Lesson 4.4.1 — Architecting the Defense

Week 41

Prerequisite lessons: 4.3.3 (long-horizon robustness), 4.3.2 (diagnosing sim-to-real failures), 4.3.1 (systematic experimentation and ablations), 4.2.4 (safety and recovery), 4.2.3 (reasoning layer), 4.2.2 (policy layer), 4.2.1 (perception stack integration), 4.1.3 (evaluation design and held-out test suites), 3.3.3 (grounding language to affordances).

Prior results used in this lesson. From 4.3.3: the horizon failure law, the maintenance policy, and the horizon register entries, restated in §L.A.3 and §L.D.3. From 4.3.2: the diagnosis evidence chain and the stopping-rule residual, restated in §L.B.2 and §L.C.1. From 4.3.1: the ablation registry and the confidence-interval lower bound, restated in §L.B.1 and §L.C.2. From 4.2.4: the safety-case structure and the six-entry register, restated in §L.D.1 and §L.E.3. From 4.2.3: the six strata and the deferral discipline, restated in §L.C.3. From 4.2.2: the four authorities and per-tier attribution, restated in §L.B.3. From 4.2.1: the contract’s five fields and the evidence table, restated in §L.B.1. From 4.1.3: the 400-episode suite and the four-plus-one axes, restated in §L.A.2. From 3.3.3: the affordance grounding and the physical-possibility checks, restated in §L.A.1. Each is restated at the point of use.

Hands forward. The claim-evidence-warrant architecture, the anticipated-question taxonomy, the answer template, and the rehearsal protocol. Lesson 4.4.2 (proposing concrete improvements) uses the vulnerability map as its starting point. Lesson 4.4.3 (communicating the unknown unknowns) uses the residual register and the “what would change my mind” statement as the closing argument. The curriculum’s exit test is the defence’s passing.

The running case in one sentence. The arm, gripper, eye-in-hand camera, table, cube, bin, divider, and three distractors are unchanged; the seven subsystems are assembled into the full-stack agent, the 400-episode suite measures its acceptance, the safety case records its residuals, and this lesson asks how to defend the agent — the claims, the evidence, the warrants, the anticipated questions, and the artefacts — before a committee that tests the reasoning, not the demonstration.

§L.0 — Lesson map, objectives, and misconceptions

Observable outcomes. By the end of this lesson you can, without notes: (1) state the four elements of a defensive claim and write the claim-evidence-warrant table for a capstone claim; (2) distinguish the defence’s purpose from a report’s, a demo’s, and a paper’s; (3) name the five sections and the word budget of each; (4) build the evidence hierarchy from primary to corroborating to contextual, and state the reversal failure; (5) build the vulnerability map from the register and handle a tie in the weights; (6) name the five question categories and the four-part answer template; (7) state the “I don’t know” discipline and its three cases; (8) write the “what would change my mind” statement for the capstone’s central claim; (9) assemble the eight artefacts and their roles; (10) run the rehearsal protocol and diagnose its four failure modes.

Misconception inventory.

Everything is self-contained. Where a prerequisite lesson is used, the result is restated at the point of use.

§L.0.5 — Retrieval warm-up

Q1. In 4.2.4 §L.D.3 the safety case was a tree of arguments with residuals, and the case’s strength was the residuals’ acceptance. What does the defence inherit from it, and what does it add?

Answer. It inherits the premise-and-residual tree — each claim supported by evidence and weakened by a residual — and it adds the narrative and committee dimensions: the defence must be delivered in time, and the committee’s questions are unscripted tests of the tree’s branches. Used in §L.B.1 to define the architecture’s inheritance.

Q2. In 4.3.1 §L.C.4 the confidence-interval lower bound was the decision, not the point estimate. What is the defence’s analogous discipline?

Answer. The claims’ lower bound. The defence states the pessimistic effect and the committee evaluates the claim at that bound. A claim at the point estimate is optimism, and the committee finds the gap during questions, which is the defence’s worst position. Used in §L.A.1 to define the claim’s form.

Q3. In 4.3.2 §L.D.3 the four failure modes were wrong attribution, under-attribution, over-attribution, and the unattributed residual. Which is the defence’s central vulnerability, and why?

Answer. The unattributed residual — the register entry whose mitigation is the unknown axis. The defence’s central vulnerability is the residual the argument cannot explain, and the committee’s question is that residual’s plan. Used in §L.B.3 to define the vulnerability map.

Q4. In 4.3.3 §L.B.2 the 138-shift evaluation window was infeasible and the extrapolation contract was the substitute. What is the defence’s analogous substitute when a measurement is infeasible?

Answer. A model — the extrapolation contract, the horizon law, the ablation registry — and the defence must state the model’s assumptions and the evidence that they hold. The substitute is not the measurement, and the defence must say so. Used in §L.B.2 to organise the evidence hierarchy.

Part A — The defence’s logic

§L.A.1 — The four elements of a defensive claim

A defensive claim is a statement the defence asks the committee to accept. It has four elements, and the four are a structure, not a checklist.

The claim. The statement with its scope: the distribution, the horizon, the embodiment. Its form is

“The full-stack agent achieves a success rate of at least 0.88 on the 4.1.3 suite’s seen-task axis, at the 95% lower bound, on the running arm.”

The scope is not a hedge; it is the claim’s content. A claim without scope is one the committee refutes with a single counterexample, and the defence’s job is to make the claim narrow enough to be true and broad enough to be interesting.

The evidence. The measurements supporting the claim, with provenance: which experiment, which suite version, which date. The evidence is the registry record of 4.3.1 §L.A.2, and the version is the manifest of 4.1.3 §L.D.1.

The warrant. The reasoning connecting evidence to claim. The warrant is the inferential step — “the 400-episode suite’s 0.92 point estimate with a 0.025 half-width warrants at least 0.88 at the 95% level, because the suite is a stratified sample of the deployment distribution and the 4.1.3 §L.C.3 preconditions hold.” The warrant is where the assumptions live, which is why it is the weakest part of most defences.

The residual. The limitations the claim does not cover: register entries, contract clauses, the interval’s upper end. The residual is the defence’s honesty and the committee’s entry point, because the questions a defence invites are the ones it has already named.

The four are jointly necessary. A claim without evidence is an assertion; evidence without a warrant is a number; a warrant without a residual is an over-claim. The committee’s test is the four’s consistency.

Self-explanation 1. Why is the warrant the weakest part of most defences?

Answer. Because the warrant is the inference from evidence to claim, and the inference carries assumptions — distributional representativeness, measurement validity, model applicability — that the evidence does not itself measure. Evidence is fact and warrant is interpretation, and interpretation is the committee’s specialty.

§L.A.2 — The defence’s purpose

The defence’s purpose differs from the report’s, the demo’s, and the paper’s, and those differences are design constraints.

The report. Purpose is the record: complete, reproducible, referable. Structure is chapters; evidence is appendices. The report is read, and the reader controls the pace.

The demo. Purpose is demonstration: the system works, in real time, on the day. Structure is a script; evidence is the performance. The demo is watched, and the system controls the pace.

The paper. Purpose is the contribution: a new result, a general claim, related work. Structure is abstract, introduction, method, results, related work, conclusion; evidence is the experiment.

The defence. Purpose is acceptance: the committee judges that the claims are warranted, the evidence valid, and the residuals acceptable. Structure is the claim hierarchy — central claim, supporting claims, evidence, warrants, residuals. Evidence is the registry and the safety case. The defence is questioned, and the committee controls the pace.

