.
- The circle at a given t is a closed null curve, but not a null geodesic.
- This is equivalent to requiring that it match a perfect fluid; i.e., we require that the components of the Einstein tensor, computed with respect to our frame, take the form This gives the conditions Plugging these into the Einstein tensor, we see that in fact we now have .
- Specifically, with a bit of foresight, let us choose .
- Suppressing in order to focus our attention on this three-manifold, let us examine how the appearance of the light cones changes as we travel out from the axis of symmetry :

Let us demand that the Einstein tensor match a dust term plus a vacuum energy term.

The circle at a given t is a closed null curve, but not a null geodesic.

This is equivalent to requiring that it match a perfect fluid; i.e., we require that the components of the Einstein tensor, computed with respect to our frame, take the form This gives the conditions Plugging these into the Einstein tensor, we see that in fact we now have .

Specifically, with a bit of foresight, let us choose .

Suppressing in order to focus our attention on this three-manifold, let us examine how the appearance of the light cones changes as we travel out from the axis of symmetry :

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Pr., 1989 Thoren, Victor E., "The Comet of 1577 and Tycho Brahe's System of the World," Archives Internationales d'Histoire des Sciences, 29 (1979): 53–67.
- Sambursky, S., The Physical World of Late Antiquity Routledge & Kegan Paul, 1962 Schofield, C., The Tychonic and Semi-Tychonic World Systems in Taton & Wilson (eds) 1989 Sorabji, Richard, Matter, Space and Motion London: Duckworth, 1988 ISBN 0-7156-2205-6 Sorabji, Richard, (ed.) Philoponus and the Rejection of Aristotelian Science London & Ithaca NY Sorabji, Richard, The Philosophy of the Commentators, 200–600 AD: Volume 2 Physics Duckworth 2004 Taliaferro, R.
- Cambridge: Cambridge University Press.
- ISBN 0-387-06995-X Pederson, Olaf (1993) [1974].
- Wilson (eds.), The General History of Astronomy: Volume 2 Planetary astronomy from the Renaissance to the rise of astrophysics Part A Tycho Brahe to Newton Cambridge: Cambridge Univ.

Pr., 1989 Thoren, Victor E., "The Comet of 1577 and Tycho Brahe's System of the World," Archives Internationales d'Histoire des Sciences, 29 (1979): 53–67.

Sambursky, S., The Physical World of Late Antiquity Routledge & Kegan Paul, 1962 Schofield, C., The Tychonic and Semi-Tychonic World Systems in Taton & Wilson (eds) 1989 Sorabji, Richard, Matter, Space and Motion London: Duckworth, 1988 ISBN 0-7156-2205-6 Sorabji, Richard, (ed.) Philoponus and the Rejection of Aristotelian Science London & Ithaca NY Sorabji, Richard, The Philosophy of the Commentators, 200–600 AD: Volume 2 Physics Duckworth 2004 Taliaferro, R.

Wilson (eds.), The General History of Astronomy: Volume 2 Planetary astronomy from the Renaissance to the rise of astrophysics Part A Tycho Brahe to Newton Cambridge: Cambridge Univ.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- 9781405131117_4_004.qxd 30/6/09 11:47 AM Page 84 a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience.
- Dean Keith Simonton (2006) even showed that U.S.
- We can find this misconception in a host of popular writings.
- 13) Some critics have charged that IQ tests predict performance only on other IQ tests.
- It is not merely book learning, a narrow academic skill, or test-taking smarts.

9781405131117_4_004.qxd 30/6/09 11:47 AM Page 84 a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience.

Dean Keith Simonton (2006) even showed that U.S.

We can find this misconception in a host of popular writings.

13) Some critics have charged that IQ tests predict performance only on other IQ tests.

It is not merely book learning, a narrow academic skill, or test-taking smarts.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- ElectromagnetismGoesLive | 251 onlycomplicationfortheelectromagneticfieldisthepresenceofLorentzindices,butthey mostlyjustgoalongfortheride,sotospeak.
- Let’sstartbyvaryingtheintegrandofthethirdtermin(6):δ(FμνF )=2FμνδF = μν μν 4Fμν∂ δA .(Thereadershouldunderstandthetwofactorsof2andhencetheconventional μ ν choiceof 1 in(6).)Thus,thevariationofthethirdtermis (cid:7) (cid:7) δ d4x(−1FμνF )= d4x∂ Fμν(x)δA (x) (8) 4 μν μ ν wherewehaveintegratedbyparts.Thefirsttermin(6)doesnotdependonthefieldand somaybeignored.Thus,werethesecondtermnotpresent,wewouldhaveobtained,by settingthevariationtozero,thefreeMaxwell’sequations ∂ Fμν=0 (9) μ Returnofthecurrent Butthesecondtermin(6),indicatingthepresenceofchargedparticles,isusuallythere.It iswrittenasanintegralovertheparticletrajectories.Incontrast,thethirdtermiswrittenas anintegraloverspacetime.Tocomparethevariationofthesecondtermwiththevariation ofthethirdterm,wehavetowritethesecondtermalsoasanintegraloverd4x,sothatthe twotermshavethesameform.Butweknowhowtodothis.Indeed,(7)providesastrong hint.UsetheDiracdeltafunctionintroducedinchapterI.1!
- (cid:8) RecallfromchapterIII.6thatthedeltafunctionisdefinedby dxδ(x−y)f(y)=f(x) foranyreasonablysmoothfunctionf(x).Therewealsogeneralizedtothe4-dimensional deltafunction,definedinanobviouswaybyδ(4)(x−X )≡δ(x0−X0)δ(x1−X1)δ(x2− a a a X2)δ(x3−X3).Inotherwords,δ(4)(x−X )vanishesunlessxμandXμareequalcompoa a a a nentbycomponent.
- (cid:8) Withthisquickreview,wenowwriteA (X )= d4xδ(4)(x−X )A (x),andthusthe μ a a μ secondtermin(6)as (cid:7) (cid:7) (cid:7) (cid:10) dXμ (cid:10) dXμ e dτ A (X ) a = d4x e dτ δ(4)(x−X )A (x) a (10) a a μ a a a a μ dτ dτ a a a a You might recognize that this form is analogous to the form of the second term in (7), exceptthatthephysicsisrelativistichereandnonrelativisticthere.
- NowvaryA (x)toobtain μ (cid:7) (cid:7) (cid:10) dXμ d4x e dτ δ(4)(x−X ) aδA (x) (11) a a a μ dτ a a Verynicely,weseethereturnofthe4-currentdefinedinchapterIII.6 (cid:7) (cid:10) dXμ Jμ(x)= e dτ δ(4)(x−X ) a (12) a a a dτ a a (cid:8) Wecanthenwrite(11)morecompactlyas d4x Jμ(x)δA (x).

ElectromagnetismGoesLive | 251 onlycomplicationfortheelectromagneticfieldisthepresenceofLorentzindices,butthey mostlyjustgoalongfortheride,sotospeak.

Let’sstartbyvaryingtheintegrandofthethirdtermin(6):δ(FμνF )=2FμνδF = μν μν 4Fμν∂ δA .(Thereadershouldunderstandthetwofactorsof2andhencetheconventional μ ν choiceof 1 in(6).)Thus,thevariationofthethirdtermis (cid:7) (cid:7) δ d4x(−1FμνF )= d4x∂ Fμν(x)δA (x) (8) 4 μν μ ν wherewehaveintegratedbyparts.Thefirsttermin(6)doesnotdependonthefieldand somaybeignored.Thus,werethesecondtermnotpresent,wewouldhaveobtained,by settingthevariationtozero,thefreeMaxwell’sequations ∂ Fμν=0 (9) μ Returnofthecurrent Butthesecondtermin(6),indicatingthepresenceofchargedparticles,isusuallythere.It iswrittenasanintegralovertheparticletrajectories.Incontrast,thethirdtermiswrittenas anintegraloverspacetime.Tocomparethevariationofthesecondtermwiththevariation ofthethirdterm,wehavetowritethesecondtermalsoasanintegraloverd4x,sothatthe twotermshavethesameform.Butweknowhowtodothis.Indeed,(7)providesastrong hint.UsetheDiracdeltafunctionintroducedinchapterI.1!

