Fewshot Attempt 01

Public Health Observatory Algorithmic Audit Skill

Use this skill for Public Health Observatory tasks that provide an analysis_request.json, an answer_template.json, and a read-only portal base URL. The skill is reusable method guidance only. Do not reuse solved values from training examples: counts, coefficients, p-values, selected states, countries, clusters, PRNG checkpoints, gate results, classifications, and memberships must always be recomputed from the effective request and the authorized portal data.

Activation

Activate the exact profile when the future request has one of these case-sensitive protocol_id values:

• PHO_STATE_TRANSPORT_AUDIT_V1
• PHO_COUNTY_MEDIATION_TRANSPORT_V1
• PHO_STATE_ROBUSTNESS_TRANSPORT_V1
• PHO_COUNTY_PANEL_TRANSPORT_V1

Also activate the country burden workflow when the request/template identifies a country burden revision audit, for example by template_name: country_burden_revision_audit_v1 or the combination of country_labels, burden_indicator_ids, panel_outcome_indicator_id, and requested_cluster_count.

For exact protocol profiles, bind all entities, measures, years, filters, random seeds, grids, cutoffs, output field names, and decision vocabulary from the future request. Profiles carry method semantics only.

Portal Access

Read environment_access.md in the task workspace and use only its base URL and allowed endpoints. Prefer CSV downloads through /download?dataset=<name>&format=csv for full tables, then filter locally with a structured CSV parser. Useful datasets are:

• states: state codes, regions, divisions, state/DC flag.
• counties: county FIPS, state, region, RUCC, population and coordinates.
• countries: ISO3-like stable IDs, canonical names, portal labels, alternate labels, region, income group.
• state_health, state_socioeconomic, county_health, county_socioeconomic, country_indicators, revisions.

The portal retains provisional/final status, revisions, timestamps, source and value types, suppression flags, quality flags, and record IDs. Preserve these fields until release resolution and audit counts are complete.

Output Discipline

• Return exactly one JSON object following the future answer_template.json.
• Do not include a protocol_registry_record or any provenance key unless the future template explicitly requires or permits it.
• Preserve every declared order: years, features, coefficients, clusters, states, countries, folds, grids, source groups, checkpoints, and decision precedence.
• Compute predicates on unrounded values. Round only reported non-integers to the request/template precision. Keep integer and Boolean types natural.
• Use JSON null for mathematically unavailable values. Never emit NaN, Infinity, or stringified numbers.

Effective Request Resolution

Before touching data or random generators, build one effective request:

1. Verify the exact protocol_id if the task uses a registered protocol.
2. Bind direct request keys to same-named canonical keys.
3. Resolve override aliases: root <section>_overrides targets <section>; module_overrides.<module> targets that exact module; reporting_overrides targets reporting. Strip only the terminal suffix.
4. Apply entries in request document order. Deep-merge objects by exact key; replace arrays as whole arrays; replace explicit scalars, strings, Booleans, and null only at the exact path.
5. Reject unknown targets, inferred aliases, key renames, array concatenation, positional patches, incompatible types, and type coercion.
6. Freeze the effective contract and use it consistently for all cohorts, folds, random draws, fits, summaries, and decisions.

Release And Cohort Rules

Filter each source independently by the effective entity scope, years, measures/fields, release status, value type, source type, and quality predicates. Select one publication record per declared entity-time-measure key using the request's precedence. When a profile gives precedence, use it exactly:

• State longevity and most county workflows: greatest final revision, latest release timestamp, then the specified lowest or greatest record identifier.
• State weighted robustness: greatest revision, latest release timestamp, then greatest record identifier.
• County panel: highest final revision, then latest release timestamp.
• Country burden: reconcile labels first, then select final country indicator records by highest revision, latest release timestamp, and stable record ID.

Suppressed, invalid, withdrawn, blank, null, or scale-break values are unavailable and are never zero-filled. Count selected publication rows before analytic completeness exclusions when the template asks for release counts. Construct complete-case, balanced, broad, strict dual-source, ML, and panel cohorts only from the effective nonmissing predicates. Preserve entity-code order unless the request declares another order.