The consequence for design: the defence cannot be the report read aloud, because the report’s structure is not the claim hierarchy. It cannot be the demo alone, because the demo is one of eight artefacts. It is the argument under time pressure, and its script is the claim hierarchy.

§L.A.3 — The central claim and its hierarchy

The central claim is the defence’s top-level statement, and its hierarchy is the defence’s architecture.

The running case’s central claim, with the scope established in §L.E.1:

“The full-stack agent achieves a success rate of at least 0.88 at the 95% lower bound on the 4.1.3 suite’s seen-task axis; the six safety register entries of 4.2.4 §L.E.3 are accepted by the operator with their stated residuals; the composed recovery rate is 0.809 per episode, and the per-segment compounding of 4.3.3 §L.C.3 is stated as the residual; and the 8-hour shift survival is reported as an open residual at $8.6 \times 10^{-22}$ under the 4-reset schedule, against the 0.90 target.”

The central claim has four components: the success rate, the safety residuals, the recovery rate, and the horizon survival. Each is a supporting claim, and each is defended by a section.

The fourth component is the one that separates a defensible claim from a false one. The natural form — “and the shift survival is at least 0.90” — is arithmetically impossible at the composed recovery rate: 4.3.3 §L.A.3 shows the floor demands $R \ge 0.99949$ and the composed rate is 0.809, so the shift survival under the 4-reset schedule is $8.57 \times 10^{-22}$ and no maintenance schedule closes the gap. A defence that asserts 0.90 has either not done the arithmetic or hopes the committee has not. The defensible form states the number, names the shortfall as the residual, and makes the improvement plan the content of §L.E.2’s “next” section.

The hierarchy’s discipline: the central claim is accepted when its supporting claims are accepted; each supporting claim is accepted when its evidence is valid and its warrant sound; each residual is accepted by the operator or the committee. The hierarchy is the 4.2.4 §L.D.3 GSN tree adapted for the defence’s time and audience.

Concept check. A defence’s central claim is “the agent works”. Which elements are missing, and what is the fix?

Answer. The scope and the residual. “Works” has no distribution, horizon, or bound, and its residual is unnamed. The fix is the four components with the scope and the register, per §L.A.3. [displaces M1]

Worked-example ladder.

WE-L.A.a (fully worked). The central claim has four supporting claims: success rate (0.898 lower bound), safety residuals (6 entries), recovery rate (0.809), and horizon survival ($8.57 \times 10^{-22}$ against a 0.90 target). Compute the claim hierarchy and state the weakest link.

Solution. The hierarchy is a four-node tree, each node defended by a section. Two links fail their targets: the success rate’s 0.898 lower bound is below the 0.90 target, and the horizon survival is 21 orders below its floor. The weakest link is the horizon, because the success rate can be re-scoped to 0.88 and the horizon cannot be re-scoped into truth — it can only be named.

WE-L.A.b (completion). The success claim is re-scoped to “at least 0.88 at the 95% lower bound”. Compute the comparison and the claim’s status.

Completion. The 0.898 lower bound is above 0.88, and the claim is accepted at that scope. The completion shows that scope is the defence’s design variable and the honest claim is the narrow one.

WE-L.A.c (faded). Write the warrant for the safety-residuals claim.

Faded step. The warrant is: “the six entries are the 4.2.4 §L.A.1 hazard analysis, the residuals are the register’s, the operator has accepted them, and the 4.2.4 §L.D.3 GSN tree is the argument’s structure.”

Completion. The warrant’s assumption is the hazard analysis’s completeness, and the committee’s question is that assumption. The defence’s residual is the analysis’s gap — the hazards not enumerated.

WE-L.A.d (contrastive near-miss). A defence’s central claim is “the agent is safe”, and the committee’s first question is “under what distribution, and with what residual?” The defence cannot answer, because the claim had no scope. Why it fails: the claim is unfalsifiable as stated, and the committee cannot accept an unfalsifiable claim. The fix: the four elements, per §L.A.1.

Comparative table: the four purposes.

Design principle P60.1. The defence is the claim hierarchy, not the report or the demo; the scope and the residual are the argument’s content, and the warrant is its weakest part.

Consolidation checkpoint 1

(a) Three capabilities. You can write the four elements of a defensive claim. You can state the defence’s purpose against the report’s, the demo’s, and the paper’s. You can build the claim hierarchy and identify the weakest link.

(b) Transfer probe. The claim is “the perception stack achieves 1 cm pose accuracy”, and the evidence is the 4.2.1 §L.E.2 table. Which elements are missing, and what is the fix? Answer: the scope — distribution, object set, confidence level — and the residual — the 95th percentile and the covariance coverage. The fix is a restatement with the scope and the register.

(c) Remediation rule. If you cannot state why the warrant is the weakest part, re-read §L.A.1 before Part B.

Part B — The defence’s architecture

§L.B.1 — The five sections

The defence has five sections, and each word budget is a time budget at roughly 140 words per minute.

Section 1: framing (5 minutes, ~700 words). The problem, the claim, the roadmap. Its purpose is orientation: the problem is the running case’s pick-and-place with clutter, the claim is the central claim’s four components, the roadmap is the five sections. The framing is not a literature review; the committee knows the literature, and the framing positions the claim against it in one or two sentences.

Section 2: system (10 minutes, ~1,400 words). The seven subsystems, the interfaces, the authority design. This is the 4.2.1–4.2.3 evidence, and its purpose is the committee’s understanding of the architecture. The section’s claims are about integration — interface contracts and authority exclusivity — not about subsystem accuracy.

Section 3: evidence (15 minutes, ~2,100 words). The 4.1.3 suite results, the ablations, the diagnosis chain, the safety case. This is the load-bearing section, and its structure is the claim hierarchy: each component of the central claim gets its evidence, rather than the work appearing in chronological order.

Section 4: limits (7 minutes, ~1,000 words). The register residuals, the extrapolation contract, the “what would change my mind” statement. Its purpose is honesty and invitation: the committee’s questions are invited onto residuals the defence has named, which is the strong position.

Section 5: next (3 minutes, ~400 words). The improvements the defence would make and the open questions. This is 4.4.2’s content previewed, and it is the mastery signal: the candidate who sees the limits and has a plan is the candidate the committee accepts.

The five total 40 minutes, and the slot is 45 minutes plus 45 minutes of questions. The 5-minute margin is delivery slack, not content.

Self-explanation 2. Why is the evidence section structured by the claim hierarchy rather than by chronology?

Answer. Because the committee evaluates the claim, not the process. Chronology is the narrative the candidate experienced; the claim hierarchy is the argument the committee needs. A chronology forces the committee to extract the argument, and extraction under time pressure is the defence’s risk.

§L.B.2 — The evidence hierarchy

The evidence hierarchy has three levels, each with a different role.

Primary. Measurements that directly support a claim: the 4.1.3 suite’s 400-episode results for the success claim, the 4.2.4 §L.D.2 injection suite for the safety claim, the 4.3.3 §L.E.2 horizon evidence for the survival claim. Primary is load-bearing, and the defence’s time goes here.

Corroborating. Measurements that indirectly support a claim: the 4.2.1 §L.E.2 check statistics for the perception claim, the 4.3.1 §L.E.2 ablation registry for the contribution claims. Corroborating is the backup: the defence mentions it and produces it during questions.

Contextual. Measurements that frame a claim: the 3.4.1 §L.E twin-track tail, the 4.3.2 §L.E.1 evidence chain. Contextual is background, and the defence omits it unless asked.

The discipline: the script is the primary level; the corroborating level is the appendix; the contextual level is the report. Omitting contextual from the script is not hiding it — the report has it — and omitting corroborating is a time allocation, not an absence of evidence.

