scripts/expose_workflows.py

#!/usr/bin/env python3
"""Expose inferred workflow labels for APEX-Agents tasks.

The public `tasks_and_rubrics.json` includes `domain` metadata but omits
workflow/sub-task labels. This script infers per-domain workflows from task
text and task file names, then applies quota-constrained assignment so each
domain matches the workflow distribution reported in Table 6 of the paper.
"""

from __future__ import annotations

import argparse
import csv
import json
import math
import re
from collections import Counter, defaultdict
from pathlib import Path
from typing import DefaultDict

import numpy as np
from scipy.optimize import linear_sum_assignment


DOMAIN_WORKFLOW_QUOTAS = {
    "Investment Banking": {
        "Comparables": 16,
        "DCF": 42,
        "Debt Model": 6,
        "LBO": 12,
        "Market / Sector Research": 3,
        "Merger Model": 7,
        "Sensitivity Analysis": 46,
        "Valuation Analysis": 28,
    },
    "Management Consulting": {
        "Benchmarking / Competitive Analysis": 26,
        "Cost Benefit Analysis": 11,
        "Market Sizing, TAM, SAM": 14,
        "Operations Analysis": 23,
        "Scenario/Sensitivity Analysis": 35,
        "Strategy Recommendations": 5,
        "Survey / Interview Analysis": 31,
        "Variance / Performance Analysis": 15,
    },
    "Law": {
        "Compliance Program Review": 16,
        "Contract Review": 30,
        "Due Diligence": 18,
        "Internal Investigations": 3,
        "Legal Research": 47,
        "Litigation Strategy": 8,
        "Motion Drafting": 6,
        "Risk Assessment": 24,
        "Other": 8,
    },
}


DOMAIN_BASE_PRIORS = {
    "Investment Banking": {
        "Comparables": 0.12,
        "DCF": 0.25,
        "Debt Model": 0.05,
        "LBO": 0.12,
        "Market / Sector Research": 0.05,
        "Merger Model": 0.07,
        "Sensitivity Analysis": 0.22,
        "Valuation Analysis": 0.18,
    },
    "Management Consulting": {
        "Benchmarking / Competitive Analysis": 0.18,
        "Cost Benefit Analysis": 0.08,
        "Market Sizing, TAM, SAM": 0.12,
        "Operations Analysis": 0.16,
        "Scenario/Sensitivity Analysis": 0.2,
        "Strategy Recommendations": 0.06,
        "Survey / Interview Analysis": 0.15,
        "Variance / Performance Analysis": 0.12,
    },
    "Law": {
        "Compliance Program Review": 0.1,
        "Contract Review": 0.2,
        "Due Diligence": 0.1,
        "Internal Investigations": 0.1,
        "Legal Research": 0.2,
        "Litigation Strategy": 0.1,
        "Motion Drafting": 0.1,
        "Risk Assessment": 0.2,
        "Other": 0.1,
    },
}