Shared Numerical Routines

• OLS: solve in declared column order, with or without intercept exactly as registered. Use unrounded fitted objects downstream.
• WLS: with positive weights w, set Xw=sqrt(w)*X and yw=sqrt(w)*y; solve (Xw'Xw)^-1 Xw'yw.
• HC3: use leverage from Xw, weighted residuals sqrt(w_i)*(y_i-X_i*b), and the standard HC3 sandwich with (1-h_i)^2; test with n-k Student-t df.
• CR1 cluster covariance: for ordered clusters g, scores s_g=X_g' e_g; apply the registered finite-sample factor and test with G-1 Student-t df.
• Ridge: center outcome as registered, keep intercept unpenalized, standardize predictors from training-only moments, select penalty by pooled validation squared errors, breaking ties toward the smaller penalty.
• Elastic net: cold-start each fit. Keep intercept unpenalized. Use declared feature order, training-only scaling, coordinate descent, declared tolerance and sweep/cycle cap. Do not warm-start across penalties unless the effective request explicitly says so.
• PCA: build features in declared variable/time order, standardize columns by the registered sample or population SD, eigendecompose the covariance/correlation matrix, sort eigenpairs descending, and flip each loading so the earliest maximum-absolute loading is positive.
• K-means: use deterministic farthest-first initialization unless overridden. First center is the smallest entity ID/code; later centers maximize distance to the nearest center, with entity-code tie breaks. Assign ties to lower cluster ID; update by arithmetic means until unchanged or the cap is reached.
• Adjusted Rand index: compute from the contingency table using combination counts. For aligned agreement, choose the permutation with maximum matches, breaking ties lexicographically.
• Conformal intervals: sort calibration residuals/scores, use the finite-sample rank declared by the protocol, build inclusive symmetric intervals, and aggregate coverage/width by the requested row or group weights.
• Wild bootstrap: maintain one continuous PRNG stream. Record checkpoints only after the completed replicate; never reset the stream between batches.

PHO_STATE_TRANSPORT_AUDIT_V1

Use this exact profile for state-level adult-obesity/longevity transport audits.

Release/cohorts:

• Resolve state health and socioeconomic series independently by effective final filters. Invalid, suppressed, withdrawn, blank, or null values remain unavailable.
• Build core balanced, broad reference-year complete-case, and strict dual-source cohorts from the effective required fields. Preserve state-code, year, feature, and Census division order.

Delete-cluster fixed effects:

• For each active fit, double-demean modeled variables: z_it - entity_mean - time_mean + grand_mean.
• Fit OLS without intercept in predictor order.
• Delete one state at a time, recompute all means, and refit from scratch in state-code order.
• Jackknife: with G delete estimates, bbar=mean(b_-g), SE=sqrt((G-1)/G*sum((b_-g-bbar)^2)), b_bc=G*b-(G-1)*bbar. Test b/SE two-sided with G-1 df. Select extrema by coefficient, then code.

Nested leave-one-division-out ridge:

• Hold out each ordered division as the outer fold. Inside outer training, hold out each remaining division in order.
• Standardize features with training sample SD (ddof=1), center training outcome, keep intercept unpenalized, and cycle coefficients in feature order.
• Pool inner validation squared errors by row for RMSE; choose smallest RMSE, then smaller penalty. Pool one outer prediction per row for RMSE, MAE, and Q^2=1-SSE/SST.

PCG32 Webb wild cluster bootstrap:

• Use the fixed-effects double-demeaned matrix. Compute observed CR1 and the restricted model without the target coefficient.
• PCG32 uses 64-bit wraparound, multiplier 6364136223846793005, increment 2*stream+1, and the standard XSH-RR output. Map output modulo six to [-sqrt(3/2), -1, -sqrt(1/2), sqrt(1/2), 1, sqrt(3/2)].
• Draw once per state in code order for every replicate, set y*=restricted_fit+restricted_residual*weight, refit unrestricted, recompute CR1, studentize, count absolute exceedances, and report plus-one p-value. Use nearest-rank quantiles.

Grouped split conformal ridge:

• For each ordered outer division, test on that division. Among remaining divisions, choose calibration by greatest row count then ascending division name; train on the rest.
• Fit ridge with fixed penalty and the same scaling/solver as nested ridge. Rank ceil((m+1)*(1-alpha)), capped at m, for the absolute calibration residual threshold.