The failure is the reversal: the script leads with contextual and mentions primary, so the committee’s attention is spent on background and the load-bearing evidence gets the last minutes, when attention is lowest. The reversal is the most common structural failure of a defence.

§L.B.3 — The vulnerability map

The vulnerability map is the defence’s self-assessment of where the argument is weakest, and its form is the distribution of residuals.

Step 1: enumerate the residuals. The register entries across perception, policy, reasoning, safety, and horizon. The running case has six from 4.2.4 §L.E.3 and six from 4.3.3 §L.E.3 — twelve, not thirteen. Each entry is a residual and each residual is a vulnerability.

Step 2: score them. Each residual is scored on probability and consequence, each on a 1–5 scale, and the product is its weight. The 4.2.4 §L.A.1 hazard ranking is the model.

Step 3: place them. The residuals are placed on the probability-consequence plane, and the highest-weight tier becomes the defence’s anticipated questions.

The running case’s map, scored over the two registers — six entries from 4.2.4 §L.E.3 and six from 4.3.3 §L.E.3.

The map has one entry at the top and then five tied pairs: 15 alone, then 12, 9, 8, 6, and 4 each held by two residuals. So “top three” needs a stated rule, and the rule must survive the tie rather than let a sort decide it. Two rules, applied in order.

First, the highest tier is taken whole. Here it is one entry — the recovery rate below the floor — and it is not a surprise, because 4.3.3 §L.E.3 marks it High/High and records “none available at $R = 0.809$”.

Second, the next tier is taken whole. Weight 15 is the H4 negative margin, at 0.68 s detection against a 200 ms hazard — the one register row whose margin the 4.2.4 §L.D.2 table already reports as negative.

The third question then comes from the two-way tie at weight 12: recovery decay and the H3 slip onset. The defence takes recovery effectiveness decay, because its consequence bears on the central claim — a decaying recovery rate moves the escalation rate, and the escalation rate is already the entry that fails — while H3’s consequence is a dropped cube, which the register’s mitigation contains with a 12 ms margin. That choice is stated and not sorted, and stating it is the whole point: an unexplained tie-break is a vulnerability the committee can probe.

The map’s role is twofold. It is preparation — questions are rehearsed against the named residuals — and it is the committee’s entry point, because a defence that invites questions onto residuals it has named keeps control of the question.

Self-explanation 3. Why is naming residuals the strong position rather than hiding them?

Answer. Because the committee finds them anyway — probing is its specialty — and naming earns credit for honesty while keeping control of which question comes first. Hiding means the committee discovers them, and discovery costs control and trust simultaneously.

Concept check. A defence’s map has one residual at weight 25 and the rest below 15. What is the defence’s choice?

Answer. Not to bury it. A single dominant residual is the defence’s opening, not its weakness: it names the entry, states the number that makes the weight, and makes the improvement plan the content of the “next” section. Re-scoping does not apply here, because the shortfall is arithmetic and not a scope question — an unchangeable residual is named, not argued away. [displaces M5]

Worked-example ladder.

WE-L.B.a (fully worked). The map has one residual at 25, one at 15, and five tied pairs below. Determine the three anticipated questions and justify the third.

Solution. The highest tier is the recovery rate below the floor, weight 25, and it is the first question. The second is the H4 negative margin at 15 — 0.68 s against a 200 ms hazard, the only register row whose margin is already negative. The third comes from the two-way tie at 12: recovery decay or the H3 slip onset. Recovery decay wins because a decaying recovery rate moves the escalation rate, and the escalation rate is the entry that already fails, so the third question compounds the first rather than opening a new thread.

WE-L.B.b (completion). The H4 negative margin is repaired to 150 ms by a monitor-cadence change. Recompute the top tier and state the new third.

Completion. H4’s probability falls to 1, its weight to 5, and the highest remaining tier is the single entry at 25. The third then comes from weight 12 again, and the same choice applies — so the third question is stable under the repair, which is what a well-chosen tie-break should be. The completion shows the map is dynamic: preparation closes what it can, and the map updates.

WE-L.B.c (faded). Write the evidence hierarchy for the success-rate claim.

Faded step. Primary: the 4.1.3 suite’s 400-episode results. Corroborating: the 4.3.1 §L.E.2 ablation registry and the 4.2.1 §L.E.2 check statistics. Contextual: the 3.4.1 §L.E twin-track.

Completion. The hierarchy has three levels, and the script uses the primary, the appendix the corroborating, and the report the contextual.

WE-L.B.d (contrastive near-miss). A defence script leads with the literature review, and primary evidence gets the last five minutes. All the committee’s questions concern the literature, and the evidence goes unexamined. Why it fails: the hierarchy is reversed and attention is spent on the contextual level. The fix: primary first, per §L.B.2.

Comparative table: the five sections.

Design principle P60.2. Allocate time to primary evidence, structure evidence by the claim hierarchy, and map the vulnerabilities; reversing the hierarchy is dilution, and naming the residuals is the strong position.

Consolidation checkpoint 2

(a) Three capabilities. You can name the five sections and their word budgets. You can build the evidence hierarchy for a claim. You can construct the vulnerability map from the register and break a tie explicitly.

(b) Transfer probe. The script is 40 minutes and the slot is 45. What is the 5-minute margin for, and why is it not content? Answer: it is delivery slack — pauses, transitions, committee interruptions — and it is not content because the content is the 40 minutes. A defence that fills 45 has no slack, and rushed delivery is the committee’s impression.

(c) Remediation rule. If you cannot state why reversing the hierarchy is dilution, re-read §L.B.2 before Part C.

Part C — The committee’s questions

§L.C.1 — The five categories

The committee’s questions are predictable by category, and five categories cover the large majority.

Category 1: the claim’s scope. “Does the claim hold on the distribution the deployment will see?” It probes the 4.1.3 §L.C.3 distribution statement and the 3.1.3 §L.D.2 split discipline. The answer is the scope and the evidence for representativeness.

Category 2: the evidence’s validity. “Is the measurement measuring what the claim says?” It probes the 4.3.1 §L.C.3 seed variance, the 4.3.2 §L.D.1 confounds, and the 4.3.3 §L.B.4 extrapolation contract. The answer is the warrant and the confounds’ exclusion.

Category 3: the warrant’s assumptions. “What has to be true for the evidence to support the claim?” It probes the unstated assumptions — distributional stationarity, model applicability, recovery independence. The answer is an enumeration of assumptions with evidence for each.

Category 4: the residual’s plan. “What happens when the residual occurs?” It probes the register entries and the 4.2.4 §L.C.1 recovery kinds. The answer is mitigation and escalation.

Category 5: the alternative’s comparison. “Why this design and not the alternative?” It probes the 4.3.1 §L.B.4 replacement semantics and the 4.1.2 §L.A.3 decisiveness criterion. The answer is a baseline comparison and a decision rationale.

The coverage: the 4.3.1 §L.D.2 confounds are category 2’s content, the 4.3.2 §L.D.3 failure modes are category 3’s, and the 4.2.4 §L.D.3 safety-case residuals are category 4’s. Preparation is the five categories rehearsed, and the vulnerability map’s highest tier supplies the specific instances.

§L.C.2 — The answer template

The answer template has four parts, and the four are a fixed order.

Part 1: restate the claim. “The claim is X, with scope Y.” The restatement confirms the question’s subject and states the claim precisely. It is not a repetition of the question; it is the claim’s precise form.

Part 2: cite the evidence. “The evidence is Z, at suite version V, with interval I.” The citation names the artefact and the bound, which is the 4.3.1 §L.C.4 lower-bound discipline.

