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

EVIDENCE:
- Ben Affleck) informs the nurse administering an eye exam that he can’t read letters because “I just get ’em backward sometimes.” And on a National Public Radio show on dyslexia in 2007, the host stated that the “simplest explanation, I suppose, is that you see things backwards” (National Public Radio, 2007).
- Dyslexia (meaning “difficulty with words”) is a learning disability marked by difficulties in processing | 90 Chapter 4 Teaching Old Dogs New Tricks

Ben Affleck) informs the nurse administering an eye exam that he can’t read letters because “I just get ’em backward sometimes.” And on a National Public Radio show on dyslexia in 2007, the host stated that the “simplest explanation, I suppose, is that you see things backwards” (National Public Radio, 2007).

Dyslexia (meaning “difficulty with words”) is a learning disability marked by difficulties in processing | 90 Chapter 4 Teaching Old Dogs New Tricks

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:
- these four isotopes, the longest-lived is 226Ra (half-life 1600 years), a decay product of natural uranium.
- Because of its relative longevity, 226Ra is the most common isotope of the element, making up about one part per trillion of the Earth's crust; essentially all natural radium is 226Ra.[30] Thus, radium is found in tiny quantities in the uranium ore uraninite and various other uranium minerals, and in even tinier quantities in thorium minerals.
- One ton of pitchblende typically yields about one seventh of a gram of radium.[31] One kilogram of the Earth's crust contains about 900 picograms of radium, and one liter of sea water contains about 89 femtograms of radium.[32] History Radium was discovered by Marie Skłodowska-Curie and her husband Pierre Curie on 21 December 1898 in a uraninite (pitchblende) sample from Jáchymov.[33] While studying the mineral earlier, the Curies removed uranium from it and found that the remaining material was still radioactive.
- In July 1898, while studying pitchblende, they isolated an element similar to bismuth which turned out to be polonium.
- They then isolated a radioactive mixture consisting of two components: compounds of

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.

these four isotopes, the longest-lived is 226Ra (half-life 1600 years), a decay product of natural uranium.

Because of its relative longevity, 226Ra is the most common isotope of the element, making up about one part per trillion of the Earth's crust; essentially all natural radium is 226Ra.[30] Thus, radium is found in tiny quantities in the uranium ore uraninite and various other uranium minerals, and in even tinier quantities in thorium minerals.

One ton of pitchblende typically yields about one seventh of a gram of radium.[31] One kilogram of the Earth's crust contains about 900 picograms of radium, and one liter of sea water contains about 89 femtograms of radium.[32] History Radium was discovered by Marie Skłodowska-Curie and her husband Pierre Curie on 21 December 1898 in a uraninite (pitchblende) sample from Jáchymov.[33] While studying the mineral earlier, the Curies removed uranium from it and found that the remaining material was still radioactive.

In July 1898, while studying pitchblende, they isolated an element similar to bismuth which turned out to be polonium.

They then isolated a radioactive mixture consisting of two components: compounds of

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:
- — Daniela walks into the guest room wearing yoga pants and a tank top and carrying a cup of tea.
- But I’d be wrong.” “Then tell me,” she says.
- “What do you think is happening to you?” “I’m not entirely sure.”
- It’s warm, soothing, faintly sweet.
- I mean, what would you think if someone were saying to you the things you’re saying to me?” “I’d think he was out of his mind.

— Daniela walks into the guest room wearing yoga pants and a tank top and carrying a cup of tea.

But I’d be wrong.” “Then tell me,” she says.

“What do you think is happening to you?” “I’m not entirely sure.”

I mean, what would you think if someone were saying to you the things you’re saying to me?” “I’d think he was out of his mind.

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:
- Terminology wormhole, compared to the amount of time it takes to reach point B from point A in the regular spacetime, wormholes are characterized as either short - going from A to B through the ambient space takes longer than going through the wormhole – or long, if the inverse is true (Figure 2.1).
- Inter-universe wormholes are by default short, since going from one universe to another without the aid of the wormhole is impossible – it would take infinite time.
- Figure taken from reference [2].
- It is important to note that an eternal wormhole might only be traversable for a certain amount of time, and a change of traversability does not require a change of topology.
- If an eternal wormhole is traversable for all time, then the wormhole is “eternally traversable”.

Terminology wormhole, compared to the amount of time it takes to reach point B from point A in the regular spacetime, wormholes are characterized as either short - going from A to B through the ambient space takes longer than going through the wormhole – or long, if the inverse is true (Figure 2.1).

Inter-universe wormholes are by default short, since going from one universe to another without the aid of the wormhole is impossible – it would take infinite time.

It is important to note that an eternal wormhole might only be traversable for a certain amount of time, and a change of traversability does not require a change of topology.

If an eternal wormhole is traversable for all time, then the wormhole is “eternally traversable”.

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:
- Suppose that a connection is given in three dimensions, with curvature 2-form and torsion 2form .
- One problem models the growth of vines, focusing on the question of how vines manage to twist around objects.[14] The vine itself is modeled as a pair of elastic filaments twisted around one another.
- In its energy-minimizing state, the vine naturally grows in the shape of a helix.
- Let be the skew-symmetric Levi-Civita tensor, and Then the Bianchi identities (?) The Bianchi identities are imply that and These are the equations satisfied by an equilibrium continuous medium with moment density .[15] Geodesics and the absorption of torsion Suppose that γ(t) is a curve on M.
- Torsion is the ambiguity of classifying connections in terms of their geodesic sprays: Two connections ∇ and ∇′ which have the same affinely parametrized geodesics (i.e., the same geodesic spray) differ only by torsion.[16] More precisely, if X and Y are a pair of tangent vectors at p ∈ M, then let

Suppose that a connection is given in three dimensions, with curvature 2-form and torsion 2form .

One problem models the growth of vines, focusing on the question of how vines manage to twist around objects.[14] The vine itself is modeled as a pair of elastic filaments twisted around one another.

In its energy-minimizing state, the vine naturally grows in the shape of a helix.

Let be the skew-symmetric Levi-Civita tensor, and Then the Bianchi identities (?) The Bianchi identities are imply that and These are the equations satisfied by an equilibrium continuous medium with moment density .[15] Geodesics and the absorption of torsion Suppose that γ(t) is a curve on M.

Torsion is the ambiguity of classifying connections in terms of their geodesic sprays: Two connections ∇ and ∇′ which have the same affinely parametrized geodesics (i.e., the same geodesic spray) differ only by torsion.[16] More precisely, if X and Y are a pair of tangent vectors at p ∈ M, then let

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:
- • Despite the abstractness of this definition.
- It contain a lot of insight of the physics and geometry of a wormhole.
- This definition describes exactly what one pictures a wormhole to ”look like” WormholePhysics QuantumWormholePhysics Summary Definition of a Wormhole • We can start with a mathematical definition of a wormhole, Definition ( Einstein-Rosen Bridge) A compact region of Minkowskian spacetime Ω is homeomorphic to R×Σ.
- Where Σ having non-trivial topology and boundary ∂Σ (cid:39) S2.
- All hyper surfaces Σ are spacelike/ The region Ω is called a Wormhole / Einstein-Rosen Bridge .

• Despite the abstractness of this definition.

It contain a lot of insight of the physics and geometry of a wormhole.

This definition describes exactly what one pictures a wormhole to ”look like” WormholePhysics QuantumWormholePhysics Summary Definition of a Wormhole • We can start with a mathematical definition of a wormhole, Definition ( Einstein-Rosen Bridge) A compact region of Minkowskian spacetime Ω is homeomorphic to R×Σ.

Where Σ having non-trivial topology and boundary ∂Σ (cid:39) S2.

All hyper surfaces Σ are spacelike/ The region Ω is called a Wormhole / Einstein-Rosen Bridge .

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:
- accessible to both laypersons and scientists from different fields.
- Prologue: A Voyage Among the Holes This science fiction narrative takes readers on an imagined expedition to explore black holes, illustrating their mysterious properties and behaviors through the eyes of the spacecraft's captain.
- The Relativity of Space and Time 1.
- Newton : Einstein's theory dismantles Newton’s view that space and time are absolute, proposing that both are relative and interdependent, fundamentally altering the understanding of motion.
- The Speed of Light : The constant speed of light leads to the conclusion that lengths contract and time dilates, revealing the interrelation of space and time.

accessible to both laypersons and scientists from different fields.

Prologue: A Voyage Among the Holes This science fiction narrative takes readers on an imagined expedition to explore black holes, illustrating their mysterious properties and behaviors through the eyes of the spacecraft's captain.

Newton : Einstein's theory dismantles Newton’s view that space and time are absolute, proposing that both are relative and interdependent, fundamentally altering the understanding of motion.

The Speed of Light : The constant speed of light leads to the conclusion that lengths contract and time dilates, revealing the interrelation of space and time.

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:
- Jason4: I followed Daniela from 44 Eleanor St.
- The conversation is much longer, with so many participants I break out in a cold sweat.
- I click No and log in with my username and password.
- Jason28: So which of you did this?
- Is she still in the police station?

Jason4: I followed Daniela from 44 Eleanor St.

The conversation is much longer, with so many participants I break out in a cold sweat.

I click No and log in with my username and password.

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:
- 1 0 The Einstein equations (20.38) applied to the two expressions (20.35c) for G01 yield evolution equations for the time and radial components of the vierbein coefficients β in any tetrad frame, m − dβ 0 =− 1 ( β Rh +4πR2T01) , (20.193a) dx ξ0 1 1 − dβ 1 = 1 ( β Rh +4πR2T01) .
- (20.192b) dx 0 1 In the evolution equation (20.192a) for ξ0, equation (20.172) has been used to convert the conformal radial derivative ∂ to the conformal time derivative ∂ , and thence to −d/dx by equation (20.174).
- 0 0 The defining equations (20.169) for the proper acceleration h and Hubble parameter h yield equations 0 1 for the evolution of the time and radial components of the conformal Killing vector ξm in any tetrad frame, dξ0 − =β −Rh , (20.192a) dx 1 0 dξ1 − =−β +Rh .
- m Self-similarityrequiresthateachfluidhaveanequationofstatewithconstantwandw ,equations(20.162), ⊥ w ≡p/ρ , w ≡p /ρ .
- (20.193b) dx ξ1 0 0 Again, in the evolution equation (20.193a) for β , equation (20.172) has been used to convert the conformal radial derivative ∂ to the conformal time derivative ∂ .

