Companion case study · real model inference · provisional result

Can synthetic moments turn five Pew marginals into richer work-and-family profiles?

This companion study starts with five observed Pew gender-attitude marginals, proposes ten additional questions about adult family and economic life, screens them with three frontier models, and generates complete response-blueprint personas. It succeeds at producing richer text. It does not yet produce a population that is both accurate and statistically dispersed.

Evidence boundary. The original five gender-comparison marginals are observed weighted estimates from Pew American Trends Panel Wave 154. Every added work-and-family marginal is model-synthetic. Generated circumstances such as relationship status and income describe synthetic support points; they are not recovered Pew respondent characteristics.

1. What is being augmented?

The foundational tutorial uses five observed questions about whether men and women are basically similar or different in hobbies, physical abilities, parenting, emotional expression, and workplace strengths. Those marginals constrain gender attitudes but do not provide enough material for profiles about household bargaining, economic circumstances, or family priorities.

The companion battery adds ten candidate moments:

relationship situation, children under 18 at home, and household income;
the personal importance of marriage, parenthood, and paid-work success;
preferred divisions of childcare and routine housework;
preferred major-financial-decision style; and
the preferred rule for deciding who reduces paid work for family needs.

The exact wording, options, and scale types are preserved in pew_work_family_candidates.json. The combined 15-question battery is pew_gender_work_family_battery.json.

2. Three models screen the new marginals

umriss prior build-marginals \
  --metadata examples/pew_w154/augmentation/pew_work_family_candidates.json \
  --tag pew_work_family_priors \
  --out examples/pew_w154/augmentation/prior_probe

umriss prior consensus \
  --predictions examples/pew_w154/augmentation/prior_probe/pew_work_family_priors_prior_predictions.csv \
  --metadata examples/pew_w154/augmentation/pew_work_family_candidates.json \
  --population us_adults_2026 \
  --minimum-models 3 \
  --max-total-variation 0.10 \
  --max-option-difference 0.10 \
  --tag pew_work_family_consensus \
  --out examples/pew_w154/augmentation/prior_probe

GPT-5.5, Claude Opus 5, and Grok 4.5 each supplied one independent distribution per question. Six of ten candidates passed the predeclared agreement thresholds:

Candidate	Maximum pairwise TV	Decision
Relationship status	0.02	Accepted
Children under 18 at home	0.06	Accepted
Household income	0.07	Accepted
Importance of parenthood	0.10	Accepted
Importance of paid-work success	0.08	Accepted
Preferred housework division	0.09	Accepted
Importance of marriage	0.12	Rejected
Preferred childcare division	0.22	Rejected
Financial decision style	0.23	Rejected
Career-sacrifice rule	0.18	Rejected

The full model-by-model predictions and decisions remain in the consensus audit. Rejected candidates remain visible and are not silently dropped from provenance.

3. Complete blueprints produce richer personas

The 11 accepted targets—five observed and six synthetic—inform the allocation of 96 complete response blueprints. Each individual prompt contains one full 15-item answer vector but no population percentages. Under the item-complete persona contract, GPT-5.5 writes a readable synthesis, one explicit second-person statement for every question, and response probabilities for all questions. The parser rejects any incomplete detail set and assembles the synthesis and all 15 statements into the exported persona.

umriss support build \
  --metadata examples/pew_w154/augmentation/pew_gender_work_family_battery.json \
  --preset target-informed-blueprints \
  --targets examples/pew_w154/augmentation/pew_augmented_targets.json \
  --n-support 96 \
  --tag pew_work_family_detailed \
  --out examples/pew_w154/augmentation/support_v2/initial

umriss support validate-blueprints \
  --support examples/pew_w154/augmentation/support_v2/initial/bank/pew_work_family_detailed_probabilities.csv \
  --plan examples/pew_w154/augmentation/support_v2/initial/pew_work_family_detailed_support_plan.csv \
  --metadata examples/pew_w154/augmentation/pew_gender_work_family_battery.json \
  --tag pew_work_family_detailed \
  --out examples/pew_w154/augmentation/support_v2/initial/validation

96/96initial blueprints passed fidelity

192/192repair blueprints passed fidelity

288personas in the merged bank

11accepted calibration marginals

4. Examples of real generated persona text

These are unedited second-person syntheses returned by GPT-5.5 during the registered item-complete support runs. Each underlying points row additionally contains all 15 explicit statements; the first example opens those statements verbatim. The displayed percentages come from the initial 288-person diagnostic fit, before the geometry-repair rounds described below; they are mixture coefficients, not literal shares of identifiable demographic types.

