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

EVIDENCE:
- This meaning is found in late medieval French, and is adopted from the French into English in the mid-16th century.
- The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines.
- The OED traces the formal, modern meaning to John Harris' Lexicon Technicum (1704), which has:
- They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.
- Etymology The English word machine comes through Middle French from Latin machina,[2] which in turn derives from the Greek (Doric μαχανά makhana, Ionic μηχανή mekhane 'contrivance, machine, engine',[3] a derivation from μῆχος mekhos 'means, expedient, remedy'[4]).[5] The word mechanical (Greek: μηχανικός) comes from the same Greek roots.

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.

This meaning is found in late medieval French, and is adopted from the French into English in the mid-16th century.

The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines.

The OED traces the formal, modern meaning to John Harris' Lexicon Technicum (1704), which has:

They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.

Etymology The English word machine comes through Middle French from Latin machina,[2] which in turn derives from the Greek (Doric μαχανά makhana, Ionic μηχανή mekhane 'contrivance, machine, engine',[3] a derivation from μῆχος mekhos 'means, expedient, remedy'[4]).[5] The word mechanical (Greek: μηχανικός) comes from the same Greek roots.

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:
- A first order ordinary differential equation suffices!
- Open and flat universes troubledhim,Wheelersaid,becausetheinfinitespaceimpliedthateverythingthatcould havehappenedwouldhavehappened.Anotherversionofyouwouldhavereadnotonly thisbook,butalsothisbookinallitsmanydrafts.Thesameargumentcouldhavebeen invokedtoruleouttheflatearthwithitsedgeinfinitelyfaraway.Aswegoonanendless questtotheedge,wewouldhaveencounteredeveryimaginablegoblinandmonstrosity.
- We have grown to be far more selfconfidentandconceitedthanhe.
- We are often awed by the power of aesthetic or “philosophic” arguments, but on the otherhand,weshouldnotsuccumbtoselectivebiasandfailtoremembertheonesthat failed.ButhasWheeler’sargumentreallyfailed?No.Theuniversehasnotbeenprovento beflat.10 TheunderlyingalgebraofphysicswasextendedfromtheGalileanalgebratotheLorentz algebra.
- As the flat earth once gave way to the round world, will the Lorentz algebra be replacedbythedeSitteralgebra?11 ——— Asforthemysteryofgravity, letusnotforgetthatweactuallyhaveaprettygoodunderstandingofgravity;inparticular,theconnectionwithspacetimecurvatureisnothingshort

A first order ordinary differential equation suffices!

We have grown to be far more selfconfidentandconceitedthanhe.

We are often awed by the power of aesthetic or “philosophic” arguments, but on the otherhand,weshouldnotsuccumbtoselectivebiasandfailtoremembertheonesthat failed.ButhasWheeler’sargumentreallyfailed?No.Theuniversehasnotbeenprovento beflat.10 TheunderlyingalgebraofphysicswasextendedfromtheGalileanalgebratotheLorentz algebra.

As the flat earth once gave way to the round world, will the Lorentz algebra be replacedbythedeSitteralgebra?11 ——— Asforthemysteryofgravity, letusnotforgetthatweactuallyhaveaprettygoodunderstandingofgravity;inparticular,theconnectionwithspacetimecurvatureisnothingshort

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:
- The escape velocity from Earth's surface is 11.23 kilometers per second.
- The minimum velocity at which this happens is the escape velocity.
- The rising body never entirely loses all, and in that case, what goes up doesn't come down because it never quite stops going up.
- There comes a point where an object rises so rapidly that its velocity decrease matches the decline in gravitational intensity.
- ** If an object is moving less than escape velocity but not less than about 70 percent of escape velocity, and if it also has a sideways motion, then it may not escape from Earth but may not drop back to the surface, either.

The escape velocity from Earth's surface is 11.23 kilometers per second.

The minimum velocity at which this happens is the escape velocity.

The rising body never entirely loses all, and in that case, what goes up doesn't come down because it never quite stops going up.

There comes a point where an object rises so rapidly that its velocity decrease matches the decline in gravitational intensity.

** If an object is moving less than escape velocity but not less than about 70 percent of escape velocity, and if it also has a sideways motion, then it may not escape from Earth but may not drop back to the surface, either.

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:
- Macías, Alfredo; Camacho, Abel (May 2008).
- Archived (https://web.archive.org/web/2 0190501213902/https://nawcc.org/index.php/main-education) from the original on 1 May 2019.
- "Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day?" (https://www.scientificamerican.com/article/experts -time-division-days-hours-minutes/).
- "Revolutionary theory finally unites quantum mechanics and Einstein's theory of general relativity" (https://www.thebrighterside.news/post/revolutionary-theory-f inally-unites-quantum-mechanics-and-einsteins-theory-of-general-relativity/).
- Bibcode:2008PhLB..663...99M (https://ui.adsabs.harvard.edu/abs/2008PhLB..663...99 M).

Macías, Alfredo; Camacho, Abel (May 2008).

Archived (https://web.archive.org/web/2 0190501213902/https://nawcc.org/index.php/main-education) from the original on 1 May 2019.

"Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day?" (https://www.scientificamerican.com/article/experts -time-division-days-hours-minutes/).

"Revolutionary theory finally unites quantum mechanics and Einstein's theory of general relativity" (https://www.thebrighterside.news/post/revolutionary-theory-f inally-unites-quantum-mechanics-and-einsteins-theory-of-general-relativity/).

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:
- To justify the “bridge” appellation, consider a spherical surface, with • constant u.
- • The net result is that the neutral “Einstein-Rosen” bridge (aka as the “Schwarzschild wormhole”) is identical to a part of the maximally extended Schwarzschild geometry.
- One defines the narrowest part of the geometry as the “throat”, while • the nearby region is denoted the bridge (or in modern terminology a “wormhole”).
- – The area of the surface is: A(u) = 4π(2M+u2 )2.
- • Non-traversable: The throat will pinch off before an observer may traverse the throat.

To justify the “bridge” appellation, consider a spherical surface, with • constant u.

• The net result is that the neutral “Einstein-Rosen” bridge (aka as the “Schwarzschild wormhole”) is identical to a part of the maximally extended Schwarzschild geometry.

One defines the narrowest part of the geometry as the “throat”, while • the nearby region is denoted the bridge (or in modern terminology a “wormhole”).

– The area of the surface is: A(u) = 4π(2M+u2 )2.

• Non-traversable: The throat will pinch off before an observer may traverse the throat.

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:
- He was also one of the first scientists to conceive the possibility of quantum computers.[155][156][157] In the 1980s he began to spend his summers working at Thinking Machines Corporation, helping to build some of the first parallel supercomputers and considering the construction of quantum computers.[158][159] Between 1984 and 1986, he developed a variational method for the approximate calculation of path integrals, which has led to a powerful method of converting divergent perturbation expansions into convergent strong-coupling expansions (variational perturbation theory) and, as a consequence, to the most accurate determination[160] of critical exponents measured in satellite experiments.[161] At Caltech, he once chalked "What I cannot create I do not understand" on his blackboard.[162] Machine technology Feynman had studied the ideas of John von Neumann while researching quantum field theory.
- showed that some 45% of the energy momentum was carried by electrically neutral particles in the nucleon.
- His most famous lecture on the subject was delivered in 1959 at the California Institute of Technology, published under
- The computational device that Feynman discovered then for gravity, "ghosts", which are "particles" in the interior of his diagrams that have the "wrong" connection between spin and statistics, have proved invaluable in explaining the quantum particle behavior of the Yang–Mills theories, for example, quantum chromodynamics and the electro-weak theory.[152] He did work on all four of the fundamental interactions of nature: electromagnetic, the weak force, the strong force and gravity.
- By analogy with the photon, which has spin 1, he investigated the consequences of a free massless spin 2 field and derived the Einstein field equation of general relativity, but little more.

He was also one of the first scientists to conceive the possibility of quantum computers.[155][156][157] In the 1980s he began to spend his summers working at Thinking Machines Corporation, helping to build some of the first parallel supercomputers and considering the construction of quantum computers.[158][159] Between 1984 and 1986, he developed a variational method for the approximate calculation of path integrals, which has led to a powerful method of converting divergent perturbation expansions into convergent strong-coupling expansions (variational perturbation theory) and, as a consequence, to the most accurate determination[160] of critical exponents measured in satellite experiments.[161] At Caltech, he once chalked "What I cannot create I do not understand" on his blackboard.[162] Machine technology Feynman had studied the ideas of John von Neumann while researching quantum field theory.

showed that some 45% of the energy momentum was carried by electrically neutral particles in the nucleon.

His most famous lecture on the subject was delivered in 1959 at the California Institute of Technology, published under

The computational device that Feynman discovered then for gravity, "ghosts", which are "particles" in the interior of his diagrams that have the "wrong" connection between spin and statistics, have proved invaluable in explaining the quantum particle behavior of the Yang–Mills theories, for example, quantum chromodynamics and the electro-weak theory.[152] He did work on all four of the fundamental interactions of nature: electromagnetic, the weak force, the strong force and gravity.

By analogy with the photon, which has spin 1, he investigated the consequences of a free massless spin 2 field and derived the Einstein field equation of general relativity, but little more.

