{
  "authorship": "Original mathematics and figures;GPT-6.1 Sol (OpenAI),Ultra;CC0 1.0",
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      "atom_weights": "2^(-j), j enumerates all atoms",
      "marker_sizes_do_not_represent_masses": true
    },
    "embedded_segment": {
      "endpoints": [
        [
          -1,
          0,
          0
        ],
        [
          1,
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        ]
      ],
      "displayed_atom_coordinates": [
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      "weights_per_atom": "2^(-m-1)",
      "physical_projection": "x_1; x_2=x_3=0",
      "full_construction_uses_all_m": true
    },
    "proof_locators": [
      "Formal Theorems3.1,4.1",
      "Learner Example3",
      "Learner Exercises5\u20137"
    ],
    "physical_axes_have_equal_scale": true
  },
  "separated_sum": {
    "f": {
      "smooth": true,
      "support": [
        -2,
        3
      ],
      "positive_on_interior": true
    },
    "u1": "delta_-1+f",
    "u2": "delta_2-f",
    "ordinary_supports": [
      [
        -2,
        3
      ],
      [
        -2,
        3
      ]
    ],
    "singular_supports": [
      [
        -1
      ],
      [
        2
      ]
    ],
    "sum": "delta_-1+delta_2",
    "sum_singular_support": [
      -1,
      2
    ],
    "sum_singular_hull": [
      -1,
      2
    ],
    "sum_indicator": "max(-eta,2*eta)",
    "diagram_vertical_positions_are_distribution_rows_not_physical_coordinates": true,
    "proof_locators": [
      "Formal Lemma2.2,Theorem6.1",
      "Learner Example2"
    ]
  },
  "cancellation": {
    "v1": "delta_0",
    "v2": "-delta_0",
    "common_singular_support": [
      0
    ],
    "sum": "zero",
    "component_indicators": [
      "zero",
      "zero"
    ],
    "sum_indicator": "collapsed minus infinity",
    "proof_locators": [
      "Learner Example4",
      "Learner Exercise10"
    ]
  },
  "references": [
    "Terence Tao,246B Notes2 and245B Notes9",
    "Lars H\u00f6rmander,Analysis of Linear Partial Differential Operators I and II"
  ]
}