{ "schema_version": "1.0.0", "ledger_id": "signal-quest-lecture-masterclass-worked-examples", "canonical_manuscript": "docs/textbook/btc-polymarket-ml/full-textbook/lecture-masterclass-manuscript.md", "epistemic_contract": "Every entry is illustrative. No entry is a measured market, model, latency, fill, calibration, or performance result.", "examples": [ { "id": "SQ-EX-001", "title": "Binary settlement label under an equality-inclusive contract", "inputs": { "start_value": 100, "end_value": 101, "equality_rule": "end_value >= start_value", "equality_case_end_value": 100 }, "formula_or_algorithm": "label = 1 if end_value >= start_value else 0", "exact_expected_outputs": { "primary_label": 1, "equality_case_label": 1, "strict_greater_than_equality_case_label": 0 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-001", "notes": "A unit-test fixture demonstrating that the equality convention is part of the estimand; values are not market observations." }, { "id": "SQ-EX-002", "title": "Bernoulli log loss with L2 regularization", "inputs": { "labels": [1, 0, 1, 0], "probabilities": [0.8, 0.3, 0.6, 0.2], "parameter_vector": [0.4, -0.2], "regularization_lambda": 0.1, "regularizer": "sum(theta_j^2)" }, "formula_or_algorithm": [ "mean_log_loss = -mean(y_i * ln(p_i) + (1-y_i) * ln(1-p_i))", "l2_squared_norm = sum(theta_j^2)", "penalty = regularization_lambda * l2_squared_norm", "regularized_objective = mean_log_loss + penalty" ], "exact_expected_outputs": { "mean_log_loss_expression": "-(ln(0.8) + ln(0.7) + ln(0.6) + ln(0.8)) / 4", "mean_log_loss_decimal": 0.32844691758328565, "l2_squared_norm": 0.2, "regularization_penalty": 0.02, "regularized_objective_expression": "-(ln(0.8) + ln(0.7) + ln(0.6) + ln(0.8)) / 4 + 0.02", "regularized_objective_decimal": 0.34844691758328566 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-002", "notes": "Demonstrates the fit-plus-complexity objective; it does not recommend a regularization setting." }, { "id": "SQ-EX-003", "title": "Temporal purge and embargo derived from support windows", "inputs": { "lookback_minutes": 3, "label_horizon_minutes": 2, "candidate_training_decision_minutes": [5, 6, 7, 8, 9], "nominal_evaluation_boundary_minute": 10, "embargo_minutes": 3, "purge_rule": "purge training decision t when t + label_horizon_minutes >= nominal_evaluation_boundary_minute" }, "formula_or_algorithm": [ "label_support_end(t) = t + 2", "surviving training decisions satisfy label_support_end(t) < 10", "first eligible evaluation decision = 10 + 3" ], "exact_expected_outputs": { "label_support_ends": [7, 8, 9, 10, 11], "surviving_training_decision_minutes": [5, 6, 7], "purged_training_decision_minutes": [8, 9], "first_eligible_evaluation_decision_minute": 13 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-003", "notes": "Durations are teaching values. A real purge and embargo must follow measured lookbacks, horizons, delays, and overlap semantics." }, { "id": "SQ-EX-004", "title": "Confusion-matrix metrics including MCC", "inputs": { "true_positives": 30, "false_positives": 10, "true_negatives": 50, "false_negatives": 10 }, "formula_or_algorithm": [ "accuracy = (TP + TN) / (TP + FP + TN + FN)", "precision = TP / (TP + FP)", "recall = TP / (TP + FN)", "specificity = TN / (TN + FP)", "false_positive_rate = FP / (FP + TN)", "f1 = 2 * TP / (2 * TP + FP + FN)", "mcc = (TP * TN - FP * FN) / sqrt((TP + FP)(TP + FN)(TN + FP)(TN + FN))" ], "exact_expected_outputs": { "sample_size": 100, "accuracy": 0.8, "precision": 0.75, "recall": 0.75, "specificity_fraction": "5/6", "specificity_decimal": 