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:
- Scientists and engineers are exploring multiple technologies for quantum computing hardware and hope to develop scalable quantum architectures, but serious obstacles remain.[93][94] A wafer of adiabatic quantum computers Challenges There are a number of technical challenges in building a large-scale quantum computer.[95] Physicist David DiVincenzo has listed these requirements for a practical quantum computer:[96] Physically scalable to increase the number of qubits Qubits that can be initialized to arbitrary values Quantum gates that are faster than decoherence time Universal gate set Qubits that can be read easily.
- This has led to the development of quantum controllers that enable interfacing with the qubits.
- Therefore, one can expect that quantum-enhanced generative models[91] including quantum GANs[92] may eventually be developed into ultimate generative chemistry algorithms.
- Sourcing parts for quantum computers is also very difficult.
- In 2023, researchers at Gero reported a hybrid quantum–classical generative model based on a restricted Boltzmann machine, implemented on a commercially available quantum annealing device, to generate novel drug-like small molecules with physicochemical properties comparable to known medicinal compounds.[89][90] However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers.

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

Scientists and engineers are exploring multiple technologies for quantum computing hardware and hope to develop scalable quantum architectures, but serious obstacles remain.[93][94] A wafer of adiabatic quantum computers Challenges There are a number of technical challenges in building a large-scale quantum computer.[95] Physicist David DiVincenzo has listed these requirements for a practical quantum computer:[96] Physically scalable to increase the number of qubits Qubits that can be initialized to arbitrary values Quantum gates that are faster than decoherence time Universal gate set Qubits that can be read easily.

This has led to the development of quantum controllers that enable interfacing with the qubits.

Therefore, one can expect that quantum-enhanced generative models[91] including quantum GANs[92] may eventually be developed into ultimate generative chemistry algorithms.

Sourcing parts for quantum computers is also very difficult.

In 2023, researchers at Gero reported a hybrid quantum–classical generative model based on a restricted Boltzmann machine, implemented on a commercially available quantum annealing device, to generate novel drug-like small molecules with physicochemical properties comparable to known medicinal compounds.[89][90] However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers.

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:
- Bibcode:2017PhT..2017k0676R (https://ui.adsabs.harvard.edu/abs/2017PhT..2017k0676R).
- doi:10.1259/dmfr/73488299 (https://doi.org/10.1259%2Fdmfr%2F734 88299).
- PMC 8454205 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8454205).
- Kasimir Fajans, "Radioactive transformations and the periodic system of the elements".
- "Early victims of X-rays: a tribute and current perception" (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3520298).

Kasimir Fajans, "Radioactive transformations and the periodic system of the elements".

"Early victims of X-rays: a tribute and current perception" (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3520298).

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:
- Many four-dimensionalists understand four-dimensionalism simply as perdurantism, together with the claim that all material objects persist in this manner.[1][4] Stage theory (exdurantism) Stage theory or exdurantism is a closely related four-dimensionalist theory that also posits temporal parts, but differs in how it identifies ordinary objects.[15][16] According to stage theory, the object ordinarily referred to at a time is an instantaneous (or short-lived) temporal stage, not the entire spacetime worm.
- The B-series orders events only by the tenseless relations earlier than, later than and simultaneous with, which do not themselves change.[17][12]
- The dispute between endurantism and four-dimensionalist theories such as perdurantism and stage theory concerns how to understand the relation between objects, time and change.
- Because of this, perdurantism is sometimes called the "worm view": a persisting object is identified with the entire spacetime "worm" composed of its temporal parts.[2][10] Perdurantism is usually taken to be a paradigmatic four-dimensionalist position about persistence.
- Stage theory thus offers a four-dimensionalist account of persistence and change, but denies that persisting objects are identical with extended spacetime worms.

Many four-dimensionalists understand four-dimensionalism simply as perdurantism, together with the claim that all material objects persist in this manner.[1][4] Stage theory (exdurantism) Stage theory or exdurantism is a closely related four-dimensionalist theory that also posits temporal parts, but differs in how it identifies ordinary objects.[15][16] According to stage theory, the object ordinarily referred to at a time is an instantaneous (or short-lived) temporal stage, not the entire spacetime worm.

The B-series orders events only by the tenseless relations earlier than, later than and simultaneous with, which do not themselves change.[17][12]

The dispute between endurantism and four-dimensionalist theories such as perdurantism and stage theory concerns how to understand the relation between objects, time and change.

Because of this, perdurantism is sometimes called the "worm view": a persisting object is identified with the entire spacetime "worm" composed of its temporal parts.[2][10] Perdurantism is usually taken to be a paradigmatic four-dimensionalist position about persistence.

Stage theory thus offers a four-dimensionalist account of persistence and change, but denies that persisting objects are identical with extended spacetime worms.

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:
- [22] mass and the time derivative of the velocity, which is the acceleration: As the acceleration is the second derivative of position with respect to time, this can also be written Newton's second law, in modern form, states that the time derivative of the momentum is the force: [23]: 4.1 When applied to systems of variable mass, the equation above is valid only for a fixed set of particles.
- Otherwise, the equilibrium is unstable.[15]: 121 [23]: 174 A free body diagram for a block on an inclined plane, illustrating the normal A common visual representation of forces acting in concert is force perpendicular to the plane (N), the the free body diagram, which schematically portrays a body of downward force of gravity (mg), and a interest and the forces applied to it by outside influences.[26] force f along the direction of the plane For example, a free body diagram of a block sitting upon an that could be applied, for example, by inclined plane can illustrate the combination of gravitational friction or a string force, "normal" force, friction, and string tension.[note 4] Newton's second law is sometimes presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating.
- To go beyond tautology, an equation detailing the force might also be specified, like Newton's law of universal gravitation.
- By inserting such an expression for into Newton's second law, an equation with predictive power can be written.[note 5] Newton's second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of matter.[15]: 134 [28]: 12-2
- A state of mechanical equilibrium is stable if, when the position of the body is changed slightly, the body remains near that equilibrium.

[22] mass and the time derivative of the velocity, which is the acceleration: As the acceleration is the second derivative of position with respect to time, this can also be written Newton's second law, in modern form, states that the time derivative of the momentum is the force: [23]: 4.1 When applied to systems of variable mass, the equation above is valid only for a fixed set of particles.

Otherwise, the equilibrium is unstable.[15]: 121 [23]: 174 A free body diagram for a block on an inclined plane, illustrating the normal A common visual representation of forces acting in concert is force perpendicular to the plane (N), the the free body diagram, which schematically portrays a body of downward force of gravity (mg), and a interest and the forces applied to it by outside influences.[26] force f along the direction of the plane For example, a free body diagram of a block sitting upon an that could be applied, for example, by inclined plane can illustrate the combination of gravitational friction or a string force, "normal" force, friction, and string tension.[note 4] Newton's second law is sometimes presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating.

To go beyond tautology, an equation detailing the force might also be specified, like Newton's law of universal gravitation.

By inserting such an expression for into Newton's second law, an equation with predictive power can be written.[note 5] Newton's second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of matter.[15]: 134 [28]: 12-2

A state of mechanical equilibrium is stable if, when the position of the body is changed slightly, the body remains near that equilibrium.

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:
- (16.123) ∂xκ pκ Invertingequation(16.123)alongthelinesofequations(16.106)–(16.110)recoverstheusualexpression(11.55) for the torsion-full tetrad connection Γ as a sum of the torsion-free connection ̊Γ given by equamnλ mnλ tion (16.110), and a contortion tensor K , mnλ Γ = ̊Γ +K , (16.124) mnλ mnλ mnλ with the contortion tensor K being related to the spin angular-momentum Σ by mnl lmn K =8π ( −Σ + 3Σ −γ Σp ) .
- Like the torsion tensor S , the λmn spin angular-momentum Σ is antisymmetric in its last two indices mn.
- Adding the variation (16.104) of λmn the gravitational action and the variation (16.121) of the matter action gives ∫ ( e−1∂(eemnκλ) ) 8π(δS +δS )= − +2Γ[men]pκλ+4πΣλmn δΓ d4x , (16.122) g m ∂xκ pκ mnλ extremization of which implies e−1∂(eemnκλ) =2Γ[men]pκλ+4πΣλmn .
- (16.125) mnl lmn 2 [lmn] l[m n]p The contortion K is related to the torsion S by equations (11.56).
- Since torsion in Einstein-Cartan theory is local, it is hard to detect.

(16.123) ∂xκ pκ Invertingequation(16.123)alongthelinesofequations(16.106)–(16.110)recoverstheusualexpression(11.55) for the torsion-full tetrad connection Γ as a sum of the torsion-free connection ̊Γ given by equamnλ mnλ tion (16.110), and a contortion tensor K , mnλ Γ = ̊Γ +K , (16.124) mnλ mnλ mnλ with the contortion tensor K being related to the spin angular-momentum Σ by mnl lmn K =8π ( −Σ + 3Σ −γ Σp ) .

Like the torsion tensor S , the λmn spin angular-momentum Σ is antisymmetric in its last two indices mn.