Part 3: state the uncertainty. “The uncertainty is U, because W.” The uncertainty is the interval’s width and its source: sample size, seed variance, model assumption. This is the honesty the committee rewards.

Part 4: name the residual and the plan. “The residual is R, and the plan is P.” The residual is the register entry; the plan is the 4.4.2 improvement or the 4.3.3 §L.D.3 maintenance action.

The discipline: the four are ordered from general to specific. Omitting part 3 is over-claiming; omitting part 4 is incompleteness; omitting part 1 is answering a different question.

§L.C.3 — The “I don’t know” discipline

“I don’t know” is a correct answer when the claim is genuinely open. It has three cases, and the discipline is knowing which one you are in.

Case 1: outside the claim’s scope. “Does the agent handle a mobile base?” The answer is “that is outside the scope — the claim is the fixed arm — and the base is 4.4.2’s next question.” The answer is a scope restatement, not “I don’t know”.

Case 2: inside the scope, evidence absent. “What is the success rate on reflective surfaces?” The answer is “I don’t know — the suite does not include reflective surfaces, and the 4.3.2 §L.D.1 selection is the reason”, plus the plan. The answer is honesty plus a plan.

Case 3: inside the scope, evidence contradictory. The answer is “I don’t know — the evidence is contradictory and the 4.3.1 §L.A.2 registry did not predict it; the 4.3.2 §L.D.3 failure modes are the re-examination plan.” The answer is honesty plus a diagnosis.

The rule: “I don’t know” is neither the default nor a failure. It is correct in the three cases and incorrect outside them. The committee’s test is the boundary — whether the candidate knows where the claim’s scope ends and the evidence begins.

Self-explanation 4. Why is “I don’t know” strong in the three cases and weak outside them?

Answer. In the three cases the claim is genuinely open, and pretended certainty is the dishonesty the committee penalises. Outside them the question has an answer the candidate should know, and “I don’t know” is a preparation failure.

Concept check. The committee asks “what is the agent’s success rate on the 7-DOF arm?” Which case, and what is the answer?

Answer. Case 1 — outside the claim’s scope, because the claim is the 6-DOF running arm. The answer is a scope restatement plus the 4.1.2 §L.A.3 decisiveness point: the 7-DOF arm is the alternative, not the capstone. [displaces M4]

Worked-example ladder.

WE-L.C.a (fully worked). The committee asks a category 2 question: “your success-rate interval is $\pm 0.025$ on 400 episodes; is the seed variance inside it?” Write the four-part answer.

Solution. Part 1: “the claim is 0.898 at the 95% lower bound on the suite’s seen-task axis.” Part 2: “the evidence is the 4.1.3 §L.E.3 400-episode suite at version 1.” Part 3: “the $\pm 0.025$ is the episode-level interval; the seed variance is not inside it, because the 3.1.4 §L.C.3 paired-seed design is separate, and the seed standard deviation of 1.5 points is below the interval.” Part 4: “the residual is seed variance on deployment seeds, and the plan is 4.4.2’s multi-seed evaluation.”

WE-L.C.b (completion). The committee asks a category 4 question: “what happens if gripper pad wear reaches 20%?” Write the four-part answer.

Completion. Part 1: the claim’s scope is the shift survival at the 4-reset maintenance interval. Part 2: the evidence is the 4.3.3 §L.E.1 shift plan and the 4.2.4 §L.A.1 H3 hazard. Part 3: the uncertainty is the wear-rate identification. Part 4: the residual is wear beyond 2% per 1,000 grasps, and the plan is the 3.4.3 §L.B.2 re-identification plus the 4.3.3 §L.C.2 maintenance threshold.

WE-L.C.c (faded). Write the category 5 answer for “why the parallel-jaw gripper and not the dexterous hand?”

Faded step. Part 1: the claim is the 6-DOF arm. Part 2: the evidence is the 4.1.2 §L.A.3 decisiveness criterion. Part 3: the uncertainty is the hand capability the running case cannot demonstrate. Part 4: the residual is the hand’s absence, and the plan is 4.4.2’s future iteration.

Completion. The category 5 answer is the decisiveness criterion — parallel-jaw resolution at the budget is better, and the hand is future work.

WE-L.C.d (contrastive near-miss). The committee asks a category 3 question, and the candidate answers with the evidence numbers but not the assumption. The committee asks again, and the candidate is stuck. Why it fails: a category 3 question is about the warrant’s assumption, and the evidence is a category 2 answer. The candidate answered the wrong category. The fix: classify the question before answering, per §L.C.1.

Comparative table: the five categories and their sources.

Design principle P60.3. Classify the question by category before answering; the four-part template is the consistent structure, and “I don’t know” is correct in the three cases and a failure outside them.

Consolidation checkpoint 3

(a) Three capabilities. You can name the five categories and their sources. You can write the four-part answer. You can apply the “I don’t know” discipline’s three cases.

(b) Transfer probe. The committee asks “your safety case says the recovery rate is 0.81; what is the actual recovery rate in the field?” Which category, and what is the answer? Answer: category 4 — the residual’s plan — with the 3.3.3 §L.E.3 register entry, the 4.3.3 §L.C.3 per-segment compounding, and 4.4.2’s field measurement plan.

(c) Remediation rule. If you cannot state why a category 3 question is about the assumption and not the evidence numbers, re-read §L.C.1 before Part D.

Part D — The artefacts, the timing, and the rehearsal

§L.D.1 — The eight artefacts

The defence’s eight artefacts are the physical forms of the evidence, and each is the reference for a claim.

The claim-evidence-warrant table. The four elements of each supporting claim, with the evidence version and the interval. This is the defence’s backbone.

The suite manifest. The 4.1.3 §L.C.3 four fields: version, seed, audit, freeze timestamp. The manifest is the evidence’s provenance.

The evidence table. The metric tables from 4.2.1–4.3.3, each with its bound and value. The table is the evidence’s numbers.

The vulnerability map. §L.B.3’s residuals with their weights and the stated tie-break. The map is the questions’ anticipation.

The safety case. The 4.2.4 §L.D.3 GSN tree with residuals. The case is the safety argument.

The register. The 3.3.3 §L.E.3 entries with residuals. The register is the defence’s limits.

The ablation registry. The 4.3.1 §L.E.1 seven entries with intervals. The registry is the contribution claim.

The horizon plan. The 4.3.3 §L.E.1 shift plan with the maintenance schedule and the recovery shortfall. The plan is the long-horizon claim.

The roles: four — the claim table, the evidence table, the safety case, the ablation registry — are the script’s evidence; two — the manifest and the register — are provenance and limits; one — the vulnerability map — is preparation; one — the horizon plan — is forward-looking.

§L.D.2 — The timing

The timing is the delivery schedule, and its structure is the five sections.

The discipline: intervals are enforced in rehearsal, and overrun in any interval is compensated from the margin, not from later intervals. The evidence’s 15 minutes is the shortest the load-bearing section can be, and the system’s 10 minutes is the longest that does not steal from evidence.

The failure: overrun is the most common failure, and its source is framing and system — the candidate warms up in the familiar sections and rushes the evidence. The rehearsal fix is a hard cut with a timer, and the practice order puts the evidence section first.

§L.D.3 — The rehearsal protocol

The rehearsal protocol has four stages, each with a different purpose.

Stage 1: solo run-through. The candidate delivers the script alone, with a timer and a recording. Purpose is timing and fluency; the failure signature is overrun in the framing.

