Orthogonal
Evan had already sampled what happened when the projector could not satisfy a target.
It did not break a law. It selected from nearby legal failures.
D-01 stood electrically open. The rotor coasted under the eddy brake. Its battery controller held the signed APPLY event without consuming it. The wall contactor had done exactly what its label promised, and the promised transition still had no feasible completion in LCA-01.
Evan considered leaving it there.
Walking away would preserve the current shutdown trajectory until the rotor stopped. It would not make P-04 true in a different way, erase the reconstructable escrow, withdraw Lena's disclosure, convert her refusal into consent, or remove D-01 from the history that had already produced the pending state. LCA-01 could solve those alternatives only by substituting another past.
He left the contactor open and finished a model offline. The event-feature scaffold, archive loader, and regularized response map already existed in his divergence notebook. Loading W-0 and the signed evidence records, then running the final decompositions, took fourteen seconds.
He named it ORTHO-01 before he had earned the word. The model operated in three live-cycle event features and D-01's two normalized control axes. It was not a map of every physically valid state, and a vector orthogonal inside it was not automatically orthogonal to a universe.
The first rejection example was CONSTRAINT-01.
He had requested two optical gates open behind one rigid steel shutter. The target had no mechanical realization. The apparatus supplied threshold chatter, a late sample, an invalid checksum, excess current, heat, and a thermal abort. It had approached the requested condition through the adjacent nuisances recorded in that run and never produced the impossible sample.
The second example was the DECOM-01 and DR-01 bundle.
The requested state had been permanent loss of projector capability. The lawful result isolated every energy path, destroyed OLD-7 and the projector-specific garage hardware, and retained the one evidence package that could reconstruct the fault build. Nothing turned itself back on. Safe handling, accountability, and retention policy preserved the missing edge.
LCA-01 supplied two modeled rejections. APPLY required software to restore actuation after a direct physical opening. HOLD preserved shutdown but made a committed live contingency inert. Both failed as complete transitions while every local device remained lawful.
For each case, Evan encoded the unsupported request and the adjacent legal result in the same event-feature order. He subtracted the result from the request and preserved that sign. The difference vectors were not things the machine had done. They were directions it had refused.
Six standardized request-minus-result vectors entered the rejection matrix. Evan removed duplicated nuisance directions with a QR decomposition and checked the result by singular-value decomposition. One singular value cleared the preregistered 0.20 cutoff. He oriented its unit vector so the mean signed source coefficient remained positive and called it the rejection axis.
The oriented axis said what the sampled legal failures looked like in his chosen features. It did not say what lay outside valid state space.
P-04 did not belong in the fit.
Its identification run and abort condition had been physically realizable. Its automatic abort had been defeated because Evan reported FOUR after he believed the peripheral depth had fallen to three. Lena then opened the independent contactor by hand. The classifier log, controller trace, audio, and contactor record agreed on the order.
His false report preserved his next decision. Her stop removed him from it.
That made P-04 a counter-sample, not another impossible-target trial. It oriented a sign.
Lena had not sent a new instruction. She had not approved ORTHO-01, supplied a current signature, or become a remote operator. Her manual stop was preserved evidence of an ordinary transition that once proceeded against Evan's preference.
He fitted an event-level projector signature from live, HOLD, broken-edge, and replay cases in the D-01 and clean-room records. The three varying features were an operator retaining next-action authority, preservation of the live feedback edge, and another consequential cycle.
Accepted cycles loaded positive on all three. P-04's manual stop oriented the opposite sign without entering the fit.
Evan had already proved that his personality was not the dominant pattern. The live projection topology operated without his code, hardware, or presence. But his own next action remained the only implementation inside the garage he could deliberately remove.
He changed the target from TERMINATE PROJECTOR to MINIMIZE NEXT-STATE OPERATOR ALIGNMENT / FIXED ONE-PULSE BUDGET.
