feat(corner-idler-bracket): graph twin of the script (graph format 1.1) (#169)

corner-idler.graph.json is a golden twin of main.py, declared as graph_file
on the corner_idler mode beside the script (owner decision D5: graph twins
coexist with scripts, parity-checked; main.py stays the rendered source and
the oracle). Digital Twins phase 8b, lane P8-TWINS-B.

Same parameters (declared in `parameters`, `mirrored` included), same
derivations (the nine clamps as ternary pairs in `derived`, `length`'s max
as a ternary, the constants under main.py's names and values) and the same
operations in the same order. `mirrored` selects the pure YZ `reflect` of
the body, as body.mirror("YZ") does.

Each _cyl_y is an XZ profile_circle extruded along +Y, turned -90 degrees
about its own axis, then translated into place. The turn puts the cylinder's
seam at +Z, where makeCylinder (gp_Ax2 with an axis along Y) puts it; the
seam decides where the tessellator puts vertices, and without it the two
meshes differ by 0.001635 mm at the counterbore floors.

y4d-spec check --render --require-openscad --parity ./corner-idler-bracket:
10 renders, parity 5/5 at 0.000000 mm (defaults + gates_9mm_right,
gates_9mm_left, belt_6mm_right, long_drop_wide_pitch; the two mirrored
presets included), frames 35/35 ok, failures 0. Frames and presets
unchanged. Assembly A validates (235/235 placed, 292/292 mates, poses
23/23); its digest moves cb80b679... -> 0839e06c... because the cartridge
gains a file.

Signed-off-by: Aldo Ruiz Luna <aldo.ruiz.luna@gmail.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