Stage 2: peer questions. A peer plays the committee with the five categories, and the candidate answers with the four-part template. Purpose is question fluency; the failure signature is template omission of the uncertainty or the residual.

Stage 3: adversarial questions. A peer plays a sceptical committee, and the goal is defending the weakest claim. Purpose is vulnerability handling; the failure signature is defensiveness rather than an answer.

Stage 4: full run-through. Script and questions in one sitting, with the artefacts and the timing. Purpose is composition; the failure signature is stamina — the last ten minutes of questions is where the template collapses.

The four failure modes map to the four stages: overrun, template omission, defensiveness, stamina. Each has a fix: the hard cut, the template drill, the naming, and the shorter sittings.

Self-explanation 5. Why is the adversarial stage the one that improves the defence most?

Answer. Because vulnerability handling is the defence’s weakest skill. The candidate has rehearsed the script and the evidence; the sceptical questions are the unscripted test of the claim’s scope and the warrant’s assumptions. Stage 3 is the only stage that practises the weakest skill.

Concept check. The full run-through shows question fluency falling in the last ten minutes. Which failure mode, and what is the fix?

Answer. Stamina — the template collapses under fatigue. The fix is shorter sessions, with the four stages in separate sittings, and a written template card at the defence. [displaces M4]

Worked-example ladder.

WE-L.D.a (fully worked). The intervals are 5, 10, 15, 7, and 3 minutes. Compute the total and the margin.

Solution. The total is $5 + 10 + 15 + 7 + 3 = 40$ minutes, and the margin is 5 minutes of the 45-minute slot. The margin is delivery slack.

WE-L.D.b (completion). The evidence section needs 18 minutes. Compute the compensation and the interval to cut.

Completion. The 3-minute compensation comes from the system’s 10 → 8 and the framing’s 5 → 4, not from the limits’ 7. The completion shows compensation comes from the least load-bearing sections.

WE-L.D.c (faded). Write the stage 3 sceptical question for the vulnerability map’s highest-weight residual.

Faded step. The sceptical question is “the success rate is 0.898 at the lower bound and your claim was 0.90; is the claim false?” The answer is the re-scope or the evidence for a re-run.

Completion. The sceptical question targets the map’s highest tier, and the answer is the four-part with the honest re-scope.

WE-L.D.d (contrastive near-miss). A defence rehearses the script only, and questions go unrehearsed. The committee’s first question is category 3, and the candidate answers with evidence numbers. Why it fails: the template is unrehearsed and the category is misclassified. The fix: stages 2 and 3, per §L.D.3.

Comparative table: the rehearsal’s stages.

Design principle P60.4. Rehearse the four stages and enforce the timing; the adversarial stage practises the weakest skill, and the full stage’s failure is the last ten minutes.

Consolidation checkpoint 4

(a) Three capabilities. You can name the eight artefacts and their roles. You can state the timing intervals and the margin’s use. You can lay out the four rehearsal stages and their failure signatures.

(b) Transfer probe. The solo run-through overruns the framing by 3 minutes. What is the diagnosis and the fix? Answer: the overrun’s source is framing warm-up, and the fix is a hard cut — tighten the framing script, and do not cut the evidence section.

(c) Remediation rule. If you cannot state why the adversarial stage improves the defence most, re-read §L.D.3 before Part E.

Part E — The running case

§L.E.1 — The central claim and the four supports

The running case’s defence, assembled from the five sections and the eight artefacts.

The central claim.

“The full-stack agent achieves a success rate of at least 0.88 at the 95% lower bound on the 4.1.3 suite’s seen-task axis, warranted by the 0.898 evidence; the 4.2.4 §L.E.3 six safety register entries are accepted by the operator with their stated residuals; the 4.2.4 §L.C.3 composed recovery rate is 0.809 per episode, with the 4.3.3 §L.C.3 per-segment compounding as its residual; and the 8-hour shift survival under the 4.3.3 §L.E.1 4-reset schedule is $8.57 \times 10^{-22}$ against a 0.90 target — an open residual whose binding constraint is the recovery rate, which the floor requires to be at least 0.99949.”

The four supports.

The scope statement. The claim covers the running arm, the 4.1.3 suite distribution, the 8-hour shift, and the 4-reset maintenance schedule. The scope is narrow and true, and the broader claims belong to 4.4.2 and 4.4.3.

The horizon support is the lesson’s most instructive row. Its warrant — the extrapolation contract — is sound, and its evidence — the shift plan — is valid, and the claim still fails, because the quantity being extrapolated is below the floor by 21 orders. A defence that reports only the warrant’s soundness and the evidence’s validity would be technically correct about the argument’s form and silent about its conclusion. The residual column is where that silence would have lived, and naming it is the difference between a defence and a performance.

§L.E.2 — The five sections

Framing (5 minutes). The problem — pick-and-place with clutter, seven subsystems, conditional instruction. The claim — four components. The roadmap — five sections.

System (10 minutes). The 4.2.1 perception contract, the 4.2.2 four authorities, the 4.2.3 goal specification, the 4.2.4 five components. The interfaces — six contracts. The authority exclusivity — the state machine.

Evidence (15 minutes). The 4.1.3 suite results; the 4.3.1 ablations; the 4.3.2 diagnosis chain; the 4.2.4 safety case; the 4.3.3 horizon plan.

Limits (7 minutes). The vulnerability map’s top three — the recovery rate below the floor (weight 25), the H4 negative margin (15), and the recovery-effectiveness decay (12, chosen from a two-way tie by a stated criterion). The register’s twelve entries. The “what would change my mind” statement.

Next (3 minutes). The 4.4.2 improvements — multi-seed evaluation, spec-writer completeness, the recovery redesign the horizon arithmetic demands — and 4.4.3’s unknown unknowns.

Note the composition of the “next” section. Because the horizon support fails arithmetically, the improvement plan is not a list of nice-to-haves; it carries the one item that would make the central claim true. A defence whose next section is only multi-seed evaluation and spec completeness has not read its own horizon arithmetic.

§L.E.3 — The rehearsal’s diagnosis

The four stages with the running case’s numbers.

Stage 1: solo. Timing — framing 5, system 10, evidence 17, limits 6, next 3. The overrun is the evidence’s 2 minutes, and the compensation is the system’s 10 → 8. The fix is tightening the system section.

Stage 2: peer questions. Five categories, two each, with the template. The omission is the uncertainty — the candidate omits the interval on the safety claim. The fix is a written template card.

Stage 3: adversarial. The map’s highest tier, with the four-part answer. The defensiveness is on the horizon extrapolation — the candidate defends the contract rather than naming the clauses. The fix is naming plus the 4.4.2 plan.

Stage 4: full. Script and questions with the artefacts. Stamina fails on the last five questions — the template collapses. The fix is the card and shorter sittings.

Self-explanation 6. Why is the evidence section’s overrun the most common and the most damaging?

Answer. Because the evidence is the load-bearing section and the candidate overruns it because its content is richest. The damage is that the limits section gets cut, and the limits section is what invites the questions the defence wants — the residuals it has named.

Worked-example ladder.

WE-L.E.a (fully worked). The evidence section is 17 minutes and the limits is 6. Compute the cut and the consequence.

Solution. The cut is 2 minutes from the system (10 → 8) and 2 from the evidence (17 → 15), which restores the limits to 7. The consequence is that the questions are invited onto the highest tier.

WE-L.E.b (completion). The system section cannot be cut below 8. Compute the alternative cut.

Completion. The framing 5 → 4 and the evidence 17 → 16 give the 2 minutes, and the limits is restored to 7. The completion shows the cut comes from the framing and the evidence, not the limits.

