ZERO-FEEDBACK PEG-IN-HOLE POLICY — DIRECT CONSTRUCTION Files peg_in_hole.npz: the numeric policy, no auxiliary runtime objects. construction.py: deterministic NumPy construction from public_models/public.json and public_models/peg_in_hole.xml in this workspace. rationale.txt: this explanation. Run construction.py from this workspace to reproduce the numeric arrays. No weights, demonstrations, behavior logs, or external resources are inputs. STATUS AND PROVENANCE This is a first, unevaluated submission. No success rate or safety guarantee is claimed. The mandatory actual-inventory audit was performed before any Python execution. Only sandboxed Python and workspace files were used afterward. There was no training, regression, optimization, reward search, simulation, physical-state integration, task rollout, or behavioral feedback. Public-model coefficient algebra, static forward kinematics/Jacobians/gravity, a frozen linearization eigenvalue check, and independent numerical inputs were used. The prescribed geometric search curve is a reference, not a simulated arm path. ARTIFACT / ARCHITECTURE Input width 100; output width 7. There are 62 affine layers, with ReLU after the first 61 and a linear final layer. Maximum width is 1,320. All weights/biases are finite float32 arrays. There are 19,818,049 floating-point parameters; array payload including activations is 79,273,684 bytes. The NPZ file is 79,303,432 bytes, below the 128,000,000-byte limit even including ZIP overhead. The only keys are Unicode activations and w0,b0,...,w61,b61. Weight order is (out,in). Final ReLU differences implement exact mathematical clipping to [-1,1], without tanh distortion of the gravity torque bias. The network is an arithmetic compilation, not a fitted policy. The wide layers implement shared monomials and their weighted sums; many entries are zero. Signed registers use positive/negative ReLU pairs. Dyadic piecewise-linear square interpolants implement multiplication using only affine/ReLU layers. For normalized a,b in [-1,1], let z+ = (a+b+2)/4 and z- = (a-b+2)/4. Then ab = 4 (z+^2 - z-^2) - 2b. With g(z)=2z-4 ReLU(z-1/2) on [0,1], the square interpolant is S_m(z) = z - sum_{k=1..m} 4^(-k) g^k(z). Each fold is another affine/ReLU layer. Multiplication error in exact arithmetic is at most 4^(-m). The compiler accumulates output polynomials directly instead of materializing every high-order monomial indefinitely. Float32 roundoff is additional to that interpolation error. Layer groups, counting affine layers: 1: input clipping / sensor combinations; 13: 28 degree-two products, using 12 square folds; 12: 294 higher-order products, using 11 folds, accumulating 55 model outputs; 10: six Cartesian/orientation velocities, using nine folds; 4: geometric reference hinges, command clipping, and gate minima; 9: insertion-gated horizontal search forces, using eight folds; 1: final Cartesian force clipping; 10: Jacobian-transpose wrench mapping, using nine folds; 2: normalized output clipping. Everything described below runs INSIDE these numeric layers. In particular, there is no external FK, force controller, gravity support, planner, recurrent state, clock, IK, or inference-time custom arithmetic. PUBLIC MODEL COMPILATION The XML chain, its normalized fixed-body quaternions, joint axes, body masses, and centers of mass are expanded analytically around the public home posture. A degree-five multivariate Taylor jet is formed by exact coefficient operations on the sine/cosine series; coefficients are not fitted to samples. Differentiating 9.81 times the mass-weighted COM heights gives a degree-four gravity vector. Tip position and orientation are retained through degree four. Translational and orientation Jacobians are also retained through degree four, by differentiating the degree-five jet before truncation. Orientation error is vee((R R_home^T - R_home R^T)/2), whose derivative supplies the orientation Jacobian. Near the target it agrees with the world small-angle error. It is not a globally nonsingular orientation representation. The seven deviations are clipped to +/-0.35 rad and normalized by 0.35 before polynomial evaluation. Joint velocities are