Weight 1.64% · repair persona 173

You are a married adult in a lower-income household who treats your marriage as a practical partnership rather than as a core personal milestone. You see men and women as basically different in several personal and family domains: hobbies and interests, physical abilities, parenting approaches, and emotional expression. At the same time, you believe men and women are basically similar in what they can be good at in the workplace. You do not have children under 18 at home, and raising children is not personally important to your sense of a good life. You place some importance on paid work or career success, but you prefer household arrangements that are pragmatic: childcare should fall more to the parent with more available time, housework should be divided about equally, the person who manages the money should usually decide major financial matters, and both adults should reduce paid work as equally as possible when work reductions are needed.

Show all 15 preserved persona dimensions

Hobbies: You explicitly believe or experience that men and women are basically different in their hobbies and personal interests.
Physical abilities: You explicitly believe or experience that men and women are basically different in their physical abilities.
Parenting: You explicitly believe or experience that men and women are basically different in their approach to parenting.
Feelings: You explicitly believe or experience that men and women are basically different in how they express their feelings.
Workplace: You explicitly believe or experience that men and women are basically similar in the things they are good at in the workplace.
Relationship: You explicitly believe or experience being married.
Children at home: You explicitly believe or experience having no children under 18 living in the household.
Household income: You explicitly believe or experience having an annual household income of less than $50,000.
Marriage: You explicitly believe or experience marriage as not at all important to you personally, even though you are married.
Parenthood: You explicitly believe or experience raising children as not at all important to you personally.
Paid work: You explicitly believe or experience paid-work or career success as somewhat important to you personally.
Childcare: You explicitly believe or experience that day-to-day childcare should be done more by the parent with more available time.
Housework: You explicitly believe or experience that routine housework should be divided about equally by both adults.
Financial decisions: You explicitly believe or experience that the person who manages the money should usually decide major household financial matters.
Career sacrifice: You explicitly believe or experience that both adults should reduce paid work as equally as possible when someone needs to cut back.

Weight 1.56% · repair persona 058

You are a married adult in a high-income household with no children under 18 at home. You see men and women as basically different in hobbies and interests, physical abilities, parenting approaches, and emotional expression, while still believing they are basically similar in what they can be good at in the workplace. You do not place very high personal importance on marriage as an institution, even though you are married, and you give moderate importance to raising children and to paid-work or career success. In family life, you prefer equal sharing of childcare and routine housework, but you think major financial decisions and career-sacrifice choices should be handled case by case rather than by a fixed rule.

Weight 1.51% · repair persona 167

You are a married adult with no children under 18 in the household and a midrange household income. Your outlook separates some areas where you see men and women as basically different from one area where you see them as basically similar: you perceive differences in hobbies, physical abilities, parenting approaches, and emotional expression, while still believing men and women are basically similar in what they can be good at in the workplace. You do not place high personal importance on marriage itself, even though you are married, but you place very high importance on raising children and on paid-work or career success. In family arrangements, you prefer practical, situation-sensitive rules: childcare should be handled more by the parent with more available time, routine housework should be divided about equally, major financial decisions should depend on the decision, and career sacrifices should depend entirely on the family.

5. Target repair improves coverage—but exposes a hard limit

The newly measured initial 96-person bank cannot reproduce the target intersection: its minimum possible worst-cell error is 6.37 percentage points. Umriss therefore uses the same 192 target-directed repair blueprints recorded in the resolved design.

umriss support augment-targets \
  --support examples/pew_w154/augmentation/support_v2/initial/validation/pew_work_family_detailed_validated_probabilities.csv \
  --targets examples/pew_w154/augmentation/pew_augmented_targets.json \
  --metadata examples/pew_w154/augmentation/pew_gender_work_family_battery.json \
  --n-add 192 \
  --tag pew_work_family_detailed_repair1 \
  --out examples/pew_w154/augmentation/support_v2/repair_1

After merging, the best possible worst-cell error improves to 4.55 points. Every individual target cell now lies within the support bank's range, but their joint intersection remains outside a one-point tolerance. The limiting residual is still the observed emotional-expression marginal, so broad cell coverage alone does not guarantee simultaneous feasibility.