Adding the variation (16.104) of λmn the gravitational action and the variation (16.121) of the matter action gives ∫ ( e−1∂(eemnκλ) ) 8π(δS +δS )= − +2Γ[men]pκλ+4πΣλmn δΓ d4x , (16.122) g m ∂xκ pκ mnλ extremization of which implies e−1∂(eemnκλ) =2Γ[men]pκλ+4πΣλmn .

(16.125) mnl lmn 2 [lmn] l[m n]p The contortion K is related to the torsion S by equations (11.56).

Since torsion in Einstein-Cartan theory is local, it is hard to detect.

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:
- For any three vectors and [45] One can in n dimensions take the product of n − 1 vectors to produce a vector perpendicular to all of them.
- The cross product A × B of the vectors A and B is a vector that is perpendicular to both and therefore normal to the plane containing them.
- Cross product The cross product or vector product is a binary operation on two vectors in three-dimensional space and is denoted by the symbol ×.
- However, there is no 'preferred' or 'canonical basis' for .
- This differs from in a subtle way.

For any three vectors and [45] One can in n dimensions take the product of n − 1 vectors to produce a vector perpendicular to all of them.

The cross product A × B of the vectors A and B is a vector that is perpendicular to both and therefore normal to the plane containing them.

Cross product The cross product or vector product is a binary operation on two vectors in three-dimensional space and is denoted by the symbol ×.

However, there is no 'preferred' or 'canonical basis' for .

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:
- When Penzias heard about Dicke’s work, he and Wilson quickly realised that their observations fit what the Princeton group were predicting.
- Thus the CMB provides a snapshot of the Universe at recombination.
- The acceleration requires the mass-energy density of the Universe to be dominated at the present time by a gravitationally repulsive component, such as a cosmological constant Λ.
- They were unaware that Robert Dicke’s group at Princeton had already realised that a hot Big Bang would have left a remnant of blackbody radiation filling the Universe, with a present-day temperature of a few Kelvin, and were setting about to try to detect it.
- 10.1.3 The Cosmic Microwave Background (CMB) The single most powerful observational constraints on the Universe come from the Cosmic Microwave Background (CMB).

When Penzias heard about Dicke’s work, he and Wilson quickly realised that their observations fit what the Princeton group were predicting.

Thus the CMB provides a snapshot of the Universe at recombination.

The acceleration requires the mass-energy density of the Universe to be dominated at the present time by a gravitationally repulsive component, such as a cosmological constant Λ.

They were unaware that Robert Dicke’s group at Princeton had already realised that a hot Big Bang would have left a remnant of blackbody radiation filling the Universe, with a present-day temperature of a few Kelvin, and were setting about to try to detect it.

10.1.3 The Cosmic Microwave Background (CMB) The single most powerful observational constraints on the Universe come from the Cosmic Microwave Background (CMB).

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:
- If charge were imaginary, then electromagnetic energy would be negative.
- 8.17 Reissner-Nordström geometry with imaginary charge It is possible formally to consider the Reissner-Nordström geometry with imaginary charge Q Q2 <0 .
- Thus particles, instead of bouncing off the singularity, are attracted to it, and it turns out to be possible to continue geodesics through the singularity.
- (8.31) This is completely unphysical.
- Mathematically, the geometry can be considered as the Kerr-Newman geometry in the limit of zero spin.

If charge were imaginary, then electromagnetic energy would be negative.

8.17 Reissner-Nordström geometry with imaginary charge It is possible formally to consider the Reissner-Nordström geometry with imaginary charge Q Q2 <0 .

Thus particles, instead of bouncing off the singularity, are attracted to it, and it turns out to be possible to continue geodesics through the singularity.

Mathematically, the geometry can be considered as the Kerr-Newman geometry in the limit of zero 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:
Design a retrieval+analysis pipeline to discover missing facts from the corpus without hallucinating.

EVIDENCE:
- VII.3 Hawking Radiation Quantumfluctuationscansetyoufree Nothingcangetoutofblackholes.Spacetimeiswarpedinsuchawaythat,onceinsidethe horizon,evenlightcanneveremerge,astheKruskaldiagramshowsforaSchwarzschild blackhole.Weworkedthispictureoutindetailintheprecedingchapters.
- Let’s put substance on this basically correct explanation by learning about the phenomenonoftherestlessvacuuminquantumfieldtheory.
- Butasyouhavenodoubtheard,thatpicture,paintedexclusivelywithclassicalphysics, nolongerholdstruewhenquantumeffectsareturnedon,aswehavealreadydiscussedin theintroductiontothistext.Blackholesradiateasblackbodies,eachwithatemperature characteristic of the specific black hole.
- Wenowtrytounderstandhowquantumeffectscouldchangethepicturesodrastically.
- Indeed, we were even able to determine, purely bydimensionalanalysissupplementedbyabitofbasicknowledgeaboutgravity,thatthe HawkingtemperatureforaSchwarzschildblackholeisgivenby 1 (cid:2)c3 T ∼ ∼ (1) H GM GM withM themassoftheblackhole.Youmaywishtogobacktotheintroductiontoreview howwedidthat.Therewealreadynotedthatthissimplyderivedresultindicatesthatblack holeradiationendsexplosively.AsM decreases,T goesup.1 From(1),usingthethermodynamicdefinitionofentropydM =TdS,weimmediately determinedtheentropytobe GM2 S∼GM2∼ (2) (cid:2)c3 Ihaveuseddimensionalanalysistorestore(cid:2) in(1)and(2), thusshowingclearlythat for(cid:2)=0,wehaveT =0andS=∞,sothatclassically,blackholesdonotradiate.

Let’s put substance on this basically correct explanation by learning about the phenomenonoftherestlessvacuuminquantumfieldtheory.

Butasyouhavenodoubtheard,thatpicture,paintedexclusivelywithclassicalphysics, nolongerholdstruewhenquantumeffectsareturnedon,aswehavealreadydiscussedin theintroductiontothistext.Blackholesradiateasblackbodies,eachwithatemperature characteristic of the specific black hole.

Indeed, we were even able to determine, purely bydimensionalanalysissupplementedbyabitofbasicknowledgeaboutgravity,thatthe HawkingtemperatureforaSchwarzschildblackholeisgivenby 1 (cid:2)c3 T ∼ ∼ (1) H GM GM withM themassoftheblackhole.Youmaywishtogobacktotheintroductiontoreview howwedidthat.Therewealreadynotedthatthissimplyderivedresultindicatesthatblack holeradiationendsexplosively.AsM decreases,T goesup.1 From(1),usingthethermodynamicdefinitionofentropydM =TdS,weimmediately determinedtheentropytobe GM2 S∼GM2∼ (2) (cid:2)c3 Ihaveuseddimensionalanalysistorestore(cid:2) in(1)and(2), thusshowingclearlythat for(cid:2)=0,wehaveT =0andS=∞,sothatclassically,blackholesdonotradiate.

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:1998PhRvL..80.1121B (https://ui.adsabs.harvard.edu/abs/1998PhRvL..80.11 21B).
- Archived (https://web.archive.org/we b/20210423204829/https://physicstoday.scitation.org/doi/10.1063/1.881360) from the original on 23 April 2021.
- Bibcode:1990AmJPh..58.1131G (https://ui.adsabs.harvard.edu/abs/1990AmJPh..58.1131G).
- doi:10.1063/1.881360 (https://doi.org/10.1063%2F1.881360).
- Boschi, D.; Branca, S.; De Martini, F.; Hardy, L.; Popescu, S.

Archived (https://web.archive.org/we b/20210423204829/https://physicstoday.scitation.org/doi/10.1063/1.881360) from the original on 23 April 2021.

Boschi, D.; Branca, S.; De Martini, F.; Hardy, L.; Popescu, S.

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:
- philosophers.[38][39] In the thirteenth century the astronomer al-'Urḍi proposed a radical change to Ptolemy's system of nesting spheres.
- In his Kitāb al-Hayáh, he recalculated the distance of the planets using parameters which he redetermined.
- Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet's diameters to the thickness of their spheres.
- As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.[34]

philosophers.[38][39] In the thirteenth century the astronomer al-'Urḍi proposed a radical change to Ptolemy's system of nesting spheres.

In his Kitāb al-Hayáh, he recalculated the distance of the planets using parameters which he redetermined.

Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet's diameters to the thickness of their spheres.

As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.[34]

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:
- its follower is a higher pair called a cam joint.
- Examples The planar one degree-of-freedom linkages assembled from N links and j hinges or sliding joints are: N = 2, j = 1 : a two-bar linkage that is the lever; N = 4, j = 4 : the four-bar linkage;
- Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints.
- The degree of freedom of a kinematic chain is computed from the number of links and the number and type of joints using the mobility formula.
- Mechanisms and robots are examples of kinematic chains.

its follower is a higher pair called a cam joint.

Examples The planar one degree-of-freedom linkages assembled from N links and j hinges or sliding joints are: N = 2, j = 1 : a two-bar linkage that is the lever; N = 4, j = 4 : the four-bar linkage;

Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints.

The degree of freedom of a kinematic chain is computed from the number of links and the number and type of joints using the mobility formula.

Mechanisms and robots are examples of kinematic chains.