1 0 The Einstein equations (20.38) applied to the two expressions (20.35c) for G01 yield evolution equations for the time and radial components of the vierbein coefficients β in any tetrad frame, m − dβ 0 =− 1 ( β Rh +4πR2T01) , (20.193a) dx ξ0 1 1 − dβ 1 = 1 ( β Rh +4πR2T01) .

(20.192b) dx 0 1 In the evolution equation (20.192a) for ξ0, equation (20.172) has been used to convert the conformal radial derivative ∂ to the conformal time derivative ∂ , and thence to −d/dx by equation (20.174).

0 0 The defining equations (20.169) for the proper acceleration h and Hubble parameter h yield equations 0 1 for the evolution of the time and radial components of the conformal Killing vector ξm in any tetrad frame, dξ0 − =β −Rh , (20.192a) dx 1 0 dξ1 − =−β +Rh .

m Self-similarityrequiresthateachfluidhaveanequationofstatewithconstantwandw ,equations(20.162), ⊥ w ≡p/ρ , w ≡p /ρ .

(20.193b) dx ξ1 0 0 Again, in the evolution equation (20.193a) for β , equation (20.172) has been used to convert the conformal radial derivative ∂ to the conformal time derivative ∂ .

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:
- 428 Action principle for electromagnetism and gravity The combined electromagnetic and charged interaction Lagrangian (16.59) can be written L= π [ d α (*F α ̄ ∧A t ̄)+ *F α ̄ ∧d t A − (d*F −4π *j) α ̄ ∧A t ̄+ *F t ̄∧(dA−F) α ̄ − 1 *F α ̄ ∧F t ̄+ 1*F t ̄∧F α ̄ +4π *j t ̄∧A α ̄ ] .
- The third and fourth terms (*F α ̄ ∧F t ̄− *F t ̄∧F α ̄ )/(8π) go over to (E2+B2)/(8π)d4x in flat space, and comprise the energy density of the electromagnetic field.
- Varying the conventional Hamiltonian (16.85) with respect to A α ̄ , A t ̄, *F α ̄ , and *F t ̄recovers Hamilton’s equations(16.76)and(16.77).Inexecutingthevariation,thetermsinvolvingthevariedderivativesδ(d A )= α α ̄ d δA and δ(d *F )=d δ*F can be integrated by parts.
- Both terms vanish on the equations of motion.
- (16.84) Dropping the total derivative term d α (*F α ̄ ∧A t ̄) from the Lagrangian (16.84), and inserting the rest into the defining equation (16.83) yields the conventional Hamiltonian H = π [ (d*F −4π *j) α ̄ ∧A t ̄− *F t ̄∧(dA−F) α ̄ + 1 *F α ̄ ∧F t ̄− 1*F t ̄∧F α ̄ −4π *j t ̄∧A α ̄ ] .

428 Action principle for electromagnetism and gravity The combined electromagnetic and charged interaction Lagrangian (16.59) can be written L= π [ d α (*F α ̄ ∧A t ̄)+ *F α ̄ ∧d t A − (d*F −4π *j) α ̄ ∧A t ̄+ *F t ̄∧(dA−F) α ̄ − 1 *F α ̄ ∧F t ̄+ 1*F t ̄∧F α ̄ +4π *j t ̄∧A α ̄ ] .

The third and fourth terms (*F α ̄ ∧F t ̄− *F t ̄∧F α ̄ )/(8π) go over to (E2+B2)/(8π)d4x in flat space, and comprise the energy density of the electromagnetic field.

Varying the conventional Hamiltonian (16.85) with respect to A α ̄ , A t ̄, *F α ̄ , and *F t ̄recovers Hamilton’s equations(16.76)and(16.77).Inexecutingthevariation,thetermsinvolvingthevariedderivativesδ(d A )= α α ̄ d δA and δ(d *F )=d δ*F can be integrated by parts.

Both terms vanish on the equations of motion.

(16.84) Dropping the total derivative term d α (*F α ̄ ∧A t ̄) from the Lagrangian (16.84), and inserting the rest into the defining equation (16.83) yields the conventional Hamiltonian H = π [ (d*F −4π *j) α ̄ ∧A t ̄− *F t ̄∧(dA−F) α ̄ + 1 *F α ̄ ∧F t ̄− 1*F t ̄∧F α ̄ −4π *j t ̄∧A α ̄ ] .

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:
- ● https://www.thesun.co.uk/news/4487506/us-navy-is-running-top-secret-programme-to-detect-alie n-spacecraft-under-the-ocean-ufo-expert-claims/ (PUBLICDOMAIN) -26October2017—MusicianTomDeLongesuggestsonapodcastheisbeing advisedbyUSAFMaj.Gen.NeilMcCasland,USAFMaj.Gen.MichaelCarey,LockheedMartinSkunk WorksEVPRobWeiss,HillaryClintoncampaignmanagerJohnPodesta,Dr.HalPuthoff,formerDeputy AssistantSecretaryofDefenseforIntelligenceChristopherK.MellonandformerOUSD(I)employeeand AATIPheadLuisElizondo,amongothersunnamed,tocarryoutslowdisclosureofUAPinformationto theAmericanpublicfromUSG/USGcontractorsources.
- (PUBLICDOMAIN) -19September2017—AstronomerMarcD’AntonioandoperatorofFXModels thathasNavalcontracts,claimstheUSNavyisrunningasecretUSOprojectknownasthe“FastMover Program.” D’AntoniostatesheaskedaseniorNavalfigureabouttheprogramandtheytoldhim“Sorry Marc,Ican’ttalkaboutthatprogram.” ThispersonthentoldhimtheprogramexistsandthatUSOsare commonbutdidn’tgetintoanymoredetails.
- ● https://media.defense.gov/2019/May/23/2002135778/-1/-1/0/WF_0067_HANS_JEFFERSON_W EHRLE MOVEMENT AND %20MANEUVER IN DEEP%20SPACE A FRAMEWORK T O_LEVERAGE_ADVANCED_PROPULSION.PDF Note:TheLockheedPZTexperimentsweredoneattheunclassifiedlevelalmost20years beforethisframeworkwaspublished.
- DeLongeclaimsUSG/USGcontractorsalreadyhavefreeenergytechnology,i.e.zero-point energy,thatwouldmakeallotherformsofenergyderivationobsolete.
- ● https://forgottenlanguages-full.forgottenlanguages.org/2017/12/axis-from-lightning-bugs-to-milor bs.html (PUBLICDOMAIN) -April2017—USAFMaj.BrainHans,Maj.ChristopherJeffersonandMaj.

● https://media.defense.gov/2019/May/23/2002135778/-1/-1/0/WF_0067_HANS_JEFFERSON_W EHRLE MOVEMENT AND %20MANEUVER IN DEEP%20SPACE A FRAMEWORK T O_LEVERAGE_ADVANCED_PROPULSION.PDF Note:TheLockheedPZTexperimentsweredoneattheunclassifiedlevelalmost20years beforethisframeworkwaspublished.

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:
- "Matter-to-Life" (https://sloan.org/programs/research/matter-to-life).
- "Confronting risks of mirror life" (https://www.scie nce.org/doi/10.1126/science.ads9158).
- unesco.org/ark:/48223/pf0000395064) (Programme and meeting document).
- "Paris Conference on Risks from Mirror Life" (https://www.parismirrorlife.org/).
- "Mirror life" (https://www.gov.uk/government/publications/mirror-life/mirror-life).

"Confronting risks of mirror life" (https://www.scie nce.org/doi/10.1126/science.ads9158).

unesco.org/ark:/48223/pf0000395064) (Programme and meeting document).

"Paris Conference on Risks from Mirror Life" (https://www.parismirrorlife.org/).

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:
- past (however, the particles or other objects experience only a finite proper time between crossing the horizon and passing the outside observer).
- The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward, which will eventually reach the black hole interior region can also pass the observer at any time.
- Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions.
- This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other

past (however, the particles or other objects experience only a finite proper time between crossing the horizon and passing the outside observer).

The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward, which will eventually reach the black hole interior region can also pass the observer at any time.

Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions.

This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other

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:
- described her as Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all.[70] Noether showed a devotion to her subject and her students that extended beyond the academic day.
- Once, when the building was closed for a state holiday, she gathered the class on the steps outside, led them through the woods, and lectured at a local coffee house.[111] Later, after Nazi Germany dismissed her from teaching, she invited students into her home to discuss their plans for the future and mathematical concepts.[112] Influential lectures Noether's frugal lifestyle was at first due to her being denied pay for her work.
- Even after the university began paying her a small salary in 1923, she continued to live a simple and modest life.
- She was paid more generously later in her life, but saved half of her salary to bequeath to her nephew, Gottfried E.

described her as Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all.[70] Noether showed a devotion to her subject and her students that extended beyond the academic day.

Once, when the building was closed for a state holiday, she gathered the class on the steps outside, led them through the woods, and lectured at a local coffee house.[111] Later, after Nazi Germany dismissed her from teaching, she invited students into her home to discuss their plans for the future and mathematical concepts.[112] Influential lectures Noether's frugal lifestyle was at first due to her being denied pay for her work.

Even after the university began paying her a small salary in 1923, she continued to live a simple and modest life.

She was paid more generously later in her life, but saved half of her salary to bequeath to her nephew, Gottfried E.

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:
- "Suppose Alice and Bob wish to exchange keys, and Darth is the adversary." 27.
- Algorithmic Aspects of Wireless Sensor Networks.
- "Mallet maintains the illusion that Alice and Bob are talking to each other rather than to him by intercepting the messages and retransmitting them." 24.
- Schneier, Bruce (September 23, 2010), "Who are Alice & Bob?" (https://www.youtube.com/watch?
- Applied Cryptography: Protocols, Algorithms, and Source Code in C.

