{
  "grade": "RELATION",
  "pdg_version": "PDG 2024 (S. Navas et al., Phys. Rev. D 110, 030001 (2024))",
  "data_freeze_date": "2024-05-31",
  "safe_wording": "This suite verifies that every observed particle is quantum-number-consistent with its geometry-derived constituents and that the parameter-free QCD symmetry relations hold against PDG-2024; it does NOT compute or claim absolute hadron masses from geometry.",
  "quantum_number_gate": {
    "passed": true,
    "findings": [
      {
        "particle": "proton",
        "quark_content": "uud",
        "field": "charge",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "proton",
        "quark_content": "uud",
        "field": "strangeness",
        "derived": 0,
        "listed": 0,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "proton",
        "quark_content": "uud",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "neutron",
        "quark_content": "udd",
        "field": "charge",
        "derived": 0.0,
        "listed": 0.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "neutron",
        "quark_content": "udd",
        "field": "strangeness",
        "derived": 0,
        "listed": 0,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "neutron",
        "quark_content": "udd",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Lambda",
        "quark_content": "uds",
        "field": "charge",
        "derived": 0.0,
        "listed": 0.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Lambda",
        "quark_content": "uds",
        "field": "strangeness",
        "derived": -1,
        "listed": -1,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Lambda",
        "quark_content": "uds",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Sigma+",
        "quark_content": "uus",
        "field": "charge",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Sigma+",
        "quark_content": "uus",
        "field": "strangeness",
        "derived": -1,
        "listed": -1,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Sigma+",
        "quark_content": "uus",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Sigma0",
        "quark_content": "uds",
        "field": "charge",
        "derived": 0.0,
        "listed": 0.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Sigma0",
        "quark_content": "uds",
        "field": "strangeness",
        "derived": -1,
        "listed": -1,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Sigma0",
        "quark_content": "uds",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Sigma-",
        "quark_content": "dds",
        "field": "charge",
        "derived": -1.0,
        "listed": -1.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Sigma-",
        "quark_content": "dds",
        "field": "strangeness",
        "derived": -1,
        "listed": -1,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Sigma-",
        "quark_content": "dds",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Xi0",
        "quark_content": "uss",
        "field": "charge",
        "derived": 0.0,
        "listed": 0.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Xi0",
        "quark_content": "uss",
        "field": "strangeness",
        "derived": -2,
        "listed": -2,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Xi0",
        "quark_content": "uss",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Xi-",
        "quark_content": "dss",
        "field": "charge",
        "derived": -1.0,
        "listed": -1.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Xi-",
        "quark_content": "dss",
        "field": "strangeness",
        "derived": -2,
        "listed": -2,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Xi-",
        "quark_content": "dss",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Delta",
        "quark_content": "uuu",
        "field": "charge",
        "derived": 2.0,
        "listed": 2.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Delta",
        "quark_content": "uuu",
        "field": "strangeness",
        "derived": 0,
        "listed": 0,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Delta",
        "quark_content": "uuu",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Sigma*",
        "quark_content": "uus",
        "field": "charge",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Sigma*",
        "quark_content": "uus",
        "field": "strangeness",
        "derived": -1,
        "listed": -1,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Sigma*",