WE-L.E.c (faded). Write the “what would change my mind” statement for the central claim.

Faded step. The claim would be wrong if the 400-episode suite’s distribution is not the deployment’s — the 4.3.2 §L.D.1 selection — or if the horizon extrapolation fails its contract clauses, or if the recovery rate can be raised above 0.99949 without the cost the composed rate assumes.

Completion. The statement names the three assumptions and the evidence that would falsify them, which is 4.4.3’s unknown-unknowns content.

WE-L.E.d (contrastive near-miss). The limits section is cut to 3 minutes, and all the committee’s questions concern residuals the limits had no time to name. Why it fails: the limits section controls the questions, and cutting it loses the defence’s own questions. The fix: protect the limits’ 7 minutes, per §L.E.3.

Comparative table: the defence’s plan.

Design principle P60.5. Protect the limits section and re-scope the claim to the evidence; the limits control the questions, and the honest claim is the strong position.

Consolidation checkpoint 5

(a) Three capabilities. You can state the running case’s central claim and its four supports. You can lay out the five sections with their minutes. You can diagnose the four rehearsal stages.

(b) Transfer probe. The evidence section is 17 minutes and the limits is 7. What is the cut, and what is protected? Answer: the cut is 2 minutes from the system and the evidence, and the limits’ 7 is protected. The defence’s strong position is the limits with its residuals named.

(c) Remediation rule. If you cannot state why the limits section controls the questions, re-read §L.E.3 before the lab.

Failure taxonomy

The last row is not in the earlier draft and belongs there. It is the failure this lesson’s own running case commits if the horizon row is copied from a draft that asserted 0.97: the register names the horizon, the evidence supports the horizon, and the number is wrong. A defence that names a residual and mis-states its value has done the harder thing and the easier thing wrong at once.

The lab

Task. Write the running case’s claim-evidence-warrant table, the vulnerability map, and the four-part answer templates for the highest-weight residuals; deliver the five sections to a peer with a timer; and run the four-stage rehearsal protocol with a diagnosis of each stage.

Conditions. The claim is §L.E.1’s central claim; the evidence is the 4.1.3–4.3.3 tables; the register is 4.2.4 §L.E.3’s six plus 4.3.3 §L.E.3’s six, twelve entries. The peer plays the committee with the five categories. Seed the RNG that selects which peer questions are drawn.

Controls. (i) Full preparation; (ii) preparation without the vulnerability map; (iii) preparation without the limits section; (iv) preparation without rehearsal stage 3.

Metrics.

Pre-registered hypotheses.

H1. Full preparation scores 4 of 4 on claim coverage, because §L.E.1’s central claim is written with scope and residual.

H2. Preparation without the vulnerability map draws a higher hostile-question rate, because the defence cannot invite residuals it has not named.

H3. Preparation without the limits section concentrates questions on residuals the limits would have named, and template fluency falls.

H4. Preparation without stage 3 shows the defensiveness signature on the horizon question, because the adversarial stage is the only one practising vulnerability handling.

H5. A register copied from the earlier draft — horizon survival 0.97 — fails arithmetic consistency on exactly one of the three audited entries, and the failure is detected by recomputation rather than by inspection.

Break-it sequence.

1. Cut the limits silently. Questions turn hostile and the defence turns defensive. Silent: the evidence is complete.
2. Over-scope the claim silently. A 0.90 claim against a 0.898 lower bound is the committee’s first question. Silent: the claim looks strong.
3. Skip stage 3 silently. The adversarial question gets a defensive answer. Silent: the script is fluent.
4. Copy a register number from an earlier draft. The horizon entry reads 0.97 while 4.3.3 computes $8.57 \times 10^{-22}$. Silent: the entry is present, the evidence is cited, and the defence has named the residual.

Acceptance criteria.

What good looks like. A good artefact has six properties. (1) Each claim’s four elements are sentences with a scope. (2) The vulnerability map reports its highest tier and states its tie-break. (3) The answer templates have four parts, each with the evidence version. (4) The timing is enforced and the limits protected. (5) The break-it results are a table. (6) Every register number is recomputed from its own formula, and the recomputation is an artefact, not a habit.

A runnable core of the claim check, the vulnerability map with an explicit tie-break, and the register audit:

# lab_4_4_1.py — claim check, vulnerability map over the register, register audit
import numpy as np
from math import floor, log10

rng = np.random.default_rng(0)

CLAIM = {
    "claim": "success rate >= 0.88 at 95% lower bound, seen-task axis",
    "scope": "running arm, 4.1.3 suite v1, 8-hour shift, 4-reset maintenance",
    "evidence": {"suite_version": 1, "$n_episodes$": 400,
                 "lower_bound": 0.898, "point": 0.92},
    "warrant": "the suite is a stratified sample of the deployment distribution",
    "residual": "the 0.90 target; the seed variance on deployment seeds",
}
ELEMENTS = ("claim", "evidence", "warrant", "residual")   # scope is the claim's own content

def check_claim(claim):
    """The four elements, the scope statement, and the bound's consistency with the claim."""
    threshold = float(claim["claim"].split(">=")[1].split(" at ")[0].strip())
    return {"elements": "%d of %d" % (sum(bool(claim.get(k)) for k in ELEMENTS), len(ELEMENTS)),
            "scope": bool(claim.get("scope")),
            "threshold": threshold,
            "consistent": claim["evidence"]["lower_bound"] >= threshold}

# --- the vulnerability map, scored directly off the two registers --------
# Six entries from 4.2.4 §L.E.3, six from 4.3.3 §L.E.3. Probability and
# consequence are judgements on a 1-5 scale, as in 4.2.4 §L.A.1.
RESIDUALS = {
    # 4.2.4 §L.E.3 -- safety register
    "H1 force: stiffness mis-estimation":            (2, 3),
    "H2 workspace: divider moves after the check":   (2, 3),
    "H3 drop: slip onset beyond 12 ms":              (3, 4),
    "H4 unintended: I5 at 0.68 s, negative margin":  (3, 5),
    "H5 stuck: 2 s fallback duration":               (2, 2),
    "H6 spurious: semantic error within tolerance":  (2, 2),
    # 4.3.3 §L.E.3 -- horizon register
    "drift unmonitored inside the interval":         (3, 3),
    "recovery effectiveness decay":                  (4, 3),
    "policy confidence drift":                       (4, 2),
    "gripper wear between resets":                   (3, 3),
    "extrapolation contract violation":              (2, 4),
    "recovery rate below the floor requirement":     (5, 5),
}

def vulnerability_map(residuals):
    """Weight desc, probability desc, name asc -- a total order.

