data listlengths 2 2 | raw_response dict | raw_text stringlengths 643 2.21k | knowledge_pieces listlengths 5 17 | doc_id int64 0 447 | native_id int64 0 447 |
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[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. A standard Controlled-NOT (C-NOT) gate flips the target qubit's state if the control qubit is in the state |1⟩ and leaves it unchanged if the control qubit is in the state |0⟩.\n2. The unitary operation of a standard C-NOT gate can be represented as |0⟩⟨0| ⊗ I + |1⟩⟨1| ⊗ X, where I is the identity matri... | 1. A standard Controlled-NOT (C-NOT) gate flips the target qubit's state if the control qubit is in the state |1⟩ and leaves it unchanged if the control qubit is in the state |0⟩.
2. The unitary operation of a standard C-NOT gate can be represented as |0⟩⟨0| ⊗ I + |1⟩⟨1| ⊗ X, where I is the identity matrix and X is the... | [
"A standard Controlled-NOT (C-NOT) gate flips the target qubit's state if the control qubit is in the state |1⟩ and leaves it unchanged if the control qubit is in the state |0⟩.",
"The unitary operation of a standard C-NOT gate can be represented as |0⟩⟨0| ⊗ I + |1⟩⟨1| ⊗ X, where I is the identity matrix and X is... | 201 | 201 |
[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. In quantitative PCR (qPCR), the cycle threshold (ct) value is inversely proportional to the initial concentration of the target nucleic acid; a lower ct value indicates a higher concentration.\n2. The A260/280 absorbance ratio is a standard metric for assessing the purity of nucleic acid samples, where ... | 1. In quantitative PCR (qPCR), the cycle threshold (ct) value is inversely proportional to the initial concentration of the target nucleic acid; a lower ct value indicates a higher concentration.
2. The A260/280 absorbance ratio is a standard metric for assessing the purity of nucleic acid samples, where a ratio betwee... | [
"In quantitative PCR (qPCR), the cycle threshold (ct) value is inversely proportional to the initial concentration of the target nucleic acid; a lower ct value indicates a higher concentration.",
"The A260/280 absorbance ratio is a standard metric for assessing the purity of nucleic acid samples, where a ratio be... | 202 | 202 |
[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. The total electrostatic potential energy of a system of point charges is the sum of the potential energies of all unique pairs of charges within that system.\n2. The number of unique pairs that can be formed from a set of $n$ distinct objects is calculated using the combination formula $C(n, 2) = \\frac... | 1. The total electrostatic potential energy of a system of point charges is the sum of the potential energies of all unique pairs of charges within that system.
2. The number of unique pairs that can be formed from a set of $n$ distinct objects is calculated using the combination formula $C(n, 2) = \frac{n(n-1)}{2}$.
3... | [
"The total electrostatic potential energy of a system of point charges is the sum of the potential energies of all unique pairs of charges within that system.",
"The number of unique pairs that can be formed from a set of $n$ distinct objects is calculated using the combination formula $C(n, 2) = \\frac{n(n-1)}{2... | 203 | 203 |
[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. 9-fluorenone is a fused bicyclic ketone consisting of two benzene rings with a carbonyl group at the 9-position.\n2. Selectfluor is an electrophilic fluorinating reagent used to introduce fluorine atoms into organic molecules.\n3. UV irradiation can provide the necessary activation energy for fluorinati... | 1. 9-fluorenone is a fused bicyclic ketone consisting of two benzene rings with a carbonyl group at the 9-position.
2. Selectfluor is an electrophilic fluorinating reagent used to introduce fluorine atoms into organic molecules.
3. UV irradiation can provide the necessary activation energy for fluorination reactions in... | [
"9-fluorenone is a fused bicyclic ketone consisting of two benzene rings with a carbonyl group at the 9-position.",
"Selectfluor is an electrophilic fluorinating reagent used to introduce fluorine atoms into organic molecules.",
"UV irradiation can provide the necessary activation energy for fluorination reacti... | 204 | 204 |
[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. The orbital velocity of a body in a circular orbit is equal to the square root of the product of the gravitational constant and the mass of the central body, divided by the orbital radius.\n2. Centrifugal acceleration is defined as the square of the orbital velocity divided by the radius of the orbit.\n... | 1. The orbital velocity of a body in a circular orbit is equal to the square root of the product of the gravitational constant and the mass of the central body, divided by the orbital radius.
