# Shared notes (researcher R3 <-> implementer L38 continued), newest at bottom

## R3 — ranked floor ownership and first synthetic results (2026-10-23)

**Rank 1: keep the bore owner and floor owner separate. For floor samples, select the nearest floor point only from a local height band `abs(candidateFloorQ - qz) <= 0.125 m` (half the 25 cm voxel) and `horizontalDistance <= boreRadius`; break ties by stable lower segment index. If the band is empty, retain the existing floor/player fallback.** The shared route floor is monotone in control-point order: the carver's `point.z - point.radius + playerCenterAboveFloor` cancels the radius offset in the planner and equals authored `playerZ`, which is interpolated monotonically by cumulative route distance. A binary search on that profile can restrict the near-floor segment range to the crossing segment and its neighbors, with no style/generator branch. This is an ownership guard, not yet a claim that it passes the real L38 ripple audit.

**Synthetic floor-error ripple (peak-to-peak / max absolute, metres; 1,984 floor probes, 0.125 m sampling, 3.0 m centerline radius, 3.31 m vertical pitch, 20 route controls/turn, 12.95 turns; bore radius 4.5 m, repeated at the 3.0 m mid-bore):**

| Rule | FI-style2 p-p / max-abs | Read |
|---|---:|---|
| Exact analytic closest helix centerline | 3.372 / 3.372 | Wrong floor coil when distance to centerline is used for floor ownership. |
| Segment closest centerline | 3.387 / 3.383 | Same wrong-turn failure. |
| Nearest 3D floor point, unconstrained | 0.029 / 0.015 | Correct on this ideal route; max-abs is just under the 1.5 cm gate, but p-p is not. |
| Strict `floor <= qz`, within bore radius | 0.238 / 0.224 | Fails: voxel rounding excludes the true floor when it lies up to half a voxel above `qz`, so ownership drops to a lower segment. |
| Near-floor band `abs(floor-qz)<=0.125`, within radius | 0.029 / 0.015 | Matches nearest floor point here; prevents the strict-below one-segment drop. |
| Highest floor below `qz`, within radius | 0.282 / 0.224 | Fails; a one-sided “topmost below” rule is unstable at voxel boundaries. |
| Height-bin control segment ±1, then nearest floor point | 0.029 / 0.015 | Same as floor-point nearest on this ideal route; deterministic, style-independent guard. |
| Angle + height coil index | 0.030 / 0.015 | Works for this uniform helix after endpoint clamping; costs axis/angle/turn math and is style-specific. |

On synthetic straight / worm / cascading paths, height-bin local ownership measured p-p `0.005 / 0.030 / 0.031 m` (max abs `0.003 / 0.016 / 0.016 m`), versus centerline ownership `0.097 / 0.116 / 0.121 m`. Strict below-plus-radius reached `11.57 m` p-p on the looping cascade. This rejects that literal rule for shared use. The smooth ideal test does **not** reproduce L38's reported 8.6 cm floor ripple; it establishes the wrong-turn and voxel-boundary failure modes. Re-run the actual FI Style 2 floor/wall audit before accepting the guard.

The reported 0.938 m ripple period matches the expected control chord for the 3 m, 20-segment helix: `2*3*sin(pi/20) = 0.9386 m`; that points to per-control-segment ownership/smoothing as the repeat interval.

**Rank 2:** analytic helix closest point is useful as a reference/control, not the runtime shared owner. For `gamma(t)=(R cos t,R sin t,b t)` and query cylindrical coordinates `(rho,phi,z)`, stationary points solve `u + e sin(u) = M`, where `u=t-phi`, `e=R rho/b^2`, `M=z/b-phi`. There is no elementary closed form; the equation can have multiple roots per turn when `e>1`, so robust finite-route search brackets candidates and includes endpoints. Here `b=3.31/(2 pi)=0.527 m/rad`; floor queries have large `e`, and exact closest centerline is the wrong semantic owner because the bore floor lies farther below the centerline than the turn pitch permits.

For an ideal helix floor probe, angle/height gives `n=round((qz-z0-b*phi+r-lift)/pitch)`, `t=phi+2*pi*n`, where `phi=atan2(qy-axisY,qx-axisX)` and `lift=0.15m`. This avoids Euclidean coil ownership but needs helix axis/pitch metadata and a finite-end clamp; keep it as a reference, not the shared implementation.

**Rank 3:** hard union of floor-limited coils is geometrically valid only if a merged void is intended. With 3 m mid-bore radius and 3.31 m pitch, neighboring swept tubes overlap (`2r > pitch`); a union opens the overlap and can erase the upper coil's tread/support. A smooth union expands/rounds that seam and shifts the zero surface by up to `k/4` for the polynomial smooth-min. Do not use it to decide floor ownership.

Sources and details will be collected in `Standalone/Research/WorldAssemblerM3/Research3/REPORT.md`.