"Suppose Alice and Bob wish to exchange keys, and Darth is the adversary." 27.

Algorithmic Aspects of Wireless Sensor Networks.

"Mallet maintains the illusion that Alice and Bob are talking to each other rather than to him by intercepting the messages and retransmitting them." 24.

Schneier, Bruce (September 23, 2010), "Who are Alice & Bob?" (https://www.youtube.com/watch?

Applied Cryptography: Protocols, Algorithms, and Source Code in C.

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:
- (2.117) κλμν κνλμ κμνλ Actually, as shown in Exercise 11.6, the third, symmetric, symmetry is a consequence of the fourth, cyclic symmetry.
- The Ricci tensor, the compressive part of the Riemann tensor, is R ≡gλνR a coordinate tensor .
- The final, cyclic symmetry of the Riemann tensor, equation (2.117), which can be abbreviated R =0 , (2.120) κ[λμν] removes 1 further degree of freedom.
- If you prefer, you can add back the products of connection coefficients in equation (2.112), and check that the claimed symmetries remain.
- 2.20 Ricci tensor, Ricci scalar The Ricci tensor R and Ricci scalar R are the essentially unique contractions of the Riemann curvature κμ tensor.

(2.117) κλμν κνλμ κμνλ Actually, as shown in Exercise 11.6, the third, symmetric, symmetry is a consequence of the fourth, cyclic symmetry.

The Ricci tensor, the compressive part of the Riemann tensor, is R ≡gλνR a coordinate tensor .

The final, cyclic symmetry of the Riemann tensor, equation (2.117), which can be abbreviated R =0 , (2.120) κ[λμν] removes 1 further degree of freedom.

If you prefer, you can add back the products of connection coefficients in equation (2.112), and check that the claimed symmetries remain.

2.20 Ricci tensor, Ricci scalar The Ricci tensor R and Ricci scalar R are the essentially unique contractions of the Riemann curvature κμ tensor.

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:
- Spin is not a rotation in real space, as can be seen from the fact that spin 1/2 particles have to be rotated over an angle 4π before coming back to the initial state, which will be shown in the next section.
- One of the main differences between angular momentum and spin isthatwherethevalueoftheangularmomentumofaparticlecanvary,thevaluesofspinofaparticle isconstant.
- WritingthesimultaneouseigenstatesofthespinoperatorsS2andS as|s,m(cid:105), (II.26)and(II.27) z can be used again, where L2 and L are replaced by S2 and S , respectively, and l by s.
- , (II.26) 2 2 L |l,m(cid:105) = (cid:126)m|l,m(cid:105) with m = −l, −l + 1, ...
- II.4.3 SPIN Thecommutationrelations(II.5)yieldforthecomponentsoftheangularmomentumL(cid:126) = (cid:126)q×p(cid:126) ofasystemin3-dimensionalspace L = −i(cid:126)(cid:178) q ∂ .

Bennett
Dirac
Zeilinger
Jian-Wei Pan
De Martini
Feynman
Popper

Spin is not a rotation in real space, as can be seen from the fact that spin 1/2 particles have to be rotated over an angle 4π before coming back to the initial state, which will be shown in the next section.

One of the main differences between angular momentum and spin isthatwherethevalueoftheangularmomentumofaparticlecanvary,thevaluesofspinofaparticle isconstant.

WritingthesimultaneouseigenstatesofthespinoperatorsS2andS as|s,m(cid:105), (II.26)and(II.27) z can be used again, where L2 and L are replaced by S2 and S , respectively, and l by s.

II.4.3 SPIN Thecommutationrelations(II.5)yieldforthecomponentsoftheangularmomentumL(cid:126) = (cid:126)q×p(cid:126) ofasystemin3-dimensionalspace L = −i(cid:126)(cid:178) q ∂ .

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:
- Chicago: The University of Chicago Press.
- doi:10.1007/s10714-009-0856-0 (https://doi.or g/10.1007%2Fs10714-009-0856-0).
- General Relativity (https://archive.org/details/generalrelativit0000wald).
- S2CID 361088 (https://api.semanticscholar.org/CorpusI D:361088).
- General Relativity and Gravitation.

Chicago: The University of Chicago Press.

S2CID 361088 (https://api.semanticscholar.org/CorpusI D:361088).

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:
- blame others for them, offer a warm and nurturing environment for our children, eat in moderation and exercise regularly, and rely on friends and other sources of social support when we’re feeling down.
- By and large, these are wise tidbits of advice, even if our grandmothers knew about them.
- The problem is that the popular psychology industry often intersperses such advice with suggestions that fly in the face of scientific evidence | Introduction 3

blame others for them, offer a warm and nurturing environment for our children, eat in moderation and exercise regularly, and rely on friends and other sources of social support when we’re feeling down.

By and large, these are wise tidbits of advice, even if our grandmothers knew about them.

The problem is that the popular psychology industry often intersperses such advice with suggestions that fly in the face of scientific evidence | Introduction 3

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- Answer:Astrophysicists realized that black holes are not just end states of massive stars but complex objects that can interact with their surroundings and influence cosmic phenomena, like the generation of gravitational waves and the acceleration of cosmic jets.
- This marked a shift in research focus to include understanding the energetic processes around them.
- Answer:Chandrasekhar returned to black hole research after a long hiatus, driven by his early confrontations with the skepticism of the astrophysical community.
- 4.Question What role did Chandrasekhar play in advancing the understanding of black holes?
- How did the dynamics of black holes change from the perspective of astrophysics during the golden age?

Answer:Astrophysicists realized that black holes are not just end states of massive stars but complex objects that can interact with their surroundings and influence cosmic phenomena, like the generation of gravitational waves and the acceleration of cosmic jets.

This marked a shift in research focus to include understanding the energetic processes around them.

Answer:Chandrasekhar returned to black hole research after a long hiatus, driven by his early confrontations with the skepticism of the astrophysical community.

4.Question What role did Chandrasekhar play in advancing the understanding of black holes?

How did the dynamics of black holes change from the perspective of astrophysics during the golden age?

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 frequency and wavelength of the gamma rays indicate that each carries 511 keV of energy (that is, the rest mass of an electron multiplied by c 2).
- If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter A video showing how scientists used There are some 500 terrestrial gamma and antimatter regions would the Fermi Gamma ray Space ray flashes daily.
- They may similarly be produced in regions like the center of the Milky Way and other galaxies, where very energetic celestial events occur (principally the interaction of relativistic jets with the interstellar medium).
- identical masses and decay lifetimes (if unstable).
- The thunderstorms blue areas indicate where potential Antiparticles are created lightning can occur for terrestrial everywhere in the universe gamma ray flashes.

The frequency and wavelength of the gamma rays indicate that each carries 511 keV of energy (that is, the rest mass of an electron multiplied by c 2).

If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter A video showing how scientists used There are some 500 terrestrial gamma and antimatter regions would the Fermi Gamma ray Space ray flashes daily.

They may similarly be produced in regions like the center of the Milky Way and other galaxies, where very energetic celestial events occur (principally the interaction of relativistic jets with the interstellar medium).

identical masses and decay lifetimes (if unstable).

The thunderstorms blue areas indicate where potential Antiparticles are created lightning can occur for terrestrial everywhere in the universe gamma ray flashes.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- The faintest red dwarfs in the cluster are absolute magnitude 15, while a 17th absolute magnitude white dwarf has been discovered.[189][190] Classification The current stellar classification system originated in the Surface temperature ranges for early 20th century, when stars were classified from A to Q different stellar classes[191] based on the strength of the hydrogen line.[192] It was Class Temperature Sample star thought that the hydrogen line strength was a simple linear function of temperature.
- Instead, it was more O 33,000 K or more Zeta Ophiuchi complicated: it strengthened with increasing temperature, B 10,500–30,000 K Rigel peaked near 9000 K, and then declined at greater A 7,500–10,000 K Altair temperatures.
- The main classifications in order of decreasing surface temperature are: O, B, A, F, G, K, and M.
- 1 15 2 48 The Sun has an apparent magnitude of −26.7, but its absolute magnitude is only +4.83.
- Sirius, the brightest star in the night sky as seen from Earth, is 3 171 approximately 23 times more luminous than the Sun, while Canopus, the 4 513 second brightest star in the night sky with an absolute magnitude of −5.53, 5 1,602 is approximately 14,000 times more luminous than the Sun.

The faintest red dwarfs in the cluster are absolute magnitude 15, while a 17th absolute magnitude white dwarf has been discovered.[189][190] Classification The current stellar classification system originated in the Surface temperature ranges for early 20th century, when stars were classified from A to Q different stellar classes[191] based on the strength of the hydrogen line.[192] It was Class Temperature Sample star thought that the hydrogen line strength was a simple linear function of temperature.

Instead, it was more O 33,000 K or more Zeta Ophiuchi complicated: it strengthened with increasing temperature, B 10,500–30,000 K Rigel peaked near 9000 K, and then declined at greater A 7,500–10,000 K Altair temperatures.

The main classifications in order of decreasing surface temperature are: O, B, A, F, G, K, and M.

1 15 2 48 The Sun has an apparent magnitude of −26.7, but its absolute magnitude is only +4.83.

Sirius, the brightest star in the night sky as seen from Earth, is 3 171 approximately 23 times more luminous than the Sun, while Canopus, the 4 513 second brightest star in the night sky with an absolute magnitude of −5.53, 5 1,602 is approximately 14,000 times more luminous than the Sun.

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:
- of the Stark effect under high field strengths helped confirm the correctness of quantum mechanics over the Bohr model.
- The prevailing theory behind this difference lies in the shapes of the orbitals of the electrons, which vary according to the energy state of the electron.
- The Bohr–Sommerfeld quantization conditions lead to questions in modern mathematics.
- Consistent semiclassical quantization condition requires a certain type of structure on the phase space, which places topological limitations on the types of symplectic manifolds which can be quantized.

of the Stark effect under high field strengths helped confirm the correctness of quantum mechanics over the Bohr model.

The prevailing theory behind this difference lies in the shapes of the orbitals of the electrons, which vary according to the energy state of the electron.

The Bohr–Sommerfeld quantization conditions lead to questions in modern mathematics.

