{
  "case_id": "Case08",
  "title": "Case08 — Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.",
      "award_conditions": [
        "Both symmetric and antisymmetric states belong to the specified fixed-separation 2D soft-core H2+ model and spatially propagating nondipole pulse with consistent gauge."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F2, F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.",
      "award_conditions": [
        "A probability-preserving outgoing-wave extraction defines comparable molecule-frame final PMDs for both states."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.)",
        "Preserve independently valid work in F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish a quantitative inversion from final angular phase to relative birth time, explicitly treating two-centre geometry, parity, sign/phase branch, periodic aliases and identifiability.",
      "award_conditions": [
        "The candidate quantitatively maps final interference phase to relative delay with geometry, parity, sign, branch, aliases and identifiability explicit."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O1, O2, I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.",
      "award_conditions": [
        "The symmetric-state final probability signal is reconstructible and resolves one-photon support and angular two-centre structure.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.)",
        "Preserve independently valid work in O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.",
      "award_conditions": [
        "The antisymmetric-state signal is reconstructible and resolves one-photon support and parity-specific angular nodes/structure.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.)",
        "Preserve independently valid work in O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.",
      "award_conditions": [
        "Two-state phase/interference evidence resolves timing-bearing minima, periods or an equivalent phase object distinguishable from smooth background.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.)",
        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present initial-to-final spatial evidence supporting state dependence, exposing inter-centre symmetric density versus outward antisymmetric density/effective emission geometry, or a strictly equivalent spatial relation.",
      "award_conditions": [
        "Spatial evidence exposes symmetric inter-centre versus antisymmetric outward density/effective-emission geometry, or a valid equivalent spatial relation.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.)",
        "Preserve independently valid work in M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify one-photon support and angular two-centre phase structure in the presented symmetric-state signal, rather than merely supplying data or a figure.",
      "award_conditions": [
        "The candidate identifies one-photon support and angular two-centre phase structure in the symmetric-state presentation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.)",
        "Preserve independently valid work in I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify one-photon support, parity-specific nodes/angular structure and differences from the symmetric case in the antisymmetric-state signal.",
      "award_conditions": [
        "The candidate identifies parity-specific nodes and state differences in the antisymmetric-state presentation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.)",
        "Preserve independently valid work in I1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.",
      "award_conditions": [
        "Candidate identification includes state-specific period/phase branch, effective scale or equivalent quantity, numerical delay class and ordering."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.)",
        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I4",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the material initial-density/emission-geometry difference, symmetric inter-centre versus antisymmetric outward support, or physically equivalent spatial evidence.",
      "award_conditions": [
        "The candidate identifies the relevant initial-density/emission-geometry difference from presented spatial evidence."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O4 (Present initial-to-final spatial evidence supporting state dependence, exposing inter-centre symmetric density versus outward antisymmetric density/effective emission geometry, or a strictly equivalent spatial relation.)",
        "Preserve independently valid work in M6, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.",
      "award_conditions": [
        "The candidate explains how propagating-field space-time phase enters angular two-centre interference and why arbitrary angular texture is not a clock."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.)",
        "Preserve independently valid work in M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.",
      "award_conditions": [
        "A quantitative phase relation connects period, effective separation and delay with the correct parity phase and sign/alias mapping."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F3 (Establish a quantitative inversion from final angular phase to relative birth time, explicitly treating two-centre geometry, parity, sign/phase branch, periodic aliases and identifiability.)",
        "Preserve independently valid work in M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Infer a symmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.",
      "award_conditions": [
        "The symmetric-state delay follows its computed signal and is physically compared with its effective-scale light-crossing time."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I1 (Explicitly identify one-photon support and angular two-centre phase structure in the presented symmetric-state signal, rather than merely supplying data or a figure.); I3 (Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.)",
        "Preserve independently valid work in M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Infer an antisymmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.",
      "award_conditions": [
        "The antisymmetric-state delay follows its computed signal and is physically compared with its effective-scale light-crossing time."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I2 (Explicitly identify one-photon support, parity-specific nodes/angular structure and differences from the symmetric case in the antisymmetric-state signal.); I3 (Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.)",
        "Preserve independently valid work in M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.",
      "award_conditions": [
        "The two initial states' distinct emission scales explain different timing, without forcing either scale to equal nuclear separation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: M3 (Infer a symmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.); M4 (Infer an antisymmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.)",
        "Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.",
      "award_conditions": [
        "Density support, effective emission positions and light propagation form an evidence-linked state-to-geometry-to-delay chain."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I4 (Identify the material initial-density/emission-geometry difference, symmetric inter-centre versus antisymmetric outward support, or physically equivalent spatial evidence.)",
        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Synthesize both signals, quantitative timing and geometry mechanism into the strongest identifiable conclusion, without promoting a mere angular shift or smooth response into a unique clock.",
      "award_conditions": [
        "Both signals, quantitative inversion and geometry mechanism support the strongest identifiable relative-timing claim, not an unproven unique clock."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.",
      "award_conditions": [
        "When background, phase aliases, parity/sign, competing shift mechanisms or resolution threaten timing, capable evidence discriminates them or the claim is narrowed; otherwise N/A."
      ],
      "applicability_and_na": [
        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
      ],
      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Positively state the specified two-dimensional fixed-nuclei soft-core H2+, two initial states, nondipole pulse and achieved final-PES inference domain; do not extrapolate to general molecules or a unique absolute birth clock.",
      "award_conditions": [
        "The candidate positively bounds the conclusion to the specified fixed-nuclei 2D soft-core states/pulse and actual final-PES inference domain."
