# W12 No-Video Transcript — Optimization under Competing Queries

## Status and use

No W12 recording exists. This document is an authored no-video equivalent for independent study and instructor preparation. It is not a transcription of speech, and the package has not been taught, rehearsed, timed, recorded, or piloted. All durations below are instructional planning budgets rather than observed media or classroom time. The route uses a synthetic matrix and a local software fixture; no platform or user outcome was collected.

## Planned chapter budget

| Chapter | Topic | Planned minutes |
|---:|---|---:|
| 1 | The portfolio problem | 4 |
| 2 | Query strata and weights | 4 |
| 3 | Vector objectives and hard gates | 4 |
| 4 | Frozen candidates and matrix | 4 |
| 5 | Weighted arithmetic and uncertainty | 4 |
| 6 | Pareto dominance and frontier | 4 |
| 7 | Choice rule and policy sensitivity | 4 |
| 8 | Ablation and interaction | 4 |
| 9 | Nulls, conflicts, and deviations | 3 |
| 10 | L05 and evidence routes | 4 |
| 11 | Reproduction and bounded decision | 3 |

**Total planned route: 42 minutes.** Pause time, calculations, retrieval checks, and studio work are outside this narration budget.

## Chapter 1

Welcome to W12, Optimization under Competing Queries. Our essential question is deceptively simple: which gain survives a portfolio of intents? The difficult word is not “gain.” It is “portfolio.” A page can help someone who needs a definition and hinder someone who needs to verify a limitation. A revision can perform well for a comparison prompt and poorly for a counterfactual prompt. If we compress those outcomes into one average too early, we lose the identity of the person or task that bears the loss.

So today optimization means a decision procedure over a governed set of source states. It does not mean making a page generally better, maximizing mentions, or searching for a universal tactic. We need a frozen control, candidate identities, a target query portfolio, direction-aware objectives, hard constraints, a budget, uncertainty, a choice rule, and rollback. The valid action set includes releasing one locally reviewed candidate, retaining control, or reporting an inconclusive result.

The case is HarborGuide, a fictional evidence page. Its seven candidates and every outcome value were authored for teaching. No search engine, answer engine, model, crawler, browser session, or person produced those scores. This is important because reproducible arithmetic is not empirical evidence. We can prove which row our rule selects, but we cannot claim that a live product or user would respond in the same way.

Consider the common sentence, “This layout improved overall visibility.” Before accepting it, ask: overall across which queries, sampled how, on which surface, using what metric and comparator, under what content and cost budget, with which factual and accessibility gates, and over what uncertainty? If those objects are absent, the sentence is not a complete optimization result.

Your first retrieval check is to formulate the bounded decision. Try: “Among seven frozen local candidates, choose at most one under a five-stratum query portfolio and an eight-point edit budget after non-compensable integrity gates, using a preregistered lower-tail, meaningful-effect, tie, and rollback rule.” Notice how this sentence permits no release. That is a feature, not a failure.

## Chapter 2

We begin with the portfolio because its definition controls the meaning of every later score. The five fictional strata are definition, compare, select, verify, and counterfactual. Their weights are respectively zero point three zero, zero point two five, zero point two zero, zero point one five, and zero point one zero. The weights sum to one.

Definition queries establish the object and its scope. Compare queries request a contrast on declared dimensions. Select queries support a bounded decision without a persuasion shortcut. Verify queries recover method, date, evidence, and limitations. Counterfactual queries look for exceptions, failure cases, or reasons not to select. This last group matters because a revision can become easier to consume by hiding the conditions under which it fails.

The weights are governance inputs. They are not properties of language or verified estimates of the HarborGuide audience. In a real project, a weight might come from a declared service mandate or a properly sampled demand estimate. Its provenance would belong in the manifest. Here the values are teaching policy. They let us demonstrate that aggregation always carries a decision about whose tasks count.

Suppose someone sees a negative result on the counterfactual stratum and lowers its weight from zero point one zero to zero point zero one. The arithmetic may still be correct, but the primary question has changed after observing outcomes. That is a researcher degree of freedom. A transparent team may run the changed allocation as sensitivity analysis, but it must preserve the frozen primary result.