0.8333333333333334, "false_positive_rate_fraction": "1/6", "false_positive_rate_decimal": 0.16666666666666666, "f1": 0.75, "mcc_numerator": 1400, "mcc_denominator": 2400, "mcc_fraction": "7/12", "mcc_decimal": 0.5833333333333334 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-004", "notes": "One hard-prediction matrix supports multiple questions but says nothing by itself about calibration, temporal validity, or decision value." }, { "id": "SQ-EX-005", "title": "Threshold sweep, ROC-AUC, and stepwise average precision", "inputs": { "score_label_pairs_descending": [ {"score": 0.9, "label": 1}, {"score": 0.8, "label": 0}, {"score": 0.7, "label": 1}, {"score": 0.4, "label": 0}, {"score": 0.3, "label": 1}, {"score": 0.1, "label": 0} ], "thresholds": [0.85, 0.65], "positive_rule": "score >= threshold", "pr_summary": "stepwise average precision" }, "formula_or_algorithm": [ "At each threshold, construct the confusion matrix from score >= threshold.", "ROC-AUC = positive-negative score wins / all positive-negative pairs; there are no ties.", "average_precision = mean(precision at each positive-ranked position)." ], "exact_expected_outputs": { "threshold_0_85": { "TP": 1, "FP": 0, "TN": 3, "FN": 2, "precision": 1, "recall_fraction": "1/3", "recall_decimal": 0.3333333333333333, "f1": 0.5, "false_positive_rate": 0, "accuracy_fraction": "2/3", "accuracy_decimal": 0.6666666666666666 }, "threshold_0_65": { "TP": 2, "FP": 1, "TN": 2, "FN": 1, "precision_fraction": "2/3", "precision_decimal": 0.6666666666666666, "recall_fraction": "2/3", "recall_decimal": 0.6666666666666666, "f1_fraction": "2/3", "f1_decimal": 0.6666666666666666, "false_positive_rate_fraction": "1/3", "false_positive_rate_decimal": 0.3333333333333333, "accuracy_fraction": "2/3", "accuracy_decimal": 0.6666666666666666 }, "positive_negative_pair_wins": 6, "positive_negative_pair_count": 9, "roc_auc_fraction": "2/3", "roc_auc_decimal": 0.6666666666666666, "positive_rank_precisions": [1, "2/3", "3/5"], "average_precision_expression": "(1 + 2/3 + 3/5) / 3", "average_precision_fraction": "34/45", "average_precision_decimal": 0.7555555555555555 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-005", "notes": "Demonstrates that equal accuracy can hide different operating behavior and that PR integration convention must be named." }, { "id": "SQ-EX-006", "title": "Reliability-bin gap, Brier score, and log loss", "inputs": { "probabilities": [0.9, 0.8, 0.4, 0.2], "labels": [1, 0, 1, 0], "high_probability_bin_indices_zero_based": [0, 1], "calibration_gap_sign": "mean prediction minus observed positive frequency" }, "formula_or_algorithm": [ "brier = mean((p_i - y_i)^2)", "log_loss = -mean(y_i * ln(p_i) + (1-y_i) * ln(1-p_i))", "bin_gap = mean(p_i in bin) - mean(y_i in bin)" ], "exact_expected_outputs": { "squared_errors": [0.01, 0.64, 0.36, 0.04], "squared_error_sum": 1.05, "brier_score": 0.2625, "log_loss_expression": "-(ln(0.9) + ln(0.2) + ln(0.4) + ln(0.8)) / 4", "log_loss_decimal": 0.7135581778200728, "high_bin_mean_prediction": 0.85, "high_bin_observed_frequency": 0.5, "high_bin_gap": 0.35 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-006", "notes": "The sample is intentionally too small for an empirical calibration claim; it is arithmetic instruction only." }, { "id": "SQ-EX-007", "title": "Conservative edge trigger and abstention", "inputs": { "case_pass": { "lower_probability_bound": 0.62, "executable_ask": 0.55, "fee_allowance": 0.02, "slippage_allowance": 0.01, "latency_allowance": 0.015, "required_margin": 0.01 }, "case_abstain": { "lower_probability_bound": 0.59, "all_other_inputs": "same