        "quark_content": "uus",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Xi*",
        "quark_content": "uss",
        "field": "charge",
        "derived": 0.0,
        "listed": 0.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Xi*",
        "quark_content": "uss",
        "field": "strangeness",
        "derived": -2,
        "listed": -2,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Xi*",
        "quark_content": "uss",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "Omega-",
        "quark_content": "sss",
        "field": "charge",
        "derived": -1.0,
        "listed": -1.0,
        "ok": true,
        "detail": "Q == sum(quark charges)"
      },
      {
        "particle": "Omega-",
        "quark_content": "sss",
        "field": "strangeness",
        "derived": -3,
        "listed": -3,
        "ok": true,
        "detail": "S == sum(quark strangeness)"
      },
      {
        "particle": "Omega-",
        "quark_content": "sss",
        "field": "baryon_number",
        "derived": 1.0,
        "listed": 1.0,
        "ok": true,
        "detail": "B == (#quarks)/3 == 1 for a baryon"
      },
      {
        "particle": "nucleon:neutron",
        "quark_content": "udd",
        "field": "charge_derivable",
        "derived": 0.0,
        "listed": "(no column)",
        "ok": true,
        "detail": "derived charge is well-formed from quark flavours"
      },
      {
        "particle": "nucleon:proton",
        "quark_content": "uud",
        "field": "charge_derivable",
        "derived": 1.0,
        "listed": "(no column)",
        "ok": true,
        "detail": "derived charge is well-formed from quark flavours"
      },
      {
        "particle": "kaon:K0",
        "quark_content": "ds",
        "field": "charge_derivable",
        "derived": -0.666667,
        "listed": "(no column)",
        "ok": true,
        "detail": "derived charge is well-formed from quark flavours"
      },
      {
        "particle": "kaon:K+",
        "quark_content": "us",
        "field": "charge_derivable",
        "derived": 0.333333,
        "listed": "(no column)",
        "ok": true,
        "detail": "derived charge is well-formed from quark flavours"
      },
      {
        "particle": "D_meson:D0",
        "quark_content": "uc",
        "field": "charge_derivable",
        "derived": 1.333333,
        "listed": "(no column)",
        "ok": true,
        "detail": "derived charge is well-formed from quark flavours"
      },
      {
        "particle": "D_meson:Dplus",
        "quark_content": "dc",
        "field": "charge_derivable",
        "derived": 0.333333,
        "listed": "(no column)",
        "ok": true,
        "detail": "derived charge is well-formed from quark flavours"
      }
    ],
    "n_checks": 42,
    "n_failed": 0
  },
  "relations": [
    {
      "relation_id": "R1",
      "name": "Gell-Mann-Okubo baryon octet mass formula",
      "grade": "RELATION",
      "formula": "2(m_N + m_Xi) = 3*m_Lambda + m_Sigma",
      "inputs": {
        "m_N_MeV": 938.918755,
        "m_Xi_MeV": 1318.285,
        "m_Lambda_MeV": 1115.683,
        "m_Sigma_MeV": 1193.153667
      },
      "predicted": 4540.202667,
      "observed": 4514.40751,
      "residual": 0.00569768,
      "residual_kind": "relative",
      "tolerance_name": "gmo_octet_rel_tol",
      "tolerance_value": 0.01,
      "tolerance_rationale": "Gell-Mann-Okubo 2(m_N+m_Xi)=3*m_Lambda+m_Sigma holds to ~0.6% in PDG-2024; second-order SU(3) breaking is sub-percent. A >1% violation falsifies the linear-breaking assumption. Source: foundation/01_mass_method_catalog.md method 3.",
      "passed": true,
      "detail": "LHS=2(m_N+m_Xi)=4514.4075 MeV; RHS=3 m_Lambda+m_Sigma=4540.2027 MeV; |LHS-RHS|=25.7952 MeV; rel=0.5698% (tol 1.00%)"
    },
    {
      "relation_id": "R2",
      "name": "Baryon decuplet equal-spacing rule",
      "grade": "RELATION",
      "formula": "m_Sigma* - m_Delta == m_Xi* - m_Sigma* == m_Omega - m_Xi*",
      "inputs": {
        "m_Delta_MeV": 1230.9,
        "m_Sigma*_MeV": 1382.83,
        "m_Xi*_MeV": 1531.8,
        "m_Omega-_MeV": 1672.45,
        "step_Sigma*-Delta_MeV": 151.93,
        "step_Xi*-Sigma*_MeV": 148.97,
        "step_Omega-Xi*_MeV": 140.65,
        "mean_step_MeV": 147.1833
      },
      "predicted": 147.1833,
      "observed": [
        151.93,
        148.97,
        140.65
      ],
      "residual": 0.04438908,
      "residual_kind": "max_relative",
      "tolerance_name": "decuplet_equal_spacing_rel_tol",
      "tolerance_value": 0.1,