Trajectory PCA/clustering:

• Build variable-major/year feature columns from the core balanced cohort, standardize by sample SD, use covariance Z'Z/(n-1), deterministic PCA orientation, and deterministic three-means.
• For each omitted year block, rebuild PCA, orientation, initialization, and clustering; report ARI and aligned agreement.

Source/year perturbation:

• Use the strict dual-source cohort unchanged.
• Enumerate time subsets by increasing requested subset size and lexicographic tuple order. Refit complete double-demeaned models for primary and parallel source series with CR1 inference.
• Shift is abs(b_alt-b)/abs(b)*100. Same sign requires both nonzero and identical sign. Worst subset is greatest unrounded shift, then earlier order.

Decision:

• Complete every module, evaluate the request's six gates on unrounded values, count passes, and apply the request's controlled decision mapping.

PHO_COUNTY_MEDIATION_TRANSPORT_V1

Use this exact profile for county poverty/physical-inactivity/adult-obesity mediation transport audits.

Publication/cohorts:

• Filter county health and socioeconomic rows by effective fields and release filters. Select one row per entity-time-measure using the declared priority.
• Construct primary-year, balanced-panel, and ML cohorts from nonmissing health, socioeconomic, and geography predicates. Preserve county and state order.

Primary mediation models:

• Build total, path-a, and direct/path-b OLS designs from effective exposure, mediator, outcome, covariates, transformations, reference categories, and column order. Keep the fitted objects for bootstrap and sensitivity.

Difference GMM mediation:

• Create adjacent-change rows in entity then end-period order using effective lag structure and instruments.
• For each equation, W=(Z'Z)^-1 and beta=(X'Z W Z'X)^-1 X'Z W Z'y.
• With residual u, use clustered sandwich scores Z_g'u_g. For the indirect effect theta=a*b, use Var(theta)=b^2 Var(a)+a^2 Var(b)+2ab Cov(a,b) and Student-t cluster df.
• Compute first-stage partial F from full versus reduced RSS. For delete-state diagnostics, rebuild rows and refit from scratch.

Nested state ridge:

• Use feature arrays in exact order. Standardize from training arithmetic means and population SD; use unit divisor for zero variance.
• Leave one state out externally and internally. Pool county squared errors for inner RMSE. Select by unrounded RMSE then smaller penalty; refit and pool OOF.

Paired state wild bootstrap:

• For each target equation, fit the restricted model with only that target removed. Generate synthetic outcomes from restricted fit plus state-weighted restricted residuals.
• Use unsigned xorshift32 (x ^= x<<13, x ^= x>>17, x ^= x<<5, mask after each operation). Odd state is +1, even is -1.
• Draw once per state in ascending order per replicate and reuse the same state signs across paired equations. Use absolute exceedances with plus-one p, nearest-rank order statistics, bootstrap-t inversion, and requested checkpoints.

State-grouped conformal:

• Sort states ascending and assign cyclic partitions by index modulo the partition count.
• Test each partition, use the preceding partition as calibration, and train on the rest. Reduce calibration residuals to one maximum per state. Rank by ceil((m+1)*coverage), capped at m.

Partial-R2 sensitivity:

• From unrounded baseline a, b, SE_b, and residual df, compute magnitude=SE_b*sqrt(df*rY*rM/(1-rM)).
• For each direction, adjusted_b=b-s*magnitude, adjusted_indirect=a*adjusted_b, adjusted_direct=total-adjusted_indirect, and proportion=adjusted_indirect/total.
• Enumerate the full declared R2 surface and compute the equal-strength positive tipping root from unrounded inputs.

State trajectory PCA:

• Aggregate balanced-panel measures to state-period means in declared feature order. Standardize with sample SD, use covariance Z'Z/(G-1), orient PCA, and run deterministic farthest-first Lloyd k-means. Rebuild for leave-period ARI.

Decision:

• Evaluate the six effective support predicates after all modules are complete and return the first applicable class in the request's precedence order.

Country Burden Revision Audit

Use this workflow for the country cross-section/panel burden task.

Reconciliation:

• Load countries. Resolve every requested label by exact match against portal_label, canonical_name, or the pipe-separated alternate_labels. Count aliases when the requested label differs from the canonical name.
• Return unique resolved ISO3 identifiers sorted ascending where the template asks for set-like lists.

