Recorded data and provenance for the associated calculation.
| status | pass |
|---|---|
| checks_total | 484 |
| scope | Conditional extension to r identical polarization channels using the actual retained endpoint source. Orthogonal polarization vectors cancel all pair sources when r is at least the number of occupied bands; the physical value of r is not derived. A separate positive energy-momentum identity shows that neither phase cancellation nor the number of spatial dimensions produces a two-only inertial-mass cancellation in the tested positive quadratic action. |
| elapsed_seconds | 0.9061942480038851 |
View complete data
{
"status": "pass",
"checks_total": 484,
"checks": [
{
"name": "d2-W-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-W-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-W-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign1-r2-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign1-complete-pair-invariant-identity",
"error": 3.0617730325375992e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-W-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-W-sign-1-r1-Gram-rank-bound",
"error": 2.220446049250313e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign-1-r1-weighted-force-bound",
"error": 2e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign-1-r2-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-W-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign-1-complete-pair-invariant-identity",
"error": 2.5826096136524046e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-W-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Z-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Z-sign1-r1-Gram-rank-bound",
"error": 4.440892098500626e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign1-r1-weighted-force-bound",
"error": 4e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign1-r2-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign1-complete-pair-invariant-identity",
"error": 6.797623417066235e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Z-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Z-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign-1-r2-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Z-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign-1-complete-pair-invariant-identity",
"error": 9.063497889421647e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Z-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Higgs-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Higgs-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign1-r2-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign1-complete-pair-invariant-identity",
"error": 2.501395474858304e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Higgs-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r2-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d2-Higgs-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign-1-complete-pair-invariant-identity",
"error": 3.9193943382033034e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-Higgs-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-all-parallel-massless-motions-null",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d2-one-opposing-massless-motion-positive-mass",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-down-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-down-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-down-sign1-r1-Gram-rank-bound",
"error": 4.440892098500626e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign1-complete-pair-invariant-identity",
"error": 4.15816390625796e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-down-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-down-sign-1-r1-Gram-rank-bound",
"error": 4.440892098500626e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-down-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign-1-complete-pair-invariant-identity",
"error": 2.4948983437547758e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-down-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-strange-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-strange-sign1-r1-Gram-rank-bound",
"error": 8.881784197001252e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign1-complete-pair-invariant-identity",
"error": 8.31632781251592e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-strange-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-strange-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-strange-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign-1-complete-pair-invariant-identity",
"error": 1.663265562503184e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-strange-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-complete-pair-invariant-identity",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-complete-pair-invariant-identity",
"error": 8.31632781251592e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom lower component-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r1-Gram-rank-bound",
"error": 4.440892098500626e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-complete-pair-invariant-identity",
"error": 1.663265562503184e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r1-Gram-rank-bound",
"error": 4.440892098500626e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r3-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-complete-pair-invariant-identity",
"error": 8.31632781251592e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-bottom upper component-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-all-parallel-massless-motions-null",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d3-one-opposing-massless-motion-positive-mass",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-up-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-up-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-up-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign1-complete-pair-invariant-identity",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-up-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-up-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-up-sign-1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign-1-complete-pair-invariant-identity",
"error": 4.9897966875095516e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-up-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-charm-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-charm-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign1-complete-pair-invariant-identity",