(cid:8) RecallfromchapterIII.6thatthedeltafunctionisdefinedby dxδ(x−y)f(y)=f(x) foranyreasonablysmoothfunctionf(x).Therewealsogeneralizedtothe4-dimensional deltafunction,definedinanobviouswaybyδ(4)(x−X )≡δ(x0−X0)δ(x1−X1)δ(x2− a a a X2)δ(x3−X3).Inotherwords,δ(4)(x−X )vanishesunlessxμandXμareequalcompoa a a a nentbycomponent.

(cid:8) Withthisquickreview,wenowwriteA (X )= d4xδ(4)(x−X )A (x),andthusthe μ a a μ secondtermin(6)as (cid:7) (cid:7) (cid:7) (cid:10) dXμ (cid:10) dXμ e dτ A (X ) a = d4x e dτ δ(4)(x−X )A (x) a (10) a a μ a a a a μ dτ dτ a a a a You might recognize that this form is analogous to the form of the second term in (7), exceptthatthephysicsisrelativistichereandnonrelativisticthere.

NowvaryA (x)toobtain μ (cid:7) (cid:7) (cid:10) dXμ d4x e dτ δ(4)(x−X ) aδA (x) (11) a a a μ dτ a a Verynicely,weseethereturnofthe4-currentdefinedinchapterIII.6 (cid:7) (cid:10) dXμ Jμ(x)= e dτ δ(4)(x−X ) a (12) a a a dτ a a (cid:8) Wecanthenwrite(11)morecompactlyas d4x Jμ(x)δA (x).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Natural uranium-238 in the Earth's crust decays through a series of solid radioactive intermediates including radium-226 to
- Andrey Lugovoy and Dmitry Kovtun.[116][117] As such, Litvinenko's death was the first (and, to date, only) confirmed instance in which polonium's extreme toxicity has been used with malicious intent.[118][119][120] In 2011, an allegation surfaced that the death of Palestinian leader Yasser Arafat, who died on 11 November 2004 of uncertain causes, also resulted from deliberate polonium poisoning,[121][122] and in July 2012, concentrations of 210Po many times more than normal were detected in Arafat's clothes and personal belongings by the Institut de Radiophysique in Lausanne, Switzerland.[123][124] Even though Arafat's symptoms were acute gastroenteritis with diarrhoea and vomiting,[125] the institute's spokesman said that despite the tests the symptoms described in Arafat's medical reports were not consistent with 210Po poisoning, and conclusions could not be drawn.[124] In 2013 the team found levels of polonium in Arafat's ribs and pelvis 18 to 36 times the average,[126][127] even though by this point in time the amount had diminished by a factor of 2 million.[128] Forensic scientist Dave Barclay stated, "In my opinion, it is absolutely certain that the cause of his illness was polonium poisoning.
- He had symptoms similar to Aleksander Litvinenko.[131] Treatment It has been suggested that chelation agents, such as British anti-Lewisite (dimercaprol), can be used to decontaminate humans.[132] In one experiment, rats were given a fatal dose of 1.45 MBq/kg (8.7 ng/kg) of 210Po; all untreated rats were dead after 44 days, but 90% of the rats treated with the chelation agent HOEtTTC remained alive for five months.[133] Detection in biological specimens Polonium-210 may be quantified in biological specimens by alpha particle spectrometry to confirm a diagnosis of poisoning in hospitalized patients or to provide evidence in a medicolegal death investigation.
- Levels in excess of 30 mBq/day are suggestive of excessive exposure to the radionuclide.[134] Occurrence in humans and the biosphere Polonium-210 is widespread in the biosphere, including in human tissues, because of its position in the uranium238 decay chain.
- What we have got is the smoking gun - the thing that caused his illness and was given to him with malice."[125][126] Subsequently, French and Russian teams claimed that the elevated 210Po levels were not the result of deliberate poisoning, and did not cause Arafat's death.[129][130] It has also been suspected that Russian businessman Roman Tsepov was killed with polonium.

Natural uranium-238 in the Earth's crust decays through a series of solid radioactive intermediates including radium-226 to

Andrey Lugovoy and Dmitry Kovtun.[116][117] As such, Litvinenko's death was the first (and, to date, only) confirmed instance in which polonium's extreme toxicity has been used with malicious intent.[118][119][120] In 2011, an allegation surfaced that the death of Palestinian leader Yasser Arafat, who died on 11 November 2004 of uncertain causes, also resulted from deliberate polonium poisoning,[121][122] and in July 2012, concentrations of 210Po many times more than normal were detected in Arafat's clothes and personal belongings by the Institut de Radiophysique in Lausanne, Switzerland.[123][124] Even though Arafat's symptoms were acute gastroenteritis with diarrhoea and vomiting,[125] the institute's spokesman said that despite the tests the symptoms described in Arafat's medical reports were not consistent with 210Po poisoning, and conclusions could not be drawn.[124] In 2013 the team found levels of polonium in Arafat's ribs and pelvis 18 to 36 times the average,[126][127] even though by this point in time the amount had diminished by a factor of 2 million.[128] Forensic scientist Dave Barclay stated, "In my opinion, it is absolutely certain that the cause of his illness was polonium poisoning.

He had symptoms similar to Aleksander Litvinenko.[131] Treatment It has been suggested that chelation agents, such as British anti-Lewisite (dimercaprol), can be used to decontaminate humans.[132] In one experiment, rats were given a fatal dose of 1.45 MBq/kg (8.7 ng/kg) of 210Po; all untreated rats were dead after 44 days, but 90% of the rats treated with the chelation agent HOEtTTC remained alive for five months.[133] Detection in biological specimens Polonium-210 may be quantified in biological specimens by alpha particle spectrometry to confirm a diagnosis of poisoning in hospitalized patients or to provide evidence in a medicolegal death investigation.

Levels in excess of 30 mBq/day are suggestive of excessive exposure to the radionuclide.[134] Occurrence in humans and the biosphere Polonium-210 is widespread in the biosphere, including in human tissues, because of its position in the uranium238 decay chain.

What we have got is the smoking gun - the thing that caused his illness and was given to him with malice."[125][126] Subsequently, French and Russian teams claimed that the elevated 210Po levels were not the result of deliberate poisoning, and did not cause Arafat's death.[129][130] It has also been suspected that Russian businessman Roman Tsepov was killed with polonium.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- readers the impression that Rosenhan’s conclusions were valid, but that she’d replicated them in a follow-up study in which she presented herself as a pseudopatient at various mental hospitals: “Let me tell you, I tried this experiment.
- I actually did it” (Slater, 2004, p.
- Spitzer and several other prominent mental health researchers repeatedly asked Slater to provide copies of records from her hospital encounters, but she didn’t comply.
- Only after Spitzer and his colleagues (Spitzer, Lilienfeld, & Miller, 2005) published a critique did Slater (2005) write | Chapter 9 Sad, Mad, and Bad 183

readers the impression that Rosenhan’s conclusions were valid, but that she’d replicated them in a follow-up study in which she presented herself as a pseudopatient at various mental hospitals: “Let me tell you, I tried this experiment.