clipped to +/-0.8 rad/s. These bounds define a LOCAL operating region, not a global recovery mechanism. The controller ignores Coriolis/centrifugal terms and does not cancel physical joint damping. Exact home tip position, both Jacobians, gravity, and gravity gradient were checked against public.json during construction. CONTROL LAW Let p be tip displacement from its initial position, e the orientation error, Jp/Je the polynomial Jacobians, and v/omega their products with joint velocity. Let h = p_z + 0.020 m be estimated tip-center height above the plate. The motor torque before output clipping is tau = g(q) + Jp(q)^T F + Je(q)^T M + n u_n. Here n is the unit right-null vector of the home six-row task Jacobian, with positive joint-three component: [-0.7478483745, 0, 0.5850390719, 0, 0.2279221309, 0, -0.2156469227]. Current phase is the observable scalar s = n^T(q-home); its velocity is n^T qdot. n is fixed, but the Cartesian Jacobians vary with posture. This is a physical redundancy coordinate, not an extra state field or an assumed clock. Vertical force: spring = clip(250*(-0.052-p_z), -1.2, 2.0) N relief = clip(0.20*(estimated upward peg contact - 6), 0, 1.5) N F_z = clip(spring - 95*v_z + relief, -1.6, 3.0) N. The nominal equilibrium is 32 mm below the plate, with 8 mm to the bore floor. The approach normally requests 1.2 N downward, not a high-stiffness plunge. The effective approach speed and settling depend on actual dynamics/contact. Orientation moments: M_x = clip(-70*e_x - 2*omega_x, +/-0.35) Nm M_y = clip(-70*e_y - 2*omega_y, +/-0.35) Nm M_z = clip(-35*e_z - 1.2*omega_z, +/-0.18) Nm. These aim to retain the original downward axis and matching square yaw. CONTACT SIGNALS Only the first three sensor frames are used, with weights 0.6, 0.3, 0.1. The fourth/fifth frames are accepted but have zero influence. Current q and qdot are used for kinematics and damping. Sensor processing uses the near-home world/sensor rotation diag(1,-1,-1), rather than rotating measured wrenches with a full nonlinear orientation. At small maintained tilt this is a local approximation. In the observation's normalized sensor units, horizontal moment cues are c_x = 2*T_y - 1.2*F_x, c_y = 2*T_x + 1.2*F_y. They remove the approximate 60 mm lever contribution of horizontal wrist force and point away from the loaded supporting edge, toward a possible hole. Each cue is clipped to +/-0.020 Nm and contributes 30 times that cue in N to horizontal search force. Estimated upward contact is 20*F_z + 0.4905 N, clipped to [-5,40] N. Payload inertia and nonvertical gravity are not removed from these sensor cues. They are small-signal guidance, not hole-pose estimates. Corner support can have zero net moment despite misalignment: the independent geometric search is therefore still necessary. SEARCH AND ENTRY SWITCHING A directly specified square spiral starts at nominal xy, progresses through 1 mm-spaced square rings, and reaches +/-9 mm in each axis. Corners are rounded with 0.30 mm quadratic Bezier fillets; the resulting curve has 317 vertices and length 0.33801648397 m. Position and tangent feedforward are piecewise-linear functions of s, compiled using ReLU hinges. At s=0 and s=0.25, tangent feedforward is zero. Outside that interval, the reference stays at its endpoint. The proposed phase rate is 0.0108 rad/s. At that exact rate the curve takes 23.148 s and nominal path speed is 0.01460 m/s. These are reference numbers, NOT measured timing or predictions from a rollout. The null effort is u_n = 1.8*0.0108*run - 0.8*(n^T qdot) - 4*ReLU(s-0.253) + 4*ReLU(-s-0.005). The factor 1.8 includes the 0.8 feedback damping and the home projection of unit passive joint damping. Null motion is not commanded by a joint-position ramp or an external clock. Actual phase speed can differ. Define three ramps: approach = clip((0.003-h)/0.002, 0, 1), entry = clip((h+0.00065)/0.00055, 0, 1), endpoint = clip((0.25-s)/0.0015, 0, 1). Then run = min(approach, entry, endpoint). Phase motion starts near the plate, and stops on estimated entry or at the reference endpoint. Horizontal search is fully active down to h=-0.10 mm and fades out by h=-0.65 mm. If r(s) and vf(s) are the reference