as case_pass" } }, "formula_or_algorithm": [ "total_cost_allowance = fee_allowance + slippage_allowance + latency_allowance", "conservative_edge = lower_probability_bound - executable_ask - total_cost_allowance", "numerical_gate_passes when conservative_edge >= required_margin", "win_net = 1 - executable_ask - total_cost_allowance", "loss_net = -executable_ask - total_cost_allowance", "expected_value = p_lower * win_net + (1-p_lower) * loss_net" ], "exact_expected_outputs": { "total_cost_allowance": 0.045, "case_pass": { "conservative_edge": 0.025, "win_net": 0.405, "loss_net": -0.595, "expected_value": 0.025, "numerical_edge_gate": "pass" }, "case_abstain": { "conservative_edge": -0.005, "numerical_edge_gate": "abstain" } }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-007", "notes": "Passing the arithmetic gate does not override data, artifact, calibration, liquidity, risk, or authority gates." }, { "id": "SQ-EX-008", "title": "Additive boosted-tree logit", "inputs": { "base_logit": 0, "tree_leaf_values": [0.8, -0.3], "learning_rate": 0.1 }, "formula_or_algorithm": [ "final_logit = base_logit + learning_rate * sum(tree_leaf_values)", "probability = 1 / (1 + exp(-final_logit))" ], "exact_expected_outputs": { "tree_contributions": [0.08, -0.03], "final_logit": 0.05, "probability_expression": "1 / (1 + exp(-0.05))", "probability_decimal": 0.5124973964842103 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-008", "notes": "Explains additive-logit mechanics without claiming to reproduce a library's full optimizer or calibration." }, { "id": "SQ-EX-009", "title": "Simplified ordered categorical target statistic", "inputs": { "category_sequence": ["A", "A", "A"], "label_sequence": [1, 0, 1], "prior_probability": 0.5, "smoothing_weight": 2, "ordering": "left to right; current and later labels excluded" }, "formula_or_algorithm": "statistic_i = (sum of earlier same-category labels + smoothing_weight * prior_probability) / (count of earlier same-category labels + smoothing_weight)", "exact_expected_outputs": { "row_1_expression": "(0 + 2 * 0.5) / (0 + 2)", "row_1_statistic": 0.5, "row_2_expression": "(1 + 2 * 0.5) / (1 + 2)", "row_2_statistic_fraction": "2/3", "row_2_statistic_decimal": 0.6666666666666666, "row_3_expression": "(1 + 0 + 2 * 0.5) / (2 + 2)", "row_3_statistic": 0.5 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-009", "notes": "A teaching simplification of ordered target-statistic intuition, not a complete reproduction of CatBoost internals." }, { "id": "SQ-EX-010", "title": "Additive SHAP-style attribution on the logit scale", "inputs": { "baseline_logit": -0.2, "feature_contributions": [0.5, -0.1, 0.2], "output_space": "logit" }, "formula_or_algorithm": [ "explained_logit = baseline_logit + sum(feature_contributions)", "probability = 1 / (1 + exp(-explained_logit))" ], "exact_expected_outputs": { "contribution_sum": 0.6, "explained_logit": 0.4, "probability_expression": "1 / (1 + exp(-0.4))", "probability_decimal": 0.598687660112452 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-010", "notes": "An additive accounting example; it makes no causal claim about feature intervention." }, { "id": "SQ-EX-011", "title": "Masked self-supervised reconstruction loss", "inputs": { "scalar_token_sequence": [2, 4, 6, 8], "masked_position_one_based": 3, "masked_target": 6, "prediction": 5.5, "loss": "squared error at the masked position" }, "formula_or_algorithm": "masked_loss = (prediction - masked_target)^2", "exact_expected_outputs": { "error": -0.5, "squared_reconstruction_loss": 0.25 