Consistent semiclassical quantization condition requires a certain type of structure on the phase space, which places topological limitations on the types of symplectic manifolds which can be quantized.

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:
- This is some crazy hallucination.
- We’re going to lift you onto a gurney now.” I look toward my feet, and the man’s face racks into focus.
- As hands slide under my shoulders, a woman says, “How’d he get out of the box?” A man responds: “No idea.
- He’s staring at me through the face shield of an aluminized hazmat suit with a self-contained breathing apparatus.
- Glancing at the woman behind my head, he says, “One, two, three.” They hoist me onto a gurney and lock padded restraints around my ankles and wrists.

We’re going to lift you onto a gurney now.” I look toward my feet, and the man’s face racks into focus.

As hands slide under my shoulders, a woman says, “How’d he get out of the box?” A man responds: “No idea.

He’s staring at me through the face shield of an aluminized hazmat suit with a self-contained breathing apparatus.

Glancing at the woman behind my head, he says, “One, two, three.” They hoist me onto a gurney and lock padded restraints around my ankles and wrists.

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:
- Curiously, though, he feels that he is floating.3Toanobserverontheground,ourfriendandhislivingroomarehurtlingtoward acrunchingrendezvouswiththeground.Ourfriend,however,isblissfullyunawareofthe impendingdisaster.Sinceheisacceleratingdownwardatthesamerateastheboxandall theobjectscontainedinside,hefeelsthatheisnotmovingdownwardatallrelativetohis surroundings.Aslightspringinhisstepandhefindshimselfdriftingtowardtheceiling.
- He thinks he isfloatingupwardbutinrealityhisdownwardplungeisacceleratingatthesamerateas before.
- Indeed,thisawfullyunethicalAprilFools’jokehasalreadybeentried:weputastronauts insideaboxcalledaspaceshipanddropitoutofthesky.Tobehumane,wegivethebox aforwardmotionsothatassoonastheboxdrops,thegroundwouldhavethegoodsense ofcurvingawaybyjusttherightamount,sotheboxstaysupatthesamealtitude.When you see on TV an astronaut floating in space, with the announcer commenting in the backgroundthattheastronautisinthezero-genvironmentofspace100milesaboveour heads,youofcourseknowbetter,sinceyouarecapableofreadingthisbook.Theastronaut is in a 0.95-g environment, subject to only 5% less gravity than we are.
- But this action is interpreted by the ground observer quite differently: our friend, by stepping on the floor, has at the same time decreased slightly his downward velocity and increased slightly the box’s downward velocity.
- wakes up, he thinks that he is in his living room.

Curiously, though, he feels that he is floating.3Toanobserverontheground,ourfriendandhislivingroomarehurtlingtoward acrunchingrendezvouswiththeground.Ourfriend,however,isblissfullyunawareofthe impendingdisaster.Sinceheisacceleratingdownwardatthesamerateastheboxandall theobjectscontainedinside,hefeelsthatheisnotmovingdownwardatallrelativetohis surroundings.Aslightspringinhisstepandhefindshimselfdriftingtowardtheceiling.

He thinks he isfloatingupwardbutinrealityhisdownwardplungeisacceleratingatthesamerateas before.

Indeed,thisawfullyunethicalAprilFools’jokehasalreadybeentried:weputastronauts insideaboxcalledaspaceshipanddropitoutofthesky.Tobehumane,wegivethebox aforwardmotionsothatassoonastheboxdrops,thegroundwouldhavethegoodsense ofcurvingawaybyjusttherightamount,sotheboxstaysupatthesamealtitude.When you see on TV an astronaut floating in space, with the announcer commenting in the backgroundthattheastronautisinthezero-genvironmentofspace100milesaboveour heads,youofcourseknowbetter,sinceyouarecapableofreadingthisbook.Theastronaut is in a 0.95-g environment, subject to only 5% less gravity than we are.

But this action is interpreted by the ground observer quite differently: our friend, by stepping on the floor, has at the same time decreased slightly his downward velocity and increased slightly the box’s downward velocity.

wakes up, he thinks that he is in his living room.

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:
- neutrinos satisfy a set of Boltzmann equations similar to the unpolarized photon Boltzmann equations (35.45a) but without scattering terms, ( ) ( N ̇ −ikμΘ ) =N ̇ +k κ lm0 N − κ l+1,m0N =G , (35.47) lm lm 2l+1 l−1,m 2l+1 l+1,m lm whereμ≡k^·p^isthecosineoftheanglebetweenthewavevectorkandtheneutrinomomentump.HereG lm are the harmonics (35.41) of the gravitational term G in the Boltzmann equation, the same as for photons.
- Equations(35.47)includenotonlyscalar(m=0)butalsovector(m=±1)andtensor(m=±2)equations.
- The scalar equations are the same as before, equations (33.91).

neutrinos satisfy a set of Boltzmann equations similar to the unpolarized photon Boltzmann equations (35.45a) but without scattering terms, ( ) ( N ̇ −ikμΘ ) =N ̇ +k κ lm0 N − κ l+1,m0N =G , (35.47) lm lm 2l+1 l−1,m 2l+1 l+1,m lm whereμ≡k^·p^isthecosineoftheanglebetweenthewavevectorkandtheneutrinomomentump.HereG lm are the harmonics (35.41) of the gravitational term G in the Boltzmann equation, the same as for photons.

The scalar equations are the same as before, equations (33.91).

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:
- Letusstartbyenvisagingthethinsphericalshellofphotons(a)inaMinkowskispacetime, and (b) in an eternal Schwarzschild spacetime.
- WewillhaveabitmoretosayaboutMinkowskispacetimeinappendix5.
- Notethatthespecific“compacting”functiontan usedtorelateavariable(P orQ, for example)withafiniterangetoavariable(porq,forexample)withaninfiniterangehardly mattersinthepresentcontext.Itisthecausalstructureofspacetimethatweareafter.For Minkowski spacetime, evidently, every timelike worldline will end up at I+ (excepting + onelinethatendsupatI ).Causalrelationshipscannowbedeterminedataglance.For example,iftheobserveratBwantstosendamessagetoanobserveratrestatr =0,the earliestthemessagecouldreachherwouldbeatpointA.Bythesametoken,iftheobserver atBwantstogettor =0,thereisnowayhecouldgettherebeforepointA.
- BlackHolesandtheCausalStructureofSpacetime | 429 i+ r = 0 i+ II i0 IV I i0 V III U i– r = 0 i– Figure7 PenrosediagramoftheSchwarzschildblackhole.
- Thus, we have tojointwodistinctspacetimestogether.

Letusstartbyenvisagingthethinsphericalshellofphotons(a)inaMinkowskispacetime, and (b) in an eternal Schwarzschild spacetime.

Notethatthespecific“compacting”functiontan usedtorelateavariable(P orQ, for example)withafiniterangetoavariable(porq,forexample)withaninfiniterangehardly mattersinthepresentcontext.Itisthecausalstructureofspacetimethatweareafter.For Minkowski spacetime, evidently, every timelike worldline will end up at I+ (excepting + onelinethatendsupatI ).Causalrelationshipscannowbedeterminedataglance.For example,iftheobserveratBwantstosendamessagetoanobserveratrestatr =0,the earliestthemessagecouldreachherwouldbeatpointA.Bythesametoken,iftheobserver atBwantstogettor =0,thereisnowayhecouldgettherebeforepointA.

BlackHolesandtheCausalStructureofSpacetime | 429 i+ r = 0 i+ II i0 IV I i0 V III U i– r = 0 i– Figure7 PenrosediagramoftheSchwarzschildblackhole.

Thus, we have tojointwodistinctspacetimestogether.

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:
- VI.2 To Cosmology as Quickly as Possible Theuniversemadeassimpleaspossible,butnotanysimpler [Ihad]againcommitted,inregardstogravity,somethingwhich putsmeindangerofbeingshutupinaninsaneasylum.
- —Einstein,writingtoPaulEhrenfestonFebruary4,1917 Newtonwasboldenoughtoapplyhismechanicstothecelestialspherewheretheplanets reside.ButtheaudacityofEinstein,thinkingthattheuniversecould1bedescribedbyan equation!Turnedoutthathewasrightandinnodangerofbeingdraggedawaybymenin whitecoats.
- In the preceding chapter, we derived, with scandalously little work, Einstein’s field equation R (x)=0 (1) μν inemptyspacetime.Wefirstdeducedongeneralgrounds,invokingsymmetryconsiderationswithgleefulabandon,whattheactionforEinsteingravitymustbe.Then,instead ofcarefullyvaryingtheactionasdutifulscholarswould,wewingeditlikealazysouthern Californian,andarrivedat(1).Wecouldnowderivethewarpedspacetimearoundamass, astarorablackhole,butIwillpostponethatuntilthenextchapter.
- Inthespiritoftheprecedingchapter,Iwouldliketogetyoutocosmologyasquicklyas possible.

VI.2 To Cosmology as Quickly as Possible Theuniversemadeassimpleaspossible,butnotanysimpler [Ihad]againcommitted,inregardstogravity,somethingwhich putsmeindangerofbeingshutupinaninsaneasylum.

In the preceding chapter, we derived, with scandalously little work, Einstein’s field equation R (x)=0 (1) μν inemptyspacetime.Wefirstdeducedongeneralgrounds,invokingsymmetryconsiderationswithgleefulabandon,whattheactionforEinsteingravitymustbe.Then,instead ofcarefullyvaryingtheactionasdutifulscholarswould,wewingeditlikealazysouthern Californian,andarrivedat(1).Wecouldnowderivethewarpedspacetimearoundamass, astarorablackhole,butIwillpostponethatuntilthenextchapter.

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 boyshowed the mastadgeyourjacket.It smelledit and came here.What do the pictures say,Jackson?' 'They tell a story that began ten thousand years ago.
- It was the only writing in the room.
- S(I;IIthatshelencu; andDanielS,ll!' inuncdiatclywhatitIms.
- Daniel felt the sign, pressed it, and theyjumped with surprise when a secret door opened.
- A boy stood below it, lifting his arms to the light.