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:
- (See figure 3.) Since worldlines a cannot go backward, the sum in (11) reduces to just one term.
- (Reneging on our earlier a a a promise,weputbackthesubscriptN hereforemphasis.) Similarly, when we do the integral in (7), we encounter pν(τ )(dqμ/dτ )/(dq0/dτ ), a a a a a a whichwewriteaspμ(τ )pν(τ )/E (τ )(sinceE =m dq a 0 =p0 isjustanothernamefor a a a a a a a dτa a p0).Thus, a (cid:10) pμ(τ )pν(τ ) Tμν(x)= a a a a δ(3)(x(cid:3)−q(cid:3) (τ )) (13) a a E (τ ) a a a The denominator E may seem a bit off to you, but you will soon see that it plays a a necessaryrole.
- For an observer going with the flow so to speak, known as a comoving observer, U0=1, Ui =0, and thus n(x) is just the number density seen by the comoving observer.
- Furthermore, the only thing we have available to construct the
- SinceUi=0andthereisnoother3-vectoravailabletoconstructT0ioutof,T0ivanishes, by rotational invariance.

(See figure 3.) Since worldlines a cannot go backward, the sum in (11) reduces to just one term.

(Reneging on our earlier a a a promise,weputbackthesubscriptN hereforemphasis.) Similarly, when we do the integral in (7), we encounter pν(τ )(dqμ/dτ )/(dq0/dτ ), a a a a a a whichwewriteaspμ(τ )pν(τ )/E (τ )(sinceE =m dq a 0 =p0 isjustanothernamefor a a a a a a a dτa a p0).Thus, a (cid:10) pμ(τ )pν(τ ) Tμν(x)= a a a a δ(3)(x(cid:3)−q(cid:3) (τ )) (13) a a E (τ ) a a a The denominator E may seem a bit off to you, but you will soon see that it plays a a necessaryrole.

For an observer going with the flow so to speak, known as a comoving observer, U0=1, Ui =0, and thus n(x) is just the number density seen by the comoving observer.

Furthermore, the only thing we have available to construct the

SinceUi=0andthereisnoother3-vectoravailabletoconstructT0ioutof,T0ivanishes, by rotational invariance.

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:
- Although position in space and velocity in space are both true vectors (in terms of their properties under rotation), as is angular velocity, angle itself is not a true vector.
- Here θ and θ are, respectively, the initial and final angular positions, ω and ω are, respectively, the i f i f initial and final angular velocities, and α is the constant angular acceleration.
- This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations.
- Point trajectories in body moving in three dimensions Important formulas in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space.
- Position In order to define these formulas, the movement of a component B of a mechanical system is defined by the set of rotations [A(t)] and translations d(t) assembled into the homogeneous transformation [T(t)]=[A(t), d(t)].

Although position in space and velocity in space are both true vectors (in terms of their properties under rotation), as is angular velocity, angle itself is not a true vector.

Here θ and θ are, respectively, the initial and final angular positions, ω and ω are, respectively, the i f i f initial and final angular velocities, and α is the constant angular acceleration.

This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations.

Point trajectories in body moving in three dimensions Important formulas in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space.

Position In order to define these formulas, the movement of a component B of a mechanical system is defined by the set of rotations [A(t)] and translations d(t) assembled into the homogeneous transformation [T(t)]=[A(t), d(t)].

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:
- According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition.
- As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck.
- In 1988, Morris, Thorne and Yurtsever worked out how to convert a wormhole traversing space into one traversing time by accelerating one of its two mouths.[35] According to general relativity, however, it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time "machine".
- Wormholes connect two points in spacetime, which means that they would in principle allow travel in time, as well as in space.
- Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in Image of a simulated traversable which a path through the wormhole can be made where the wormhole that connects the square in traversing path does not pass through a region of exotic front of the physical institutes of matter.

According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition.

As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck.

In 1988, Morris, Thorne and Yurtsever worked out how to convert a wormhole traversing space into one traversing time by accelerating one of its two mouths.[35] According to general relativity, however, it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time "machine".

Wormholes connect two points in spacetime, which means that they would in principle allow travel in time, as well as in space.

Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in Image of a simulated traversable which a path through the wormhole can be made where the wormhole that connects the square in traversing path does not pass through a region of exotic front of the physical institutes of matter.

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:
- Withsix eyes,wecouldhaveprecisestereoscopicvisioninalldirections at once, including straight up.
- Newton’sLaws | 31 ∗ hereindicateshowtheNewtonianorbit (andalsotheEinsteinianorbit,aswewillseein partVI)couldbedetermined.Seeexercise2.
- What he did with ma=GMm/r2 was to compare the moon’s acceleration withtheapple’sacceleration:a R2 =GM =a R2 .Buttowrite moon lunarorbit earth apple radiusofearth GM =a R2 ,hehadtoprovewhatissometimesreferredtoasthefirstof earth apple radiusofearth Newton’stwo“superbtheorems,”namelythatwiththeinversesquarelawthegravitational forceexertedbyasphericalmassdistributionactsasiftheentiremasswereconcentrated inapointatthecenterofthedistribution.(Seeexercise4.)Evenwithhisabilities,Newton hadtostruggleforalmost20years,thelengthofwhichcontributedtothebitterpriority fighthehadwithHookeontheinversesquarelaw,withNewtonclaimingthathehadthe lawalongtimebeforepublication.Youshouldbeabletodoitfasterbyafactorof∼104as anexercise.
- Ahistoricaldigressionontheso-calledNewton’sconstant Wouldn’twebebetteroffwiththetwoeyeswenowhaveplusa thirdthatwouldtelluswhatissneakingupbehind?
- ∗Ontheoldonepoundnote,aportraitofNewtontogetherwithhisorbitsappearsontheback.Amusingly, theartistfeltcompelledtoputthesunatthecenter,ratherthanoneofthefoci,oftheellipse.

Withsix eyes,wecouldhaveprecisestereoscopicvisioninalldirections at once, including straight up.

Newton’sLaws | 31 ∗ hereindicateshowtheNewtonianorbit (andalsotheEinsteinianorbit,aswewillseein partVI)couldbedetermined.Seeexercise2.

What he did with ma=GMm/r2 was to compare the moon’s acceleration withtheapple’sacceleration:a R2 =GM =a R2 .Buttowrite moon lunarorbit earth apple radiusofearth GM =a R2 ,hehadtoprovewhatissometimesreferredtoasthefirstof earth apple radiusofearth Newton’stwo“superbtheorems,”namelythatwiththeinversesquarelawthegravitational forceexertedbyasphericalmassdistributionactsasiftheentiremasswereconcentrated inapointatthecenterofthedistribution.(Seeexercise4.)Evenwithhisabilities,Newton hadtostruggleforalmost20years,thelengthofwhichcontributedtothebitterpriority fighthehadwithHookeontheinversesquarelaw,withNewtonclaimingthathehadthe lawalongtimebeforepublication.Youshouldbeabletodoitfasterbyafactorof∼104as anexercise.

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:
- Hawking gradually lost the use of his hand, and in 2005 he began to control his communication device with movements of his cheek muscles,[319][320][321] with a rate of about one word per minute.[320] With this decline there was a risk of him developing locked-in syndrome, so Hawking worked with Intel researchers on systems that could translate his brain patterns or facial expressions into switch activations.
- After several prototypes did not perform as planned, they settled on an adaptive word predictor made by the London-based startup SwiftKey, which used a system similar to his original technology.
- Hawking had an easier time adapting to the new system, which was further developed after inputting large amounts of Hawking's papers and other written materials and uses predictive software similar to other smartphone keyboards.[178][311][321][322] By 2009, he could no longer drive his wheelchair independently, but the same people who created his new typing mechanics were working on a method to drive his chair using movements made by his chin.
- This proved difficult, since Hawking could not move his neck, and trials showed that while he could indeed drive the chair, the movement was sporadic and jumpy.[311][323] Near the end of his life, Hawking experienced increased breathing difficulties, often resulting in his requiring the usage of a ventilator, and being regularly hospitalised.[178] Hawking continued to travel widely, including trips to Chile, Easter Island, South Africa, Spain (to receive the Fonseca Prize in 2008),[324][325] Canada,[326] and numerous trips to the United States.[327] For practical reasons related to his disability, Hawking in 2008 Hawking increasingly travelled by private jet, and by 2011, that had become his only mode of international travel.[328] Disability outreach Starting in the 1990s, Hawking accepted the mantle of role model for disabled people, lecturing and participating in fundraising activities.[329] At the turn of the century, he and eleven other humanitarians signed the Charter for the Third Millennium on Disability, which called on governments to prevent disability and protect the rights of disabled people.[330][331] In 1999, Hawking was awarded the Julius Edgar Lilienfeld Prize of the American Physical Society.[332] In August 2012, Hawking narrated the "Enlightenment" segment of the 2012 Summer Paralympics opening ceremony in London.[333] In 2013, the biographical documentary film Hawking, in which Hawking himself is featured, was released.[334] In September 2013, he expressed support for the legalisation of assisted suicide for the terminally ill.[335] In August 2014, Hawking accepted the Ice Bucket Challenge to promote ALS/MND awareness and raise contributions for research.
- As he had pneumonia in 2013, he was advised not

Hawking gradually lost the use of his hand, and in 2005 he began to control his communication device with movements of his cheek muscles,[319][320][321] with a rate of about one word per minute.[320] With this decline there was a risk of him developing locked-in syndrome, so Hawking worked with Intel researchers on systems that could translate his brain patterns or facial expressions into switch activations.