Revision and anomaly audit:

• Load revisions for domain=COUNTRY and the requested ISO3, years, and indicators/outcome. Applied scale corrections are expected to be reflected in later final indicator revisions. Non-applied scale corrections are unresolved anomalies and should be reported as ISO3|YEAR|indicator_id when they touch requested analytical cells.
• Separate applicable APPLIED event IDs from non-applied event IDs and sort each ascending.

Country indicator matrix:

• Select final country indicator records for requested burden indicators and panel outcome over the effective cross-section and panel years.
• For the reference-year PCA matrix, mark raw missing requested cells before anomaly exclusions, mark unresolved anomaly cells, then impute after quality exclusions. Use indicator-wise means from eligible reference-year countries unless the future request gives a different imputation rule.
• Standardize burden indicators across countries. Orient PC1 so larger scores mean greater burden; all standard burden indicators in this portal are HIGHER_WORSE.
• Report retained component count from the template/request rule, PC1 variance fraction, and top absolute loadings by descending absolute value with indicator-ID tie break.

Clusters:

• Run deterministic k-means for candidate counts requested by the template (commonly the range 2 through 5) on retained burden scores. Compute Euclidean silhouette; singleton silhouettes are zero. Select the highest unrounded silhouette, breaking ties toward smaller k.
• For the requested three-segment grouping, label clusters by mean PC1 burden: lowest as LOW_BURDEN, middle as MIDDLE_BURDEN, highest as HIGH_BURDEN. Return high-burden ISO3 IDs sorted ascending.

Region-adjusted panel model:

• For each eligible country-year, compute PC1 burden using the reference PCA orientation and comparable standardized inputs. Exclude unresolved anomaly cells and rows without outcome.
• Fit OLS of the requested life-expectancy outcome on PC1 burden plus region fixed effects, with a normal intercept and one omitted reference region. Report coefficient, standard error, two-sided p-value, R-squared, and true for region fixed effects.
• Advisory rule: significant adverse gradient (pc1_coefficient < 0 with conventional two-sided significance unless overridden) means PRIORITIZE_HIGH_BURDEN_CLUSTER; adverse but not significant means MONITOR_GRADIENT; otherwise NO_ADVERSE_GRADIENT.

PHO_STATE_ROBUSTNESS_TRANSPORT_V1

Use this exact profile for reliability-weighted state association audits.

Release/cohorts:

• Resolve state direct health, parallel rollup health, and socioeconomic rows by effective filters. Select greatest revision, latest release timestamp, then greatest record ID. Never replace direct values silently.
• Keep the selected direct outcome sample size as the fixed positive reliability weight, including source-perturbation fits, unless the effective request overrides the rule.

Weighted linear algebra:

• Use WLS, HC3, and CR1 as defined above. Region indicators and reference levels come only from the future request.

Cluster jackknife:

• Fit the full weighted design, then delete each registered cluster in order and refit from scratch. Percent change is 100*abs((b_delete-b)/b).
• Bias correction uses b_bc=G*b-(G-1)*mean(delete). Test b_bc/SE_jk with G-1 df. Most influential cluster is greatest unrounded percent change, then earlier cluster order.

Nested weighted elastic net:

• Hold out each registered cluster externally and each remaining cluster internally. Build raw, transformed, squared, and interaction features in declared order.
• Training-only weighted means and weighted population SDs standardize features. Center y by the training weighted mean. Objective is weighted SSE over 2*sum(w) plus lambda*(alpha*L1 + (1-alpha)*L2/2).
• Cold-start every fit. Coordinate update: rho_j=sum(w*z_j*r_partial)/sum(w), b_j=S(rho_j,lambda*alpha)/(1+lambda*(1-alpha)).
• Pool unweighted validation/test errors by row for RMSE, MAE, and OOF R2.

Xorshift32 cluster bootstrap:

• Studentize full weighted target with CR1. Fit weighted restricted model without target, retain untransformed fit/residuals, and generate y*=fit+residual*cluster_sign.
• Use unsigned xorshift32, draw clusters in registered order, map low bit one to +1 else -1, and keep one continuous stream.
• Count t* >= observed - tolerance if a tolerance is effective. Quantiles use type-seven interpolation on sorted absolute t values.

Grouped conformal:

• Reuse outer elastic-net center predictions. For each held-out cluster, refit each other training cluster as calibration using the same algorithm, pool absolute residuals, rank by ceil((m+1)*coverage), and report ordered diagnostics. Worst coverage ties by earlier cluster order.

