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"electric_weights": [ "-1/2", "1/2" ] }, { "color_grade": 6, "weak_grade": 0, "color_rank": 210, "weak_rank": 1, "hypercharge": "-3/5", "electric_weights": [ "-3/5" ] }, { "color_grade": 6, "weak_grade": 2, "color_rank": 210, "weak_rank": 1, "hypercharge": "2/5", "electric_weights": [ "2/5" ] }, { "color_grade": 7, "weak_grade": 1, "color_rank": 120, "weak_rank": 2, "hypercharge": "-1/5", "electric_weights": [ "-7/10", "3/10" ] }, { "color_grade": 8, "weak_grade": 0, "color_rank": 45, "weak_rank": 1, "hypercharge": "-4/5", "electric_weights": [ "-4/5" ] }, { "color_grade": 8, "weak_grade": 2, "color_rank": 45, "weak_rank": 1, "hypercharge": "1/5", "electric_weights": [ "1/5" ] }, { "color_grade": 9, "weak_grade": 1, "color_rank": 10, "weak_rank": 2, "hypercharge": "-2/5", "electric_weights": [ "-9/10", "1/10" ] }, { "color_grade": 10, "weak_grade": 0, "color_rank": 1, "weak_rank": 1, "hypercharge": "-1", "electric_weights": [ "-1" ] }, { "color_grade": 10, "weak_grade": 2, "color_rank": 1, "weak_rank": 1, "hypercharge": "0", "electric_weights": [ "0" ] } ], "trace_y": "0", "trace_y_cubed": "0", "su2_squared_y_trace": "0", "number_of_weak_doublets": 512, "minimal_family_match": false, "geometric_fundamental_doublet": [ "9/10", "-1/10" ], "minimal_family_doublet": [ "11/20", "-9/20" ], "minimal_subfamily_cubic_trace": null, "minimal_subfamily_weak_trace": null, "additional_full_carrier_components": null, "colorless_weak_doublet_present": false, "anomaly_traces_exclude_higher_complete_carriers": false } }, { "geometry": "one compatible physical nested flag", "parameters": { "depths": [ 2, 3, 4, 5, 6, 10 ] }, "measurements": { "pencil_normal_plane_is_physical_Q6": false, "extra_normal_line_needed": true, "ambient_su3_stabilizer_of_Q6_dimension": 4, "ambient_su3_stabilizer_of_Q5_dimension": 3 } } ], "scope": "Bounded spatial Clifford algebra and exact stabilizers; classical field amplitudes, no particle simulations.", "assumptions": [ "Two orthogonal same-chirality spinors span an everywhere-pure local pencil.", "One spinor is fixed exactly while the other is fixed projectively.", "The earlier universal nonzero alternating normal-vector channel is imposed on the complement." ], "limitations": [ "Pure pencils exist at every even parent depth at least four; their presence alone does not select ten.", "The normal channel criterion selects ten only in combination with the pencil premise.", "The normal six-plane is not the nested physical depth-six sector.", "The pair itself shares a normal vacuum and does not generate the additional normal frame.", "Charge characters are representation weights, not derived occupied-particle electric charges.", "Full higher-rank carriers retain extra representations and cancel the displayed anomaly traces.", "Preserving fixed lower-sector flags reduces ambient spatial SU3; an independent color action requires its own dynamics." ], "sources": { "experiments/pure-pencil-geometry-checks.py": "5dbdcbaa6b81cf5bed9d00536111ef6e6b1f9013bfe841b9d914398153b846c7", "experiments/spinor-hodge-source-checks.py": "c1a9212b8dd1f0e9e525e36db80c322b9487986ca656aa028c2a4cbb8456b38e" } }