Spitzer and several other prominent mental health researchers repeatedly asked Slater to provide copies of records from her hospital encounters, but she didn’t comply.

Only after Spitzer and his colleagues (Spitzer, Lilienfeld, & Miller, 2005) published a critique did Slater (2005) write | Chapter 9 Sad, Mad, and Bad 183

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- While in the Army, Puharich took part in a variety of parapsychology experiments, and he lectured Army, Air Force and Navy groups on possibilities for mind warfare.
- Spontaneous deformation of the metal specimens was observed at the PK session conducted during the INSCOM retreat, causing a great deal of excitement among those present.
- Numerous government science advisors and senior military officials took part in and/or witnessed these events, which took place at the Pentagon, at officers’ or scientists’ homes, and at one quarterly INSCOM retreat attended by the commanding general and a group of colonels and generals commanding INSCOM units around the globe.
- Puharich had an interest in clairvoyance and PK, and dabbled in theories for electronically and pharmaceutically enhancing and synthesizing psychic abilities.
- Alexander (USA ret.) credits professional aerospace engineer Jack Houck for “capturing PK phenomenon and transitioning it into an observable form” (Houck, 1982, 1984a, b; Alexander et al., 1990; Alexander, 2003).

While in the Army, Puharich took part in a variety of parapsychology experiments, and he lectured Army, Air Force and Navy groups on possibilities for mind warfare.

Spontaneous deformation of the metal specimens was observed at the PK session conducted during the INSCOM retreat, causing a great deal of excitement among those present.

Numerous government science advisors and senior military officials took part in and/or witnessed these events, which took place at the Pentagon, at officers’ or scientists’ homes, and at one quarterly INSCOM retreat attended by the commanding general and a group of colonels and generals commanding INSCOM units around the globe.

Puharich had an interest in clairvoyance and PK, and dabbled in theories for electronically and pharmaceutically enhancing and synthesizing psychic abilities.

Alexander (USA ret.) credits professional aerospace engineer Jack Houck for “capturing PK phenomenon and transitioning it into an observable form” (Houck, 1982, 1984a, b; Alexander et al., 1990; Alexander, 2003).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- We might in each case seize it by its gravitational field, tug it in the wake of some massive object, and set it up in an orbit around the Earth (if a nervous humanity will allow it).
- To be sure, it is exceedingly unlikely we will find massive black holes that we can use as a universal furnace.
- The mini-black hole will then prove the simplest and most foolproof nuclearfusion reactor possible, and the energy it produces can be stored and sent down to Earth.
- A stream of frozen hydrogen pellets can then be aimed past the mini-black hole so that it skims the Schwarzschild radius without entering it.
- Perhaps it is better, until such time as our technology advances sufficiently, to make do with one of the much more common (if they exist at all) mini-black holes and make use of more conventional means of gaining energy.

We might in each case seize it by its gravitational field, tug it in the wake of some massive object, and set it up in an orbit around the Earth (if a nervous humanity will allow it).

To be sure, it is exceedingly unlikely we will find massive black holes that we can use as a universal furnace.

The mini-black hole will then prove the simplest and most foolproof nuclearfusion reactor possible, and the energy it produces can be stored and sent down to Earth.

A stream of frozen hydrogen pellets can then be aimed past the mini-black hole so that it skims the Schwarzschild radius without entering it.

Perhaps it is better, until such time as our technology advances sufficiently, to make do with one of the much more common (if they exist at all) mini-black holes and make use of more conventional means of gaining energy.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- (38.6) The spin properties of the components of a tensor are thus manifest when expressed in a spin basis.
- The general rule is that the spin weight s of any tensor component is equal to the number of + covariant indices minus the number of − covariant indices: spin weight s=number of + minus − covariant indices .
- 970 The super geometric algebra 38.2 Spin weight An object is defined to have spin weight s if it varies by e−isθ (38.3) under a right-handed rotation by angle θ in the γγ –γγ plane.
- 38.3 Pauli representation of spin basis vectors InthePaulirepresentation(13.112),thespinbasisvectorsγγ arerepresentedbythereal2×2Paulimatrices ± 1 √ ( 0 1 ) 1 √ ( 0 0 ) γγ =σ ≡ √ (σ +iσ )= 2 , γγ =σ ≡ √ (σ −iσ )= 2 .
- Sometimes the term spin weight is abbreviated to spin, when there is no ambiguity.

(38.6) The spin properties of the components of a tensor are thus manifest when expressed in a spin basis.

The general rule is that the spin weight s of any tensor component is equal to the number of + covariant indices minus the number of − covariant indices: spin weight s=number of + minus − covariant indices .

970 The super geometric algebra 38.2 Spin weight An object is defined to have spin weight s if it varies by e−isθ (38.3) under a right-handed rotation by angle θ in the γγ –γγ plane.

38.3 Pauli representation of spin basis vectors InthePaulirepresentation(13.112),thespinbasisvectorsγγ arerepresentedbythereal2×2Paulimatrices ± 1 √ ( 0 1 ) 1 √ ( 0 0 ) γγ =σ ≡ √ (σ +iσ )= 2 , γγ =σ ≡ √ (σ −iσ )= 2 .

Sometimes the term spin weight is abbreviated to spin, when there is no ambiguity.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- The Milky Way galaxy and the nearby Andromeda Galaxy are Hubble eXtreme Deep Field moving toward each other at about 130 km/s, and—depending upon (XDF) the lateral movements—the two might collide in about five to six billion years.
- Several thousand galaxies, each consisting of billions of stars, are Future trends in this small view.
- Spiral galaxies, like the Milky Way, produce new generations of stars as long as they have dense molecular clouds of interstellar hydrogen in their spiral arms.[210] Elliptical galaxies are largely devoid of this gas, and so form few new stars.[211] The supply of star-forming material is finite; once stars have converted the available supply of hydrogen into heavier elements, new star formation will come to an end.[212][213] The current era of star formation is expected to continue for up to XDF (2012) view: Each light one hundred billion years, and then the "stellar age" will wind down speck is a galaxy, some of which after about ten trillion to one hundred trillion years (1013– are as old as 13.2 billion 1014 years), as the smallest, longest-lived stars in the visible years[201] – the observable universe is estimated to contain universe, tiny red dwarfs, begin to fade.
- At the end of the stellar age, 200 billion to two trillion galaxies.
- As time passes, mergers of two systems of equal size become less common.

The Milky Way galaxy and the nearby Andromeda Galaxy are Hubble eXtreme Deep Field moving toward each other at about 130 km/s, and—depending upon (XDF) the lateral movements—the two might collide in about five to six billion years.

Several thousand galaxies, each consisting of billions of stars, are Future trends in this small view.

Spiral galaxies, like the Milky Way, produce new generations of stars as long as they have dense molecular clouds of interstellar hydrogen in their spiral arms.[210] Elliptical galaxies are largely devoid of this gas, and so form few new stars.[211] The supply of star-forming material is finite; once stars have converted the available supply of hydrogen into heavier elements, new star formation will come to an end.[212][213] The current era of star formation is expected to continue for up to XDF (2012) view: Each light one hundred billion years, and then the "stellar age" will wind down speck is a galaxy, some of which after about ten trillion to one hundred trillion years (1013– are as old as 13.2 billion 1014 years), as the smallest, longest-lived stars in the visible years[201] – the observable universe is estimated to contain universe, tiny red dwarfs, begin to fade.

At the end of the stellar age, 200 billion to two trillion galaxies.