'The boyshowed the mastadgeyourjacket.It smelledit and came here.What do the pictures say,Jackson?' 'They tell a story that began ten thousand years ago.

Daniel felt the sign, pressed it, and theyjumped with surprise when a secret door opened.

A boy stood below it, lifting his arms to the light.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- The Spirit of Asilomar and the Future of Biotechnology summit (http s://doi.org/10.25611/X89A-D947) (Report).
- G.; Kay, Michael S.; Lenski, Richard E.; Liu, Chenli; Medzhitov, Ruslan; Nicotra, Matthew L.; Oehm, Sebastian B.; Pannu, Jaspreet; Relman, David A.; Schwille, Petra; Smith, James A.; Suga, Hiroaki; Szostak, Jack W.; Talbot, Nicholas J.; Tiedje, James M.; Venter, J.
- doi:10.1126/science.ads9158 (https://doi.org/10.1126%2Fscience.ads9158).
- "Paris Conference on Risks from Mirror Life" (https://www.parismirrorlife.org/).
- "Confronting risks of mirror life" (https://www.scie nce.org/doi/10.1126/science.ads9158).

The Spirit of Asilomar and the Future of Biotechnology summit (http s://doi.org/10.25611/X89A-D947) (Report).

G.; Kay, Michael S.; Lenski, Richard E.; Liu, Chenli; Medzhitov, Ruslan; Nicotra, Matthew L.; Oehm, Sebastian B.; Pannu, Jaspreet; Relman, David A.; Schwille, Petra; Smith, James A.; Suga, Hiroaki; Szostak, Jack W.; Talbot, Nicholas J.; Tiedje, James M.; Venter, J.

"Paris Conference on Risks from Mirror Life" (https://www.parismirrorlife.org/).

"Confronting risks of mirror life" (https://www.scie nce.org/doi/10.1126/science.ads9158).

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:
- (23.59) It is convenient to call such an orbit circular even if the orbit is at finite inclination (not confined to the equatorial plane) about a rotating black hole, and therefore follows the surface of a spheroid (in BoyerLindquist coordinates).
- 23.10 Circular orbits in the Kerr-Newman geometry For simplicity, this section 23.10 is restricted to Kerr-Newman black holes with zero magnetic charge and cosmological constant, Q =Λ=0 .
- The solutions with L = 0 are those of the freely-falling observers that define the Doran coordinate system, §9.18.
- Solving dP2/dy = 0 yields the condition between y y energy E and angular momentum L √ L2 E =± m2+ .
- The condition P2 = 0 sets the value of the Carter integral K.

(23.59) It is convenient to call such an orbit circular even if the orbit is at finite inclination (not confined to the equatorial plane) about a rotating black hole, and therefore follows the surface of a spheroid (in BoyerLindquist coordinates).

23.10 Circular orbits in the Kerr-Newman geometry For simplicity, this section 23.10 is restricted to Kerr-Newman black holes with zero magnetic charge and cosmological constant, Q =Λ=0 .

The solutions with L = 0 are those of the freely-falling observers that define the Doran coordinate system, §9.18.

Solving dP2/dy = 0 yields the condition between y y energy E and angular momentum L √ L2 E =± m2+ .

The condition P2 = 0 sets the value of the Carter integral K.

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:
- 826 | Index conservation(continued) 424–425,432–433;Kruskal-Szekeres-like,635; momentumtensor,384;current,226,253;energy lightcone,146–147,170–171,427–429,704; (seeenergyconservation);energymomentum(see locallyflat,130,132,278,288,552,557;notation, energymomentumconservation);momentum 62n,117;Painlev ́e-Gullstrand,417;poorchoice (seemomentumconservation);andrelativistic of,590;primedandunprimed,18,38,39f,71– fluiddynamics,233;andsymmetry,150–155 73;pseudo-time,657;relationsbetweendifferent, conservationlaws,155;fromactionprinciple,141; 159;Rindler,446;roleexchangeof,athorizon, andKillingvectors,589;formotionincurved 419;ofspecificpoint,Ferminormalcoordinates, spacetime,310;inNewtonianmechanics,35–37 559;static,634,636,652;time,652;traditional conservedquantities:inNewtonianmechanics,30; “names”of,25;warpedpolar,613e Noether’stheorem,152 coordinates,“crazy,”94e consistencycondition,anddeterminationof coordinatization,ofdeSitterspacetime,634 potential,36 Copernicanprinciple,491 constantlatitude/longitude,circlesof,onsphere,105 corotation/counterrotation:lightrays,461,469; constantvectorfields,covariantderivativeof,331 particles,474 constants,fundamental,12 correlation:angular,cosmicmicrowavebackground constraintsonmetric,403 fluctuations,474;ofquantumfluctuations,447 container:ofantideSitterspacetime,649;rectilinear, cosetmanifolds,590;andclassificationofspaceand infinitesimalvolumeof,80e spacetime,666;grouptheoryofuniverse,644; continuityequation,forcurrentconservation,225 andmaximalsymmetry,625;andspontaneous continuummechanics,notationsofcoordinates,117 symmetrybreaking,593 contractedBianchiidentity,393;derivedfrom cosmiccensorship,479–480 Einstein-Hilbertaction,394 cosmicclock,universe’sambienttemperatureas, contraction:ofindices,46n,345;ofrepeatedindices, 504 58n;ofspacetimeindices,metricfor,719;tensors, cosmiccoincidenceproblem,andcosmological 316 constantparadox,751 contravariantindices,72,315 “cosmicconspiracy,”297 contravariantvectors,183 cosmicdiagram,496,502,503f;flowin,510–512; coordinatedifferentials,312 phaseboundariesin,513–514;stableattractorand coordinateinvariance:general,305–306,672;local, fixedpoints,511f inhigherdimensionaltheories,682 cosmicexpansion.Seeexpandinguniverse coordinatepatches,tocoverentirespace,76 cosmicmicrowavebackground,236e,517;angular coordinatescalars,toformametric,708–709 correlationoffluctuationsof,523f;density coordinatesingularities:comparedtophysical fluctuationsinearlyuniverse,521–522;first singularities,91–92;andEinstein-Rosenbridge, acousticpeak,523–525;fluctuations,effectof 92f;Kerrblackholes,467;Schwarzschildmetric, curvatureon,525–526;temperature,515 365–366 cosmicpotential,508f;BigBanganalyzedwith, coordinatesystems:failureof,76–77;natural,134 508–509 coordinatetransformations:5-dimensional,gauge cosmicrayparticle,lifetimeof,198 transformationsas,673;acceleratedframes, cosmictime,295;andconformaltime,632;and 285;changeofmetricunder,70–71;Christoffel horizonproblem,530 symbols,bybruteforce,329;incurvedspace Cosmicomics(Calvino),554 andcurvedspacetime,317;indifferentialforms, cosmologicalaction:derivationofenergymomentum 597;freedomof,62;Galilean,ofacceleration, conservation,387e;variationof,391 276–277;general,68–71,312,314,318,384;for cosmologicalconstant:for2-branemodel,701;added gravitationalwaves,similaritytoelectromagnetic byEinstein,360;incosmicdiagram,502–503,513; gaugetransformations,564;andindices(upper indeSitterspacetime,456;decaying,756;and andlower),73–74; andJacobian,75; and decelerationofcosmicexpansion,507;deletion Mercatormap,79e;nonlinear,69;aspassive of,Feynmandiagramsfor,756–757;dependence diffeomorphism,398 ofequationofstateparameteron,359;different coordinates:angular,422,426,627;Boyer-Lindquist, spatialcurvature,634;Einstein’sfieldequationin 476;changeof,64–65,641;chooseofappropriate, presenceof,357;andEinstein-Hilbertcurvature 631;comoving,290,298;conceptof,byDescartes, term,754;andenergyconditions,557;essential 48;dimensionless,665;Eddington-Finkelstein, roleplayedby,512;andexpandinguniverse,392; 431; effectofmotionon,160; geometric ininflationarycosmology,534;introductionof, significanceof,68;hyperbolic,661;hyperbolic 356,393;asLagrangemultiplierforvolumeof radial,653–654;internal,675;Kruskal-Szekeres, spacetime,756;massscaleof,700;mysteryof,

