{
  "source": "2013 author manuscript, 19 pages; publisher record 24(1\u20134):320\u2013338",
  "figures": [
    {
      "number": 1,
      "title": "Video feedback and the mathematical model",
      "source_pages": [
        2
      ],
      "cases": [
        "fig1_60",
        "fig1_90",
        "fig1_135",
        "fig1_144"
      ],
      "note": "Historical video feedback alongside mathematical specimens with specified branch parameters. The photographs motivate the model rather than calibrating its coefficients.",
      "plates": [
        "figures/2013/fig01_feedback.pdf",
        "figures/2013/fig01_local_models.pdf"
      ]
    },
    {
      "number": 2,
      "title": "The binary locus in two reciprocal charts",
      "source_pages": [
        3
      ],
      "cases": [
        "fig1_60",
        "fig1_90",
        "gold_108",
        "gold_120",
        "fig1_135",
        "fig1_144"
      ],
      "note": "Both the inner contraction chart and the outer expansion chart are shown. The unit circle is excluded; these are reciprocal parameter charts, not a continuation of the same contractive maps through it.",
      "plates": [
        "figures/2013/fig02_exterior_plane.pdf"
      ]
    },
    {
      "number": 3,
      "title": "Angle\u2013expansion chart and golden references",
      "source_pages": [
        5
      ],
      "cases": [
        "fig1_60",
        "gold_108",
        "gold_120",
        "fig1_144",
        "fig1_90"
      ],
      "note": "All four golden trees and both tile junctions are retained; increasing R means shorter branches.",
      "plates": [
        "figures/2013/fig03_angle_R.pdf",
        "figures/2013/fig03_golden_specimens.pdf"
      ]
    },
    {
      "number": 4,
      "title": "The original 50\u00b0 contact calculation",
      "source_pages": [
        6
      ],
      "cases": [
        "fig4_50"
      ],
      "note": "The highlighted point is the infinite tip, not a finite vertex. Its expansion satisfies R\u00b3 \u2212 2R \u2212 2cos(50\u00b0) = 0.",
      "plates": [
        "figures/2013/fig04_address_50.pdf"
      ]
    },
    {
      "number": 5,
      "title": "Even backward-centred fans",
      "source_pages": [
        9
      ],
      "cases": [
        "fig5_Beven"
      ],
      "note": "An even backward-centred fan: local directions, adjacent addresses, and the B4\u2013B6 contact equations, illustrated at 60\u00b0.",
      "plates": [
        "figures/2013/fig05_fan_and_contact.pdf"
      ]
    },
    {
      "number": 6,
      "title": "Backward contact equations and full-fan reference points",
      "source_pages": [
        11
      ],
      "cases": [
        "B_reference_2",
        "B_reference_3",
        "B_reference_4",
        "B_reference_5",
        "B_reference_6",
        "B_reference_7"
      ],
      "note": "Integer-arity contact blocks, continuous transition tracks, and the regular-fan reference points. The reference rays have exact hull and connectedness-threshold proofs.",
      "plates": [
        "figures/2013/fig06_B_catalogue.pdf",
        "figures/2013/fig06_regular_references.pdf"
      ]
    },
    {
      "number": 7,
      "title": "Odd backward-centred fans",
      "source_pages": [
        13
      ],
      "cases": [
        "fig7_Bodd"
      ],
      "note": "The central backward multiplier is \u22121/R. Its branch retraces part of the trunk at every R; canopy contact is a different statement.",
      "plates": [
        "figures/2013/fig07_fan_and_contact.pdf"
      ]
    },
    {
      "number": 8,
      "title": "Even forward-centred fans",
      "source_pages": [
        14
      ],
      "cases": [
        "fig8_Feven"
      ],
      "note": "The two high-angle quadratic periods are kept distinct. The displayed parameter is an explicitly specified representative.",
      "plates": [
        "figures/2013/fig08_fan_and_contact.pdf"
      ]
    },
    {
      "number": 9,
      "title": "The four even forward contact classes",
      "source_pages": [
        15
      ],
      "cases": [
        "fig8_Feven",
        "fig1_60"
      ],
      "note": "F7, F8, F9 and F10 are all present, with separate repeating periods and admissible indices. The binary subfamily has a complete radial theorem.",
      "plates": [
        "figures/2013/fig09_F_even_catalogue.pdf"
      ]
    },
    {
      "number": 10,
      "title": "Odd forward-centred fans",
      "source_pages": [
        16
      ],
      "cases": [
        "fig10_Fodd",
        "ternary_F60"
      ],
      "note": "The axial branch is C+; contact is on the appropriate adjacent bisector, not necessarily the trunk axis.",
      "plates": [
        "figures/2013/fig10_fan_and_contact.pdf"
      ]
    },
    {
      "number": 11,
      "title": "Odd forward equations and regular references",
      "source_pages": [
        17
      ],
      "cases": [
        "F_reference_3",
        "F_reference_5",
        "F_reference_7"
      ],
      "note": "F11 and the explicitly re-derived F12 are both covered. Reference polygons are exact convex hulls, not claims that every canopy fills them.",
      "plates": [
        "figures/2013/fig11_F_odd_catalogue.pdf",
        "figures/2013/fig11_regular_references.pdf"
      ]
    }
  ],
  "equations": [
    {
      "source_equation": 1,
      "adapted_label": "2013.1",
      "proof": "chapters/article2013.tex",
      "status": "Exact reciprocal address derivation"
    },
    {
      "source_equation": 2,
      "adapted_label": "2013.2",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    },
    {
      "source_equation": 3,
      "adapted_label": "2013.3",
      "proof": "chapters/article2013.tex",
      "status": "Exact reciprocal address derivation"
    },
    {
      "source_equation": 4,
      "adapted_label": "2013.4",
      "proof": "chapters/article2013.tex",
      "status": "Exact reciprocal address derivation"
    },
    {
      "source_equation": 5,
      "adapted_label": "2013.5",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    },
    {
      "source_equation": 6,
      "adapted_label": "2013.6",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    },
    {
      "source_equation": 7,
      "adapted_label": "2013.7",
      "proof": "chapters/article2013.tex",
      "status": "Exact reciprocal address derivation"
    },
    {
      "source_equation": 8,
      "adapted_label": "2013.8",
      "proof": "chapters/article2013.tex",
      "status": "Exact reciprocal address derivation"
    },
    {
      "source_equation": 9,
      "adapted_label": "2013.9",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    },
    {
      "source_equation": 10,
      "adapted_label": "2013.10",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    },
    {
      "source_equation": 11,
      "adapted_label": "2013.11",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    },
    {
      "source_equation": 12,
      "adapted_label": "2013.12",
      "proof": "chapters/article2013.tex",
      "status": "Corrected address derivation, not a verbatim assertion of equivalence to every printed source variant"
    }
  ],
  "global_scope": "Complete binary radial classification, exact regular-fan support test and complete full-fan rays. General higher-arity selector minimality and full-skeleton no-crossing are not claimed."
}