As time passes, mergers of two systems of equal size become less common.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- As usual in the tetrad formalism, coordinate indices are lowered and raised with the coordinate metric, tetrad indices are lowered and raised with the tetrad metric, and coordinate and tetrad indices can be transformed to each other with the vierbein and its inverse.
- (17.7) α a The ADM line-element is ds2 =−α2dt2+g (dxα−βαdt) ( dxβ −ββdt ) , (17.8) αβ where g is the spatial coordinate metric αβ g =γ ea eb .
- (17.11) dτ 0 α The proper time derivative d/dτ in the tetrad rest frame is just equal to the directed derivative ∂ in the time direction γγ , d ∂ =uμ =∂ .
- (17.9) αβ ab α β Essentially all the tetrad formalism developed in Chapter 11 carries through, subject only to the conditions (17.2) and (17.3).
- Physically, the lapse α is the rateatwhichthepropertimeτ ofthetetradrestframeelapsesperunitcoordinatetimet,whiletheshiftβα is the velocity at which the tetrad rest frame moves through the spatial coordinates xα per unit coordinate time t, dτ dxα α= , βα = .

As usual in the tetrad formalism, coordinate indices are lowered and raised with the coordinate metric, tetrad indices are lowered and raised with the tetrad metric, and coordinate and tetrad indices can be transformed to each other with the vierbein and its inverse.

(17.7) α a The ADM line-element is ds2 =−α2dt2+g (dxα−βαdt) ( dxβ −ββdt ) , (17.8) αβ where g is the spatial coordinate metric αβ g =γ ea eb .

(17.11) dτ 0 α The proper time derivative d/dτ in the tetrad rest frame is just equal to the directed derivative ∂ in the time direction γγ , d ∂ =uμ =∂ .

(17.9) αβ ab α β Essentially all the tetrad formalism developed in Chapter 11 carries through, subject only to the conditions (17.2) and (17.3).

Physically, the lapse α is the rateatwhichthepropertimeτ ofthetetradrestframeelapsesperunitcoordinatetimet,whiletheshiftβα is the velocity at which the tetrad rest frame moves through the spatial coordinates xα per unit coordinate time t, dτ dxα α= , βα = .

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Consider a canonical transformation with generator infinitesimally shifted from the identity transformation, with ε an infinitesimal parameter, G=qμp′ +εg(q,p′) .
- Equation (4.140) becomes in α the conventional case df ∂f = +[f,H] .
- (4.141) dt ∂t 4.21 Infinitesimal canonical transformations A canonical transformation generated by G=qμp′ is the identity transformation, since it leaves the coordiμ nates and momenta unchanged.
- (4.143) ∂p′ ∂p′ μ ∂qμ μ ∂qμ μ μ Because ε is infinitesimal, the term ε∂g/∂p′ can be replaced by ε∂g/∂p to linear order, yielding μ μ ∂g ∂g q′μ =qμ+ε , p′ =p −ε .
- The same derivation holds in the conventional case where λ is taken to be time t, but generically the function f(t,qα,p ) and conventional Hamiltonian H(t,qα,p ) must be allowed to be explicit functions of α α time t as well as of generalized spatial coordinates and momenta qα and p .

Consider a canonical transformation with generator infinitesimally shifted from the identity transformation, with ε an infinitesimal parameter, G=qμp′ +εg(q,p′) .

Equation (4.140) becomes in α the conventional case df ∂f = +[f,H] .

(4.141) dt ∂t 4.21 Infinitesimal canonical transformations A canonical transformation generated by G=qμp′ is the identity transformation, since it leaves the coordiμ nates and momenta unchanged.

(4.143) ∂p′ ∂p′ μ ∂qμ μ ∂qμ μ μ Because ε is infinitesimal, the term ε∂g/∂p′ can be replaced by ε∂g/∂p to linear order, yielding μ μ ∂g ∂g q′μ =qμ+ε , p′ =p −ε .

The same derivation holds in the conventional case where λ is taken to be time t, but generically the function f(t,qα,p ) and conventional Hamiltonian H(t,qα,p ) must be allowed to be explicit functions of α α time t as well as of generalized spatial coordinates and momenta qα and p .

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- "Bianchini's planisphere" (https://brunelleschi.imss.fi.it/galileopalazzostrozzi/object/BianchinisPlani sphere.html).
- Archived (https://web.archive.org/web/20180227062732/https://brunelleschi.i mss.fi.it/galileopalazzostrozzi/object/BianchinisPlanisphere.html) from the original on 27 February 2018.
- "Minor Planet Naming Guidelines (Rules and Guidelines for naming non-cometary small SolarSystem bodies) – v1.0" (https://www.wgsbn-iau.org/documentation/NamesAndCitations.pdf) (PDF).
- "The origin of the symbols of the planets".
- issn.1673-8578.2018.03.015) from the original on 5 May 2023.

"Bianchini's planisphere" (https://brunelleschi.imss.fi.it/galileopalazzostrozzi/object/BianchinisPlani sphere.html).

Archived (https://web.archive.org/web/20180227062732/https://brunelleschi.i mss.fi.it/galileopalazzostrozzi/object/BianchinisPlanisphere.html) from the original on 27 February 2018.

"Minor Planet Naming Guidelines (Rules and Guidelines for naming non-cometary small SolarSystem bodies) – v1.0" (https://www.wgsbn-iau.org/documentation/NamesAndCitations.pdf) (PDF).

"The origin of the symbols of the planets".

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Great Books of the Western World.
- Journal for the History of Astronomy.
- S., The Discarded Image: An Introduction to Medieval and Renaissance Literature, Cambridge: Cambridge University Press 1964 ISBN 0-521-09450-X Lindberg, David C.
- ISBN 0-521-56762-9 Grasshoff, Gerd (2012).
- 1150," Journal for the History of Astronomy, 28(1997): 235–258.

S., The Discarded Image: An Introduction to Medieval and Renaissance Literature, Cambridge: Cambridge University Press 1964 ISBN 0-521-09450-X Lindberg, David C.

1150," Journal for the History of Astronomy, 28(1997): 235–258.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- became one of the fundamental aspects of quantum field theory and is seen as a criterion for a theory's general acceptability.
- Even though renormalization works well in practice, Feynman was never entirely comfortable with its mathematical validity, referring to renormalization as a "shell game" and "hocus pocus".[2]: 128 Neither Feynman nor Dirac were happy with that way to approach the observations made in theoretical physics, above all in quantum mechanics.[24] QED is the model and template for all subsequent quantum field theories.
- Based on Bethe's intuition and fundamental papers on the subject by Shin'ichirō Tomonaga,[16] Julian Schwinger,[17][18] Richard Feynman[1][19][20] and Freeman Dyson,[21][22] it was finally possible to Hans Bethe produce fully covariant formulations that were finite at any order in a perturbation series of quantum electrodynamics.
- The idea was simply to attach infinities to corrections of mass and charge that were actually fixed to a finite value by experiments.
- A first indication of a possible solution was given by Hans Bethe in 1947.[14][15] He made the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Willis Lamb and Robert Retherford.[14] Despite limitations of the computation, agreement was excellent.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

became one of the fundamental aspects of quantum field theory and is seen as a criterion for a theory's general acceptability.

Even though renormalization works well in practice, Feynman was never entirely comfortable with its mathematical validity, referring to renormalization as a "shell game" and "hocus pocus".[2]: 128 Neither Feynman nor Dirac were happy with that way to approach the observations made in theoretical physics, above all in quantum mechanics.[24] QED is the model and template for all subsequent quantum field theories.

Based on Bethe's intuition and fundamental papers on the subject by Shin'ichirō Tomonaga,[16] Julian Schwinger,[17][18] Richard Feynman[1][19][20] and Freeman Dyson,[21][22] it was finally possible to Hans Bethe produce fully covariant formulations that were finite at any order in a perturbation series of quantum electrodynamics.