Author: aldoruizluna

corner-idler-bracket/corner-idler.graph.json

@@ -0,0 +1,121 @@
+{
+  "version": "1.1.0",
+  "units": "mm",
+  "meta": {
+    "title": "Corner Idler Bracket (graph twin)",
+    "notes": "Golden twin of main.py (graph format 1.1): the same parameters, the same derivations and the same operations in the same order. main.py stays the oracle; y4d-spec --parity compares the two at the defaults and at every preset. Constants keep main.py's names and values, and their sources are main.py's: ISO 7380-1 M5x30 (Keller & Kalmbach 157380530: SCREW_D 5, SCREW_L 30, HEAD_DK 9.5, HEAD_K 2.75), MISUMI HFS5 T-slot (SLOT_LIP_T 2, PILOT_D 4.2, PROFILE 20), MISUMI HNTAP5-5 (TNUT_L 15); HOLE_CLEAR, HEAD_CLEAR, TAB_W, POCKET_RADIAL, AXLE_WALL, HEEL_GAP, MOUNT_X1 and EDGE are main.py's labelled conventions. Clamps max(lo, min(x, hi)) and length's max are ternaries, because the expression dialect has no function calls. _cyl_y (makeCylinder along +Y) is an XZ profile_circle at (x, z) extruded by -(y1 - y0), since the XZ normal is -Y, then translated to y0. `mirrored` selects the pure YZ reflection of the body, as body.mirror(\"YZ\") does."
+  },
+  "parameters": {
+    "idler_width": {"default": 14.0},
+    "idler_od": {"default": 18.0},
+    "idler_clear": {"default": 0.5},
+    "idler_offset": {"default": 13.0},
+    "idler_drop": {"default": 24.0},
+    "front_arm": {"default": 5.0},
+    "mount_grip": {"default": 24.5},
+    "mount_pitch": {"default": 20.0},
+    "heel_reach": {"default": 18.0},
+    "mirrored": {"default": false}
+  },
+  "derived": [
+    {"id": "SCREW_D", "expr": "5.0"},
+    {"id": "SCREW_L", "expr": "30.0"},
+    {"id": "HEAD_DK", "expr": "9.5"},
+    {"id": "HEAD_K", "expr": "2.75"},
+    {"id": "SLOT_LIP_T", "expr": "2.0"},
+    {"id": "PILOT_D", "expr": "4.2"},
+    {"id": "PROFILE", "expr": "20.0"},
+    {"id": "TNUT_L", "expr": "15.0"},
+    {"id": "HOLE_CLEAR", "expr": "0.25"},
+    {"id": "HEAD_CLEAR", "expr": "0.5"},
+    {"id": "TAB_W", "expr": "5.8"},
+    {"id": "POCKET_RADIAL", "expr": "1.0"},
+    {"id": "AXLE_WALL", "expr": "7.0"},
+    {"id": "HEEL_GAP", "expr": "0.5"},
+    {"id": "MOUNT_X1", "expr": "10.0"},
+    {"id": "EDGE", "expr": "4.75"},
+    {"id": "iw_cap", "expr": "idler_width < 20 ? idler_width : 20"},
+    {"id": "iw", "expr": "9 > iw_cap ? 9 : iw_cap"},
+    {"id": "od_cap", "expr": "idler_od < 24 ? idler_od : 24"},
+    {"id": "od", "expr": "12 > od_cap ? 12 : od_cap"},
+    {"id": "ic_cap", "expr": "idler_clear < 2 ? idler_clear : 2"},
+    {"id": "ic", "expr": "0.2 > ic_cap ? 0.2 : ic_cap"},
+    {"id": "fa_cap", "expr": "front_arm < 8 ? front_arm : 8"},
+    {"id": "fa", "expr": "3 > fa_cap ? 3 : fa_cap"},
+    {"id": "gap", "expr": "iw + 2 * ic"},
+    {"id": "rear_arm", "expr": "SCREW_L - fa - gap"},
+    {"id": "pocket_r", "expr": "od / 2 + POCKET_RADIAL"},
+    {"id": "io_cap", "expr": "idler_offset < 40 ? idler_offset : 40"},
+    {"id": "io", "expr": "(pocket_r + 1) > io_cap ? (pocket_r + 1) : io_cap"},
+    {"id": "idrop_cap", "expr": "idler_drop < 60 ? idler_drop : 60"},
+    {"id": "idrop", "expr": "(pocket_r + 8) > idrop_cap ? (pocket_r + 8) : idrop_cap"},
+    {"id": "mg_cap", "expr": "mount_grip < (SCREW_L - HEAD_K - 0.5) ? mount_grip : (SCREW_L - HEAD_K - 0.5)"},
+    {"id": "mg", "expr": "(SCREW_L - 8) > mg_cap ? (SCREW_L - 8) : mg_cap"},
+    {"id": "mp_cap", "expr": "mount_pitch < 60 ? mount_pitch : 60"},
+    {"id": "mp", "expr": "(TNUT_L + 1) > mp_cap ? (TNUT_L + 1) : mp_cap"},
+    {"id": "hr_cap", "expr": "heel_reach < PROFILE ? heel_reach : PROFILE"},
+    {"id": "hr", "expr": "(PROFILE / 2 + TAB_W / 2 + 2) > hr_cap ? (PROFILE / 2 + TAB_W / 2 + 2) : hr_cap"},
+    {"id": "DEPTH", "expr": "SCREW_L"},
+    {"id": "TOP", "expr": "PROFILE / 2"},
+    {"id": "z_axle", "expr": "-idrop"},
+    {"id": "z_bottom", "expr": "z_axle - AXLE_WALL"},
+    {"id": "x2", "expr": "MOUNT_X1 + mp"},
+    {"id": "length_a", "expr": "x2 + (HEAD_DK / 2 + HEAD_CLEAR) + EDGE"},
+    {"id": "length_b", "expr": "io + pocket_r + 4"},
+    {"id": "length", "expr": "length_a > length_b ? length_a : length_b"},
+    {"id": "heel_top", "expr": "-PROFILE / 2 - HEEL_GAP"},
+    {"id": "hole_d", "expr": "SCREW_D + 2 * HOLE_CLEAR"},
+    {"id": "cbore_d", "expr": "HEAD_DK + 2 * HEAD_CLEAR"}
+  ],
+  "nodes": [
+    {"id": "block_blank", "type": "box", "params": {"w": {"expr": "length - 0"}, "d": {"expr": "DEPTH - 0"}, "h": {"expr": "TOP - z_bottom"}}},
+    {"id": "block", "type": "translate", "inputs": {"shape": "block_blank"}, "params": {"x": {"expr": "(0 + length) / 2"}, "y": {"expr": "(0 + DEPTH) / 2"}, "z": {"expr": "(z_bottom + TOP) / 2"}}},
+    {"id": "heel_blank", "type": "box", "params": {"w": {"expr": "0.5 - -hr"}, "d": {"expr": "DEPTH - 0"}, "h": {"expr": "heel_top - z_bottom"}}},
+    {"id": "heel", "type": "translate", "inputs": {"shape": "heel_blank"}, "params": {"x": {"expr": "(-hr + 0.5) / 2"}, "y": {"expr": "(0 + DEPTH) / 2"}, "z": {"expr": "(z_bottom + heel_top) / 2"}}},
+    {"id": "body_1", "type": "union", "inputs": {"a": "block", "b": "heel"}},
+    {"id": "corner_tongue_blank", "type": "box", "params": {"w": {"expr": "0.5 - -SLOT_LIP_T"}, "d": {"expr": "DEPTH - 2 - 2"}, "h": {"expr": "TAB_W / 2 - (-TAB_W / 2)"}}},
+    {"id": "corner_tongue", "type": "translate", "inputs": {"shape": "corner_tongue_blank"}, "params": {"x": {"expr": "(-SLOT_LIP_T + 0.5) / 2"}, "y": {"expr": "(2 + (DEPTH - 2)) / 2"}, "z": {"expr": "(-TAB_W / 2 + (TAB_W / 2)) / 2"}}},