826 | Index conservation(continued) 424–425,432–433;Kruskal-Szekeres-like,635; momentumtensor,384;current,226,253;energy lightcone,146–147,170–171,427–429,704; (seeenergyconservation);energymomentum(see locallyflat,130,132,278,288,552,557;notation, energymomentumconservation);momentum 62n,117;Painlev ́e-Gullstrand,417;poorchoice (seemomentumconservation);andrelativistic of,590;primedandunprimed,18,38,39f,71– fluiddynamics,233;andsymmetry,150–155 73;pseudo-time,657;relationsbetweendifferent, conservationlaws,155;fromactionprinciple,141; 159;Rindler,446;roleexchangeof,athorizon, andKillingvectors,589;formotionincurved 419;ofspecificpoint,Ferminormalcoordinates, spacetime,310;inNewtonianmechanics,35–37 559;static,634,636,652;time,652;traditional conservedquantities:inNewtonianmechanics,30; “names”of,25;warpedpolar,613e Noether’stheorem,152 coordinates,“crazy,”94e consistencycondition,anddeterminationof coordinatization,ofdeSitterspacetime,634 potential,36 Copernicanprinciple,491 constantlatitude/longitude,circlesof,onsphere,105 corotation/counterrotation:lightrays,461,469; constantvectorfields,covariantderivativeof,331 particles,474 constants,fundamental,12 correlation:angular,cosmicmicrowavebackground constraintsonmetric,403 fluctuations,474;ofquantumfluctuations,447 container:ofantideSitterspacetime,649;rectilinear, cosetmanifolds,590;andclassificationofspaceand infinitesimalvolumeof,80e spacetime,666;grouptheoryofuniverse,644; continuityequation,forcurrentconservation,225 andmaximalsymmetry,625;andspontaneous continuummechanics,notationsofcoordinates,117 symmetrybreaking,593 contractedBianchiidentity,393;derivedfrom cosmiccensorship,479–480 Einstein-Hilbertaction,394 cosmicclock,universe’sambienttemperatureas, contraction:ofindices,46n,345;ofrepeatedindices, 504 58n;ofspacetimeindices,metricfor,719;tensors, cosmiccoincidenceproblem,andcosmological 316 constantparadox,751 contravariantindices,72,315 “cosmicconspiracy,”297 contravariantvectors,183 cosmicdiagram,496,502,503f;flowin,510–512; coordinatedifferentials,312 phaseboundariesin,513–514;stableattractorand coordinateinvariance:general,305–306,672;local, fixedpoints,511f inhigherdimensionaltheories,682 cosmicexpansion.Seeexpandinguniverse coordinatepatches,tocoverentirespace,76 cosmicmicrowavebackground,236e,517;angular coordinatescalars,toformametric,708–709 correlationoffluctuationsof,523f;density coordinatesingularities:comparedtophysical fluctuationsinearlyuniverse,521–522;first singularities,91–92;andEinstein-Rosenbridge, acousticpeak,523–525;fluctuations,effectof 92f;Kerrblackholes,467;Schwarzschildmetric, curvatureon,525–526;temperature,515 365–366 cosmicpotential,508f;BigBanganalyzedwith, coordinatesystems:failureof,76–77;natural,134 508–509 coordinatetransformations:5-dimensional,gauge cosmicrayparticle,lifetimeof,198 transformationsas,673;acceleratedframes, cosmictime,295;andconformaltime,632;and 285;changeofmetricunder,70–71;Christoffel horizonproblem,530 symbols,bybruteforce,329;incurvedspace Cosmicomics(Calvino),554 andcurvedspacetime,317;indifferentialforms, cosmologicalaction:derivationofenergymomentum 597;freedomof,62;Galilean,ofacceleration, conservation,387e;variationof,391 276–277;general,68–71,312,314,318,384;for cosmologicalconstant:for2-branemodel,701;added gravitationalwaves,similaritytoelectromagnetic byEinstein,360;incosmicdiagram,502–503,513; gaugetransformations,564;andindices(upper indeSitterspacetime,456;decaying,756;and andlower),73–74; andJacobian,75; and decelerationofcosmicexpansion,507;deletion Mercatormap,79e;nonlinear,69;aspassive of,Feynmandiagramsfor,756–757;dependence diffeomorphism,398 ofequationofstateparameteron,359;different coordinates:angular,422,426,627;Boyer-Lindquist, spatialcurvature,634;Einstein’sfieldequationin 476;changeof,64–65,641;chooseofappropriate, presenceof,357;andEinstein-Hilbertcurvature 631;comoving,290,298;conceptof,byDescartes, term,754;andenergyconditions,557;essential 48;dimensionless,665;Eddington-Finkelstein, roleplayedby,512;andexpandinguniverse,392; 431; effectofmotionon,160; geometric ininflationarycosmology,534;introductionof, significanceof,68;hyperbolic,661;hyperbolic 356,393;asLagrangemultiplierforvolumeof radial,653–654;internal,675;Kruskal-Szekeres, spacetime,756;massscaleof,700;mysteryof,

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:
- "Feld und Materie" (https://zenodo.org/record/1424373).
- Other computer-rendered images and animations of traversable wormholes can be seen on this page (http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html) by the creator of the image in the article, and this page (https://web.archive.org/web/20151228145356/https://www.vis.uni-stut tgart.de/~muelleta/MTvis/) has additional renderings.
- Just maybe, a holographic cosmos" (https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologr am.html).
- Black holes and time warps: Einstein's outrageous legacy.
- doi:10.1002/andp.19213701405 (https://doi.org/10.1002%2Fandp.19213701405).

"Feld und Materie" (https://zenodo.org/record/1424373).

Other computer-rendered images and animations of traversable wormholes can be seen on this page (http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html) by the creator of the image in the article, and this page (https://web.archive.org/web/20151228145356/https://www.vis.uni-stut tgart.de/~muelleta/MTvis/) has additional renderings.

Just maybe, a holographic cosmos" (https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologr am.html).

Black holes and time warps: Einstein's outrageous legacy.

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:
- Then what do these guys call the first fundamental form?
- μν μν Thus,wehaveaconstrainedextremizationproblem.
- For each curve, calculateκ .Followingthegreatman,wearesupposedtofindtheextremalvaluesofκ .
- μν Next,differentiatet(cid:3).n(cid:3)=0toobtain(using(14)) dn(cid:3) dt(cid:3) t(cid:3).
- Gauss’s idea was to look at all curves passing through the point P.

Then what do these guys call the first fundamental form?

For each curve, calculateκ .Followingthegreatman,wearesupposedtofindtheextremalvaluesofκ .

μν Next,differentiatet(cid:3).n(cid:3)=0toobtain(using(14)) dn(cid:3) dt(cid:3) t(cid:3).

Gauss’s idea was to look at all curves passing through the point P.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- invariant C and Dynkin index S of U(1) are dimensionful quantities equal to the square of the 2 2 U(1) charge, equations (42.40) and (42.41).
- Representations of Spin(3).ThegroupSpin(3)ofrotationsin3spatialdimensionsisthe simplest irreducible Lie group with non-vanishing commutators.
- Use the Cartan-Weyl-Dynkin approach to find all representations of Spin(3).
- Given that Spin(3) is isomorphic to SU(2), is there any difference between their representations?
- ThegroupSpin(3)has3generators,whichinanorthonormalbasisare 1γγ withindicesaandbdrawn 2 [ab]

invariant C and Dynkin index S of U(1) are dimensionful quantities equal to the square of the 2 2 U(1) charge, equations (42.40) and (42.41).

Representations of Spin(3).ThegroupSpin(3)ofrotationsin3spatialdimensionsisthe simplest irreducible Lie group with non-vanishing commutators.

Use the Cartan-Weyl-Dynkin approach to find all representations of Spin(3).

Given that Spin(3) is isomorphic to SU(2), is there any difference between their representations?

ThegroupSpin(3)has3generators,whichinanorthonormalbasisare 1γγ withindicesaandbdrawn 2 [ab]

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:
- ProvedbyB.Carter,G.F.R.Ellis,S.Hawking,R.Penrose,andmanyothers.Ireferyoutomoreadvanced monographsbysomeoftheseauthors.
- Justtogiveyouaflavorofthiskindoftheorem, letmementionthatonetheoremstatesthat, withthe strongenergycondition,ifametrichasatrappedsurfacefromwhichlightrayscannotescape,theneither asingularityoraclosedtimelikecurveispresent.
- Hereisahandwavingunderstandingofthesolution.SinceA(r)→1−2GMasr→∞,Mrepresentsthetotal r mass,includingtheelectromagneticcontribution.Asrdecreases,byNewton’ssecondsuperbtheorem(see (cid:8) chapterI.1),weshouldsubtractofftheelectromagneticcontribution∼4π ∞ drr21Q2 =2πQ2 anddefine, r 2 r4 r heuristically,aneffectivemassM ̃ (r)∼M−2πQ2 .WethenguessthatA(r)∼1−2GM ̃ =1−2GM +4πGQ2 .
- Rev.D41(1990),p.1796,andD.Marolf,arXiv:1005.2999.PoissonandIsraelfoundaninstabilityassociated withtheinnerhorizonofclose-to-extremalbutstillsubextremalblackholes.Marolf,referringtothisasthe “dangersofextremes,”suggeststhatthemoreremarkablefeaturesoftheinteriorspacetimeofextremal blackholeswouldinfactnotsurviveanyquantumfluctuation.
- ThisiswhyIgiveyouthephysicsfirst,unlikesomeotherauthors.

Hereisahandwavingunderstandingofthesolution.SinceA(r)→1−2GMasr→∞,Mrepresentsthetotal r mass,includingtheelectromagneticcontribution.Asrdecreases,byNewton’ssecondsuperbtheorem(see (cid:8) chapterI.1),weshouldsubtractofftheelectromagneticcontribution∼4π ∞ drr21Q2 =2πQ2 anddefine, r 2 r4 r heuristically,aneffectivemassM ̃ (r)∼M−2πQ2 .WethenguessthatA(r)∼1−2GM ̃ =1−2GM +4πGQ2 .

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 Schwarzschild metric is ds2 =−Δ(r)dt2+ dr2+r2(dθ2+sin2θdφ2) , (7.33) Δ(r) where Δ(r) is the horizon function 2M Δ(r)=1− .
- (7.32) According to equation (7.28), this happens at r =r , which is the Schwarzschild radius, as it should be.
- Geodesics in the Schwarzschild geometry.
- It is striking that the mathematics was known long before physical understanding emerged.
- Unlike Schwarzschild coordinates, there is no singularity at the horizon in Gullstrand-Painlevé coordinates.

The Schwarzschild metric is ds2 =−Δ(r)dt2+ dr2+r2(dθ2+sin2θdφ2) , (7.33) Δ(r) where Δ(r) is the horizon function 2M Δ(r)=1− .

(7.32) According to equation (7.28), this happens at r =r , which is the Schwarzschild radius, as it should be.

Geodesics in the Schwarzschild geometry.

It is striking that the mathematics was known long before physical understanding emerged.

Unlike Schwarzschild coordinates, there is no singularity at the horizon in Gullstrand-Painlevé coordinates.

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:
- At the end of the ramp, I take a brutal left turn through a stop sign —tires squealing, rubber burning.
- Through the bullet-riddled glass, I see the lake straight ahead.
- I say, “Hang on, we’re almost there.” I make a hard right onto Pulaski Drive, and as a trio of bullets peppers the rear passenger door, I cut the lights.
- We tear through the vacated streets of South Chicago.
- As I drive across the overpass, I count five sets of flashing lights on the interstate, the closest SUV now speeding onto the exit ramp with two Humvees in tow.

At the end of the ramp, I take a brutal left turn through a stop sign —tires squealing, rubber burning.

Through the bullet-riddled glass, I see the lake straight ahead.

I say, “Hang on, we’re almost there.” I make a hard right onto Pulaski Drive, and as a trio of bullets peppers the rear passenger door, I cut the lights.

We tear through the vacated streets of South Chicago.