The idea was simply to attach infinities to corrections of mass and charge that were actually fixed to a finite value by experiments.

A first indication of a possible solution was given by Hans Bethe in 1947.[14][15] He made the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Willis Lamb and Robert Retherford.[14] Despite limitations of the computation, agreement was excellent.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- von Glasenapp, Helmuth (1999).
- Jainism: An Indian Religion of Salvation (https://books.google.co m/books?id=WzEzXDk0v6sC&pg=PA181).
- 115 (https://archive.org/details/understandingpri0000wenh/page/115).
- Further analyzed by Maurice A.
- "Fundamental constituents of matter" (h ttps://books.google.com/books?id=rJe4k8tkq7sC&pg=PA9).

Jainism: An Indian Religion of Salvation (https://books.google.co m/books?id=WzEzXDk0v6sC&pg=PA181).

"Fundamental constituents of matter" (h ttps://books.google.com/books?id=rJe4k8tkq7sC&pg=PA9).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Overbye, Dennis (30 January 2015).
- Archived from the original (https:// www.nytimes.com/2015/01/31/us/a-speck-of-interstellar-dust-rebuts-a-big-bang-theory.html) on 1 January 2022.
- Overbye, Dennis (17 March 2014).
- "Study confirms criticism of Big Bang finding" (https://ghos tarchive.org/archive/20220101/https://www.nytimes.com/2014/09/23/science/space/study-confirms -criticism-of-big-bang-finding.html).
- "Cosmic inflation: Confidence lowered for Big Bang signal" (http s://www.bbc.com/news/science-environment-27935479).

Archived from the original (https:// www.nytimes.com/2015/01/31/us/a-speck-of-interstellar-dust-rebuts-a-big-bang-theory.html) on 1 January 2022.

"Study confirms criticism of Big Bang finding" (https://ghos tarchive.org/archive/20220101/https://www.nytimes.com/2014/09/23/science/space/study-confirms -criticism-of-big-bang-finding.html).

"Cosmic inflation: Confidence lowered for Big Bang signal" (http s://www.bbc.com/news/science-environment-27935479).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- org/article/emmy-noether-theorem-legacy-physics-math) from the original on 26 March 2023, retrieved 2 July 2018
- The nickname was not always used in a well-meaning manner.[77] In Noether's obituary, Hermann stated that The power of your genius seemed to transcend the bounds of your sex, which is why we in Göttingen, in awed mockery, often spoke of you in the masculine form as "der Noether."[40][78] d.
- Tollmien, Cordula, "Emmy Noether (1882–1935) – Lebensläufe" (https://web.archive.org/web/2007 0929100418/http://www.physikerinnen.de/noetherlebenslauf.html), physikerinnen.de, archived from the original (http://www.physikerinnen.de/noetherlebenslauf.html) on 29 September 2007, retrieved 13 April 2024 3.
- This can be seen in the résumé submitted by Noether to the University of Erlangen–Nuremberg in 1907.[1][2] Sometimes Emmy is mistakenly reported as a short form for Amalie, or misreported as Emily; for [3] example, the latter was used by Lee Smolin in a letter for The Reality Club.
- 41) states that he died "some time in 1939 or 40" and Ding, Kang & Tan (1999) state that he died in November 1940, but a local newspaper recorded his date of death as 1 October 1940.[101] f.

org/article/emmy-noether-theorem-legacy-physics-math) from the original on 26 March 2023, retrieved 2 July 2018

The nickname was not always used in a well-meaning manner.[77] In Noether's obituary, Hermann stated that The power of your genius seemed to transcend the bounds of your sex, which is why we in Göttingen, in awed mockery, often spoke of you in the masculine form as "der Noether."[40][78] d.

Tollmien, Cordula, "Emmy Noether (1882–1935) – Lebensläufe" (https://web.archive.org/web/2007 0929100418/http://www.physikerinnen.de/noetherlebenslauf.html), physikerinnen.de, archived from the original (http://www.physikerinnen.de/noetherlebenslauf.html) on 29 September 2007, retrieved 13 April 2024 3.

This can be seen in the résumé submitted by Noether to the University of Erlangen–Nuremberg in 1907.[1][2] Sometimes Emmy is mistakenly reported as a short form for Amalie, or misreported as Emily; for [3] example, the latter was used by Lee Smolin in a letter for The Reality Club.

41) states that he died "some time in 1939 or 40" and Ding, Kang & Tan (1999) state that he died in November 1940, but a local newspaper recorded his date of death as 1 October 1940.[101] f.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- ANEC is violated along geodesics going in the compact direction.
- • Unruh vacuum and evaporating black holes - Ford and Roman described situations in which ANEC is violated in this context: in 4D, it is violated for outgoing null geodesics and orbiting null geodesics, while in 2D it is violated for half-complete outgoing radial null geodesics and orbiting null geodesics on the horizon.
- The idea of a traversable wormhole is no longer pure
- This violation can happen both anomalously and in a nonanomalous way [29].
- • Hartle-Hawking vacuum - the ANEC is violated for circular curves existing between the event horizon of the Schwarzschild black hole and the r = 3M unstable circular photon orbit [1], [31].

ANEC is violated along geodesics going in the compact direction.

• Unruh vacuum and evaporating black holes - Ford and Roman described situations in which ANEC is violated in this context: in 4D, it is violated for outgoing null geodesics and orbiting null geodesics, while in 2D it is violated for half-complete outgoing radial null geodesics and orbiting null geodesics on the horizon.

The idea of a traversable wormhole is no longer pure

This violation can happen both anomalously and in a nonanomalous way [29].

• Hartle-Hawking vacuum - the ANEC is violated for circular curves existing between the event horizon of the Schwarzschild black hole and the r = 3M unstable circular photon orbit [1], [31].

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- between points doubled every 10-37 seconds; the expansion lasted at least 10-35 seconds, but its full duration is not certain.
- All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10-29 m then grew to a sphere with a radius around 0.9 m by the end of inflation.[10]: 202 At the end of inflation the driving field converts to particles, leading to a quark-soup phase of the universe, a phase that retains small density variations due to quantum fluctuations in the original small smooth patch of the universe.[11]

between points doubled every 10-37 seconds; the expansion lasted at least 10-35 seconds, but its full duration is not certain.

All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10-29 m then grew to a sphere with a radius around 0.9 m by the end of inflation.[10]: 202 At the end of inflation the driving field converts to particles, leading to a quark-soup phase of the universe, a phase that retains small density variations due to quantum fluctuations in the original small smooth patch of the universe.[11]

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- That was over a month ago.” “When I walked out the door of our house that night, that’s the last time I saw you, until five minutes ago when I came through those doors.” “Jason, I’ve seen you every day since that night.” “That man isn’t me.” Her face becomes dark.
- It’s three minutes out.” I glance around the lobby.
- The officer who escorted me here from the booking room is gone, and at the moment, we’re the only occupants aside from the woman at the welcome window.
- But she’s sitting behind a thick wall of protective glass, so I feel reasonably sure she can’t hear us.
- Looking up at me finally, she says, “Done.

That was over a month ago.” “When I walked out the door of our house that night, that’s the last time I saw you, until five minutes ago when I came through those doors.” “Jason, I’ve seen you every day since that night.” “That man isn’t me.” Her face becomes dark.

It’s three minutes out.” I glance around the lobby.

The officer who escorted me here from the booking room is gone, and at the moment, we’re the only occupants aside from the woman at the welcome window.

But she’s sitting behind a thick wall of protective glass, so I feel reasonably sure she can’t hear us.