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-011", "notes": "Pretext-task arithmetic only; low reconstruction loss would not establish downstream usefulness." }, { "id": "SQ-EX-012", "title": "Causal masking and row-wise softmax", "inputs": { "unmasked_attention_logits": [ [1, 2, 3], [0, 1, 2], [2, 1, 0] ], "mask": "lower triangular; logits above the diagonal become negative infinity" }, "formula_or_algorithm": [ "masked_logits[t,j] = logits[t,j] when j <= t else -infinity", "attention_weights[t] = softmax(masked_logits[t])" ], "exact_expected_outputs": { "masked_logits_symbolic": [ [1, "-Infinity", "-Infinity"], [0, 1, "-Infinity"], [2, 1, 0] ], "attention_weights": [ [1, 0, 0], [0.2689414213699951, 0.7310585786300049, 0], [0.6652409557748219, 0.24472847105479764, 0.09003057317038046] ], "each_row_sum": [1, 1, 1] }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-012", "notes": "Verifies masking arithmetic only. It cannot make a future-derived token causally admissible." }, { "id": "SQ-EX-013", "title": "Replay latency, depth consumption, partial fill, and fee", "inputs": { "intent_units": 120, "ask_levels_before_latency": [ {"price": 0.54, "units": 40}, {"price": 0.56, "units": 35}, {"price": 0.6, "units": 50} ], "units_removed_from_first_level_during_latency": 20, "fee_rate_on_gross_acquisition_cost": 0.01, "settlement_payout_per_filled_unit": 1 }, "formula_or_algorithm": [ "Consume remaining ask depth from best to worse until intent is filled or visible depth is exhausted.", "gross_cost = sum(filled_units_at_level * level_price)", "vwap = gross_cost / total_filled_units", "fee = fee_rate * gross_cost", "net_settlement_result = payout_per_unit * total_filled_units - gross_cost - fee" ], "exact_expected_outputs": { "post_latency_ask_levels": [ {"price": 0.54, "units": 20}, {"price": 0.56, "units": 35}, {"price": 0.6, "units": 50} ], "fills": [ {"price": 0.54, "units": 20, "cost": 10.8}, {"price": 0.56, "units": 35, "cost": 19.6}, {"price": 0.6, "units": 50, "cost": 30} ], "total_filled_units": 105, "unfilled_units": 15, "gross_acquisition_cost": 60.4, "vwap_fraction": "60.4/105", "vwap_decimal": 0.5752380952380952, "fee": 0.604, "total_acquisition_cost": 61.004, "gross_settlement_payout": 105, "net_settlement_result": 43.996 }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-013", "notes": "A paper-replay fixture, not an observed fill or profitability result. Queue priority, impact, and production mechanics are not claimed." }, { "id": "SQ-EX-014", "title": "Monitoring freshness predicate and bounded containment", "inputs": { "freshness_budget_seconds": 2, "last_valid_receive_time": "10:00:00.0", "monitor_evaluation_time": "10:00:03.2", "stale_predicate": "evaluation_time - last_valid_receive_time > freshness_budget_seconds" }, "formula_or_algorithm": [ "observed_staleness_seconds = evaluation_time - last_valid_receive_time", "budget_excess_seconds = observed_staleness_seconds - freshness_budget_seconds", "If stale, execute the allowlisted reversible containment path and escalate." ], "exact_expected_outputs": { "observed_staleness_seconds": 3.2, "budget_excess_seconds": 1.2, "stale_predicate_result": true, "policy_result": "abstain", "containment_actions": [ "stop affected data consumer", "mark dependent policy evaluations ineligible", "record predicate evidence", "verify containment", "escalate to data-contract owner" ] }, "epistemic_status": "illustrative", "manuscript_anchor": "#sq-ex-014", "notes": "A runbook teaching trace, not a production freshness budget or observed incident. No remediation or execution authority is granted." } ] }