+    {"id": "body_2", "type": "union", "inputs": {"a": "body_1", "b": "corner_tongue"}},
+    {"id": "heel_tongue_blank", "type": "box", "params": {"w": {"expr": "-PROFILE / 2 + TAB_W / 2 - (-PROFILE / 2 - TAB_W / 2)"}, "d": {"expr": "0.5 - -SLOT_LIP_T"}, "h": {"expr": "heel_top - 2 - (z_bottom + 2)"}}},
+    {"id": "heel_tongue", "type": "translate", "inputs": {"shape": "heel_tongue_blank"}, "params": {"x": {"expr": "(-PROFILE / 2 - TAB_W / 2 + (-PROFILE / 2 + TAB_W / 2)) / 2"}, "y": {"expr": "(-SLOT_LIP_T + 0.5) / 2"}, "z": {"expr": "(z_bottom + 2 + (heel_top - 2)) / 2"}}},
+    {"id": "body_3", "type": "union", "inputs": {"a": "body_2", "b": "heel_tongue"}},
+    {"id": "mount_hole_1_outline", "type": "profile_circle", "params": {"plane": "XZ", "r": {"expr": "hole_d / 2"}}},
+    {"id": "mount_hole_1_blank", "type": "extrude", "inputs": {"profile": "mount_hole_1_outline"}, "params": {"height": {"expr": "-(DEPTH + 1 - -1)"}}},
+    {"id": "mount_hole_1_seam", "type": "rotate", "inputs": {"shape": "mount_hole_1_blank"}, "params": {"axis": "y", "angle": -90.0}},
+    {"id": "mount_hole_1", "type": "translate", "inputs": {"shape": "mount_hole_1_seam"}, "params": {"x": {"expr": "MOUNT_X1"}, "y": -1.0}},
+    {"id": "body_4", "type": "cut", "inputs": {"a": "body_3", "b": "mount_hole_1"}},
+    {"id": "mount_cbore_1_outline", "type": "profile_circle", "params": {"plane": "XZ", "r": {"expr": "cbore_d / 2"}}},
+    {"id": "mount_cbore_1_blank", "type": "extrude", "inputs": {"profile": "mount_cbore_1_outline"}, "params": {"height": {"expr": "-(DEPTH + 1 - mg)"}}},
+    {"id": "mount_cbore_1_seam", "type": "rotate", "inputs": {"shape": "mount_cbore_1_blank"}, "params": {"axis": "y", "angle": -90.0}},
+    {"id": "mount_cbore_1", "type": "translate", "inputs": {"shape": "mount_cbore_1_seam"}, "params": {"x": {"expr": "MOUNT_X1"}, "y": {"expr": "mg"}}},
+    {"id": "body_5", "type": "cut", "inputs": {"a": "body_4", "b": "mount_cbore_1"}},
+    {"id": "mount_hole_2_outline", "type": "profile_circle", "params": {"plane": "XZ", "r": {"expr": "hole_d / 2"}}},
+    {"id": "mount_hole_2_blank", "type": "extrude", "inputs": {"profile": "mount_hole_2_outline"}, "params": {"height": {"expr": "-(DEPTH + 1 - -1)"}}},
+    {"id": "mount_hole_2_seam", "type": "rotate", "inputs": {"shape": "mount_hole_2_blank"}, "params": {"axis": "y", "angle": -90.0}},
+    {"id": "mount_hole_2", "type": "translate", "inputs": {"shape": "mount_hole_2_seam"}, "params": {"x": {"expr": "x2"}, "y": -1.0}},
+    {"id": "body_6", "type": "cut", "inputs": {"a": "body_5", "b": "mount_hole_2"}},
+    {"id": "mount_cbore_2_outline", "type": "profile_circle", "params": {"plane": "XZ", "r": {"expr": "cbore_d / 2"}}},
+    {"id": "mount_cbore_2_blank", "type": "extrude", "inputs": {"profile": "mount_cbore_2_outline"}, "params": {"height": {"expr": "-(DEPTH + 1 - mg)"}}},
+    {"id": "mount_cbore_2_seam", "type": "rotate", "inputs": {"shape": "mount_cbore_2_blank"}, "params": {"axis": "y", "angle": -90.0}},
+    {"id": "mount_cbore_2", "type": "translate", "inputs": {"shape": "mount_cbore_2_seam"}, "params": {"x": {"expr": "x2"}, "y": {"expr": "mg"}}},
+    {"id": "body_7", "type": "cut", "inputs": {"a": "body_6", "b": "mount_cbore_2"}},
+    {"id": "idler_pocket_blank", "type": "box", "params": {"w": {"expr": "io + pocket_r - (io - pocket_r)"}, "d": {"expr": "rear_arm + gap - rear_arm"}, "h": {"expr": "z_axle + pocket_r - (z_bottom - 1)"}}},
+    {"id": "idler_pocket", "type": "translate", "inputs": {"shape": "idler_pocket_blank"}, "params": {"x": {"expr": "(io - pocket_r + (io + pocket_r)) / 2"}, "y": {"expr": "(rear_arm + (rear_arm + gap)) / 2"}, "z": {"expr": "(z_bottom - 1 + (z_axle + pocket_r)) / 2"}}},
+    {"id": "body_8", "type": "cut", "inputs": {"a": "body_7", "b": "idler_pocket"}},
+    {"id": "axle_clearance_outline", "type": "profile_circle", "params": {"plane": "XZ", "r": {"expr": "hole_d / 2"}}},
+    {"id": "axle_clearance_blank", "type": "extrude", "inputs": {"profile": "axle_clearance_outline"}, "params": {"height": {"expr": "-(DEPTH + 1 - (rear_arm + gap - 0.5))"}}},
+    {"id": "axle_clearance_seam", "type": "rotate", "inputs": {"shape": "axle_clearance_blank"}, "params": {"axis": "y", "angle": -90.0}},
+    {"id": "axle_clearance", "type": "translate", "inputs": {"shape": "axle_clearance_seam"}, "params": {"x": {"expr": "io"}, "y": {"expr": "rear_arm + gap - 0.5"}, "z": {"expr": "z_axle"}}},
+    {"id": "body_9", "type": "cut", "inputs": {"a": "body_8", "b": "axle_clearance"}},
+    {"id": "axle_pilot_outline", "type": "profile_circle", "params": {"plane": "XZ", "r": {"expr": "PILOT_D / 2"}}},
+    {"id": "axle_pilot_blank", "type": "extrude", "inputs": {"profile": "axle_pilot_outline"}, "params": {"height": {"expr": "-(rear_arm + 0.5 - -1)"}}},
+    {"id": "axle_pilot_seam", "type": "rotate", "inputs": {"shape": "axle_pilot_blank"}, "params": {"axis": "y", "angle": -90.0}},
+    {"id": "axle_pilot", "type": "translate", "inputs": {"shape": "axle_pilot_seam"}, "params": {"x": {"expr": "io"}, "y": -1.0, "z": {"expr": "z_axle"}}},
+    {"id": "body_10", "type": "cut", "inputs": {"a": "body_9", "b": "axle_pilot"}},
+    {"id": "body_mirrored", "type": "reflect", "inputs": {"shape": "body_10"}, "params": {"plane": "YZ"}},
+    {"id": "corner_idler", "type": "select", "inputs": {"if_true": "body_mirrored", "if_false": "body_10"}, "params": {"when": {"expr": "mirrored"}}}
+  ],
+  "outputs": {
+    "corner_idler": "corner_idler"
+  }
+}