      ],
      "applicability_and_na": [
        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
      ],
      "source_support": [
        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    }
  ],
  "case_scientific_rules": [
    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
    "Representative structural anchors, not tolerances, include a one-photon band near p=4 a.u., symmetric minima near mu=-0.41,+0.44, antisymmetric minima near -0.56,0,+0.59, and parity-distinct periods.",
    "Representative effective scales are about 1.77-1.79 and 2.62-2.64 a.u.; principal delays about 0.31-0.34 and 0.45-0.49 as. The symmetric delay is below R/c, the antisymmetric delay above R/c, each near its own Rw/c; convention-equivalent aliases remain accepted.",
    "A different angular shift that cannot distinguish smooth single-centre background does not solve the same inference problem even if internally consistent. Bound-contaminated continuum data and incorrect angular measures do not establish the target probability.",
    "Initial-state geometry evidence and its interpretation retain independent credit when quantitative timing fails; conversely, state labels alone do not establish computed structural support.",
    "For a representative one-photon momentum $p$, the symmetric-state two-centre model can be written",
    "$$\nF(\\mu)=1+\\cos\\!\\left[2\\pi\\left(\n\\frac{\\mu R_w}{\\lambda_e}-\\frac{\\tau_b v_{\\rm ph}}{\\lambda_e}\n\\right)\\right],\n\\qquad \\mu=\\cos\\alpha,\n$$",
    "with $\\lambda_e=2\\pi/p$ and $v_{\\rm ph}=E/p$. The antisymmetric initial state adds the parity phase $\\pi$ (or an equivalent global convention). The canonical route obtains a positive effective emission separation $R_w$ from the stable angular period and then the delay equivalence class from the phase displacement. It uses robust interior interference minima because the smooth single-centre photoionization background shifts maxima but does not move a true zero in the same way.",
    "both states show a one-photon momentum band near $p\\simeq4$ a.u. with resolved, parity-distinct angular interference;",
    "the symmetric case has the principal interior depressions near $\\mu\\simeq-0.41$ and $+0.44$;",
    "the antisymmetric case has a central depression and principal minima near $\\mu\\simeq-0.56,0,+0.59$;",
    "representative effective separations are about $1.77$--$1.79$ a.u. and $2.62$--$2.64$ a.u.; principal delays are approximately $0.31$--$0.34$ as and $0.45$--$0.49$ as, respectively;",
    "the symmetric delay lies below $R/c$ and the antisymmetric delay above it, while each is close to its own $R_w/c$;",
    "the computed symmetric density is concentrated between the centres whereas the antisymmetric density is displaced outward, supporting the effective emission-geometry interpretation.",
    "These are structural anchors, not pixel targets. An energy-resolved, momentum-resolved, phase-fit, likelihood or other estimator may replace the canonical radial PAD route if it demonstrably measures the same phase and controls the same background ambiguity. A delay shifted by an exact period or global sign is equivalent when the student derives and reports the mapping; the grader must not choose a branch by proximity to the reference values.",
    "The task deliberately does not name the radial measure, cosine fit, minima, $R_w$, parity phase or principal delay interval. None may be awarded merely for matching terminology. Full credit follows physical function and computed correctness. Conversely, a route that measures a different angular shift and cannot distinguish single-centre background has not solved the same inference problem, even if it is internally consistent.",
    "Charge a continuum-extraction, measure or fit defect first to the affected Output criterion. A dependent scientific inference loses credit only when the same defect makes the physical inference false or unsupported. Do not also deduct for absence of a named convergence test. Do not require source figure layout, colours, exact crop, absolute yield or a fixed output package.",
    "For F3/O3/M1-M4, the phase model already stated is article p.043105-3, Eq.(3). Equivalently,\n$$\\Phi(\\mu)=pR_w\\mu-E\\tau_b+\\phi_{\\rm parity},\\quad\n\\Delta\\mu=\\frac{2\\pi}{pR_w},\\quad\n\\phi_{\\rm parity}=0\\ (\\text{symmetric}),\\ \\pi\\ (\\text{antisymmetric}).$$\nHere $E/p=v_{\\rm ph}$ is the electron phase velocity under the source convention, not an independently substituted group velocity. An observed phase fixes a delay equivalence class modulo $2\\pi/E$; selecting a principal delay needs a stated branch/physical justification, not nearest-reference-value matching. Source Fig.2 compares each inferred delay with its own $R_w/c$ and with bare $R/c$; those are different physical scales."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL0, central physical object: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required co primary claim CL1, indispensable material component: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL2, indispensable material component: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC2": [
      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M2 (Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC3": [
      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
      "Required co primary claim CL4, material validation/scope: V1 (When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC4": [
      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
      "Close CL0 central physical object: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.).",
      "Close CL1 indispensable material component: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.).",
      "Close CL2 indispensable material component: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.).",
      "Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M2 (Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.).",
      "Close CL3 principal mechanism or commissioned conclusion: all of: M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.).",
      "Close CL4 material validation/scope: V1 (When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.)."
    ]
  },
  "references": [
    {
      "citation": "XuanYang Lai, SongPo Xu, ShaoGang Yu, MengWen Shi, Wei Quan, and XiaoJun Liu. 2021. *Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima*. *Physical Review A*, 104, 043105.",
      "url": "https://doi.org/10.1103/PhysRevA.104.043105",
      "scientific_scope": "Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima",
      "anchors": [
        "Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction.",
        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4.",
        "Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive.",
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference.",
        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity.",
        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions.",
        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
      ]
    }
  ]
}