The first wording claimed control over the operation. The second specified a descent step. It did not claim that one pulse could solve an absolute operator component to zero.
W-0 supplied the response Jacobian. The two columns described standardized retained changes from stator phase and brake-command timing. Their singular values were 0.030 and 0.010, both below the 0.080 threshold. Under the fixed unit-norm pulse budget, the smaller right singular vector combined a positive phase step with an equal negative brake-timing step.
Both components were ordinary. Each remained inside its calibrated envelope. Together they were predicted to produce a visible transient with the smallest retained difference D-01 could command.
When W-0 committed, the isolated sequencer had automatically frozen an event-command map before the signed event arrived: APPLY selected positive u*; HOLD kept the output gate closed. The map then had no self-erasure meaning. It was simply the next bounded response probe. By the time Evan named a target, APPLY had already been authenticated and the waveform's sign and shape could no longer change. He could still leave the wall contactor open or abort on a hard trip.
A regularized three-by-two map fitted from the live, HOLD, broken-edge, and replay cases translated the two normalized controls into the three event features. Applied to positive u*, its point estimate was [-0.400, -0.349, -0.300]: less operator next-action authority, less live-edge retention, and less next-cycle retention. Replay-bootstrap intervals crossed zero for each feature. The claimed direction belonged to that uncertain model, not directly to volts, radians, or heat.
The event-vector point estimate had norm 0.610. Its signed projection onto the oriented rejection axis was positive 0.609. Its dot product with the unit operator signature was negative 0.606. Both bootstrap intervals crossed zero.
Evan called that orthogonal steering. The artifact called it a local extrapolation with unresolved sign stability.
ORTHO-01 / RESPONSE-JACOBIAN AND TERMINAL INTERPRETATION
scope: D-01 terminal contingent step
claim type: OPERATIONAL / LOCAL / EXTRAPOLATIVE
maximum actuation count: 1
independent hard trips: ARMED
independent one-shot output gate: ARMED / ONE PULSE
new participation or authorization by L. Varga: NONE
normalized control basis:
u[0] stator phase relative to heat front
u[1] brake-command timing relative to heat front
control constraint: ||u||2 = 1.000 / FIXED PULSE BUDGET
W-0 standardized retained-response Jacobian:
u[0] u[1]
retained mode 1 +0.0212 +0.0212
retained mode 2 +0.0071 -0.0071
singular values: 0.030 / 0.010
retained-response threshold: 0.080 / DIMENSIONLESS
authorized retained-response rank: 0
for u*: ||J u*|| point estimate: 0.010
replay-bootstrap 95% interval: 0.000 .. 0.074
event-feature order:
OPERATOR_NEXT_ACTION / LIVE_EDGE / NEXT_CYCLE
standardized control-to-event map K_event:
u[0] u[1]
OPERATOR_NEXT_ACTION -0.283 +0.283
LIVE_EDGE -0.247 +0.247
NEXT_CYCLE -0.212 +0.212
map fit cases: LIVE / HOLD / BROKEN EDGE / REPLAY
map feature scaling: REPLAY Z-SCORES
map fit rank: 1
map status: FROZEN / RIDGE-REGULARIZED / LOCAL
for u* = +0.707 u[0] - 0.707 u[1]:
K_event u* = [-0.400, -0.349, -0.300]
bootstrap 95%:
OPERATOR_NEXT_ACTION [-0.71, +0.08]
LIVE_EDGE [-0.68, +0.11]
NEXT_CYCLE [-0.63, +0.14]
event-vector norm: 0.610
unit fitted operator signature P-OP:
[+0.5774, +0.5774, +0.5774]
P-04 manual-abort counter-sample:
sign orientation: - / - / -
source audio / classifier / controller / contactor: VERIFIED
use: SIGN ORIENTATION ONLY
consent or current instruction inferred: NO
rejection-axis sources:
CONSTRAINT-01 adjacent legal failures OBSERVED
DECOM-01 / DR-01 retained path OBSERVED
LCA-01 APPLY / HOLD infeasibility MODEL
P-04 COUNTER-SAMPLE / EXCLUDED FROM FIT
rejection difference vectors: 6 / STANDARDIZED