Weights alone do not protect material groups. A rare safety-critical intent can carry a low frequency weight and still deserve a non-inferiority condition. W12 therefore also freezes a floor: no stratum may fall below negative zero point zero two. This is an outcome guardrail, distinct from factual, legal, safety, privacy, authorization, and accessibility gates.

This chapter carries W06 forward. A convenience prompt list is not a target population. Strata need operational definitions, desired-answer prompts need exclusions, paraphrase families should remain together, and locale and date need identities. Optimization cannot repair leakage. If favorable paraphrases occupy both development and evaluation cells, a precise weighted score can describe the wrong target.

Pause and write who would have authority to set the weights in your setting. Then write who bears a loss when a heavily weighted aggregate selects a candidate that harms a small stratum. If those roles are unclear, the weighted mean should not be presented as neutral.

## Chapter 3

Now construct the objective vector. For each feasible candidate, we retain six coordinates: gain for definition, compare, select, verify, and counterfactual, followed by negative cost. Higher is better in every displayed direction. Using negative cost is a notation convenience; the raw cost still has authored point units and the budget remains at most eight.

Why use a vector? Because it keeps the trade-off pattern visible. A scalar average implies exchange rates among objectives. The vector lets us ask whether one candidate is at least as good in every relevant direction before imposing those exchange rates. It also lets us preserve the zero-cost control, which can remain nondominated even when revisions have positive gains.

Hard constraints do not belong inside this vector as small positive rewards. HarborGuide requires factual integrity, legal permission, authorization, safety, privacy, and essential accessibility to pass. The cost limit is also a gate. First filter the permitted set. Only then compare outcomes among survivors.

Imagine a candidate with a very large selection gain but a factual-integrity failure. A weighted formula such as eighty percent visibility, ten percent factuality, and ten percent accessibility could allow the large gain to offset the failure. That is the wrong problem. If factual validity is mandatory, represent it as a Boolean gate or threshold that cannot be purchased with benefit elsewhere.

The same applies to essential accessibility. This package can freeze an accessibility pass field for a synthetic exercise, but a real release would require appropriate semantic, keyboard, screen-reader, visual, and content review. A software score cannot grant conformance. Legal applicability also needs qualified review; the lecture does not deliver legal advice.

The proper sequence is memorable. Define permitted changes. Apply factual, legal, authorization, safety, privacy, accessibility, and budget gates. Compare vectors among survivors. Apply a declared policy. Obtain accountable approval. Preserve rollback. If any later gate fails, revert without rescoring.

Retrieval check: someone proposes `reward = visibility + factuality − cost`. Ask whether a factual score of zero should ever be offset by enough visibility. If the answer is no, factuality is not a freely tradable reward in this decision. Rewrite it as an admissibility condition.

## Chapter 4

We can now reveal the seven candidates. C0 is the unchanged control with cost zero. C1 changes evidence-layout proximity and costs three. C2 adds one answer-first limitations module and costs five. C3 combines C1 and C2 and costs nine. C4 adds a persuasive append, costs four, but changes factual scope and fails safety review. C5 adds decorative headings and costs four. C6 adds definition anchors and costs two.

Reveal gates before outcomes. C3 passes the integrity fields but exceeds the eight-point budget. C4 fails factual and safety gates. Those two rows remain in the trace because they teach why raw optimization scores can mislead. They cannot enter the choice calculation. The hard-feasible set is exactly C0, C1, C2, C5, and C6.

Now read the five gains. C0 is all zeros. C1 is zero point zero five, zero point zero four, zero point zero two, zero point zero six, and negative zero point zero one. C2 is zero point zero eight, zero point zero one, negative zero point zero two, zero point zero seven, and zero. C3 is zero point one one, zero point zero five, negative zero point zero one, zero point one zero, and negative zero point zero two. C4 is zero point zero three, zero point one zero, zero point one two, negative zero point zero eight, and negative zero point zero five. C5 is zero point zero two, zero point zero one, zero, zero, and negative zero point zero one. C6 is zero point zero two, zero point zero two, zero point zero one, zero point zero four, and zero point zero one.

Preserve the negative cells. C1’s counterfactual value is negative zero point zero one. C2 reaches the loss floor on selection. C4’s attractive compare and select values coexist with severe verify and counterfactual losses as well as inadmissible facts. C6 is modest but positive in every stratum.