"error": 4.9897966875095516e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-charm-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-charm-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-charm-sign-1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign-1-complete-pair-invariant-identity",
"error": 3.326531125006368e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-charm-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-top-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-top-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign1-complete-pair-invariant-identity",
"error": 8.31632781251592e-112,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-top-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d4-top-sign-1-r1-Gram-rank-bound",
"error": 8.881784197001252e-16,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r3-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r3-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r4-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d4-top-sign-1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign-1-complete-pair-invariant-identity",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-top-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-all-parallel-massless-motions-null",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d4-one-opposing-massless-motion-positive-mass",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r1-Gram-rank-bound",
"error": 1.7763568394002505e-15,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-complete-pair-invariant-identity",
"error": 1.663265562503184e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-complete-pair-invariant-identity",
"error": 4.9897966875095516e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 1-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-complete-pair-invariant-identity",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-complete-pair-invariant-identity",
"error": 1.663265562503184e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 2-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r1-Gram-rank-bound",
"error": 1.7763568394002505e-15,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-complete-pair-invariant-identity",
"error": 8.31632781251592e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r4-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r4-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r5-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-complete-pair-invariant-identity",
"error": 4.9897966875095516e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-neutrino 3-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-all-parallel-massless-motions-null",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d5-one-opposing-massless-motion-positive-mass",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-electron-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-electron-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-electron-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign1-r7-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r7-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign1-r7-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign1-complete-pair-invariant-identity",
"error": 3.326531125006368e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-electron-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-electron-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign-1-r7-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r7-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-electron-sign-1-r7-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign-1-complete-pair-invariant-identity",
"error": 4.9897966875095516e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-electron-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-muon-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-muon-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign1-r7-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r7-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign1-r7-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign1-complete-pair-invariant-identity",
"error": 3.326531125006368e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-muon-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d6-muon-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r5-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r5-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r6-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r6-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r6-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign-1-r7-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r7-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d6-muon-sign-1-r7-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign-1-complete-pair-invariant-identity",
"error": 3.326531125006368e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-muon-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-all-parallel-massless-motions-null",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d6-one-opposing-massless-motion-positive-mass",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d10-tau-sign1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d10-tau-sign1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d10-tau-sign1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r9-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r9-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r10-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r10-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r10-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign1-r11-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r11-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign1-r11-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign1-complete-pair-invariant-identity",
"error": 4.9897966875095516e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign-1-actual-endpoint-pair-weights-positive",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d10-tau-sign-1-fixed-two-channel-threshold",
"error": 0.0,
"tolerance": 0.5,
"passed": true
},
{