After several prototypes did not perform as planned, they settled on an adaptive word predictor made by the London-based startup SwiftKey, which used a system similar to his original technology.

Hawking had an easier time adapting to the new system, which was further developed after inputting large amounts of Hawking's papers and other written materials and uses predictive software similar to other smartphone keyboards.[178][311][321][322] By 2009, he could no longer drive his wheelchair independently, but the same people who created his new typing mechanics were working on a method to drive his chair using movements made by his chin.

This proved difficult, since Hawking could not move his neck, and trials showed that while he could indeed drive the chair, the movement was sporadic and jumpy.[311][323] Near the end of his life, Hawking experienced increased breathing difficulties, often resulting in his requiring the usage of a ventilator, and being regularly hospitalised.[178] Hawking continued to travel widely, including trips to Chile, Easter Island, South Africa, Spain (to receive the Fonseca Prize in 2008),[324][325] Canada,[326] and numerous trips to the United States.[327] For practical reasons related to his disability, Hawking in 2008 Hawking increasingly travelled by private jet, and by 2011, that had become his only mode of international travel.[328] Disability outreach Starting in the 1990s, Hawking accepted the mantle of role model for disabled people, lecturing and participating in fundraising activities.[329] At the turn of the century, he and eleven other humanitarians signed the Charter for the Third Millennium on Disability, which called on governments to prevent disability and protect the rights of disabled people.[330][331] In 1999, Hawking was awarded the Julius Edgar Lilienfeld Prize of the American Physical Society.[332] In August 2012, Hawking narrated the "Enlightenment" segment of the 2012 Summer Paralympics opening ceremony in London.[333] In 2013, the biographical documentary film Hawking, in which Hawking himself is featured, was released.[334] In September 2013, he expressed support for the legalisation of assisted suicide for the terminally ill.[335] In August 2014, Hawking accepted the Ice Bucket Challenge to promote ALS/MND awareness and raise contributions for research.

As he had pneumonia in 2013, he was advised not

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:
- Genes and environment in personality development.
- American Psychologist, 35, 409–420.
- The myth of repressed memory: False memories and accusations of sexual abuse.
- A tremor in the blood: Uses and abuses of the lie detector (2nd ed.).
- Public conceptions of mental illness: Labels, causes, dangerousness and social distance.

Genes and environment in personality development.

The myth of repressed memory: False memories and accusations of sexual abuse.

A tremor in the blood: Uses and abuses of the lie detector (2nd ed.).

Public conceptions of mental illness: Labels, causes, dangerousness and social distance.

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:
- In 4πr thesecondcase, inintegratingoverk0, wehavetospecifywhattodowiththepolesatk0=±|k (cid:3)|.Foradetailedexplanation, seeanybookonmathematicalphysicsorfieldtheory.12Itturnsoutthatthecorrectprocedure is to interpret k2 as −(k0)2+k (cid:3)2+iεsign(k0), with the sign function defined as usual and with ε a positive infinitesimal to be set to 0 after the integral has been done.
- Physically, we keep only the outgoing piece, so that G=f(t−r)/r, with some unknown functionf.
- Therichmanrecognizesthat(25)and(26)aremembersofalargeclassoflinearequationseasilysolved by Fourier analysis.
- In the first case, the integral over d3k can be done without too much difficulty and reproduces the result G(x(cid:3))=− 1 .
- This procedure reproduces the result G=−θ(t)δ(t−r)/(4πr).

In 4πr thesecondcase, inintegratingoverk0, wehavetospecifywhattodowiththepolesatk0=±|k (cid:3)|.Foradetailedexplanation, seeanybookonmathematicalphysicsorfieldtheory.12Itturnsoutthatthecorrectprocedure is to interpret k2 as −(k0)2+k (cid:3)2+iεsign(k0), with the sign function defined as usual and with ε a positive infinitesimal to be set to 0 after the integral has been done.

Physically, we keep only the outgoing piece, so that G=f(t−r)/r, with some unknown functionf.

Therichmanrecognizesthat(25)and(26)aremembersofalargeclassoflinearequationseasilysolved by Fourier analysis.

In the first case, the integral over d3k can be done without too much difficulty and reproduces the result G(x(cid:3))=− 1 .

This procedure reproduces the result G=−θ(t)δ(t−r)/(4πr).

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:
- are, it seems, brought about by quantum theoretical indeterminacy (including radiation effects).
- Accordingly, they are also probabilistic and not in themselves originally selected or adequate, but on them there subsequently operates natural selection which eliminates inappropriate mutations.
- Now we could conceive of a similar process with respect to new ideas and to free-will decisions, and similar things.
- That is to say, a range of possibilities is brought about by a probabilistic and quantum mechanically characterised set of proposals, as it were—of possibilities brought forward by the brain.
- On these there then operates a kind of selective procedure which eliminates those

are, it seems, brought about by quantum theoretical indeterminacy (including radiation effects).

Accordingly, they are also probabilistic and not in themselves originally selected or adequate, but on them there subsequently operates natural selection which eliminates inappropriate mutations.

Now we could conceive of a similar process with respect to new ideas and to free-will decisions, and similar things.

That is to say, a range of possibilities is brought about by a probabilistic and quantum mechanically characterised set of proposals, as it were—of possibilities brought forward by the brain.

On these there then operates a kind of selective procedure which eliminates those

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:
- WormholePhysics QuantumWormholePhysics Summary Wormholes as Time Machines • Let’s have a traversable wormhole with two mouths , A and B.
- If B is accelerated with respect to A, or put near an enormous gravity.
- The latter will be in different ”time” than the first.
- Hence, A and B are not only spatially separated, but also temporally.

WormholePhysics QuantumWormholePhysics Summary Wormholes as Time Machines • Let’s have a traversable wormhole with two mouths , A and B.

If B is accelerated with respect to A, or put near an enormous gravity.

The latter will be in different ”time” than the first.

Hence, A and B are not only spatially separated, but also temporally.

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:
- SpaceandTimeUnified t ∂V ∂V q a x V Figure4 Countingthenumberofparticlesinsidesome3-volume V atsometimet.Here∂V indicatestheboundaryofV.
- Anotherinstructiveexerciseistointegraten0(t,x(cid:3))oversome3-volumeV atsometime (cid:8) t (figure4).Weencounterδ(t −q0(τ )) d3xδ(3)(x(cid:3)−q(cid:3) (τ )),withtheintegralgiving1 a a V a a iftheparticleisinsideV atthattimeand0ifnot.Notethetimedeltafunction“slices”the worldlineandfixesτ tobethatvalueatwhichq0(τ )=t.Thus, a a a (cid:7) (cid:7) (cid:7) (cid:10) dq0 (cid:10) (cid:10) d3xn0(x)= dτ aδ(t−q0(τ ))= dq0δ(t−q0)= 1=N (t) V (a(cid:8)V) a dτ a a a (a(cid:8)V) a a (a(cid:8)V) V givingpreciselythenumberofparticlesinsideV.Youmayfindthisallquiteinvolved,but it is actually just telling you the obvious.
- Furthermore, applying (4), we have d N (t)= (cid:8) (cid:8) (cid:8) dt V d3x d n0(x)=− d3x∂ni =− dS ni(usingthedivergencetheorem):thechange V dt V ∂xi ∂V i inN (t)withtimeisofcoursegivenbyintegratingthenumbercurrentniflowingthrough V thesurfaceelementdS formingthesurface∂V enclosingV.
- i Wewentthroughthenumbercurrentindetailtosaveworklater.Indeed,wecannow write down the relativistic form of the electromagnetic current without further ado by simplyincludingthechargee carriedbytheathparticle: a (cid:7) (cid:10) dqμ Jμ(x)= e dτ a δ(4)(x−q (τ )) (5) a a a a dτ a a Bythesameconsiderationsasabove, weobtaintheconservationoftheelectromagnetic current ∂ Jμ=0 (6) μ Energymomentumtensor Movingonfromthenumberdensity,wecannoweasilystudyenergydensity.Asbefore, consider a bunch of particles sitting in a box.
- As is obvious by now, in nonrelativistic

SpaceandTimeUnified t ∂V ∂V q a x V Figure4 Countingthenumberofparticlesinsidesome3-volume V atsometimet.Here∂V indicatestheboundaryofV.

Anotherinstructiveexerciseistointegraten0(t,x(cid:3))oversome3-volumeV atsometime (cid:8) t (figure4).Weencounterδ(t −q0(τ )) d3xδ(3)(x(cid:3)−q(cid:3) (τ )),withtheintegralgiving1 a a V a a iftheparticleisinsideV atthattimeand0ifnot.Notethetimedeltafunction“slices”the worldlineandfixesτ tobethatvalueatwhichq0(τ )=t.Thus, a a a (cid:7) (cid:7) (cid:7) (cid:10) dq0 (cid:10) (cid:10) d3xn0(x)= dτ aδ(t−q0(τ ))= dq0δ(t−q0)= 1=N (t) V (a(cid:8)V) a dτ a a a (a(cid:8)V) a a (a(cid:8)V) V givingpreciselythenumberofparticlesinsideV.Youmayfindthisallquiteinvolved,but it is actually just telling you the obvious.