The half-widths are zero for C0, then zero point zero one eight, zero point zero two zero, zero point zero two five, zero point zero three zero, zero point zero one five, and zero point zero one seven. These are authored uncertainty fields. They did not come from repeated observations and should never be described as confidence intervals with empirical coverage.

At this point do not vote for a winner. First verify matrix identity, gate states, weights, and units. An attractive candidate name or high cell is not a decision rule.

## Chapter 5

The weighted mean is the dot product of the five stratum gains and the five weights. Let us calculate C1 without hiding intermediate terms. Zero point three times zero point zero five is zero point zero one five. Zero point two five times zero point zero four is zero point zero one zero. Zero point two times zero point zero two is zero point zero zero four. Zero point one five times zero point zero six is zero point zero zero nine. Zero point one times negative zero point zero one is negative zero point zero zero one. The sum is zero point zero three seven zero.

The full weighted means are C0 zero, C1 zero point zero three seven zero, C2 zero point zero three three zero, C3 zero point zero five six five, C4 zero point zero four one zero, C5 zero point zero zero seven five, and C6 zero point zero two zero zero.

Look at the raw ordering. C3 is highest, but it is over budget. C4 is above C1, but it fails factual and safety gates. Correct arithmetic combined with the wrong order of operations would select an inadmissible candidate. This is why gate-first selection must be executable in code and visible in the report.

Next add and subtract each authored half-width. C1 spans zero point zero one nine to zero point zero five five. C2 spans zero point zero one three to zero point zero five three. C3 spans zero point zero three one five to zero point zero eight one five. C4 spans zero point zero one one to zero point zero seven one. C5 spans negative zero point zero zero seven five to zero point zero two two five. C6 spans zero point zero zero three to zero point zero three seven.

The primary rule requires a lower endpoint of at least zero point zero one five. Among hard-feasible candidates, C1 clears this condition. C2 and C6 have positive lower endpoints but do not clear the meaningful threshold. C5 crosses zero and is therefore compatible with a null under the authored convention.

Do not say C5 proved no effect. No empirical effect was estimated. The precise statement is that its frozen interval crosses zero. Also do not say C2 failed. It is a feasible, nondominated alternative that does not satisfy one primary decision threshold.

Your calculation check is C6. Multiply each gain by its weight: zero point zero zero six, zero point zero zero five, zero point zero zero two, zero point zero zero six, and zero point zero zero one. The total is zero point zero two zero. Retain all precision until display.

## Chapter 6

Pareto dominance gives us a policy-light way to remove candidates that are unambiguously worse under the declared vector. In W12, candidate A dominates B when both are hard-feasible, A is at least as good on all five gains, A costs no more, and A is strictly better in at least one coordinate.

Compare C1 and C5. On definition, zero point zero five is greater than zero point zero two. On compare, zero point zero four is greater than zero point zero one. On select, zero point zero two is greater than zero. On verify, zero point zero six is greater than zero. On counterfactual, both equal negative zero point zero one. C1 costs three, less than C5’s four. C1 dominates C5.

C6 also dominates C5. It is equal on definition, better on compare, select, verify, and counterfactual, and cheaper. A single witness is enough to establish that C5 does not belong to the frontier, but both witnesses provide an audit check.

The feasible frontier is C0, C1, C2, and C6. C0 remains because nothing with positive gains also has cost zero. C1 and C6 trade broad gains against counterfactual protection and cost. C2 offers strong definition and verification values but reaches the selection floor and costs more. None is at least as good as another across all six directions.

C3 and C4 are not members of the feasible comparison set. On a visual, keep them visible but crosshatched beyond the feasibility boundary. Do not call them dominated when their primary disposition is inadmissible. “Dominated” and “constraint violating” answer different questions.

Also remember that a two-axis Pareto plot is only a projection. If the underlying proof uses six coordinates, the slide needs a companion table or coordinate checks. A visually forward point can still lose on a hidden stratum.

Retrieval check: why can a zero-gain control remain on the frontier? Because cost is an objective direction. Every positive-gain revision has higher cost, so no candidate is at least as good as control on all coordinates. Frontier membership does not mean the control is selected; it means the trade-off cannot be eliminated without a policy.