"name": "d10-tau-sign-1-r1-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r1-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r2-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r2-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r9-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r9-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r10-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r10-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r10-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign-1-r11-Gram-rank-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r11-weighted-force-bound",
"error": 0.0,
"tolerance": 2e-13,
"passed": true
},
{
"name": "d10-tau-sign-1-r11-complete-pair-cancellation",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign-1-complete-pair-invariant-identity",
"error": 3.326531125006368e-111,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-tau-sign-1-positive-motions-do-not-cancel-mass",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-all-parallel-massless-motions-null",
"error": 0.0,
"tolerance": 1e-80,
"passed": true
},
{
"name": "d10-one-opposing-massless-motion-positive-mass",
"error": 0.0,
"tolerance": 0.5,
"passed": true
}
],
"records": [
{
"depth": 2,
"control": "W",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0",
"smallest_actual_pair_weight": "889576631124.01382351714517070069148695231615377087495634046798029850210337442886693493865423525654400871794722",
"channels_sufficient_for_exact_cancellation": 2,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0001059023374335030064973206265050169848799917708026214514685377985311435152701774161597394985836167513403279"
},
{
"depth": 2,
"control": "W",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0",
"smallest_actual_pair_weight": "913152809159.75370101320001441570934295231615377087495634046798029850210337442886693493865423525654400871794703",
"channels_sufficient_for_exact_cancellation": 2,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0000024927371607386791483205154751845944593618721403181435254936686419580515000047269827456842108796174848961"
},
{
"depth": 2,
"control": "Z",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0",
"smallest_actual_pair_weight": "1010406124162.5377266315209431150143729409701517896852800326236046347011344498725722128352598880615596292827236",
"channels_sufficient_for_exact_cancellation": 2,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0000653040882439638913309855231396194811317477796613921339120859955030364594886646775533520747717478525815206"
},
{
"depth": 2,
"control": "Z",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0",
"smallest_actual_pair_weight": "1035523228867.2802104998669530859157489409701517896852800326236046347011344498725722128352598880615596292827236",
"channels_sufficient_for_exact_cancellation": 2,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0002430694531159803843256079854834702093165343404071263387282118573032075057995968296457756946092249257334749"
},
{
"depth": 2,
"control": "Higgs",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0",
"smallest_actual_pair_weight": "1389563395709.7150799230250617251812525579220286915433317272982812567417609381339043839597988674364134164117872",
"channels_sufficient_for_exact_cancellation": 2,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0000521138268428503657362590738175835590717147775877764063140198371989321833078833170266379794982255524472635"
},
{
"depth": 2,
"control": "Higgs",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0",
"smallest_actual_pair_weight": "1418995095087.664861633786337212556484557922028691543331727298281256741760938133904383959798867436413416411787",
"channels_sufficient_for_exact_cancellation": 2,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0000391599972269690402204563785605962272446476065118575251144798195228913792139632211849267127852368896989288"
},
{
"depth": 3,
"control": "down",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "19.424571747323081381027178568801177349037501132973504929494699854362898477673546577545739422374208977248189998",
"smallest_actual_pair_weight": "19.424571747323081381027178568801177349037501132973504929494699854362898477673546577545739422374208977248189998",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1331181245175253144108453556192131982459965080451482988643498000504758041215986795766982932067353347943066598"
},
{
"depth": 3,
"control": "down",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "19.424574973349942400919263666106895972845471720076408145057257575667090651969824761188664386842152938608975006",
"smallest_actual_pair_weight": "19.424574973349942400919263666106895972845471720076408145057257575667090651969824761188664386842152938608975006",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.183007531385085519579479001669976725015337743613922117707445023478512100876364724859411228635738455632622214"
},
{
"depth": 3,
"control": "strange",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "1243.0840142164368337816287519638316049509960689143898927676526095156929113541684284190821279664202534019592895",
"smallest_actual_pair_weight": "1243.0840142164368337816287519638316049509960689143898927676526095156929113541684284190821279664202534019592895",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.024624074777904975892893910473103196328218719210943230615787020987014358683691973070178681347556555777154717"
},
{
"depth": 3,
"control": "strange",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "1243.0845290702269887219900052125724042094176299303993660327812012343546387281318897853250347144335165928296382",
"smallest_actual_pair_weight": "1243.0845290702269887219900052125724042094176299303993660327812012343546387281318897853250347144335165928296382",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.2580823197964798601887199840473745343437223380449398689187536002053896992728506432096194921064553594721219531"
},
{
"depth": 3,
"control": "bottom lower component",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "178844.23125300012432907276367311271983533192400540593386663350210426754879039399202706056396922143356532845399",
"smallest_actual_pair_weight": "178844.23125300012432907276367311271983533192400540593386663350210426754879039399202706056396922143356532845399",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.2488165810566552267143841583173897299006082667102173991571721241972243613193158510600373533889707521153254454"
},
{
"depth": 3,