Furthermore, applying (4), we have d N (t)= (cid:8) (cid:8) (cid:8) dt V d3x d n0(x)=− d3x∂ni =− dS ni(usingthedivergencetheorem):thechange V dt V ∂xi ∂V i inN (t)withtimeisofcoursegivenbyintegratingthenumbercurrentniflowingthrough V thesurfaceelementdS formingthesurface∂V enclosingV.

i Wewentthroughthenumbercurrentindetailtosaveworklater.Indeed,wecannow write down the relativistic form of the electromagnetic current without further ado by simplyincludingthechargee carriedbytheathparticle: a (cid:7) (cid:10) dqμ Jμ(x)= e dτ a δ(4)(x−q (τ )) (5) a a a a dτ a a Bythesameconsiderationsasabove, weobtaintheconservationoftheelectromagnetic current ∂ Jμ=0 (6) μ Energymomentumtensor Movingonfromthenumberdensity,wecannoweasilystudyenergydensity.Asbefore, consider a bunch of particles sitting in a box.

As is obvious by now, in nonrelativistic

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:
- are then M− = 4πr3ρ , m“ =4πr2ρ“, M+ =M , (20.112) 3 Λ where the vacuum density ρ , shell density ρ“, and the mass M are all constants.
- The mass M is the mass Λ of the bubble perceived by an observer in the empty space outside the bubble.
- Equations (20.102) for the energy per unit mass β± inside (−) and outside (+) the shell, and their average β ̄ , become 1 1 M − 4πr3(ρ ±6πρ“2) M − 4πr3ρ β± = 3 Λ , β ̄ = 3 Λ .

are then M− = 4πr3ρ , m“ =4πr2ρ“, M+ =M , (20.112) 3 Λ where the vacuum density ρ , shell density ρ“, and the mass M are all constants.

The mass M is the mass Λ of the bubble perceived by an observer in the empty space outside the bubble.

Equations (20.102) for the energy per unit mass β± inside (−) and outside (+) the shell, and their average β ̄ , become 1 1 M − 4πr3(ρ ±6πρ“2) M − 4πr3ρ β± = 3 Λ , β ̄ = 3 Λ .

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:
- 54 Fundamentals of General Relativity y x θ φ Figure 2.2 The 2-sphere is a 2-manifold, a topological space that is locally homeomorphic to Euclidean 2-space R2.
- misbehaves at the north and south poles, Figure 2.2.
- At least two charts are requiredtocoverthesurfaceofa2-sphere,asillustratedinthemiddlepanel,whereonechartcoversthenorthpole, theotherthesouthpole.Wherethetwochartsoverlap,thetwosetsofcoordinatesarerelateddifferentiably.Theright panelshowsstandardpolarcoordinatesθ,φonthe2-sphere.Thepolarcoordinatizationfailsatthenorthandsouth poles,wherelinesoflongitudecross,theazimuthalangleφisnotunique,andapersonpassingsmoothlythroughthe polewouldseetheazimuthalanglejumpbyπ.Suchmisbehavingpoints,calledcoordinatesingularities,arehowever innocuous:theycanberemovedbycuttingoutapatcharoundthecoordinatesingularity,andpastingonaseparate chart.
- Generalrelativitypostulates,§2.10.1,thatinalocallyinertialframethefirstderivativesnotonlyofthemetric,butalsoof thetangentaxesthemselves,vanish.SeealsoConceptquestion2.5.
- 2.2.2 Principle of equivalence The weak principle of equivalence states that: “Gravitating mass equals inertial mass.” General relativity satisfies the weak principle of equivalence, but then so also does Newtonian gravity.

54 Fundamentals of General Relativity y x θ φ Figure 2.2 The 2-sphere is a 2-manifold, a topological space that is locally homeomorphic to Euclidean 2-space R2.

misbehaves at the north and south poles, Figure 2.2.

2.2.2 Principle of equivalence The weak principle of equivalence states that: “Gravitating mass equals inertial mass.” General relativity satisfies the weak principle of equivalence, but then so also does Newtonian gravity.

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 mid-to-late 1970s were a period of growing public interest in black holes and the physicists who were studying them.
- Hawking was regularly interviewed for print and television.[121][122] He also received increasing academic recognition of his work.[123] In 1975, he was awarded both the Eddington Medal and the Pius XI Gold Medal,[124] and in 1976 the Dannie Heineman Prize, the Maxwell Medal and Prize, and
- "have an entropy") from gravitational waves and increasing angular momentum from their rotation, which can both reduce its surface area, the total surface area of two merged black holes must increase or remain the same.[104] Around this time, Hawking moved into the study of quantum gravity and quantum mechanics.[105][95] This 0:35 was spurred by a visit to Moscow, in which he talked A simulation of a black hole merger with Yakov Zeldovich and Alexei Starobinsky, whose work showed that, according to the uncertainty principle, rotating black holes emit particles.[106] To Hawking's annoyance, his calculations to prove their work produced findings that contradicted his second law.
- It did, however, support Jacob Bekenstein's 1972 theory that black holes have an entropy proportional to 1:14 the area of the event horizon.[106][107][108] Hawking's law was nonetheless validated in 2025 by analysis of A simulation showing gravitational waves— black hole merger GW250114.[109][110] waves of curved spacetime—forming due to the changing gravitational field around a merger In 1974, Hawking claimed that black holes emit radiation, known today as Hawking radiation, which may continue until they exhaust their energy and evaporate.[111][112][113] Initially, Hawking radiation was controversial.
- Following the publication of further research, by the late 1970s, the discovery was widely accepted as a significant breakthrough in theoretical physics.[114][115][116] Hawking was appointed to the Sherman Fairchild Distinguished Visiting Professorship at the California Institute of Technology (Caltech) in 1974.[117] He worked with a friend on the faculty, Kip Thorne,[118][6] and engaged him in a scientific wager about whether the X-ray source Cygnus X-1 was a black hole.

The mid-to-late 1970s were a period of growing public interest in black holes and the physicists who were studying them.

Hawking was regularly interviewed for print and television.[121][122] He also received increasing academic recognition of his work.[123] In 1975, he was awarded both the Eddington Medal and the Pius XI Gold Medal,[124] and in 1976 the Dannie Heineman Prize, the Maxwell Medal and Prize, and

"have an entropy") from gravitational waves and increasing angular momentum from their rotation, which can both reduce its surface area, the total surface area of two merged black holes must increase or remain the same.[104] Around this time, Hawking moved into the study of quantum gravity and quantum mechanics.[105][95] This 0:35 was spurred by a visit to Moscow, in which he talked A simulation of a black hole merger with Yakov Zeldovich and Alexei Starobinsky, whose work showed that, according to the uncertainty principle, rotating black holes emit particles.[106] To Hawking's annoyance, his calculations to prove their work produced findings that contradicted his second law.

It did, however, support Jacob Bekenstein's 1972 theory that black holes have an entropy proportional to 1:14 the area of the event horizon.[106][107][108] Hawking's law was nonetheless validated in 2025 by analysis of A simulation showing gravitational waves— black hole merger GW250114.[109][110] waves of curved spacetime—forming due to the changing gravitational field around a merger In 1974, Hawking claimed that black holes emit radiation, known today as Hawking radiation, which may continue until they exhaust their energy and evaporate.[111][112][113] Initially, Hawking radiation was controversial.

Following the publication of further research, by the late 1970s, the discovery was widely accepted as a significant breakthrough in theoretical physics.[114][115][116] Hawking was appointed to the Sherman Fairchild Distinguished Visiting Professorship at the California Institute of Technology (Caltech) in 1974.[117] He worked with a friend on the faculty, Kip Thorne,[118][6] and engaged him in a scientific wager about whether the X-ray source Cygnus X-1 was a black hole.

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:
- Minkowski, aware of the fundamental restatement of the theory which he had made, said The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength.
- Causal structure Where v is velocity, x, y, and z are Cartesian coordinates in 3-dimensional space, c is the constant representing the universal speed limit, and t is time, the four-dimensional vector v = (ct, x, y, z) = (ct, r) is classified according to the sign of c2t2 − r2 .
- He was still far from the study of curvilinear coordinates and Riemannian geometry, and the heavy mathematical apparatus entailed.[6] For further historical information see references Galison (1979), Corry (1997) and Walter (1999).
- The Minkowski inner product below appears unnamed when referring to orthogonality (which he calls normality) of certain vectors, and the Minkowski norm squared is referred to as "sum" (a word choice that might be attributable to language translation).
- For these special topics, see the referenced articles, as the presentation below will be principally confined to the mathematical structure (Minkowski metric and from it derived quantities and the Poincaré group as symmetry group of spacetime) following from the invariance of the spacetime interval on the spacetime manifold as consequences of the postulates of special relativity, not to specific application or derivation of the invariance of the spacetime interval.

Minkowski, aware of the fundamental restatement of the theory which he had made, said The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength.