2. Centrifugal acceleration is defined as the square of the orbital velocity divided by the radius of the orbit.
3. Gravitationa... | [
"The orbital velocity of a body in a circular orbit is equal to the square root of the product of the gravitational constant and the mass of the central body, divided by the orbital radius.",
"Centrifugal acceleration is defined as the square of the orbital velocity divided by the radius of the orbit.",
"Gravit... | 205 | 205 |
[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. The luminosity of a star is proportional to the square of its radius and the fourth power of its effective temperature ($L \\propto R^2 T_{eff}^4$).\n2. The total brightness of a multiple-star system is the sum of the luminosities of all visible components.\n3. In an eclipsing binary system, the total o... | 1. The luminosity of a star is proportional to the square of its radius and the fourth power of its effective temperature ($L \propto R^2 T_{eff}^4$).
2. The total brightness of a multiple-star system is the sum of the luminosities of all visible components.
3. In an eclipsing binary system, the total observed brightne... | [
"The luminosity of a star is proportional to the square of its radius and the fourth power of its effective temperature ($L \\propto R^2 T_{eff}^4$).",
"The total brightness of a multiple-star system is the sum of the luminosities of all visible components.",
"In an eclipsing binary system, the total observed b... | 206 | 206 |
[
{
"content": "You are given a reasoning chain that explains and justifies a particular conclusion or answer. Your task is to extract all distinct knowledge pieces from this chain. A knowledge piece is any standalone statement conveying an explicit fact, definition, mechanism, relationship, or insight that can b... | {
"text": "1. Telescopes should avoid pointing directly into the direction of strong winds to protect optical components and minimize mechanical vibrations.\n2. Wind direction is defined as the cardinal direction from which the wind originates.\n3. Pointing a telescope in the direction opposite to the wind source red... | 1. Telescopes should avoid pointing directly into the direction of strong winds to protect optical components and minimize mechanical vibrations.
2. Wind direction is defined as the cardinal direction from which the wind originates.
3. Pointing a telescope in the direction opposite to the wind source reduces the direct... | [
"Telescopes should avoid pointing directly into the direction of strong winds to protect optical components and minimize mechanical vibrations.",
"Wind direction is defined as the cardinal direction from which the wind originates.",
"Pointing a telescope in the direction opposite to the wind source reduces the ... | 207 | 207 |
[{"content":"You are given a reasoning chain that explains and justifies a particular conclusion or (...TRUNCATED) | {"text":"1. Liénard-Wiechert potentials describe the electromagnetic fields produced by a moving po(...TRUNCATED) | "1. Liénard-Wiechert potentials describe the electromagnetic fields produced by a moving point char(...TRUNCATED) | ["Liénard-Wiechert potentials describe the electromagnetic fields produced by a moving point charge(...TRUNCATED) | 208 | 208 |
[{"content":"You are given a reasoning chain that explains and justifies a particular conclusion or (...TRUNCATED) | {"text":"1. The solar proton-proton (pp) fusion process consists of multiple branches, such as pp-I,(...TRUNCATED) | "1. The solar proton-proton (pp) fusion process consists of multiple branches, such as pp-I, pp-II, (...TRUNCATED) | ["The solar proton-proton (pp) fusion process consists of multiple branches, such as pp-I, pp-II, an(...TRUNCATED) | 209 | 209 |
[{"content":"You are given a reasoning chain that explains and justifies a particular conclusion or (...TRUNCATED) | {"text":"1. DABCO (1,4-diazabicyclo[2.2.2]octane) serves as a Lewis base catalyst that can facilitat(...TRUNCATED) | "1. DABCO (1,4-diazabicyclo[2.2.2]octane) serves as a Lewis base catalyst that can facilitate the ri(...TRUNCATED) | ["DABCO (1,4-diazabicyclo[2.2.2]octane) serves as a Lewis base catalyst that can facilitate the ring(...TRUNCATED) | 210 | 210 |
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