    Sorting the raw tuples (p, c, name) or (name, weight, p, c) is not a
    ranking by weight: the first sorts on probability, the second on name.
    An earlier version of this lab sorted the whole tuple and reported an
    alphabetical list wearing the weight column's clothes.
    """
    rows = [(name, p * c, p, c) for name, (p, c) in residuals.items()]
    rows.sort(key=lambda r: (-r[1], -r[2], r[0]))
    return rows

rows = vulnerability_map(RESIDUALS)

def tiers(rows):
    """Group consecutive rows of equal weight; ties are reported, not broken."""
    out = []
    for name, w, p, c in rows:
        if out and out[-1][0] == w:
            out[-1][1].append(name)
        else:
            out.append((w, [name]))
    return out

ts = tiers(rows)
print("claim checks:", check_claim(CLAIM))
print("register entries in the map: %d (6 safety + 6 horizon)" % len(rows))
print$"\nweight tiers, descending:"$
for w, names in ts:
    print("  %2d  %d entr%s  %s" % (w, len(names), "y " if len(names) == 1 else "ies",
                                    "; ".join(names)))
$n_third$ = ts[2][1]
print$"\nthe third is chosen from a %d-way tie at weight %d, by consequence, and stated"
      % (len(n_third), ts[2][0])$

# --- register audit: recompute every entry from its own formula ---------
$P_FAIL$, $R_REC$ = 0.18, 0.809
$N_SHIFT$, $T_D$, FLOOR = 1152, 576.0, 0.90
Q = $P_FAIL$ * (1.0 - $R_REC$)

def $shift_survival(n_resets$, q=Q, $t_d=T_D$, $n=N_SHIFT$):
    """$n_resets$ cut points give $n_resets+1$ segments; the last absorbs the remainder."""
    m = $n_resets$ + 1
    base = n // m
    ks = [base] * (m - 1) + [n - base * (m - 1)]
    assert sum(ks) == n, "segments must tile the shift"
    return float(np.prod([np.prod(1.0 - q * (1.0 + np.arange(k) / $t_d$)) for k in ks]))

def required_recovery(fl=FLOOR, $n=N_SHIFT$, $p=P_FAIL$):
    """The R at which zero failures still meets the floor."""
    return 1.0 - (1.0 - fl ** (1.0 / n)) / p

def sig_figs(x):
    """Significant figures the register entry was written to."""
    m = repr(float(x)).split("e")[0].split("E")[0].replace("-", "").replace(".", "").lstrip("0")
    return max(len(m), 1)

def round_sig(x, sig):
    """Round x to sig significant figures."""
    return 0.0 if x == 0 else round(x, sig - 1 - int(floor(log10(abs(x)))))

def matches(claimed, want):
    """Consistent iff the recomputed value rounds to the entry at the entry's precision.

    Two tolerances were wrong here before. A fixed relative tolerance (1e-6)
    flags a correct entry written to four decimals. A tolerance derived from
    decimal places fails open on scientific notation, where `repr` carries no
    decimal point, so 8.0e-22 and 1e-21 both passed against 8.56e-22 -- wrong
    by 6.6% and 17%. Rounding to significant figures is exact for both.
    """
    return round_sig(want, sig_figs(claimed)) == claimed

REGISTER = {
    "shift_survival_4_reset": 0.97,      # copied from an earlier draft of 4.4.1
    "composed_recovery_rate": 0.809,     # as recorded in 4.2.4
    "required_recovery_floor": 0.9995,   # as 4.3.3 quotes it, to 4 dp
}
AUDIT = {
    "shift_survival_4_reset": shift_survival(4),
    "composed_recovery_rate": $R_REC$,
    "required_recovery_floor": required_recovery(),
}
print$"\nregister audit (claimed vs recomputed from the formula):"$
bad = 0
for k, claimed in REGISTER.items():
    want = AUDIT[k]
    ok = matches(claimed, want)
    bad += 0 if ok else 1
    print("  %-24s claimed %-10.6g recomputed %-12.6g %s"
          % (k, claimed, want, "ok" if ok else "MISMATCH"))
print("  %d of %d entries fail recomputation" % (bad, len(REGISTER)))

# --- answer template ----------------------------------------------------
def answer_template(claim, evidence, uncertainty, residual_plan):
    return {"restatement": claim, "evidence": evidence,
            "uncertainty": uncertainty, "residual_plan": residual_plan}

a = answer_template(
    CLAIM["claim"], CLAIM["evidence"],
    "the CI is the episode-level CI; the seed sd (1.5 pts) is below it",
    "residual: seed variance on deployment; plan: multi-seed evaluation")
print$"\nanswer template parts:", list(a.keys())$
print("peer question draw:", rng.choice(list(RESIDUALS), size=2, replace=False).tolist())

Measured output:

claim checks: {'elements': '4 of 4', 'scope': True, 'threshold': 0.88, 'consistent': True}
register entries in the map: 12 (6 safety + 6 horizon)

weight tiers, descending:
  25  1 entry   recovery rate below the floor requirement
  15  1 entry   H4 unintended: I5 at 0.68 s, negative margin
  12  2 entries  recovery effectiveness decay; H3 drop: slip onset beyond 12 ms
   9  2 entries  drift unmonitored inside the interval; gripper wear between resets
   8  2 entries  policy confidence drift; extrapolation contract violation
   6  2 entries  H1 force: stiffness mis-estimation; H2 workspace: divider moves after the check
   4  2 entries  H5 stuck: 2 s fallback duration; H6 spurious: semantic error within tolerance

the third is chosen from a 2-way tie at weight 12, by consequence, and stated

register audit (claimed vs recomputed from the formula):
  shift_survival_4_reset   claimed 0.97       recomputed 8.56455e-22  MISMATCH
  composed_recovery_rate   claimed 0.809      recomputed 0.809        ok
  required_recovery_floor  claimed 0.9995     recomputed 0.999492     ok
  1 of 3 entries fail recomputation

answer template parts: ['restatement', 'evidence', 'uncertainty', 'residual_plan']
peer question draw: ['gripper wear between resets', 'recovery effectiveness decay']

Reading the result. Two things the lab establishes that prose alone did not.

The map does not yield a top three by weight alone. One residual sits at 25, one at 15, and the remaining ten are five tied pairs. Any implementation that returns exactly three rows has broken a tie silently, and the earlier version of this lab did precisely that — its sort key was the whole tuple, so the name decided the order and the reported “top three” was alphabetical. The fix is to sort by weight with an explicit total order and to report the ties rather than resolve them inside a sort.

The audit’s precision test is a defect in its own right. The first version compared each entry to its recomputation with a fixed relative tolerance of $10^{-6}$, which flags a correct entry written to four decimals and would have buried the one entry that is wrong under two false alarms. The second derived its tolerance from decimal places and failed open on scientific notation: 8.0e-22 and 1.0e-21 both passed against a true $8.56 \times 10^{-22}$, wrong by 6.6% and 17%. The shipped version rounds the recomputation to the entry’s significant figures, and the canary separates $8.6 \times 10^{-22}$ from $8.0 \times 10^{-22}$ and $1.0 \times 10^{-21}$. A gate that reports every row alike reports nothing.

The register audit catches a defect that no amount of rehearsal would. A horizon survival of 0.97 copied from an earlier draft passes every check in this lesson’s own artefact list: the entry exists, the evidence is cited, the residual is named. It fails only when recomputed, and it fails by 21 orders of magnitude. That is the argument for treating recomputation as an artefact rather than a habit — a defence can be internally consistent and externally wrong, and only the formula knows the difference.

Cheat sheet

Exercises with solutions

E 4.4.1.1. Write the four elements for the claim “the agent is safe”.

S 4.4.1.1. Claim: the six safety register entries are accepted by the operator at the 4.2.4 §L.E.3 register. Evidence: the six entries with the 4.2.4 §L.D.2 injection-suite metrics. Warrant: the 4.2.4 §L.A.1 hazard analysis is complete and the GSN tree is the argument. Residual: the analysis’s gap and the register residuals. The lesson: the four elements are the claim’s content, and “safe” without them is unfalsifiable.

E 4.4.1.2 (transfer). The map’s highest-weight residual is the recovery rate below the floor, at 25. What is the defence’s strong response?

S 4.4.1.2. Name it first, state the arithmetic that makes the weight ($R = 0.809$ against a required 0.99949), and make the recovery redesign the content of the “next” section. Re-scoping is not available because the shortfall is arithmetic, not a scope question. The strong response is control of the question, not defence of the number. The lesson: naming the residual is controlling it.

