Fr0zkaandClaude Opus 5.5
945225d942
Read-only study for L38: a synthetic FI Style 2 helix (3 m radius, 3.31 m pitch) shows Euclidean closest-centerline ownership is wrong when bore radius > pitch/2; a floor-near (+-0.125 m, within bore radius) nearest-floor-point owner gives 2.9 cm p-p on helix and style-like paths. The L38 0.94 m ripple period equals the 20-segment chord. L38's continuation applied it: floor ripple 0; wall ripple open. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016dhxM43dnWvUu2B5Ph1iG1
4.6 KiB
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.