Looking up at me finally, she says, “Done.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- ytisrevinU aveneG euqitpO PAG I.
- Marcikic et al., Nature, teleportation setup 421, 509-513, 2003 & InGaAs C Creation of a qubit Ge InGaAs β A B Creation of an entangled pair Beam splitter 50:50 α Creation of a photon WDM Creation of any qubit RG filter WDM RG filter to be teleported LBO LBO The Bell measurement Analysis of the teleported Φ qubit Mode locked Ti:Saphire Coincidence electronics Femto-second laser Pulse width =150 fs 3-fold 4-fold

Marcikic et al., Nature, teleportation setup 421, 509-513, 2003 & InGaAs C Creation of a qubit Ge InGaAs β A B Creation of an entangled pair Beam splitter 50:50 α Creation of a photon WDM Creation of any qubit RG filter WDM RG filter to be teleported LBO LBO The Bell measurement Analysis of the teleported Φ qubit Mode locked Ti:Saphire Coincidence electronics Femto-second laser Pulse width =150 fs 3-fold 4-fold

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Separation between infallers who fall in at different times.
- 142 Schwarzschild Black Hole the infaller.
- The infall velocity is lessthanthespeedoflightoutsidethehorizon,equaltothespeedoflightatthehorizon,andfasterthanlightinside thehorizon.Theinfallvelocitytendstoinfinityatthecentralsingularity.
- The region accessible to an infaller is cusp-like near the singularity.
- After tetrads, it will become clear that the standard Horizon Singularity Figure 7.2 The Gullstrand-Painlevé metric for the Schwarzschild geometry encodes locally inertial frames (tetrads) that free-fall radially into the black hole at the Newtonian escape velocity β, equation (7.28).

Separation between infallers who fall in at different times.

142 Schwarzschild Black Hole the infaller.

The infall velocity is lessthanthespeedoflightoutsidethehorizon,equaltothespeedoflightatthehorizon,andfasterthanlightinside thehorizon.Theinfallvelocitytendstoinfinityatthecentralsingularity.

The region accessible to an infaller is cusp-like near the singularity.

After tetrads, it will become clear that the standard Horizon Singularity Figure 7.2 The Gullstrand-Painlevé metric for the Schwarzschild geometry encodes locally inertial frames (tetrads) that free-fall radially into the black hole at the Newtonian escape velocity β, equation (7.28).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- physical world and its model provided by Euclidean geometry; presently a geometric space, or simply a space is a mathematical structure on which some geometry is defined.
- History The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC.[5][6] Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.
- The earliest known texts on geometry are the

physical world and its model provided by Euclidean geometry; presently a geometric space, or simply a space is a mathematical structure on which some geometry is defined.

History The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC.[5][6] Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.

The earliest known texts on geometry are the

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- The Pauli exclusion principle forbids fermions such as quarks from occupying the same position and energy level.
- Strange matter comes about as a way to relieve degeneracy pressure.
- It could conceivably be non-strange quark matter, if the effective mass of the strange quark were too high.
- would probably be strange matter.
- When the particle density is high enough that all energy levels below the available thermal energy are already occupied, increasing the density further requires raising some to higher, unoccupied energy levels.

The Pauli exclusion principle forbids fermions such as quarks from occupying the same position and energy level.

Strange matter comes about as a way to relieve degeneracy pressure.

It could conceivably be non-strange quark matter, if the effective mass of the strange quark were too high.

When the particle density is high enough that all energy levels below the available thermal energy are already occupied, increasing the density further requires raising some to higher, unoccupied energy levels.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- What happens beyond the horizon of our Universe?
- What happened before the Big Bang?
- What about a semi-relativistic distribution?
- What will be the fate of the Universe?
- How does a blackbody (Planck) distribution change with the expansion of the Universe?

What happens beyond the horizon of our Universe?

What about a semi-relativistic distribution?

How does a blackbody (Planck) distribution change with the expansion of the Universe?

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- as defining the 6 redundant components of the spatial Lorentz connection Γ in terms of spatial exterior derivatives d e of the spatial line interval α ̄ α α ̄ e .
- These 6 redundant components, denoted Γ/ (with a slash), can be called the gravomagnetic field, α ̄ α ̄ equation (16.334), since the situation is analogous to that in electromagnetism, where the 3-component magnetic field is redundant because it can be replaced by the spatial exterior derivative of the spatial

as defining the 6 redundant components of the spatial Lorentz connection Γ in terms of spatial exterior derivatives d e of the spatial line interval α ̄ α α ̄ e .

These 6 redundant components, denoted Γ/ (with a slash), can be called the gravomagnetic field, α ̄ α ̄ equation (16.334), since the situation is analogous to that in electromagnetism, where the 3-component magnetic field is redundant because it can be replaced by the spatial exterior derivative of the spatial

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- These technical problems are truly insurmountable unless totally new physics becomes available.
- Such wavelengths are in the gamma ray part of the spectrum, and this becomes a major technical problem for us because at present there is no gamma ray electro-optics with which to work with.
- It is called quantum teleportation, which is based on the well-known concept of quantum entanglement.
- To resolve atomic/subatomic particles requires wavelengths smaller than the size of these constituents, which will typically be 1 Å – 1 fm.
- and record their configurations.

These technical problems are truly insurmountable unless totally new physics becomes available.

Such wavelengths are in the gamma ray part of the spectrum, and this becomes a major technical problem for us because at present there is no gamma ray electro-optics with which to work with.

It is called quantum teleportation, which is based on the well-known concept of quantum entanglement.

To resolve atomic/subatomic particles requires wavelengths smaller than the size of these constituents, which will typically be 1 Å – 1 fm.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- Mukhanov, Viatcheslav; Winitzki, Sergei (2007).
- General Relativity: An Introduction for Physicists (https://books.google.com/books?id=5dryXCWR7EIC).
- The Renaissance of General Relativity and Cosmology: A Survey to Celebrate the 65th Birthday of Dennis Sciama (https://books.google.com/ books?id=5dryXCWR7EIC).
- The Large Scale Structure of Space-Time (http s://books.google.com/books?id=QagG_KI7Ll8C).
- Hobson, Michael Paul; Efstathiou, George; Lasenby, Anthony N.

Mukhanov, Viatcheslav; Winitzki, Sergei (2007).

General Relativity: An Introduction for Physicists (https://books.google.com/books?id=5dryXCWR7EIC).

The Renaissance of General Relativity and Cosmology: A Survey to Celebrate the 65th Birthday of Dennis Sciama (https://books.google.com/ books?id=5dryXCWR7EIC).

The Large Scale Structure of Space-Time (http s://books.google.com/books?id=QagG_KI7Ll8C).

Hobson, Michael Paul; Efstathiou, George; Lasenby, Anthony N.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Kruskal–Szekeres coordinates - Wikipedia.pdf


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- Reheating During inflation, any pre-existing thermal bath is diluted to negligible levels.
- Together, these effects are called the inflationary "no-hair theorem"[35] by analogy with the no hair theorem for black holes.
- Reheating is the process of converting this energy density into a thermal bath of Standard Model particles, necessary to initiate the Hot Big Bang.
- This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.
- In an expanding universe, energy densities generally fall, or get diluted, as the volume of the Universe increases.

Reheating During inflation, any pre-existing thermal bath is diluted to negligible levels.

Together, these effects are called the inflationary "no-hair theorem"[35] by analogy with the no hair theorem for black holes.

Reheating is the process of converting this energy density into a thermal bath of Standard Model particles, necessary to initiate the Hot Big Bang.

This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.

In an expanding universe, energy densities generally fall, or get diluted, as the volume of the Universe increases.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- Bibcode:2007SHPMP..38..514C (https://ui.adsabs.harvard.edu/abs/2007SHPM P..38..514C).
- Niels Bohr: Collected Works (https://ww w.nbarchive.dk/publications/bcw/).
- or took part in the discussions during the crucial years.
- 6: Foundations of Quantum Physics I (1926-1932).
- Bohr, Niels (1985) [May 16, 1947].