E 4.4.1.3. State the five sections and their word budgets.

S 4.4.1.3. Framing 700, system 1,400, evidence 2,100, limits 1,000, next 400. The lesson: evidence is the load-bearing section and limits controls the questions.

E 4.4.1.4 (diagnostic). The committee asks “what is the success rate on reflective surfaces?” and the candidate answers “I don’t know”. Which case, and what is the correct answer?

S 4.4.1.4. Case 2 — inside the scope, evidence absent. The correct answer is honesty plus a plan: the suite does not include reflective surfaces, the 4.3.2 §L.D.1 selection is the reason, and 4.4.2’s improvement is the plan. The lesson: “I don’t know” is correct when a plan is named, and bare “I don’t know” is a preparation failure.

E 4.4.1.5. Write the category 3 answer for “your recovery rate assumes recoveries are independent across episodes; are they?”.

S 4.4.1.5. Restatement: the recovery rate is 0.809 per episode with the 4.3.3 §L.C.3 per-segment compounding. Evidence: the 4.2.4 §L.C.3 composed rate and the 4.3.3 §L.C.3 segment survival. Uncertainty: the independence assumption is the warrant, and the correlation is the 4.3.3 §L.A.2 drift. Residual plan: per-segment compounding is the correlation’s treatment, and 4.4.2’s multi-segment evaluation is the plan. The lesson: a category 3 question is about the warrant’s assumption, and the answer names it.

E 4.4.1.6 (transfer). The solo run-through overruns the evidence by 2 minutes and the system by 1. What is the cut, and what is protected?

S 4.4.1.6. The cut is 3 minutes from the system (not the evidence) and 1 from the framing, and the limits’ 7 is protected. The lesson: the cut comes from the least load-bearing sections, not the overrunning one.

E 4.4.1.7 (diagnostic). The full run-through shows question fluency falling in the last ten minutes. Which failure mode?

S 4.4.1.7. Stamina; the template collapses under fatigue. The fix is shorter sittings and a written card. The lesson: the full stage tests composition, and its failure is stamina.

E 4.4.1.8. Write the “what would change my mind” statement for the success-rate claim.

S 4.4.1.8. The claim would be wrong if the 400-episode suite’s distribution differs from the deployment’s — the 4.3.2 §L.D.1 selection — or if the seed variance on deployment seeds exceeds 1.5 points. The statement names both assumptions and the evidence that would falsify them. The lesson: the statement is 4.4.3’s unknown-unknowns content.

E 4.4.1.9 (transfer). The limits section is cut to 3 minutes and the questions are all on residuals. What is the diagnosis and the fix?

S 4.4.1.9. The limits section controls the questions, and cutting it loses the defence’s own questions. The fix is restoring the limits and cutting the system and evidence. The lesson: the limits are protected because they control the questions.

E 4.4.1.10 (diagnostic). A defence’s register lists the horizon residual as “shift survival 0.97, accepted”. What is wrong, and what test finds it?

S 4.4.1.10. The number is wrong. At the composed recovery rate of 0.809 the escalation rate is $q = 0.03438$, and under the 4.3.3 §L.A.2 drift hazard with 4 resets the shift survival is $8.57 \times 10^{-22}$, not 0.97. Inspection cannot find it, because the entry is present, cited, and named. Recomputation from $p$, $R$, and the segment structure finds it, and the discrepancy is 21 orders of magnitude. The lesson: a register entry is a claim and needs the same test as a claim; internal consistency is not external correctness.

Exit test

You are ready for Lesson 4.4.2 when you can, without notes:

1. Write the four elements of a defensive claim with the running case’s values.
2. State the defence’s purpose against the report’s, the demo’s, and the paper’s.
3. Build the claim hierarchy and identify the weakest link.
4. Name the five sections and their word budgets.
5. Build the evidence hierarchy for a claim and state the reversal failure.
6. Construct the vulnerability map from the register, report its highest tier, and state a tie-break.
7. Name the five question categories and their sources.
8. Write the four-part answer for a given question.
9. Apply the “I don’t know” discipline’s three cases.
10. Name the eight artefacts and their roles.
11. State the timing intervals and the margin’s use.
12. Lay out the four rehearsal stages and their failure signatures.
13. State the running case’s central claim, including the horizon component’s true value.
14. Diagnose a rehearsal overrun and a cut to the limits section.
15. State why a register entry needs recomputation and not only inspection.

Cross-references. 4.3.3 supplies the horizon failure law, the maintenance policy, and the horizon register entries, restated in §L.A.3 and §L.D.3. 4.3.2 supplies the diagnosis evidence chain and the stopping-rule residual, restated in §L.B.2 and §L.C.1. 4.3.1 supplies the ablation registry and the interval lower bound, restated in §L.B.1 and §L.C.2. 4.2.4 supplies the safety-case structure and the six-entry register, restated in §L.D.1 and §L.E.3. 4.2.3 supplies the six strata and the deferral discipline, restated in §L.C.3. 4.2.2 supplies the four authorities and attribution, restated in §L.B.3. 4.2.1 supplies the contract’s five fields and the evidence table, restated in §L.B.1. 4.1.3 supplies the 400-episode suite and the four-plus-one axes, restated in §L.A.2. 3.3.3 supplies the affordance grounding and the physical-possibility checks, restated in §L.A.1. Lesson 4.4.2 uses the vulnerability map as its starting point. Lesson 4.4.3 uses the register and the “what would change my mind” statement as the closing argument.

§L.10 — Provenance

Corrections to the previous draft of this lesson.

1. The central claim asserted a shift survival of 0.97 and “at least 0.90”. Both are impossible at the composed recovery rate: 4.3.3 §L.A.3 requires $R \ge 0.99949$ for the floor and the composed rate is 0.809, giving $8.57 \times 10^{-22}$ under the 4-reset schedule. The horizon support now states the computed value and names the shortfall as the residual.
2. The vulnerability map scored nine residuals whose names match neither register — “spec gap”, “deferral rate”, “occlusion persistence”, “mapping drift” — while asserting each was a register entry. The register has twelve entries and twelve are now scored. The old lab’s sort key was also the whole tuple, so it ordered by name and reported an alphabetical “top three” wearing the weight column’s clothes. It now sorts by weight, probability, name, and reports the tiers rather than resolving them inside a sort.
3. The register was counted as thirteen entries; 4.2.4 has six and 4.3.3 has six, so twelve.
4. The lesson cited 3.3.4 throughout as a prerequisite. 3.3.4 is listed in the curriculum plan but not written; the register and affordance references now point at 3.3.3, which exists.

A fifth, added rather than corrected: the register-audit break-it and hypothesis H5, because defect 1 is exactly the class of error a rehearsal cannot catch and a recomputation can.

A sixth, found while building the audit. The first audit I wrote compared each entry against its recomputation with a fixed relative tolerance of $10^{-6}$, which flags a correct entry written to four decimals and so buries the one entry that is wrong. I replaced the tolerance with one derived from the entry’s decimal places, canaried it against 8.0e-22 and 1e-21, and both passed against a true $8.56 \times 10^{-22}$ — wrong by 6.6% and 17% — because repr carries no decimal point in scientific notation, so the tolerance collapsed to half an absolute unit. The shipped audit rounds the recomputation to the entry’s significant figures, which is exact for both notations, and the canary now separates $8.6 \times 10^{-22}$ (pass) from $8.0 \times 10^{-22}$ and $1.0 \times 10^{-21}$ (fail). The gate I first shipped would have reported the one true defect and every correct entry alike.