      "tolerance_rationale": "Decuplet equal-spacing steps (Sigma*-Delta, Xi*-Sigma*, Omega-Xi*) agree to ~7% in PDG-2024; the spacing has known curvature in m_s. Steps differing by >10% beyond curvature falsify equal spacing. Source: foundation/01_mass_method_catalog.md method 4.",
      "passed": true,
      "detail": "steps = [151.93, 148.97, 140.65] MeV; mean=147.18 MeV; max deviation from mean = 6.53 MeV (4.44%, tol 10%)"
    },
    {
      "relation_id": "R3",
      "name": "Isospin-splitting signs consistent with m_d>m_u + EM",
      "grade": "RELATION",
      "formula": "sign(m_member_heavier - m_member_lighter) == expected_sign (per multiplet)",
      "inputs": {
        "multiplets": [
          {
            "multiplet": "nucleon",
            "member_heavier": "neutron",
            "member_lighter": "proton",
            "mass_heavier_MeV": 939.565421,
            "mass_lighter_MeV": 938.272089,
            "observed_diff_MeV": 1.293332,
            "observed_sign": "positive",
            "expected_sign": "positive",
            "mechanism": "n(udd) has one more d, one fewer u than p(uud); QCD piece (m_d>m_u) wins over EM => m_n>m_p",
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): m_n-m_p = 1.2933321(5) MeV (positive)",
            "ok": true
          },
          {
            "multiplet": "kaon",
            "member_heavier": "K0",
            "member_lighter": "K+",
            "mass_heavier_MeV": 497.611,
            "mass_lighter_MeV": 493.677,
            "observed_diff_MeV": 3.934,
            "observed_sign": "positive",
            "expected_sign": "positive",
            "mechanism": "K0(d-sbar) vs K+(u-sbar): replacing u by d adds (m_d-m_u)>0 and removes EM self-energy of charged K => m_K0>m_K+",
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): m_K0=497.611(13), m_K+=493.677(13) MeV",
            "ok": true
          },
          {
            "multiplet": "D_meson",
            "member_heavier": "D0",
            "member_lighter": "Dplus",
            "mass_heavier_MeV": 1864.84,
            "mass_lighter_MeV": 1869.66,
            "observed_diff_MeV": -4.82,
            "observed_sign": "negative",
            "expected_sign": "negative",
            "mechanism": "D0(c-ubar) vs D+(c-dbar): the spectator light quark is ubar/dbar; charm dominates, and the charged D+ is HEAVIER (m_D+>m_D0), i.e. m_D0-m_D+<0 — opposite ordering to the kaon case",
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): m_D0=1864.84(5), m_D+=1869.66(5) MeV",
            "ok": true
          }
        ]
      },
      "predicted": [
        "positive",
        "positive",
        "negative"
      ],
      "observed": [
        "positive",
        "positive",
        "negative"
      ],
      "residual": "0 sign mismatch(es)",
      "residual_kind": "sign_match_count",
      "tolerance_name": "(exact sign match required)",
      "tolerance_value": 0,
      "tolerance_rationale": "The SIGN of each isospin splitting is the parameter-free RELATION; 0 mismatches are tolerated. Magnitudes are LATTICE-IMPORTED and not tested here.",
      "passed": true,
      "detail": "nucleon: neutron(939.565421) - proton(938.272089) = 1.2933 MeV => positive (expected positive) [OK]; kaon: K0(497.611) - K+(493.677) = 3.9340 MeV => positive (expected positive) [OK]; D_meson: D0(1864.84) - Dplus(1869.66) = -4.8200 MeV => negative (expected negative) [OK]"
    },
    {
      "relation_id": "R4:N_orbital",
      "name": "Regge linearity (N_orbital, M^2 vs J)",
      "grade": "RELATION",
      "formula": "M^2 = slope*J + intercept (least squares)",
      "inputs": {
        "axis": "J",
        "points": [
          {
            "state": "N(939)",
            "j": 0.5,
            "mass_MeV": 938.9188,
            "M2_MeV2": 881568.43,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): nucleon ground state, (m_p+m_n)/2 = 938.9188 MeV"
          },
          {
            "state": "N(1680)",
            "j": 2.5,
            "mass_MeV": 1685.0,
            "M2_MeV2": 2839225.0,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): N(1680) 5/2+ Breit-Wigner mass ~1685 MeV"
          },
          {
            "state": "N(2220)",
            "j": 4.5,
            "mass_MeV": 2250.0,
            "M2_MeV2": 5062500.0,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): N(2220) 9/2+ Breit-Wigner mass ~2250 MeV"
          }
        ],
        "n_points": 3
      },
      "predicted": {
        "slope_MeV2_per_unit": 1045232.893,
        "intercept_MeV2": 314682.244,
        "alpha_prime_GeV-2": 0.9567
      },
      "observed": {
        "R_squared": 0.998656