Niels Bohr: Collected Works (https://ww w.nbarchive.dk/publications/bcw/).

or took part in the discussions during the crucial years.

6: Foundations of Quantum Physics I (1926-1932).

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.

Copenhagen interpretation - Wikipedia.pdf


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a quantum fluctuation.
- Don Page was an outspoken critic of inflation because of this anomaly.[114] He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely.
- According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.
- Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle–Hawking initial state.[115] Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe.[4][116]: 223–225 However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-

that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a quantum fluctuation.

Don Page was an outspoken critic of inflation because of this anomaly.[114] He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely.

According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.

Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle–Hawking initial state.[115] Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe.[4][116]: 223–225 However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- null infinity.[180] Just as in classical physics, it can be shown that these masses are positive.[181] Corresponding global definitions exist for momentum and angular momentum.[182] There have also been a number of attempts to define quasi-local quantities, such as the mass of an isolated system formulated using only quantities defined within a finite region of space containing that system.
- The hope is to obtain a quantity useful for general statements about isolated systems, such as a more precise formulation of the hoop conjecture.[183]

null infinity.[180] Just as in classical physics, it can be shown that these masses are positive.[181] Corresponding global definitions exist for momentum and angular momentum.[182] There have also been a number of attempts to define quasi-local quantities, such as the mass of an isolated system formulated using only quantities defined within a finite region of space containing that system.

The hope is to obtain a quantity useful for general statements about isolated systems, such as a more precise formulation of the hoop conjecture.[183]

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- In a minute, we’re going back into that corridor.
- Then he actually brought me back to his world.
- It’s Human Behavior 101.” She must sense my rage building, because she says, “Jason, you don’t have the luxury of freaking out right now.
- If he did this to you, he would have rationalized it somehow.
- I’m saying that’s how a good man works himself up to do a terrible thing.

In a minute, we’re going back into that corridor.

Then he actually brought me back to his world.

It’s Human Behavior 101.” She must sense my rage building, because she says, “Jason, you don’t have the luxury of freaking out right now.

If he did this to you, he would have rationalized it somehow.

I’m saying that’s how a good man works himself up to do a terrible thing.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- That’s hardly surprising, because brain functioning also changes during relaxation, fatigue, heightened attention, and a host of other states that differ only in degree from normal awareness.
- For example, American psychiatrist Milton Erickson (1980) claimed that hypnosis is marked by several unique features, including “literalism”—the tendency to take questions literally, such as responding “Yes” to the question “Can you tell me what time it is?” Yet research demonstrates that most highly hypnotizable subjects don’t display literalism while hypnotized.
- Moreover, participants asked to simulate (roleplay) hypnosis display h igher rates of literalism than hypnotized subjects (Green et al., 1990).
- So the next time you see a Hollywood movie in which the CIA transforms an average Joe into a sleepwalking zombie who prevents World War III by assassinating an evil dictator, be skeptical.
- Although interesting, these findings “do not indicate a discrete state of hypnosis” (Hawegawa & Jamieson, 2000, p.

That’s hardly surprising, because brain functioning also changes during relaxation, fatigue, heightened attention, and a host of other states that differ only in degree from normal awareness.

For example, American psychiatrist Milton Erickson (1980) claimed that hypnosis is marked by several unique features, including “literalism”—the tendency to take questions literally, such as responding “Yes” to the question “Can you tell me what time it is?” Yet research demonstrates that most highly hypnotizable subjects don’t display literalism while hypnotized.

Moreover, participants asked to simulate (roleplay) hypnosis display h igher rates of literalism than hypnotized subjects (Green et al., 1990).

So the next time you see a Hollywood movie in which the CIA transforms an average Joe into a sleepwalking zombie who prevents World War III by assassinating an evil dictator, be skeptical.

Although interesting, these findings “do not indicate a discrete state of hypnosis” (Hawegawa & Jamieson, 2000, p.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- φ Christoffel Symbols Γ αβ The metric elements are g = −1, g = 1, g = b2+r2, g = (b2+r2)sin2θ.
- tt rr θθ φφ Let α = φ and xα = φ, then (cid:20) (cid:21) 1 ∂g ∂g ∂g g Γδ = φβ + φγ − βγ .
- φδ βγ 2 ∂xγ ∂xβ ∂φ Thus, δ = φ and we take β = φ due to symmetry.
- So, we have (cid:20) (cid:21) 1 ∂g ∂g ∂g g Γφ = φφ + φγ − φγ φφ φγ 2 ∂xγ ∂φ ∂φ 1∂g φφ = .
- 2 ∂xγ Since g = (b2+r2)sin2θ, then γ = r or γ = θ.

φ Christoffel Symbols Γ αβ The metric elements are g = −1, g = 1, g = b2+r2, g = (b2+r2)sin2θ.

tt rr θθ φφ Let α = φ and xα = φ, then (cid:20) (cid:21) 1 ∂g ∂g ∂g g Γδ = φβ + φγ − βγ .

φδ βγ 2 ∂xγ ∂xβ ∂φ Thus, δ = φ and we take β = φ due to symmetry.

So, we have (cid:20) (cid:21) 1 ∂g ∂g ∂g g Γφ = φφ + φγ − φγ φφ φγ 2 ∂xγ ∂φ ∂φ 1∂g φφ = .

2 ∂xγ Since g = (b2+r2)sin2θ, then γ = r or γ = θ.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- The individual metrics coincide in the overlapping transition regions.
- The actual wormhole (red part) will be characterized by a metric similar to that of the throat of a near extremal black hole - after all, the wormhole was obtained by connecting two such throats.
- TRAVERSABLE WORMHOLE WITH FERMIONS Section 5.
- - this is the “global” coordinate system which covers the whole Penrose diagram of AdS .
- The asymptotic regions of this metric (ρ >> 1) will be matched to the metric of the magnetically charged extremal black hole (r −r << r ) - this overlap corresponds e e to the red-blue transition zone on the diagram in figure 5.3.

The individual metrics coincide in the overlapping transition regions.

The actual wormhole (red part) will be characterized by a metric similar to that of the throat of a near extremal black hole - after all, the wormhole was obtained by connecting two such throats.

TRAVERSABLE WORMHOLE WITH FERMIONS Section 5.

- this is the “global” coordinate system which covers the whole Penrose diagram of AdS .

The asymptotic regions of this metric (ρ >> 1) will be matched to the metric of the magnetically charged extremal black hole (r −r << r ) - this overlap corresponds e e to the red-blue transition zone on the diagram in figure 5.3.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Evaluate a proposed wormhole construction claim and produce an evidence-bounded assessment plus verification plan.

EVIDENCE:
- It is moot whether the signal from a naked singularity, whatever it might be, would be discernible against the cacophony of astrophysical processes.
- Singularity theorems, Chapter 18, indicate that general relativity fails inside black holes (more generally, wherever a trapped surface has formed).
- 20.17 Thin spherical shells Sections 20.15 and 20.16 addressed matter that falls freely without shell crossing.
- Figure 20.1 is a spacetime diagram that illustrates the formation of a naked singularity in self-similar collapse of dust for the case a=18, which slightly exceeds the threshold (20.91).
- However, the collapse of a real black hole is one of the most violent events in observational astronomy, attended by supernovae and gamma-ray bursts.

It is moot whether the signal from a naked singularity, whatever it might be, would be discernible against the cacophony of astrophysical processes.

Singularity theorems, Chapter 18, indicate that general relativity fails inside black holes (more generally, wherever a trapped surface has formed).