Stage	Support	Minimum possible worst-cell error	Interpretation
Initial target-informed blueprints	96	6.37 points	Fails one-point feasibility
After target-directed repair	288	4.55 points	Passes only at a declared five-point tolerance
After two ordinary geometry cuts	416	4.44 points	Argmax fidelity alone creates weak vertices
After first high-certainty cut	448	2.39 points	Every intended cell is at least 0.80
After second high-certainty cut	480	1.38 points	Approaches the declared tolerance
After final high-certainty cut	496	0.83 points	Passes one-point feasibility

6. Iterative geometry repair crosses the missing hull faces

augment-targets repairs every marginal independently. That put each target cell inside the support range but did not put their joint intersection inside the convex hull. augment-geometry instead solves the minimax feasibility problem, extracts its LP dual separating certificate, and generates complete blueprints that cross the exposed hull face. After each measured round, feasibility is solved again because a new face may become limiting.

The first two 64-person rounds required only argmax blueprint fidelity and barely moved the gap. The decisive change was a geometry-only probability contract: every intended answer had to receive at least 0.80 probability, checked item by item before merging. Two 32-person cuts and one 16-person cut then reduced the gap from 4.44 to 0.83 points. All 80 high-certainty personas passed all 15 per-cell gates.

umriss support augment-geometry \
  --support examples/pew_w154/augmentation/support_v2/geometry_final_bank_480/pew_work_family_geometry_480_probabilities.csv \
  --targets examples/pew_w154/augmentation/pew_augmented_targets.json \
  --metadata examples/pew_w154/augmentation/pew_gender_work_family_battery.json \
  --n-add 16 \
  --tag pew_work_family_geometry5 \
  --out examples/pew_w154/augmentation/support_v2/geometry_repair_5

umriss support validate-blueprints \
  --support examples/pew_w154/augmentation/support_v2/geometry_repair_5/bank/pew_work_family_geometry5_probabilities.csv \
  --plan examples/pew_w154/augmentation/support_v2/geometry_repair_5/pew_work_family_geometry5_support_plan.csv \
  --metadata examples/pew_w154/augmentation/pew_gender_work_family_battery.json \
  --minimum-intended-cell-probability 0.8 \
  --tag pew_work_family_geometry5 \
  --out examples/pew_w154/augmentation/support_v2/geometry_repair_5/validation

7. Fit acceptance now includes target accuracy

umriss targets fit \
  --targets examples/pew_w154/augmentation/pew_augmented_targets.json \
  --support examples/pew_w154/augmentation/support_v2/geometry_final_bank_496/pew_work_family_geometry_496_probabilities.csv \
  --metadata examples/pew_w154/augmentation/pew_gender_work_family_battery.json \
  --minimum-effective-support 50 \
  --maximum-weight 0.05 \
  --maximum-target-residual 0.06 \
  --require-convergence \
  --tag pew_work_family_geometry_496_accepted \
  --out examples/pew_w154/augmentation/support_v2/geometry_final_bank_496/accepted_fit

101.25effective support

3.17%largest fitted weight

0.01selected entropy penalty

5.44 ptslargest fitted target residual

Feasibility asks whether some mixture can reach the targets; it does not require that mixture to be dispersed. The feasibility witness has effective support 8.78 and a 19.97% largest weight. The accepted entropy fit deliberately spreads mass much more broadly, so it does not attain the witness's 0.83-point bound. A new --maximum-target-residual gate prevents the selector from choosing an extremely diffuse but inaccurate fit: the accepted candidate has effective support 101.25, a 3.17% largest weight, convergence, and a 5.44-point worst target residual. Tighter accuracy would require relaxing the concentration gates or adding support that lets accurate fits remain diffuse.

Conclusion. Adding screened marginals now creates text personas whose detail scales with the battery, including all five Pew gender views. Complete blueprints and item-complete prose prevent silent textual compression. Independent marginal repair is not enough for joint feasibility; iterative LP-dual geometry cuts with a high-certainty per-cell gate reduced the minimax gap from 4.55 to 0.83 points and passed the declared stopping rule. Fit acceptance now exposes the remaining accuracy-versus-dispersion tradeoff rather than silently selecting a diffuse, inaccurate population.