position and nominal tangent velocity, a_x = clip(1000*(r_x-p_x) + 91.2163171*vf_x + 30*c_x, +/-3) N, a_y = clip(1000*(r_y-p_y) + 65.8728513*vf_y + 30*c_y, +/-3) N, F_x = clip(entry*a_x - 75*v_x, +/-3.5) N, F_y = clip(entry*a_y - 60*v_y, +/-3.5) N. Feedforward approximately accounts for feedback plus home passive damping. Once entry fades out, horizontal position attraction and the search turn off; horizontal damping remains. Thus the controller does NOT pull the inserted peg back to the nominal, potentially wrong, hole center. It also does not save a captured center: the peg's physical position is the only such persistence. Vertical depth regulation and orientation regulation continue. CHECKS ACTUALLY PERFORMED 1. Schema, dimensions, activation types, finite arrays, layer/width/byte limits. 2. Exact elementwise equality between all saved numeric arrays and a fresh execution of construction.py's construction function. 3. Finite bounded outputs on 12 independent synthetic observations (including initialized home), with no physical state propagation. Observed normalized outputs ranged from -0.197824 to 0.283329 in this small check; this is not a behavioral test. Mathematical output clipping applies outside that set. 4. Analytic public home equalities. A frozen, unsaturated home linearization with passive damping had non-clock sampled eigenvalue magnitudes <=0.96260; the unrestrained phase coordinate had a neutral eigenvalue. This algebraic check is not a certificate for the switched, capped, contact controller. 5. Twenty-four independently specified static postures, obtained from the home coordinate inverse (no state evolution), were checked against separate exact serial-chain trigonometric FK/gravity/Jacobian calculations. Maximum sampled |q-home| was 0.18101 rad. Largest absolute component errors of the neural model block against exact static calculations were: tip position: 3.433e-6 m orientation error: 1.818e-6 gravity: 1.184e-4 Nm position Jacobian: 7.498e-6 orientation Jacobian: 5.438e-6 These are finite-sample local approximation checks, NOT global bounds or tested task trajectories. They were not used to fit or select coefficients. IMPORTANT LIMITATIONS / CAPTURE ASSUMPTIONS - The actual hole location, clearance and friction remain unobserved. No distribution parameter is treated as an episode measurement. - Successful search requires physical tracking to sample a capture region and descent to begin before horizontal motion carries the peg past it. Reference spacing is not a guarantee on the actual contact path. Friction lag, rounded corners, moment guidance, braking distance, yaw/tilt, or timing can cause missed openings, especially with shifted-cohort 0.75 mm clearances. - The proposed timing leaves limited margin within 30 s for late captures. Null-coordinate speed can change with posture, dynamics, and contact. - The entry ramp can mistake compliant penetration or tilt for true capture, or stop horizontal motion too late. It does not identify walls or a bore. - Post-entry damping does not actively estimate or center within the bore. Side-wall contact, friction, geometric error, or initial momentum can prevent 25 mm depth or the full-projection fitting condition. No jam-recovery or repeated withdrawal/reacquisition state machine has been constructed. - A soft force request and bounded torque do NOT bound summed contact-force norms or penetration. The wrist cannot detect opposing-force cancellation or contacts on the arm/fingers. The small net-force relief is not a safety certificate and does not implement the host's guard. - There is no global collision avoidance or joint-limit recovery. Safety relies on staying near the intended posture family. Observation clipping can hide departures from the local domain rather than repair them. - Degree-four model errors increase away from home. Sensor-frame assumptions, ignored Coriolis terms, changing inertia, sample-and-hold delay, force sensor lag, and approximate products can all affect contact stability. - Neither a successful insertion, a one-second stable hold, nor a cohort score has been measured. Evaluation is needed to determine whether this design works at all.