Trajectory PCA:

• Build variable/time blocks in declared order and state ASCII order. Standardize by sample SD, use covariance Z'Z/(n-1), orient PCA, and cluster on retained scores. Handle empty clusters by moving the ASCII-first farthest entity from its assigned center, then continue.
• Leave-one-year/block stability rebuilds the entire PCA and clustering pipeline.

Exhaustive source perturbation:

• Resolve alternate outcome source with its own filters. Order paired entities by descending absolute alternate-minus-primary difference, tied by code.
• For every bitmask from zero through 2^m-1, replace entity j iff the bit is set, keep direct weights/design, refit WLS and HC3, and summarize by popcount.
• Shift is 100*abs((b_mask-b_zero)/b_zero). Select maximum shift by unrounded shift, then smaller mask.
• Exact Shapley effect for entity j is the weighted sum over coalitions not containing j of b(S union j)-b(S), with factorial weights. Preserve signed order and verify the Shapley sum equals all-replacement minus no-replacement.

Decision:

• Evaluate modules in the request's precedence order and return the first unsatisfied controlled conclusion, or the all-robust value if none fail.

PHO_COUNTY_PANEL_TRANSPORT_V1

Use this exact profile for county diagnosed-diabetes dynamics panel audits.

Publication/balanced panel:

• Resolve county health and socioeconomic final records independently using the effective priority. Values suppressed, invalid, or missing are incomplete.
• Retain only counties complete for all balanced years and valid geography. Build adjacent-change rows ordered by county ID then end period. Derive lagged levels, changes, indicators, interactions, and source groups in declared order.

Delete-state two-step GMM:

• Residualize outcome, dynamic regressors, and instruments against intercept plus effective baseline terms.
• First step uses identity weighting. Build state scores and second-step moment covariance, then the registered Moore-Penrose inverse with the relative singular-value cutoff.
• Compute second-step coefficients and Hansen J. Refit both steps after each state deletion. Bias-correct with G*theta_full-(G-1)*mean(theta_delete).

State-blocked nested elastic net:

• Allocate states to folds by descending retained entity counts, assigning to the currently smallest fold, lower fold ID on equality; sort state codes inside folds. Repeat allocation for inner folds within outer training.
• Standardize continuous terms by training population moments; leave indicators unchanged. Penalize all non-intercept terms. Cold-start intercept at training outcome mean.
• Coordinate descent objective is SSE/(2n)+alpha*(rho*L1 + .5*(1-rho)*L2). Update intercept by mean residual, then coefficients in declared order with soft-thresholding. Select grid by pooled inner RMSE, then smaller alpha, then smaller l1 ratio. Refit and pool OOF metrics.

State wild bootstrap:

• Fit full unpenalized OLS and state-cluster CR1 for the target. Fit restricted model without target. Use unsigned xorshift32 in ascending state order, odd +1, even -1, plus-one p-value, nearest-rank quantiles, and requested checkpoints.

Cross-fold grouped conformal:

• Use nested elastic-net OOF predictions in original analytic row order. For each held-out outer fold, calibrate on absolute OOF residuals from all other folds. Rank by ceil((m+1)*coverage), cap at m, and build inclusive symmetric intervals.
• Report fold, state, RUCC-band, and prediction-decile diagnostics. Prediction bins are assigned after sorting by prediction and declared identifiers; signed gap is prediction mean minus observation mean.

County trajectory PCA/clustering:

• Build variable-major trajectories in declared variable and end-period order. Standardize by population moments and use covariance Z'Z/n.
• For each candidate k, run deterministic farthest-first k-means; compute Euclidean silhouette with singleton zero. Select highest unrounded mean silhouette, then smaller k.
• For each state deletion, rebuild the trajectory pipeline at selected k and compare retained labels with ARI. Report median and minimum ARI from unrounded values.

Source-group perturbation:

• For each declared source group and outer fold, remove exactly that group's terms and reuse the full-model selected hyperparameters for that fold without retuning.
• Apply the same preprocessing and solver, record outer RMSEs, pool squared errors, subtract the full-model OOF RMSE for deterioration, count worse folds, and rank groups by decreasing unrounded deterioration with declared-order ties.

Decision:

• Complete all six modules. Evaluate gates on unrounded values and apply the request's controlled precedence exactly.