rejection-matrix singular values: 1.82 / 0.12 / 0.04
retention cutoff: 0.20
rejection-axis rank: 1
orientation rule: MEAN SIGNED SOURCE COEFFICIENT > 0
unit r_reject: [-0.6281, -0.5758, -0.5234]
oriented-axis dot point estimate: +0.609
oriented-axis cosine point estimate: +0.999
oriented-axis dot-product bootstrap 95%: [-0.10, +1.05]
P-OP dot-product point estimate: -0.606
P-OP cosine point estimate: -0.993
P-OP dot-product bootstrap 95%: [-1.02, +0.19]
sign stability: UNRESOLVED
terminal target:
preserve P-04 / DECOM-01+DR-01 / C-01 / NLE-01 / D-01 anchors
minimize next-state P-OP alignment under fixed one-pulse budget
Ruth household exposure: PRESENT / REFUSED
care continuity after self-erasure: NOT SATISFIED / NOT MODELED
self-erasure interpretation: EVAN / NOT MEASURED
empty successor set observed: NO
factorization predicted or observed: NO
execution envelope: AT MOST ONE PULSE / NOT FORCED
W-0 response commit: C0 / BEFORE EVENT
event-command-map commit: C1 / BEFORE EVENT
event authentication: C2 / APPLY
terminal interpretation commit: C3 / AFTER AUTHENTICATION
event map: APPLY -> +u* / HOLD -> NO PULSE
waveform / sign after C1: IMMUTABLE
operator execution or abort authority: RETAINED
post-commit waveform selection: NONE
The target could not restore the Quitter family. It could not undo Evan's false report, return Ruth's incompatible memories to their unselected lives, or convert Lena's refusal into permission.
Ruth's prestart line still read HOUSEHOLD EXPOSURE: PRESENT / REFUSED. Her evening medication and overnight plan still depended on Evan that night. If his interpretation meant death or incapacity, the pulse would leave her without him after he had again acted inside her home over her refusal. ORTHO-01 did not solve that consequence.
It could fail by killing him. It could fail by preserving him without authority. It could fail by finding another implementation of the same operation. ORTHO-01 assigned no probabilities to those outcomes.
He signed beneath SELF-ERASURE INTERPRETATION and left MEASURED OUTPUT blank.
The rotor remained above the minimum controllable speed. Brake temperature was below its continuous limit. The heat front had flattened but not vanished. One bounded pulse remained physically available.
Evan checked the polycarbonate shield, the touchdown bearing, the hard-trip battery, and the clear floor inside the yellow line. He did not alter a limit or bypass a latch.
The isolated one-shot gate used for the audit probes sat in series with the software output. Commit C1 had preset it to pass one phase-synchronized pulse and then open regardless of the controller or analyzer. The stator driver waited precharged at its neutral state so the contactor could close at the zero-torque boundary.
He closed the wall contactor.
The blades seated. D-01 accepted power at its base state. The queued APPLY event moved from authenticated to consumed and selected the one committed command. Evan no longer had a branch in the controller that could replace it with HOLD.
The stator phase advanced. Brake-command timing retreated by the matched amount. Current rose within the envelope. The rotor gained less speed than one ordinary audit probe had produced. Heat moved into the eddy brake and chamber jacket according to their measured capacities.
The hard trips remained armed.
At the end of the committed interval, the isolated output gate opened. It did not wait for a result code. No second command could reach the stator.
The command entered the live edge. Its physical response shaped the state D-01 was required to retain for the next cycle.
The retained-state analyzer opened its output buffer.
ORTHO-01 had defined one terminal target and one execution. The result schema allowed one accepted state, one rejected target, or one safety abort.
The result block acquired a header without a state address.