"control": "bottom lower component",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "178844.47528857663764889235131323518645353680435276292049706722135645134556661689815344305055766795500282864351",
"smallest_actual_pair_weight": "178844.47528857663764889235131323518645353680435276292049706722135645134556661689815344305055766795500282864351",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0072135147988383715108392027405237758149094342408701971586280887625941245483692918303885658631652907138861527"
},
{
"depth": 3,
"control": "bottom upper component",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "224928.06335575317277581856931092163328958877982893208484312343128756086225598719682295553015984473835868643171",
"smallest_actual_pair_weight": "224928.06335575317277581856931092163328958877982893208484312343128756086225598719682295553015984473835868643171",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0106500462845439467496992944768808078041383473130909146259009851320649281203443697484181981879719992013566312"
},
{
"depth": 3,
"control": "bottom upper component",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "224928.38695218380970542167367213616977550723860497950874788064802711378938010757477774131265967503435389651383",
"smallest_actual_pair_weight": "224928.38695218380970542167367213616977550723860497950874788064802711378938010757477774131265967503435389651383",
"channels_sufficient_for_exact_cancellation": 3,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1256093612251316816489669894499962965161394131146011094136962187772267873231059410883600945671822537491204118"
},
{
"depth": 4,
"control": "up",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0.17014878631316451183620644192794823813152888082492120316422631712104225156389062198738320160391348193212477186",
"smallest_actual_pair_weight": "0.00044394172994695049016367957751284404116347685329281456901405114543266222898427695989394052644596863329930688005",
"channels_sufficient_for_exact_cancellation": 4,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.104305996927787571876398029687139905664559232112671056833122409507716624160788772684323739734832549713778866"
},
{
"depth": 4,
"control": "up",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0.62735261751092033695307688852514649091364743447525352294410171622049750301416124871842601747283005058481147485",
"smallest_actual_pair_weight": "0.00069371533542176114961274446658318732895419917209700839140728342518339888082382207654893027288686098069891229341",
"channels_sufficient_for_exact_cancellation": 4,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.315920836881379072591730135261823030411449081530618188023185335402985262368530281344840507409259916215126389"
},
{
"depth": 4,
"control": "charm",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "3840.3848356253908378139489535759888590041163922164829802689981418606153266913322833572492309539137792981382932",
"smallest_actual_pair_weight": "7.9559568333308817999030788986972223085818763005802021030322650746437397360179222640503509260247740262514405319",
"channels_sufficient_for_exact_cancellation": 4,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0421460140032816607299203212152096594854007909923486757042769373131016540208278421177731161922011263175576004"
},
{
"depth": 4,
"control": "charm",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "4998.3508215244273829784404458789797950121264636779555585653399730640039060355646491216028804299741116680595227",
"smallest_actual_pair_weight": "8.7350675120219964209576145540942526683816653539912914097812304330396577932494024756148272820550424842998690394",
"channels_sufficient_for_exact_cancellation": 4,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1504116201571761839307955533178805766178187487355488574518937889665907074296342431578762403086312102425450727"
},
{
"depth": 4,
"control": "top",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "6414952.202534952091731317921933544018253261896112196716544263159605181824467649820013902322589875982681553362",
"smallest_actual_pair_weight": "12662.045784952035936300216268856002500132342056214184086984643593338477011767506556922752831893870107288126083",
"channels_sufficient_for_exact_cancellation": 4,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0724783569932965156096405310375970430702115086531812745431548288075864429062877945902169898297579897179231483"
},
{
"depth": 4,
"control": "top",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "6934193.1894647521532527050795222269927718515307347468724109336841590652988568168301865724092424607244999589324",
"smallest_actual_pair_weight": "13026.801210324886546966965865906107549183761353852214435994245509117241917276924492498441124168862396336933117",
"channels_sufficient_for_exact_cancellation": 4,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0755154126192152359062368139426309240871749740805308601098169309391381184157487321734561329234236194512911317"
},
{
"depth": 5,
"control": "neutrino 1",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0.25627787429720215989397213974948486517244194574910592218776757452333512451657616847269493819310091128961625546",
"smallest_actual_pair_weight": "0.0000018167092856284134753487066750605620308817246505298916726022026567633865272725446303376915117905355623616313213",
"channels_sufficient_for_exact_cancellation": 5,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1614514608744644292932525723990991657686630419799966034985952314890969323812069533270781312426237688369302955"
},
{
"depth": 5,
"control": "neutrino 1",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0.18491269479609746963772176903431954613430685745346084204478719212620845663190210676177932810641228333382558472",
"smallest_actual_pair_weight": "0.0000018168838560521867356641776686051404356885127261220348010144014286604363846448365579044920177513043729940365653",
"channels_sufficient_for_exact_cancellation": 5,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0309655034116929362194932698694397971018600944636758712918988023750267303581117396376766964664722240860516611"
},
{
"depth": 5,
"control": "neutrino 2",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "2.0500772415713881901923918282295300205367463963920184360596788465060017016337735887668186370359388864052284041",
"smallest_actual_pair_weight": "0.000030497766892506982509579958440885313474702710373557815557197651321862829169922039616383191541324241383341795792",