As I drive across the overpass, I count five sets of flashing lights on the interstate, the closest SUV now speeding onto the exit ramp with two Humvees in tow.

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:
- Onthatoccasionwiththeflyinthecar,Iwasridinginthebackseat,andIhadacamera3 with me.
- I have underlined this by (cid:5) writingmexplicitlyin(6)and(8).Thereisnom.Galileanrelativityrequiresthatdifferent observersmeasurethesamemass.
- In his monumental work, Maxwell finally gave a precise elucidation of the mystery of light, revealing it to be an undulating electromagnetic field.
- I took a picture of a friend riding in the front seat next to the driver and the
- SpaceandTimeUnified Evensomeoneasdumbasaflywouldfeeltheadditionalforcemdu(cid:3) asitsmashesintothe dt windshield.Unfortunateaswellasdumb.

I have underlined this by (cid:5) writingmexplicitlyin(6)and(8).Thereisnom.Galileanrelativityrequiresthatdifferent observersmeasurethesamemass.

In his monumental work, Maxwell finally gave a precise elucidation of the mystery of light, revealing it to be an undulating electromagnetic field.

I took a picture of a friend riding in the front seat next to the driver and the

SpaceandTimeUnified Evensomeoneasdumbasaflywouldfeeltheadditionalforcemdu(cid:3) asitsmashesintothe dt windshield.Unfortunateaswellasdumb.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- The Geometry of Special Relativity: The Minkowski Space – Time Light Cone (https://web.archive.
- "§ 6.6 Minkowski space, § 6.7,8 Canonical forms pp 221–242".
- External links Media related to Minkowski diagrams at Wikimedia Commons Animation clip (https://www.youtube.com/watch?v=C2VMO7pcWhg) on YouTube visualizing Minkowski space in the context of special relativity.
- http://www.archive.org/details/opticalgeometryoOOrobbrich.
- Linear Algebra and Group Representations (https://archive.org/details/linearalgebragro0000shaw).

The Geometry of Special Relativity: The Minkowski Space – Time Light Cone (https://web.archive.

"§ 6.6 Minkowski space, § 6.7,8 Canonical forms pp 221–242".

External links Media related to Minkowski diagrams at Wikimedia Commons Animation clip (https://www.youtube.com/watch?v=C2VMO7pcWhg) on YouTube visualizing Minkowski space in the context of special relativity.

Linear Algebra and Group Representations (https://archive.org/details/linearalgebragro0000shaw).

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:
- As another example, if a physical experiment works the same way at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively.[206][207] At the time, physicists were not familiar with Sophus Lie's theory of continuous groups, on which Noether had built.
- I'm impressed that such things can be understood in such a general way.
- Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws.
- Many physicists first learned of Noether's theorem from an article by Edward Lee Hill that presented only a special case of it.
- Consequently, the full scope of her result was not immediately appreciated.[208] During the latter half of the 20th century, Noether's theorem became a fundamental tool of modern theoretical physics, because of the insight it gives into conservation laws, and also as a practical calculation tool.

As another example, if a physical experiment works the same way at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively.[206][207] At the time, physicists were not familiar with Sophus Lie's theory of continuous groups, on which Noether had built.

I'm impressed that such things can be understood in such a general way.

Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws.

Many physicists first learned of Noether's theorem from an article by Edward Lee Hill that presented only a special case of it.

Consequently, the full scope of her result was not immediately appreciated.[208] During the latter half of the 20th century, Noether's theorem became a fundamental tool of modern theoretical physics, because of the insight it gives into conservation laws, and also as a practical calculation tool.

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:
- "Luminous and Variable Stars in M31 and M33.
- Archived from the original (http://cwp.library.ucla.edu/Phase2/Payne-Gapo schkin,_Cecilia_Helena@861234567.html) on 18 March 2005.
- Hubeny, Ivan; Mihalas, Dimitri (2014).
- Gordon, Michael S.; Humphreys, Roberta M.; Jones, Terry J.
- "" Payne-Gaposchkin, Cecilia Helena." CWP" (https://web.archive.org/web/20050318221903/htt p://cwp.library.ucla.edu/Phase2/Payne-Gaposchkin,_Cecilia_Helena@861234567.html).

"Luminous and Variable Stars in M31 and M33.

Archived from the original (http://cwp.library.ucla.edu/Phase2/Payne-Gapo schkin,_Cecilia_Helena@861234567.html) on 18 March 2005.

Gordon, Michael S.; Humphreys, Roberta M.; Jones, Terry J.

"" Payne-Gaposchkin, Cecilia Helena." CWP" (https://web.archive.org/web/20050318221903/htt p://cwp.library.ucla.edu/Phase2/Payne-Gaposchkin,_Cecilia_Helena@861234567.html).

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:
- There is a necessary and sufficient condition for a two-qubit density matrix to violate the CHSH inequality, expressed by the maximum attainable polynomial S defined in Eq.
- We also calculate the acute angle to obtain the bases that maximize Eq.
- 2.[13] This is important in entanglement-based max quantum key distribution, where the secret key rate depends on the degree of measurement correlations.[14] Let us introduce a 3×3 real matrix with elements , where are the Pauli matrices.
- Then, the expected correlation in bases a, b is The numerical values of the basis vectors, when found, can be directly translated to the configuration of the projective measurements.[16] The optimal set of bases for the state is found by taking the two greatest eigenvalues and the corresponding eigenvectors of , and finding the auxiliary unit vectors where is a free parameter.
- The choice of this measurement basis can be parametrized by a real unit vector and the Pauli vector by expressing .

There is a necessary and sufficient condition for a two-qubit density matrix to violate the CHSH inequality, expressed by the maximum attainable polynomial S defined in Eq.

We also calculate the acute angle to obtain the bases that maximize Eq.

2.[13] This is important in entanglement-based max quantum key distribution, where the secret key rate depends on the degree of measurement correlations.[14] Let us introduce a 3×3 real matrix with elements , where are the Pauli matrices.

Then, the expected correlation in bases a, b is The numerical values of the basis vectors, when found, can be directly translated to the configuration of the projective measurements.[16] The optimal set of bases for the state is found by taking the two greatest eigenvalues and the corresponding eigenvectors of , and finding the auxiliary unit vectors where is a free parameter.

The choice of this measurement basis can be parametrized by a real unit vector and the Pauli vector by expressing .

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:
- Negative mass cosmic string The standard model of a cosmic string is a geometrical structure with an angle deficit, which thus is in tension and hence has positive mass.
- It is now calculated that their contribution to the structure formation in the universe is less than 10%.
- During the expansion of the universe, cosmic strings would form a network of loops, and in the past it was thought that their gravity could have been responsible for the original clumping of matter into galactic superclusters.
- A closed cosmic string gravitates in a more conventional way.
- A cosmic string about a kilometer in length may be more massive than the Earth.

Negative mass cosmic string The standard model of a cosmic string is a geometrical structure with an angle deficit, which thus is in tension and hence has positive mass.

It is now calculated that their contribution to the structure formation in the universe is less than 10%.

During the expansion of the universe, cosmic strings would form a network of loops, and in the past it was thought that their gravity could have been responsible for the original clumping of matter into galactic superclusters.

A closed cosmic string gravitates in a more conventional way.

A cosmic string about a kilometer in length may be more massive than the Earth.

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:
- Alice and Bob will use this entangled pair in their strategy as described below.
- 180° (with 180° and 0° being the same state).
- Upon receiving the bit from Charlie, Alice will measure her qubit in the basis or in the basis , conditionally on whether or , respectively.
- 0 1 0 1 0 At what value of y does Bob test for the state?
- The following table shows how the game is played.

Alice and Bob will use this entangled pair in their strategy as described below.

180° (with 180° and 0° being the same state).

Upon receiving the bit from Charlie, Alice will measure her qubit in the basis or in the basis , conditionally on whether or , respectively.

0 1 0 1 0 At what value of y does Bob test for the state?

The following table shows how the game is played.

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:
- internal vertices connected with four edges and represented by dots (here labeled ).
- Every vertex corresponds to a single field factor at the corresponding point in spacetime, while the edges correspond to the propagators between the spacetime points.
- For every internal vertex , write down a factor .
- However, naïve computation of loop diagrams such as the one shown above will result in divergent momentum integrals, which seems to imply that almost all terms in the perturbative expansion are infinite.
- For every edge that connects two vertices and , write down a factor .

internal vertices connected with four edges and represented by dots (here labeled ).

Every vertex corresponds to a single field factor at the corresponding point in spacetime, while the edges correspond to the propagators between the spacetime points.

For every internal vertex , write down a factor .

However, naïve computation of loop diagrams such as the one shown above will result in divergent momentum integrals, which seems to imply that almost all terms in the perturbative expansion are infinite.

For every edge that connects two vertices and , write down a factor .

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 example, if a sphere passed through a sheet of paper, beings in the paper would see first a single point.
- From the perspective of this square, a three-dimensional being has seemingly godlike powers, such as ability to remove objects from a safe without breaking it open (by moving them across the third dimension), to see everything that A net of a tesseract from the two-dimensional perspective is enclosed behind walls, and to remain completely invisible by standing a few inches away in the third dimension.
- A circle gradually grows larger, until it reaches the diameter of the sphere, and then gets smaller again, until it shrinks to a point and disappears.
- Rudy Rucker illustrates this in his novel Spaceland, in which the protagonist encounters four-dimensional beings who demonstrate such powers.
- For example, a hypersphere would appear first as a point, then as a growing sphere (until it reaches the "hyperdiameter" of the hypersphere), with the sphere then shrinking to a single point and then disappearing.[22]

For example, if a sphere passed through a sheet of paper, beings in the paper would see first a single point.

From the perspective of this square, a three-dimensional being has seemingly godlike powers, such as ability to remove objects from a safe without breaking it open (by moving them across the third dimension), to see everything that A net of a tesseract from the two-dimensional perspective is enclosed behind walls, and to remain completely invisible by standing a few inches away in the third dimension.

A circle gradually grows larger, until it reaches the diameter of the sphere, and then gets smaller again, until it shrinks to a point and disappears.