20.17 Thin spherical shells Sections 20.15 and 20.16 addressed matter that falls freely without shell crossing.

Figure 20.1 is a spacetime diagram that illustrates the formation of a naked singularity in self-similar collapse of dust for the case a=18, which slightly exceeds the threshold (20.91).

However, the collapse of a real black hole is one of the most violent events in observational astronomy, attended by supernovae and gamma-ray bursts.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.
- Frank Wilczek has suggested calling attention to this assumption by designating it "Newton's Zeroth Law".[37] Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant.[38] Likewise, the idea that forces add like vectors (or in other words obey the superposition principle), and the idea that forces change the energy of a body, have both been described as a "fourth law".[note 8]

For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.

Frank Wilczek has suggested calling attention to this assumption by designating it "Newton's Zeroth Law".[37] Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant.[38] Likewise, the idea that forces add like vectors (or in other words obey the superposition principle), and the idea that forces change the energy of a body, have both been described as a "fourth law".[note 8]

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Explain quantum teleportation rigorously and outline an experimental validation checklist.

EVIDENCE:
- [7] 7 tightly bound than normal nuclei; for example, the lithium hypernucleus Li is 19% smaller than Λ the normal nucleus 6Li.[8][9] However, the hyperons can decay via the weak force; the mean lifetime of a free Λ is 263±2 ps, and that of a Λ hypernucleus is usually slightly shorter.[10] A generalized mass formula developed for both the non-strange normal nuclei and strange hypernuclei can estimate masses of hypernuclei containing Λ, ΛΛ, Σ, and Ξ hyperon(s).[11][12] The neutron and proton driplines for hypernuclei are predicted and existence of some exotic hypernuclei beyond the normal neutron and proton driplines are suggested.[7] This generalized mass formula was named the "Samanta formula" by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in heavy-ion collisions.[13] Types Λ hypernuclei The simplest, and most well understood, type of hypernucleus includes only the lightest hyperon, the Λ.[6] While two nucleons can interact through the nuclear force mediated by a virtual pion, the Λ becomes a Σ baryon upon emitting a pion,[a] so the Λ–nucleon interaction is mediated solely by more massive mesons such as the η and ω mesons, or through the simultaneous exchange of two or more mesons.[15] This means that the Λ–nucleon interaction is weaker and has a shorter range than the standard nuclear force, and the potential well of a Λ in the nucleus is shallower than that of a nucleon;[16] in hypernuclei, the depth of the Λ potential is approximately 30 MeV.[17] However, onepion exchange in the Λ–nucleon interaction does cause quantum-mechanical mixing of the Λ and Σ baryons in hypernuclei (which does not happen in free space), especially in neutron-rich hypernuclei.[18][19][20] Additionally, the three-body force between a Λ and two nucleons is expected to be more important than the three-body interaction in nuclei, since the Λ can exchange two pions with a virtual Σ intermediate, while the equivalent process in nucleons requires a relatively heavy delta baryon (Δ) intermediate.[15] Like all hyperons, Λ hypernuclei can decay through the weak interaction, which changes it to a lighter baryon and emits a meson or a lepton–antilepton pair.
- In free space, the Λ usually decays via the weak force to a proton and a π– meson, or a neutron and a π0, with a total half-life of 263±2 ps.[21] A nucleon in the hypernucleus can cause the Λ to decay via the weak force without emitting a pion; this process becomes dominant in heavy hypernuclei, due to suppression of the pion-emitting decay mode.[22] The half-life of the Λ in a hypernucleus

[7] 7 tightly bound than normal nuclei; for example, the lithium hypernucleus Li is 19% smaller than Λ the normal nucleus 6Li.[8][9] However, the hyperons can decay via the weak force; the mean lifetime of a free Λ is 263±2 ps, and that of a Λ hypernucleus is usually slightly shorter.[10] A generalized mass formula developed for both the non-strange normal nuclei and strange hypernuclei can estimate masses of hypernuclei containing Λ, ΛΛ, Σ, and Ξ hyperon(s).[11][12] The neutron and proton driplines for hypernuclei are predicted and existence of some exotic hypernuclei beyond the normal neutron and proton driplines are suggested.[7] This generalized mass formula was named the "Samanta formula" by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in heavy-ion collisions.[13] Types Λ hypernuclei The simplest, and most well understood, type of hypernucleus includes only the lightest hyperon, the Λ.[6] While two nucleons can interact through the nuclear force mediated by a virtual pion, the Λ becomes a Σ baryon upon emitting a pion,[a] so the Λ–nucleon interaction is mediated solely by more massive mesons such as the η and ω mesons, or through the simultaneous exchange of two or more mesons.[15] This means that the Λ–nucleon interaction is weaker and has a shorter range than the standard nuclear force, and the potential well of a Λ in the nucleus is shallower than that of a nucleon;[16] in hypernuclei, the depth of the Λ potential is approximately 30 MeV.[17] However, onepion exchange in the Λ–nucleon interaction does cause quantum-mechanical mixing of the Λ and Σ baryons in hypernuclei (which does not happen in free space), especially in neutron-rich hypernuclei.[18][19][20] Additionally, the three-body force between a Λ and two nucleons is expected to be more important than the three-body interaction in nuclei, since the Λ can exchange two pions with a virtual Σ intermediate, while the equivalent process in nucleons requires a relatively heavy delta baryon (Δ) intermediate.[15] Like all hyperons, Λ hypernuclei can decay through the weak interaction, which changes it to a lighter baryon and emits a meson or a lepton–antilepton pair.

In free space, the Λ usually decays via the weak force to a proton and a π– meson, or a neutron and a π0, with a total half-life of 263±2 ps.[21] A nucleon in the hypernucleus can cause the Λ to decay via the weak force without emitting a pion; this process becomes dominant in heavy hypernuclei, due to suppression of the pion-emitting decay mode.[22] The half-life of the Λ in a hypernucleus

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


Prompt:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- By definition, the initial action S is constant for each null hypersurface, so dS = 0 over each null hypersurface.
- As discussed in §18.7, in the massless limit the momentum is not only orthogonal but also tangent to the limiting null hypersurface, and equation (23.128) need be imposed only over each 3-dimensional null hypersurface projected from 2-dimensional surfaces of constant action S i on the initial 3-dimensional hypersurface, not over the entire 4-dimensional spacetime.
- 698 Trajectories in ideal rotating black holes Comparing equations (23.127) and (23.129) shows that a timelike congruence is hypersurface-orthogonal if and only if (Xα−Xα)dC =0 .
- For a timelike congruence, the action S and 3 comoving coordinates Xα can be used, if desired, as the 4 coordinates along the congruence.
- α The condition (23.129) for hypersurface-orthogonality can continue to be imposed in the massless limit, where the congruence becomes null.

By definition, the initial action S is constant for each null hypersurface, so dS = 0 over each null hypersurface.

As discussed in §18.7, in the massless limit the momentum is not only orthogonal but also tangent to the limiting null hypersurface, and equation (23.128) need be imposed only over each 3-dimensional null hypersurface projected from 2-dimensional surfaces of constant action S i on the initial 3-dimensional hypersurface, not over the entire 4-dimensional spacetime.

698 Trajectories in ideal rotating black holes Comparing equations (23.127) and (23.129) shows that a timelike congruence is hypersurface-orthogonal if and only if (Xα−Xα)dC =0 .

For a timelike congruence, the action S and 3 comoving coordinates Xα can be used, if desired, as the 4 coordinates along the congruence.

α The condition (23.129) for hypersurface-orthogonality can continue to be imposed in the massless limit, where the congruence becomes null.

If proposing a design, label as hypothesis and provide validation steps.

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.