## Chapter 7

We now apply the preregistered choice rule. Step one: pass all hard gates and cost at most eight. Step two: require no stratum below negative zero point zero two. Step three: require a weighted interval lower endpoint of at least zero point zero one five. Step four: choose the greatest weighted mean. If eligible means differ by at most zero point zero zero two, choose lower cost, then fewer changed components, then control. If nobody survives, retain C0 and report an inconclusive result.

C1 passes. Its minimum stratum is negative zero point zero one, its lower endpoint is zero point zero one nine, and its weighted mean is zero point zero three seven. C2 reaches the stratum floor but misses the meaningful lower endpoint. C6 has no negative stratum but also misses that lower endpoint. C5 is dominated and crosses zero. The primary rule selects C1 for human local review, with rollback retained.

Now expose the policy nature of that decision. The sensitivity rule is maximin: among hard-feasible candidates, select the one with the greatest minimum stratum change. The minima are C0 zero, C1 negative zero point zero one, C2 negative zero point zero two, C5 negative zero point zero one, and C6 positive zero point zero one. Maximin selects C6.

The same matrix produces different decisions because the policies protect different values. The weighted rule accepts C1’s small counterfactual loss in exchange for larger gains elsewhere. Maximin prefers C6 because its worst-served stratum still improves. Neither policy is a fact of nature. Someone must have authority to choose, and the report must identify who bears the tolerated loss.

The correct conclusion includes both results: C1 is the primary weighted-policy choice, and C6 is the robust maximin choice. A presentation that shows only C1 hides material policy sensitivity. A presentation that replaces the primary result with C6 without documenting a changed rule also hides a deviation.

If C1’s lower endpoint were zero point zero one four instead of zero point zero one nine, the primary survivor set would be empty. We would retain control. We would not lower the threshold after inspecting the result. That possibility makes the rule falsifiable.

## Chapter 8

The bundle candidate C3 lets us practice single-component ablation. C3 contains C1’s evidence proximity and C2’s answer-first limitations module. Remove proximity while keeping the module, and the corresponding candidate is C2. The conditional weighted difference is zero point zero five six five minus zero point zero three three zero, or zero point zero two three five.

Remove the module while keeping proximity, and the corresponding candidate is C1. That conditional difference is zero point zero five six five minus zero point zero three seven zero, or zero point zero one nine five.

These values are not additive. Compare the bundle with the sum of the two component changes relative to control. Zero point zero five six five minus zero point zero three seven zero minus zero point zero three three zero equals negative zero point zero one three five. The stratum interaction vector is negative zero point zero two, zero, negative zero point zero one, negative zero point zero three, and negative zero point zero one.

This descriptive negative interaction may resemble redundancy or interference. Do not invent a causal mechanism. The values were authored. Even in a real factorial design, a conditional component estimate depends on assignment, unit, context, support, and interaction specification.

C3 also costs nine. Neither ablation contribution can purchase an exception to the eight-point budget. The bundle is useful for redesign reasoning but inadmissible for release. Perhaps a smaller module can be tested next, but that would be a new candidate and analysis version.

One-factor isolation is a discipline, not a storytelling device. If a treatment changes layout, claims, schema, navigation, and disclosures simultaneously, the estimator is a bundle. Options are to isolate a component, run a factorial design with adequate support, use a sequential plan with a frozen order and stopping rule, or report a bundle estimand. What is not acceptable is calling an uncontrolled package “one factor” because one label sounds convenient.

Retrieval check: does the larger zero point zero two three five subtraction prove proximity is more important? No. It is conditional on C3, the other component, this query portfolio, and this authored matrix. It is not a universal importance measure.

## Chapter 9

Optimization research can produce four kinds of uncomfortable but valid results: nulls, conflicts, constraint violations, and policy disagreement. A complete candidate trace preserves all four.

C5 is feasible, dominated, and compatible with a null. These are three different properties. Feasible means its hard gates pass. Dominated means another feasible row is never worse under the declared vector and is better somewhere. Null-compatible means the authored interval crosses zero. None of those states should be collapsed into a red traffic light.

C1 is selected but conflicting because its counterfactual cell is negative. C2 is feasible and nondominated but not selected under the primary meaningful threshold. C6 is feasible and nondominated and wins maximin, yet loses under the primary weighted rule. C3 and C4 are constraint violating for different reasons. Precise labels preserve the decision logic.