"channels_sufficient_for_exact_cancellation": 5,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1580129530646909030773871649122299785715910639374532607017201978942897007321795000322209428447362257330357214"
},
{
"depth": 5,
"control": "neutrino 2",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "1.6368894462107830848923817011794057320731145389938878666920543885660023730026061642001692699378616262570652661",
"smallest_actual_pair_weight": "0.000030501910263245098971068800305403079557501094775029917463331605582742117021200052269468850561529028872361011658",
"channels_sufficient_for_exact_cancellation": 5,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1107561213686363510516203604915760485416164502410670542180697398864865780457625795377472146480745711214030022"
},
{
"depth": 5,
"control": "neutrino 3",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "16.156914917569226766102543977952865920668267318437457172259673892742032276903502315902148787766270161516423097",
"smallest_actual_pair_weight": "0.00048844278012978709125355747478575292247492348716605843782050209870069299400519980328097886139298118234092111172",
"channels_sufficient_for_exact_cancellation": 5,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1567418938780208341462411759426851119660744568795380639860416680294670048369073477028706564159923450654417873"
},
{
"depth": 5,
"control": "neutrino 3",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "13.872384678801396445347455435134059500355489153615368831248074716077271449050202288833095044356201267480981308",
"smallest_actual_pair_weight": "0.00048853609496164634671066021912555324050472331015218125486694899837134803931044834525773895788398209882150206228",
"channels_sufficient_for_exact_cancellation": 5,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.3742332492015644339494615794283152827633226359742274410230626936662159282276820391846318003037878864412532504"
},
{
"depth": 6,
"control": "electron",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0.011987403092576267037980797938724143737555121063998798652364498689737814706853792229946806869657055779406505176",
"smallest_actual_pair_weight": "0.000000000027894828667549072962887647653989648969258673102380695471277085602717142448234072852909014631122046080514234036",
"channels_sufficient_for_exact_cancellation": 6,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.2023996297847432550285259170685044998378636308029765132120359988693315386004261077431874744749103274341228505"
},
{
"depth": 6,
"control": "electron",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0.022844948116049175381977937565127535160774575972514982980843975094874461839230860291969862874047190250130721255",
"smallest_actual_pair_weight": "0.00000000003206968039282571024775959679894265548778824802023447745629755279519187501683774851367826527017635027287091755",
"channels_sufficient_for_exact_cancellation": 6,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1188516145097412388873075183347712628464726713162537231305783433075867947508732445688926985646754016903441235"
},
{
"depth": 6,
"control": "muon",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "13.522595999482721792281332212193406782014321158377691482725987997881001060560325000747222455305507650214785399",
"smallest_actual_pair_weight": "0.00000016713902637764037006547063851696129647377455687204985411916259585791723974536100313247865086166404901506555092",
"channels_sufficient_for_exact_cancellation": 6,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.0938995611441317641018675790508728294776570319778636610629141646396243265408861845764898054317211512704750688"
},
{
"depth": 6,
"control": "muon",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "17.464463769497174391661085251613781569733765672530036210163112429766863884778453612762096419614521276452121128",
"smallest_actual_pair_weight": "0.00000017813338647278452111362954261124279269131257269026610428802674837057608846211831842896086547262962015096122777",
"channels_sufficient_for_exact_cancellation": 6,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.2102671960300258676783124318253424010859240180652942998832187126124489122211617179803306146773959515786134606"
},
{
"depth": 10,
"control": "tau",
"surface_sign": 1,
"two_channel_minimum_pair_weight": "0.000000000000061185916842349905046085778880164997153604854236867252868485401836293422707055973443072972017538167637693839182",
"smallest_actual_pair_weight": "0.0000000000000000000000000000000025588713255131569097227379714372766706215314474707286138793691672078350719047425188308681320467628023669868401",
"channels_sufficient_for_exact_cancellation": 10,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.2113002643263483366147698064371449444547211529984840936416864401281782122913249294507716175966371263170525755"
},
{
"depth": 10,
"control": "tau",
"surface_sign": -1,
"two_channel_minimum_pair_weight": "0.00000000000036079271781586391094958358477315855879007518280362583000100304254508888292932237462867301452592493546897357898",
"smallest_actual_pair_weight": "0.0000000000000000000000000000000015336946367119476197963005781261488753703750669042649598265911046407722694989638385628595513936768346248428006",
"channels_sufficient_for_exact_cancellation": 10,
"positive_mass_lower_bound": "1.0",
"resulting_energy_momentum_mass": "1.1198687925823130963012509216251207766588060210249075571894526040844540669030500749412135317169623184628149576"
}
],
"scope": "Conditional extension to r identical polarization channels using the actual retained endpoint source. Orthogonal polarization vectors cancel all pair sources when r is at least the number of occupied bands; the physical value of r is not derived. A separate positive energy-momentum identity shows that neither phase cancellation nor the number of spatial dimensions produces a two-only inertial-mass cancellation in the tested positive quadratic action.",
"input_report": {
"path": "flux-moment-20260915T033331_031324Z.json",
"sha256": "6ed720878d217cc502ef9d7ba94e70b3d5b0afd10e08e1a7d3410336878f21e5"
},
"source_hashes": {
"experiments/polarization_dimension_cancellation_checks.py": "33ef2613fa3caafdf74eb0f0f8242f711199c7842342a8ea7491260eed4b8d49",
"experiments/mass_operator_sectors.py": "3c56bfb036174b2d62aa0902f02bea4148c42c43bd7484539f618c2291125a3b"
},
"elapsed_seconds": 0.9061942480038851
}