corner-idler-bracket/docs/README.md

@@ -100,6 +100,13 @@ That closure is the assembly A's top corner should use.
 - **Long Drop, Wide T-Nut Spacing.** Left-hand: the axle 36 mm down and 20 mm from the corner,
   with the T-nuts 30 mm apart.
 
+## Graph twin
+
+`corner-idler.graph.json` is a node-graph twin of `main.py` (graph format 1.1). It has the same parameters, the same derivations and the same operations in the same order. Each `_box` is a centred `box` translated to its centre, and each clamp a min/max ternary pair in `derived`. Each `_cyl_y` is an XZ `profile_circle` extruded along +Y (the XZ normal is −Y, so the height is negative), turned −90° about its own axis so the cylinder's seam sits at +Z where `makeCylinder` puts it, then translated into place; the seam decides where the tessellator puts vertices, so without the turn the two meshes differ by 0.0016 mm. `mirrored` is a `select` between the body and its pure YZ `reflect`, as `body.mirror("YZ")`. The constants keep `main.py`'s names, values and sources.
+- **Declaration.** The mode declares it as `graph_file` next to the script.
+- **Verification.** `y4d-spec check --render --parity` compares the two at the defaults and at every preset (`gates_9mm_right`, `gates_9mm_left`, `belt_6mm_right`, `long_drop_wide_pitch`; the two mirrored presets included); they agree to 0.000000 mm.
+- **Which one renders.** `main.py` stays the source the platform renders and the oracle the graph is checked against. A script retires only after parity holds across the nightly sweep (owner decision D5, 2026-10-04).
+
 ## Hyperobject Profile
 
 - **Domain:** industrial.

corner-idler-bracket/project.json

@@ -42,6 +42,7 @@
       },
       "scad_file": "main.py",
       "cq_file": "main.py",
+      "graph_file": "corner-idler.graph.json",
       "parts": [
         "corner_idler"
       ],