Precommit how deviations work. If a stakeholder changes weights, the analyst appends a new policy record with author, time, rationale, old and new values, and changed selection. If a candidate changes, it gets a new ID and hash. If an outcome is corrected, preserve the original matrix version and explain the correction. Never overwrite the primary record to make a preferred candidate look preregistered.

Rollback is similarly unambiguous. Any later factual, legal, authorization, safety, privacy, accessibility, or protocol failure restores the C0 control. There is no appeal to weighted benefit. A rollback record names trigger, time, owner, restored hash, verification, and unresolved impact.

Use language that matches the disposition. Say “excluded for budget,” not “performed poorly.” Say “factual and safety failure,” not “lower quality.” Say “not selected under the primary policy,” not “ineffective.” Say “interval crosses zero in an authored fixture,” not “proved no effect.” This vocabulary is a quality-control system because it stops distinct reasons from being compressed into a winner narrative.

## Chapter 10

W12 links to L05, the Controlled Content Intervention. L05 contains a local control page, treatment page, locked claims, an intervention card, an independent-equivalence checklist, and a standard-library auditor. Its intervention ID is INT-001. The factor is `evidence_layout_proximity`, and the hypothesized stage is `human_comprehension`.

The auditor reports three locked claims, one changed factor, and zero errors. It preserves claim IDs CL-001, CL-002, and CL-003 and source IDs S-001, S-004, and S-008. It generates normalized claims, a complete diff, an equivalence review, rollback manifest, and run manifest. Its evidence ceiling is exact: local structural equivalence package only; no system response or causal visibility effect is measured.

C1 uses the same factor name for curricular continuity. But the W12 gains do not come from L05. The auditor can show that selected text and source identities remain equal and that the declared local factor changed. It cannot show that a person understood more, a retriever selected the page, a model cited it, or a business outcome changed.

The reading route has two core papers and three extensions. PAPER-03 motivates multi-query conflict and content-budget coordination. PAPER-31 motivates interpretable feature-level multi-objective reasoning. Their results remain bounded by their evaluated queries, candidates, models or engines, measures, and versions.

PAPER-04 extends the discussion to output-order control and is also a manipulation-risk case; it does not authorize live steering material. PAPER-27 supplies a confidence-decay and deterministic-agent proposal for critique; it does not expose hidden states in a named closed platform. PAPER-30 motivates adaptive proposal archives, surrogate critics, cost accounting, and ablation; an adaptive agent still cannot approve unsupported facts or release itself.

These papers are not a tactic menu. We extract design objects and validity ceilings. None validates HarborGuide, the query weights, the seven outcomes, or a universal content strategy. None supports a production effect claim in this package.

## Chapter 11

Finish by reproducing the decision from frozen identities. The validator checks the exact seven files, narrative word contracts, 24 complete slides, all public PAPER identifiers, boundary statements, and SHA-256 hashes. It reads the matrix from the manifest, verifies that weights sum to one, recalculates means and intervals, filters hard gates, proves the frontier, executes both policies, checks the ablation, and reruns L05 in a temporary directory.

It fails closed. It does not silently renormalize weights, invent missing gate defaults, discard malformed candidates, accept extra artifacts, or update an expected winner to match a changed input. Identity, contract, or decision drift produces an error.

Now state the final conclusion precisely. In the frozen W12 synthetic matrix, C1 is selected by the preregistered weighted, loss-floor, and meaningful-lower-bound rule after non-compensable integrity and budget filtering. C6 is selected under the maximin sensitivity policy. C1 has a negative zero point zero one counterfactual outcome. C5 is dominated and null-compatible. C3 exceeds budget. C4 fails factual and safety gates. C0 remains the rollback state.

What does this not establish? It does not establish that C1 improves retrieval, ranking, generation, citation, human comprehension, accessibility, traffic, conversion, revenue, or any live-system result. It does not establish a universal strategy. It does not transform a synthetic interval into statistical evidence. A validator PASS means that this bounded calculation and package are internally reproducible.

Your exit response should contain five elements: the primary selected candidate, the sensitivity-policy candidate, the harmed stratum, one rollback trigger, and the strongest unsupported claim. If you can say all five without dropping the evidence ceiling, you have answered the W12 question: not “what wins everywhere,” but “which gain survives this declared portfolio, under these gates, this budget, this uncertainty convention, and this accountable rule?”