      },
      "residual": 0.998656,
      "residual_kind": "min_r_squared",
      "tolerance_name": "regge_r2_floor",
      "tolerance_value": 0.97,
      "tolerance_rationale": "M^2 vs J (orbital) and M^2 vs n (radial) are linear to ~5-10% across PDG light-meson and N* towers. We require the least-squares coefficient of determination R^2 >= 0.97 for the linearity RELATION to PASS. Source: foundation/01_mass_method_catalog.md method 6.",
      "passed": true,
      "detail": "3-point fit M^2 vs J: slope=1045232.9 MeV^2/unit (positive), R^2=0.99866 (floor 0.97) => PASS"
    },
    {
      "relation_id": "R4:pi_radial",
      "name": "Regge linearity (pi_radial, M^2 vs N)",
      "grade": "RELATION",
      "formula": "M^2 = slope*N + intercept (least squares)",
      "inputs": {
        "axis": "N",
        "points": [
          {
            "state": "pi(140)",
            "n": 0.0,
            "mass_MeV": 139.5704,
            "M2_MeV2": 19479.89,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): pi+- 1-(0-) mass 139.57039(18) MeV"
          },
          {
            "state": "pi(1300)",
            "n": 1.0,
            "mass_MeV": 1300.0,
            "M2_MeV2": 1690000.0,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): pi(1300) 1-(0-+) BW mass 1300(100) MeV (our estimate)"
          },
          {
            "state": "pi(1800)",
            "n": 2.0,
            "mass_MeV": 1810.0,
            "M2_MeV2": 3276100.0,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): pi(1800) 1-(0-+) mass 1810(+9-11) MeV"
          }
        ],
        "n_points": 3
      },
      "predicted": {
        "slope_MeV2_per_unit": 1628310.053,
        "intercept_MeV2": 33549.911,
        "alpha_prime_GeV-2": null
      },
      "observed": {
        "R_squared": 0.999776
      },
      "residual": 0.999776,
      "residual_kind": "min_r_squared",
      "tolerance_name": "regge_r2_floor",
      "tolerance_value": 0.97,
      "tolerance_rationale": "M^2 vs J (orbital) and M^2 vs n (radial) are linear to ~5-10% across PDG light-meson and N* towers. We require the least-squares coefficient of determination R^2 >= 0.97 for the linearity RELATION to PASS. Source: foundation/01_mass_method_catalog.md method 6.",
      "passed": true,
      "detail": "3-point fit M^2 vs N: slope=1628310.1 MeV^2/unit (positive), R^2=0.99978 (floor 0.97) => PASS"
    },
    {
      "relation_id": "R4:rho_orbital",
      "name": "Regge linearity (rho_orbital, M^2 vs J)",
      "grade": "RELATION",
      "formula": "M^2 = slope*J + intercept (least squares)",
      "inputs": {
        "axis": "J",
        "points": [
          {
            "state": "rho(770)",
            "j": 1.0,
            "mass_MeV": 775.26,
            "M2_MeV2": 601028.07,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): rho(770) I^G(J^PC)=1+(1--) BW mass 775.26(23) MeV"
          },
          {
            "state": "a2(1320)",
            "j": 2.0,
            "mass_MeV": 1318.2,
            "M2_MeV2": 1737651.24,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): a2(1320) 1-(2++) BW mass 1318.2(6) MeV"
          },
          {
            "state": "rho3(1690)",
            "j": 3.0,
            "mass_MeV": 1688.8,
            "M2_MeV2": 2852045.44,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): rho3(1690) 1+(3--) mass 1688.8(2.1) MeV"
          },
          {
            "state": "a4(1970)",
            "j": 4.0,
            "mass_MeV": 1967.0,
            "M2_MeV2": 3869089.0,
            "pdg_source": "PDG 2024 (Phys. Rev. D 110, 030001 (2024)): a4(1970) 1-(4++) mass 1967(16) MeV"
          }
        ],
        "n_points": 4
      },
      "predicted": {
        "slope_MeV2_per_unit": 1091857.7,
        "intercept_MeV2": -464690.812,
        "alpha_prime_GeV-2": 0.9159
      },
      "observed": {
        "R_squared": 0.999353
      },
      "residual": 0.999353,
      "residual_kind": "min_r_squared",
      "tolerance_name": "regge_r2_floor",
      "tolerance_value": 0.97,
      "tolerance_rationale": "M^2 vs J (orbital) and M^2 vs n (radial) are linear to ~5-10% across PDG light-meson and N* towers. We require the least-squares coefficient of determination R^2 >= 0.97 for the linearity RELATION to PASS. Source: foundation/01_mass_method_catalog.md method 6.",
      "passed": true,
      "detail": "4-point fit M^2 vs J: slope=1091857.7 MeV^2/unit (positive), R^2=0.99935 (floor 0.97) => PASS"
    }
  ],
  "totals": {
    "relations_evaluated": 6,
    "relations_passed": 6,
    "relations_failed": 0
  },
  "overall_pass": true
}