Recorded data and provenance for the associated calculation.
| title | Pure spatial spinor pencils and their four-plane, stabilizer and charge character |
|---|---|
| created_utc | 2026-10-09T22:57:52.850348+00:00 |
| checks_passed | 3900 |
| scope | Bounded spatial Clifford algebra and exact stabilizers; classical field amplitudes, no particle simulations. |
View complete data
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"hypercharge": "1/8",
"electric_weights": [
"-3/8",
"5/8"
]
},
{
"color_grade": 4,
"weak_grade": 0,
"color_rank": 70,
"weak_rank": 1,
"hypercharge": "-1/2",
"electric_weights": [
"-1/2"
]
},
{
"color_grade": 4,
"weak_grade": 2,
"color_rank": 70,
"weak_rank": 1,
"hypercharge": "1/2",
"electric_weights": [
"1/2"
]
},
{
"color_grade": 5,
"weak_grade": 1,
"color_rank": 56,
"weak_rank": 2,
"hypercharge": "-1/8",
"electric_weights": [
"-5/8",
"3/8"
]
},
{
"color_grade": 6,
"weak_grade": 0,
"color_rank": 28,
"weak_rank": 1,
"hypercharge": "-3/4",
"electric_weights": [
"-3/4"
]
},
{
"color_grade": 6,
"weak_grade": 2,
"color_rank": 28,
"weak_rank": 1,
"hypercharge": "1/4",
"electric_weights": [
"1/4"
]
},
{
"color_grade": 7,
"weak_grade": 1,
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"weak_rank": 2,
"hypercharge": "-3/8",
"electric_weights": [
"-7/8",
"1/8"
]
},
{
"color_grade": 8,
"weak_grade": 0,
"color_rank": 1,
"weak_rank": 1,
"hypercharge": "-1",
"electric_weights": [
"-1"
]
},
{
"color_grade": 8,
"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": 128,
"minimal_family_match": false,
"geometric_fundamental_doublet": [
"7/8",
"-1/8"
],
"minimal_family_doublet": [
"9/16",
"-7/16"
],
"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
}
},
{
"real_depth": 22,
"geometry": "complete even exterior carrier for a derived two-plus-k complex split",
"parameters": {
"complex_normal_rank": 9,
"normal_real_depth": 18
},
"measurements": {
"branching": [
{
"color_grade": 0,
"weak_grade": 0,
"color_rank": 1,
"weak_rank": 1,
"hypercharge": "0",
"electric_weights": [
"0"
]
},
{
"color_grade": 0,
"weak_grade": 2,
"color_rank": 1,
"weak_rank": 1,
"hypercharge": "1",
"electric_weights": [
"1"
]
},
{
"color_grade": 1,
"weak_grade": 1,
"color_rank": 9,
"weak_rank": 2,
"hypercharge": "7/18",
"electric_weights": [
"-1/9",
"8/9"
]
},
{
"color_grade": 2,
"weak_grade": 0,
"color_rank": 36,
"weak_rank": 1,
"hypercharge": "-2/9",
"electric_weights": [
"-2/9"
]
},
{
"color_grade": 2,
"weak_grade": 2,
"color_rank": 36,
"weak_rank": 1,
"hypercharge": "7/9",
"electric_weights": [
"7/9"
]
},
{
"color_grade": 3,
"weak_grade": 1,
"color_rank": 84,
"weak_rank": 2,
"hypercharge": "1/6",
"electric_weights": [
"-1/3",
"2/3"
]
},
{
"color_grade": 4,
"weak_grade": 0,
"color_rank": 126,
"weak_rank": 1,
"hypercharge": "-4/9",
"electric_weights": [
"-4/9"
]
},
{
"color_grade": 4,
"weak_grade": 2,
