{
  "schema": "AN02-joint-convolution-original-geometry195/v1",
  "atomic": {
    "u": [
      [
        0,
        1
      ],
      [
        1,
        1
      ]
    ],
    "v": [
      [
        0,
        1
      ],
      [
        1,
        -1
      ]
    ],
    "convolution": [
      [
        0,
        1
      ],
      [
        2,
        -1
      ]
    ],
    "cancelled_mass": {
      "location": 1,
      "sum": 0
    },
    "input_carriers": [
      [
        0,
        1
      ],
      [
        0,
        1
      ]
    ],
    "output_carrier": [
      0,
      2
    ],
    "input_indicators": "max(0,eta)",
    "output_indicator": "2 max(0,eta)",
    "persistent_real_zero_sequence": "c_j=2*pi*j for v and u*v",
    "canonical_profile_at_z0": 0,
    "exact_transform_log_at_z0": "minus infinity",
    "proof_locators": [
      "Learner Worked example2",
      "Formal Lemmas2.1\u20132.4",
      "Formal Theorem1.1"
    ]
  },
  "crossed": {
    "p_support": {
      "x1": 0,
      "x2_interval": [
        -1,
        1
      ]
    },
    "q_support": {
      "x1_interval": [
        -1,
        1
      ],
      "x2": 0
    },
    "convolution_ordinary_support": [
      [
        -1,
        1
      ],
      [
        -1,
        1
      ]
    ],
    "smooth_probability_density": "f(t)=C exp(-1/(1-t^2)) for |t|<1,otherwise0",
    "C_numerical_decimal": "2.2522836210435810104997812555598307300741954382887667026737202943",
    "convolution_function": "f(x1)*f(x2)",
    "convolution_singular_support": [],
    "convolution_logarithmic_carrier": [],
    "frequency_rays": [
      {
        "c": "(t,0),t->infinity",
        "joint_status_after_extraction": [
          "proper",
          "collapsed"
        ]
      },
      {
        "c": "(0,t),t->infinity",
        "joint_status_after_extraction": [
          "collapsed",
          "proper"
        ]
      },
      {
        "c": "(t,t),t->infinity",
        "joint_status": [
          "collapsed",
          "collapsed"
        ]
      }
    ],
    "individual_carrier_qualification": "A proper carrier is a nonempty compact convex subset of its component segment;the plot does not classify every such subset.",
    "heatmap_qualification": "257 by257 numerical samples of the specified actual smooth probability density product,inside its exact support square.",
    "proof_locators": [
      "Learner Worked example3",
      "Formal Lemma2.3",
      "Formal Theorem1.1"
    ]
  },
  "Blender_assessment": "Signed one-dimensional masses,two-dimensional support geometry and a shared real-frequency plane are fully represented in exact vector plots;an added third spatial dimension would not explain the synchronization."
}