Causal structure Where v is velocity, x, y, and z are Cartesian coordinates in 3-dimensional space, c is the constant representing the universal speed limit, and t is time, the four-dimensional vector v = (ct, x, y, z) = (ct, r) is classified according to the sign of c2t2 − r2 .

He was still far from the study of curvilinear coordinates and Riemannian geometry, and the heavy mathematical apparatus entailed.[6] For further historical information see references Galison (1979), Corry (1997) and Walter (1999).

The Minkowski inner product below appears unnamed when referring to orthogonality (which he calls normality) of certain vectors, and the Minkowski norm squared is referred to as "sum" (a word choice that might be attributable to language translation).

For these special topics, see the referenced articles, as the presentation below will be principally confined to the mathematical structure (Minkowski metric and from it derived quantities and the Poincaré group as symmetry group of spacetime) following from the invariance of the spacetime interval on the spacetime manifold as consequences of the postulates of special relativity, not to specific application or derivation of the invariance of the spacetime interval.

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:
- Retrieved 15 June original (http://www.geocities.com/CapeCanav 2018.
- l.ac.uk/news/180588/stephen-hawking-award Retrieved 11 December 2012.
- Archived (https://web.archiv 2012.
- "Time to unveil Corpus Clock" (http://www.ca www.theguardian.com/world/2009/aug/13/oba mbridgenetwork.co.uk/news/time-to-unveil-cor ma-hawking-medal-freedom) from the original pus-clock/).
- Hawking Science Knighthood" (https://inews.co.uk/news/scienc Museum in San Salvador Central America e/why-professor-stephen-hawking-never-had- Honours the Fortitude of a Great Living a-knighthood/).

Retrieved 15 June original (http://www.geocities.com/CapeCanav 2018.

l.ac.uk/news/180588/stephen-hawking-award Retrieved 11 December 2012.

"Time to unveil Corpus Clock" (http://www.ca www.theguardian.com/world/2009/aug/13/oba mbridgenetwork.co.uk/news/time-to-unveil-cor ma-hawking-medal-freedom) from the original pus-clock/).

Hawking Science Knighthood" (https://inews.co.uk/news/scienc Museum in San Salvador Central America e/why-professor-stephen-hawking-never-had- Honours the Fortitude of a Great Living a-knighthood/).

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:
- Concerningpositionandmomentumoftheparticlesinparticular,thequestioniswhethertheuncertaintieswillcauseproblemsinfirstmeasuring,andlaterrebuilding,aperson’sconfigurationafterit isbrokendowntotheparticlelevel,sincethisprocedureseeminglyencompassesexactmeasurements ofbothpositionandmomentum.
- It would require very complex logistical procedurestoputalldifferentkindsofmoleculesahumanbodyconsistsofreadyathandattheplace of reassembly, apart from the inclination we would undoubtedly have to exclude the teleportation of viralDNA andotherunwantedmolecules,leavingthislevelofteleportationtophysicians.
- Next,ifwetakesafetyasourhighestpriorityinchoosingbetweentheotherthreelevels,thelevel containingtheleastnumberofparticlestobeteleported,i.e.
- Especially in the case that we want to teleport to a planetwhichisuninhabitedbyotherusersofteleporters,thereforehavingtomakeuseofsomedevice beingsentahead,wehavetobecarefulthatthisdevicewillnot,whilecollectingandassemblinglocal electronsandnucleons,accidentallydisassemblesanindigenouslife-form!
- theatomiclevel,ispreferablesincemore simple calculations help to minimize the error level.

It would require very complex logistical procedurestoputalldifferentkindsofmoleculesahumanbodyconsistsofreadyathandattheplace of reassembly, apart from the inclination we would undoubtedly have to exclude the teleportation of viralDNA andotherunwantedmolecules,leavingthislevelofteleportationtophysicians.

Especially in the case that we want to teleport to a planetwhichisuninhabitedbyotherusersofteleporters,thereforehavingtomakeuseofsomedevice beingsentahead,wehavetobecarefulthatthisdevicewillnot,whilecollectingandassemblinglocal electronsandnucleons,accidentallydisassemblesanindigenouslife-form!

theatomiclevel,ispreferablesincemore simple calculations help to minimize the error level.

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:
- LusarclaimsGermansaucertechnology weredevelopedinBreslau,PolandandPrague,Czechoslovakiaandonceachievedanaltitudeof12,400m andaspeedof2000km/hr.
- MISScraftandtheUSAFhiresItekCorp.tobuildahigh-poweredcamerasystemforthecraft.
- LusaralsoclaimsGermanscientistswere workingondirectenergyweaponsandsoundweapons,andalso“flyingsaucers.” LusarclaimsGermanybegandevelopingsaucertechnologyin1941withscientistsSchriever, Habermohl,MietheandItalianengineerBellonzo/Belluzzo.
- LusarclaimedMiethewastakentoWright-PattersonAFBintheUS,whileHabermohlwas allegedlycapturedbyUSSRandmovedtoaSovietdesignbureaueastofMoscow,butCook foundnocorroborationofthis.
- SchrieveralsomadecommentstoWestGermanmediain1950thataflyingmachineheworked onataHeinkelfacilityatMarienehewouldhavechangedthecourseofthewar.

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:
- everywhere, implying Y has a "constant" changing rate on the radial direction.
- Before the advent of coordinate-independent methods, it was necessary to work with vector fields by embedding their respective Euclidean vectors into an atlas.
- Here on the punctured 2-dimensional Euclidean between 1880 and the turn of the 20th century.
- These components can be differentiated, but the derivatives do not transform in a manageable way under changes of coordinates.
- The red Tensor calculus really came to life, however, with the advent vector field Y sends the one-form rdθ to of Albert Einstein's theory of general relativity in 1915.

everywhere, implying Y has a "constant" changing rate on the radial direction.

Before the advent of coordinate-independent methods, it was necessary to work with vector fields by embedding their respective Euclidean vectors into an atlas.

Here on the punctured 2-dimensional Euclidean between 1880 and the turn of the 20th century.

These components can be differentiated, but the derivatives do not transform in a manageable way under changes of coordinates.

The red Tensor calculus really came to life, however, with the advent vector field Y sends the one-form rdθ to of Albert Einstein's theory of general relativity in 1915.

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 this reason, the superoperator is called the Lindbladian superoperator or the Liouvillian superoperator.[3]
- Definition Diagonal form The Lindblad master equation for system's density matrix ρ can be written as[1][3] (eq.2.1) where is the anticommutator.
- are a set of non-negative real coefficients called damping rates.
- The shape of the jump operators describes how the environment acts on the system, and must either be determined from microscopic models of the system-environment dynamics, or phenomenologically modelled.
- If all one recovers the von Neumann equation describing unitary dynamics, which is the quantum analog of the classical Liouville equation.

For this reason, the superoperator is called the Lindbladian superoperator or the Liouvillian superoperator.[3]

Definition Diagonal form The Lindblad master equation for system's density matrix ρ can be written as[1][3] (eq.2.1) where is the anticommutator.

are a set of non-negative real coefficients called damping rates.

The shape of the jump operators describes how the environment acts on the system, and must either be determined from microscopic models of the system-environment dynamics, or phenomenologically modelled.

If all one recovers the von Neumann equation describing unitary dynamics, which is the quantum analog of the classical Liouville equation.

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:
- This is quite surprising since the quantum part of the transferseemstohavehappenendbeforethestatetobetransferredexists.
- Furthermore, teleportation is not merely a simple swapping of quantum states: it does notneedaquantumchanneltobeopenatthetimethetransferiscarriedout.
- Blatt1,2 1Institut fu ̈r Experimentalphysik, Innsbruck, Austria 2Institut fu ̈r Quantenoptik und Quanteninformation, O ̈sterreichische Akademie der Wissenschaften, Austria 3 Theoretical Division T-4, Los Alamos National Laboratory, Los Alamos NM 87545, United States Abstract Theteleportationofanatomicstateaccomplishesthecompletetransfer of information from one particle to another, employing the non-local propertiesofquantummechanics.
- Inaddition to the motivation to demonstrate and to understand quantum physics, teleportation might have also considerable impact on a future quantum computer as it facilitates the scalability of many quantum computer designs [2].
- FollowingcloselytheoriginalproposalofBennettetal.[1],ahighly entangledpairofionsiscreated,acompleteBell-stateprojectivemeasurementinvolvingthesourceionandoneoftheentangledpairiscarriedout, and state reconstruction conditioned on this measurement is performed on the other half of the entangled pair.

This is quite surprising since the quantum part of the transferseemstohavehappenendbeforethestatetobetransferredexists.

Furthermore, teleportation is not merely a simple swapping of quantum states: it does notneedaquantumchanneltobeopenatthetimethetransferiscarriedout.

Blatt1,2 1Institut fu ̈r Experimentalphysik, Innsbruck, Austria 2Institut fu ̈r Quantenoptik und Quanteninformation, O ̈sterreichische Akademie der Wissenschaften, Austria 3 Theoretical Division T-4, Los Alamos National Laboratory, Los Alamos NM 87545, United States Abstract Theteleportationofanatomicstateaccomplishesthecompletetransfer of information from one particle to another, employing the non-local propertiesofquantummechanics.