"color_rank": 126,
"weak_rank": 1,
"hypercharge": "5/9",
"electric_weights": [
"5/9"
]
},
{
"color_grade": 5,
"weak_grade": 1,
"color_rank": 126,
"weak_rank": 2,
"hypercharge": "-1/18",
"electric_weights": [
"-5/9",
"4/9"
]
},
{
"color_grade": 6,
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"weak_rank": 1,
"hypercharge": "-2/3",
"electric_weights": [
"-2/3"
]
},
{
"color_grade": 6,
"weak_grade": 2,
"color_rank": 84,
"weak_rank": 1,
"hypercharge": "1/3",
"electric_weights": [
"1/3"
]
},
{
"color_grade": 7,
"weak_grade": 1,
"color_rank": 36,
"weak_rank": 2,
"hypercharge": "-5/18",
"electric_weights": [
"-7/9",
"2/9"
]
},
{
"color_grade": 8,
"weak_grade": 0,
"color_rank": 9,
"weak_rank": 1,
"hypercharge": "-8/9",
"electric_weights": [
"-8/9"
]
},
{
"color_grade": 8,
"weak_grade": 2,
"color_rank": 9,
"weak_rank": 1,
"hypercharge": "1/9",
"electric_weights": [
"1/9"
]
},
{
"color_grade": 9,
"weak_grade": 1,
"color_rank": 1,
"weak_rank": 2,
"hypercharge": "-1/2",
"electric_weights": [
"-1",
"0"
]
}
],
"trace_y": "0",
"trace_y_cubed": "0",
"su2_squared_y_trace": "0",
"number_of_weak_doublets": 256,
"minimal_family_match": false,
"geometric_fundamental_doublet": [
"8/9",
"-1/9"
],
"minimal_family_doublet": [
"5/9",
"-4/9"
],
"minimal_subfamily_cubic_trace": "-9/2",
"minimal_subfamily_weak_trace": "3/2",
"additional_full_carrier_components": 984,
"colorless_weak_doublet_present": true,
"anomaly_traces_exclude_higher_complete_carriers": false
}
},
{
"real_depth": 24,
"geometry": "complete even exterior carrier for a derived two-plus-k complex split",
"parameters": {
"complex_normal_rank": 10,
"normal_real_depth": 20
},
"measurements": {
"branching": [
{
"color_grade": 0,
"weak_grade": 0,
"color_rank": 1,
"weak_rank": 1,
"hypercharge": "0",
"electric_weights": [
"0"
]
},
{
"color_grade": 0,
"weak_grade": 2,
"color_rank": 1,
"weak_rank": 1,
"hypercharge": "1",
"electric_weights": [
"1"
]
},
{
"color_grade": 1,
"weak_grade": 1,
"color_rank": 10,
"weak_rank": 2,
"hypercharge": "2/5",
"electric_weights": [
"-1/10",
"9/10"
]
},
{
"color_grade": 2,
"weak_grade": 0,
"color_rank": 45,
"weak_rank": 1,
"hypercharge": "-1/5",
"electric_weights": [
"-1/5"
]
},
{
"color_grade": 2,
"weak_grade": 2,
"color_rank": 45,
"weak_rank": 1,
"hypercharge": "4/5",
"electric_weights": [
"4/5"
]
},
{
"color_grade": 3,
"weak_grade": 1,
"color_rank": 120,
"weak_rank": 2,
"hypercharge": "1/5",
"electric_weights": [
"-3/10",
"7/10"
]
},
{
"color_grade": 4,
"weak_grade": 0,
"color_rank": 210,
"weak_rank": 1,
"hypercharge": "-2/5",
"electric_weights": [
"-2/5"
]
},
{
"color_grade": 4,
"weak_grade": 2,
"color_rank": 210,
"weak_rank": 1,
"hypercharge": "3/5",
"electric_weights": [
"3/5"
]
},
{
"color_grade": 5,
"weak_grade": 1,
"color_rank": 252,
"weak_rank": 2,
"hypercharge": "0",
"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"
}
}