Rudy Rucker illustrates this in his novel Spaceland, in which the protagonist encounters four-dimensional beings who demonstrate such powers.

For example, a hypersphere would appear first as a point, then as a growing sphere (until it reaches the "hyperdiameter" of the hypersphere), with the sphere then shrinking to a single point and then disappearing.[22]

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:
- Ifyoudothis,asIdidwhilewritingthischapter,youwilltrulyunderstandthecounting above.
- †Thisisalsoconfirmedbytheintuitiveexamplein(1)and(2).
- ∼∂∂g..;sincethenumberofcomponentsgrowsquartically withD,wecanevenguessthatitwillcarry4indices.Verynice:thisisallconsistentwith thecurvaturebeingrelatedtoB .
- Tocalculatetheintrinsiccurvature,weneedtoknowonlythemetricg ;wedon’tneed μν toknowtheembeddingfunctionsXA(xμ).WhenthegreatGaussdiscoveredthisfactfor curvedsurfacesin1828, hewassostruckbyitthathecalledittheTheoremaEgregium ∗SinceB μν,λσarenothingbutthesecondorderTaylorcoefficientsinanexpansionofg μνaroundthepointP.
- The great insight of Carl Friedrich Gauss and other pioneers of differential geometry, not to mention the mite professors of geometry, is that given the metric, we should be abletodeterminetheintrinsiccurvaturewithoutworryinghowthesurfaceisembedded, as was already explained in the preceding chapter.

Tocalculatetheintrinsiccurvature,weneedtoknowonlythemetricg ;wedon’tneed μν toknowtheembeddingfunctionsXA(xμ).WhenthegreatGaussdiscoveredthisfactfor curvedsurfacesin1828, hewassostruckbyitthathecalledittheTheoremaEgregium ∗SinceB μν,λσarenothingbutthesecondorderTaylorcoefficientsinanexpansionofg μνaroundthepointP.

The great insight of Carl Friedrich Gauss and other pioneers of differential geometry, not to mention the mite professors of geometry, is that given the metric, we should be abletodeterminetheintrinsiccurvaturewithoutworryinghowthesurfaceisembedded, as was already explained in the preceding chapter.

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:
- Journal of Physics: Conference Series OPEN ACCESS Related content Wormhole Dynamics -Lectures on General Relativity, Cosmology and Quantum Black Holes: General relativity essentials B Ydri To cite this article: Hisa-aki Shinkai and Takashi Torii 2015 J.
- 574 012056 -Can a sub-quantum medium be provided by General Relativity?
- Thomas C Andersen -Wormhole in higher-dimensional spaceView the article online for updates and enhancements.
- time Hisa-aki Shinkai and Takashi Torii Recent citations -Negative tension branes as stable thin shell wormholes Takafumi Kokubu and Tomohiro Harada This content was downloaded from IP address 168.151.137.97 on 28/11/2017 at 17:26

Journal of Physics: Conference Series OPEN ACCESS Related content Wormhole Dynamics -Lectures on General Relativity, Cosmology and Quantum Black Holes: General relativity essentials B Ydri To cite this article: Hisa-aki Shinkai and Takashi Torii 2015 J.

574 012056 -Can a sub-quantum medium be provided by General Relativity?

Thomas C Andersen -Wormhole in higher-dimensional spaceView the article online for updates and enhancements.

time Hisa-aki Shinkai and Takashi Torii Recent citations -Negative tension branes as stable thin shell wormholes Takafumi Kokubu and Tomohiro Harada This content was downloaded from IP address 168.151.137.97 on 28/11/2017 at 17:26

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:
- “Hello?” “Where’s Daniela?” “I think you misdialed.” I recite Daniela’s cell phone number, and he says, “Yeah, that’s the number you called, but it’s my number.” “How is that possible?” He hangs up.
- A wave of exhaustion hits me like a haymaker to the jaw.
- I never actually dial Daniela’s cell-phone number, so it takes me a moment to recall, but I finally punch it in.
- No idea where my mobile phone is, but there’s a landline on the bedside table.
- I need a shave, my eyes are bloodshot, but I’m still me.

“Hello?” “Where’s Daniela?” “I think you misdialed.” I recite Daniela’s cell phone number, and he says, “Yeah, that’s the number you called, but it’s my number.” “How is that possible?” He hangs up.

A wave of exhaustion hits me like a haymaker to the jaw.

I never actually dial Daniela’s cell-phone number, so it takes me a moment to recall, but I finally punch it in.

No idea where my mobile phone is, but there’s a landline on the bedside table.

I need a shave, my eyes are bloodshot, but I’m still me.

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 only other way into the house is through the French doors that lead from the screened-in porch into the living room.
- Daniela and Charlie will be looking to me to tell them what’s next.
- Both of you head to our bedroom, get dressed, start getting our things together.
- As I reach the living room, my thoughts come in a raging stream of consciousness.
- “Yeah.” “What’s happening?” “They found us.” “Who?” “I did.” “How is that possible?” “We have to leave right now.

The only other way into the house is through the French doors that lead from the screened-in porch into the living room.

Daniela and Charlie will be looking to me to tell them what’s next.

Both of you head to our bedroom, get dressed, start getting our things together.

As I reach the living room, my thoughts come in a raging stream of consciousness.

“Yeah.” “What’s happening?” “They found us.” “Who?” “I did.” “How is that possible?” “We have to leave right now.

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:
- ψ ..τ(S −1)ζ η ...(S −1)ψ κ (10) You get the idea before I run out of Greek letters!
- κ ..ω=Sμ ρ Sν σ ...Sω τ T ζ ρ .
- Upper and lowerindicestransformoppositely.
- TensorsinGeneralRelativity | 315 GiventwovectorsW andU,wecanform,inanalogywithordinaryEuclid3-vectorsand Lorentz4-vectors,thedotproductW Uμ=g WνUμ.Inlightoftheprecedingremark, μ μν weexpectW Uμtotransformlikeascalar,thatis,itdoesnottransformatall:indeed, μ W (cid:5) U (cid:5)ρ=W (S −1)μSρUν=W Uμ (9) ρ μ ρ ν μ Asfarasthetransformationpropertiesareconcerned, thesummed-overpairofindices effectivelydisappear.Indeed,wecandefineφ(x)≡W (x)Uμ(x),andittransformslikea μ scalarφ (cid:5) (x (cid:5) )=φ(x).
- Nowthatweknowhowavectorwithalowerindextransforms,wecandefinetensors withlowerindices.Forexample,thetensorT transformsasifitwere(eventhoughitis μνρ not)builtupofthreevectorsW V U .Indeed,wecanclearlydefinetensorswitharbitrary μ ν ρ numbersofupperandlowerindices,transforminglike T (cid:5) η μ .

ψ ..τ(S −1)ζ η ...(S −1)ψ κ (10) You get the idea before I run out of Greek letters!

TensorsinGeneralRelativity | 315 GiventwovectorsW andU,wecanform,inanalogywithordinaryEuclid3-vectorsand Lorentz4-vectors,thedotproductW Uμ=g WνUμ.Inlightoftheprecedingremark, μ μν weexpectW Uμtotransformlikeascalar,thatis,itdoesnottransformatall:indeed, μ W (cid:5) U (cid:5)ρ=W (S −1)μSρUν=W Uμ (9) ρ μ ρ ν μ Asfarasthetransformationpropertiesareconcerned, thesummed-overpairofindices effectivelydisappear.Indeed,wecandefineφ(x)≡W (x)Uμ(x),andittransformslikea μ scalarφ (cid:5) (x (cid:5) )=φ(x).

Nowthatweknowhowavectorwithalowerindextransforms,wecandefinetensors withlowerindices.Forexample,thetensorT transformsasifitwere(eventhoughitis μνρ not)builtupofthreevectorsW V U .Indeed,wecanclearlydefinetensorswitharbitrary μ ν ρ numbersofupperandlowerindices,transforminglike T (cid:5) η μ .

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:
- if spinors satisfy a local gauge symmetry, then the associated gauge field arises as a connection in a gauge-covariant derivative, and must be a Lorentz vector.
- On the other hand, an electroweak Higgs field that acquires a non-zero vacuum expectation value must be a scalar, since otherwise it would impose a preferred spatial direction and rest frame, breaking Lorentz symmetry in contradiction to observation.

if spinors satisfy a local gauge symmetry, then the associated gauge field arises as a connection in a gauge-covariant derivative, and must be a Lorentz vector.

On the other hand, an electroweak Higgs field that acquires a non-zero vacuum expectation value must be a scalar, since otherwise it would impose a preferred spatial direction and rest frame, breaking Lorentz symmetry in contradiction to observation.

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

Anything not in evidence is unknown; retrieve more.

Derivations, tests, or experiments implied by evidence.


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

EVIDENCE:
- "The Maya Long Count Calendar: An Introduction".
- Archived (https://web.archive.org/web/20160802075828/http://www.
- Archived (https://web.archive.org/web/20 250308214916/https://www.britannica.com/science/French-republican-calendar) from the original on 8 March 2025.
- "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/).
- Macías, Alfredo; Camacho, Abel (May 2008).

"The Maya Long Count Calendar: An Introduction".

Archived (https://web.archive.org/web/20 250308214916/https://www.britannica.com/science/French-republican-calendar) from the original on 8 March 2025.

"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/).

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

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:
- O'Neil seemed to be the only one who wasn't frightened.
- Kawalsky ordered Feretti,Brown and Porro to go next.
- Daniel shut his eyes, walked into the wall of light, and suddenly saw himself flying among stars, millions of them.
- Daniel, O'Neil, Kawalsky and three other soldiers, Feretti, Brown and Porro, stood waiting with boxes full of things they needed.
- He was the first to walk into the circle oflight and disappear.

O'Neil seemed to be the only one who wasn't frightened.

Kawalsky ordered Feretti,Brown and Porro to go next.

Daniel shut his eyes, walked into the wall of light, and suddenly saw himself flying among stars, millions of them.

Daniel, O'Neil, Kawalsky and three other soldiers, Feretti, Brown and Porro, stood waiting with boxes full of things they needed.

He was the first to walk into the circle oflight and disappear.

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.