Inaddition to the motivation to demonstrate and to understand quantum physics, teleportation might have also considerable impact on a future quantum computer as it facilitates the scalability of many quantum computer designs [2].

FollowingcloselytheoriginalproposalofBennettetal.[1],ahighly entangledpairofionsiscreated,acompleteBell-stateprojectivemeasurementinvolvingthesourceionandoneoftheentangledpairiscarriedout, and state reconstruction conditioned on this measurement is performed on the other half of the entangled pair.

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:
- Thus, in this theory electrons are quite clearly particles.
- excluded the possibility that any extension of quantum theory (not necessarily in the form of local hidden variables) can help predict the outcomes of any measurement on any quantum state.
- In this sense, we show the following: under the assumption that measurement settings can be chosen freely, quantum theory really is complete".
- theorem, any deterministic hidden-variable theory that is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster-than-light relations (correlations) between physically separated entities.
- an electron, and a hidden 'guiding wave' that governs its motion.

Thus, in this theory electrons are quite clearly particles.

excluded the possibility that any extension of quantum theory (not necessarily in the form of local hidden variables) can help predict the outcomes of any measurement on any quantum state.

In this sense, we show the following: under the assumption that measurement settings can be chosen freely, quantum theory really is complete".

theorem, any deterministic hidden-variable theory that is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster-than-light relations (correlations) between physically separated entities.

an electron, and a hidden 'guiding wave' that governs its motion.

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 following is a positive matrix in : The image of this matrix under is which is clearly not positive, having determinant −1.
- Moreover, the eigenvalues of this matrix are 1,1,1 and −1.
- Given the algebras and of complex-valued continuous functions on compact Hausdorff spaces , every positive map is completely positive.
- See also Choi's theorem on completely positive maps References 1.
- Davidson: C*-Algebras by Example, American Mathematical Society (1996), ISBN 0-82180599-1, Thm.

The following is a positive matrix in : The image of this matrix under is which is clearly not positive, having determinant −1.

Moreover, the eigenvalues of this matrix are 1,1,1 and −1.

Given the algebras and of complex-valued continuous functions on compact Hausdorff spaces , every positive map is completely positive.

See also Choi's theorem on completely positive maps References 1.

Davidson: C*-Algebras by Example, American Mathematical Society (1996), ISBN 0-82180599-1, Thm.

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:
- As seen in equation (2.3) κ and κ are simply related to the two principal radii of curvature ρ and ρ 1 2 1 2 (defined to be the eigenvalues of Ki) of the two-dimensional spacelike hypersurface ∂Ω (see Figure 3).
- It j should be noted that a convex surface has positive radii of curvature, while a concave surface has negative radii of curvature.
- Approved for public release; distribution unlimited.

As seen in equation (2.3) κ and κ are simply related to the two principal radii of curvature ρ and ρ 1 2 1 2 (defined to be the eigenvalues of Ki) of the two-dimensional spacelike hypersurface ∂Ω (see Figure 3).

It j should be noted that a convex surface has positive radii of curvature, while a concave surface has negative radii of curvature.

Approved for public release; distribution unlimited.

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:
- 9.2 Oblate spheroidal coordinates Boyer-Lindquistcoordinatesr,θ,φareoblate spheroidalcoordinates(notpolarcoordinates).Corresponding Cartesian coordinates are x = Rsinθcosφ , y = Rsinθsinφ , (9.7) z = rcosθ .
- In the locally inertial frame defined by the Boyer-Lindquist tetrad, the energy-momentum tensor (which is non-vanishing for charged Kerr-Newman) and the Weyl tensor are both diagonal.
- Surfaces of constant r are confocal oblate spheroids, satisfying x2+y2 z2 + =1 .
- For positive a, the black hole rotates right-handedly about its polar axis θ =0.
- The Boyer-Lindquist coordinates and tetrad are carefully chosen to exhibit the symmetries of the geometry.

9.2 Oblate spheroidal coordinates Boyer-Lindquistcoordinatesr,θ,φareoblate spheroidalcoordinates(notpolarcoordinates).Corresponding Cartesian coordinates are x = Rsinθcosφ , y = Rsinθsinφ , (9.7) z = rcosθ .

In the locally inertial frame defined by the Boyer-Lindquist tetrad, the energy-momentum tensor (which is non-vanishing for charged Kerr-Newman) and the Weyl tensor are both diagonal.

Surfaces of constant r are confocal oblate spheroids, satisfying x2+y2 z2 + =1 .

For positive a, the black hole rotates right-handedly about its polar axis θ =0.

The Boyer-Lindquist coordinates and tetrad are carefully chosen to exhibit the symmetries of the geometry.

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:
- Quaoar is named after a Tongva god).
- There are a few exceptions which continue the Roman and Greek scheme, notably including Eris as it had initially been considered a tenth planet.[250][251] The moons (including the planetary-mass ones) are generally given names with some association with their parent planet.
- Most of the trans-Neptunian objects are named after gods and goddesses from other cultures (e.g.
- (The lettering starts at b, with a considered to represent the parent star.)[254] Symbols The written symbols for Most common planetary symbols Mercury, Venus, Jupiter, Saturn, Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune and possibly Mars have been or traced to forms found in late Greek papyrus texts.[255] The symbols for Jupiter and Saturn are identified as monograms of the corresponding Greek names, and the symbol for Mercury is a stylized caduceus.[255] According to Annie Scott Dill Maunder, antecedents of the planetary symbols were used in art to represent the gods associated with the classical planets.
- Mercury has a caduceus; Venus has, attached to her necklace, a cord connected to another necklace; Mars, a

There are a few exceptions which continue the Roman and Greek scheme, notably including Eris as it had initially been considered a tenth planet.[250][251] The moons (including the planetary-mass ones) are generally given names with some association with their parent planet.

Most of the trans-Neptunian objects are named after gods and goddesses from other cultures (e.g.

(The lettering starts at b, with a considered to represent the parent star.)[254] Symbols The written symbols for Most common planetary symbols Mercury, Venus, Jupiter, Saturn, Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune and possibly Mars have been or traced to forms found in late Greek papyrus texts.[255] The symbols for Jupiter and Saturn are identified as monograms of the corresponding Greek names, and the symbol for Mercury is a stylized caduceus.[255] According to Annie Scott Dill Maunder, antecedents of the planetary symbols were used in art to represent the gods associated with the classical planets.

Mercury has a caduceus; Venus has, attached to her necklace, a cord connected to another necklace; Mars, a

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:
- All four regions can be seen in a spacetime diagram that uses Kruskal–Szekeres coordinates (see figure).[9] In this spacetime, it is possible to come up with coordinate systems such that if one picks a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole.[9] Depending on where the space-like hypersurface is chosen, the EinsteinRosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region).
- When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region.[10] But because the equations of general relativity are time-reversible – they exhibit Time reversal symmetry – general relativity must also allow the timereverse of this type of "realistic" black hole that forms from collapsing matter.
- Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric.
- The time-reversed case would be a white hole that has existed since the beginning of the universe, and that emits matter until it finally "explodes" and disappears.[11] Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation; they could exist only if they were built into the initial conditions of the Big Bang.[11] Additionally, it is predicted that such a white hole would be highly
- one), and likewise particles from the interior white-hole region can escape into either universe.

All four regions can be seen in a spacetime diagram that uses Kruskal–Szekeres coordinates (see figure).[9] In this spacetime, it is possible to come up with coordinate systems such that if one picks a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole.[9] Depending on where the space-like hypersurface is chosen, the EinsteinRosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region).

When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region.[10] But because the equations of general relativity are time-reversible – they exhibit Time reversal symmetry – general relativity must also allow the timereverse of this type of "realistic" black hole that forms from collapsing matter.

Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric.

The time-reversed case would be a white hole that has existed since the beginning of the universe, and that emits matter until it finally "explodes" and disappears.[11] Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation; they could exist only if they were built into the initial conditions of the Big Bang.[11] Additionally, it is predicted that such a white hole would be highly

one), and likewise particles from the interior white-hole region can escape into either 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:
- This is what we would expect if the dust particles are in fact rotating about one another.
- The absolute future The null geodesics spiral According to Hawking and Ellis (see monograph cited below), counterclockwise toward an observer on all light rays emitted from an event on the symmetry axis the axis of symmetry.
- This shows them reconverge at a later event on the axis, with the null geodesics from "above".
- spiral inwards in the manner shown above means that when our observer, when looking radially outwards, sees nearby dust particles not at their current locations, but at their earlier locations.
- Cosmological interpretation Following Gödel, we can interpret the dust particles as galaxies, so that the Gödel solution becomes a cosmological model of a rotating universe.

This is what we would expect if the dust particles are in fact rotating about one another.

The absolute future The null geodesics spiral According to Hawking and Ellis (see monograph cited below), counterclockwise toward an observer on all light rays emitted from an event on the symmetry axis the axis of symmetry.

This shows them reconverge at a later event on the axis, with the null geodesics from "above".

spiral inwards in the manner shown above means that when our observer, when looking radially outwards, sees nearby dust particles not at their current locations, but at their earlier locations.

Cosmological interpretation Following Gödel, we can interpret the dust particles as galaxies, so that the Gödel solution becomes a cosmological model of a rotating 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.