# (signal_name, regex, weight)
DOMAIN_SIGNALS = {
    "Investment Banking": {
        "Comparables": [
            ("comparables_term", r"\bcomparables?\b|\bcomps?\b|\bpublic comparables?\b", 4.2),
            ("precedent_transactions", r"\bprecedent transactions?\b|\bprecedents?\b", 3.2),
            ("peer_group", r"\bpeer group\b|\bpeer set\b|\bpeer analysis\b", 2.6),
            ("multiple_focus", r"\bev/?ebitda\b|\bev/?ebit\b|\bp/?e\b|\bev/?fcf\b|\btrading multiples?\b", 1.8),
        ],
        "DCF": [
            ("dcf_term", r"\bdcf\b|\bdiscounted cash flow\b", 4.6),
            ("wacc_terminal", r"\bwacc\b|\bterminal value\b|\bterminal growth\b|\bperpetuity\b", 2.7),
            ("discount_build", r"\bcost of equity\b|\brisk[- ]free rate\b|\bbeta\b|\bequity risk premium\b", 2.3),
            ("discounted_fcf", r"\bdiscounted free cash flow\b|\b(un)?levered free cash flow\b|\bpv of free cash flows?\b", 2.2),
        ],
        "Debt Model": [
            ("debt_model_term", r"\bdebt model\b|\bdebt schedule\b", 4.8),
            ("debt_instruments", r"\brevolver\b|\bterm loan\b|\bdebenture\b|\bcoupon\b|\bamortization\b|\bprincipal\b", 3.0),
            ("debt_metrics", r"\binterest coverage\b|\bleverage ratio\b|\bnet debt\b|\bdebt capacity\b", 2.4),
        ],
        "LBO": [
            ("lbo_term", r"\blbo\b|\bleveraged buyout\b", 4.8),
            ("returns_terms", r"\birr\b|\bmoic\b|\bsponsor equity\b", 3.5),
            ("entry_exit_terms", r"\bentry multiple\b|\bexit multiple\b|\bpremium paid\b|\bability to pay\b", 2.2),
        ],
        "Market / Sector Research": [
            ("market_sector_research_term", r"\bmarket (?:or )?sector research\b|\bsector research\b", 4.2),
            ("industry_outlook", r"\bindustry outlook\b|\bsector outlook\b|\bmarket outlook\b", 3.1),
            ("addressable_market", r"\baddressable market\b|\btam\b|\bsam\b", 2.0),
        ],
        "Merger Model": [
            ("merger_model_term", r"\bmerger model\b|\baccretion dilution model\b", 4.5),
            ("accretion_dilution", r"\baccretion\b|\bdilution\b", 3.6),
            ("proforma_exchange", r"\bpro[\s-]?forma\b|\bexchange ratio\b|\bcombined company\b", 3.0),
            ("consideration_mix", r"\bcash consideration\b|\bstock consideration\b|\bstock portion\b", 2.1),
        ],
        "Sensitivity Analysis": [
            ("sensitivity_term", r"\bsensitivity\b|\bscenario\b", 3.4),
            ("scenario_cases", r"\bupside\b|\bdownside\b|\blow case\b|\bmid case\b|\bhigh case\b", 2.7),
            ("shock_flex", r"\bshock\b|\bstep-?up\b|\bstep-?down\b|\bflex(?:ing)?\b|\bcritical point\b", 2.6),
            ("assumption_change", r"\bassuming\b|\badjust\b|\bwhat if\b", 1.4),
        ],
        "Valuation Analysis": [
            ("valuation_term", r"\bvaluation\b|\bfair value\b", 2.9),
            ("implied_value", r"\bimplied share price\b|\benterprise value\b|\bprice per share\b|\boffer price\b", 2.6),
            ("premium_discount", r"\bpremium\b|\bdiscount\b|\bimplied upside/downside\b", 2.0),
            ("npv_present_value", r"\bnpv\b|\bnet present value\b|\bpresent value\b", 1.8),
        ],
    },
    "Management Consulting": {
        "Benchmarking / Competitive Analysis": [
            ("benchmarking_term", r"\bbenchmark(?:ing)?\b", 3.7),
            ("competitive_term", r"\bcompetitive\b|\bcompetitor(?:s)?\b|\bpeer(?:s)?\b|\blandscape\b", 3.0),
            ("ranking_compare", r"\brank(?:ing)?\b|\bcompare\b|\bversus\b|\bagainst\b", 1.9),
            ("market_share_compare", r"\bmarket share\b", 1.7),
        ],
        "Cost Benefit Analysis": [
            ("cost_benefit_term", r"\bcost[- ]benefit\b|\bcost benefit\b", 4.8),
            ("payback_roi", r"\bpayback period\b|\broi\b", 3.3),
            ("npv_term", r"\bnpv\b|\bnet present value\b", 3.1),
            ("savings_investment", r"\btotal savings\b|\bone-time investment\b|\bannual benefit\b|\bprofit opportunity\b", 2.2),
        ],
        "Market Sizing, TAM, SAM": [
            ("market_sizing_term", r"\bmarket sizing\b|\bmarket size\b", 4.1),
            ("tam_sam_som", r"\btam\b|\bsam\b|\bsom\b|\baddressable market\b", 4.6),
            ("implied_share_size", r"\bimplied market share\b|\btotal market size\b", 2.2),
        ],
        "Operations Analysis": [
            ("operations_term", r"\boperations?\b|\boperational\b|\bproductivity\b|\bworkforce\b|\bstaffing\b|\bheadcount\b", 2.8),
            ("plant_asset_maintenance", r"\bplant\b|\bequipment\b|\bmaintenance\b|\bdowntime\b|\bscrap\b|\byield\b|\basset\b", 2.5),
            ("throughput_capacity", r"\bcapacity\b|\butilization\b|\bthroughput\b|\bspan of control\b", 2.0),
            ("regression_term", r"\bregression\b|\bcorrelated\b", 1.8),
        ],
        "Scenario/Sensitivity Analysis": [
            ("scenario_term", r"\bscenario\b|\bsensitivity\b", 3.8),
            ("case_terms", r"\blow case\b|\bmid case\b|\bhigh case\b|\bstress case\b", 2.8),
            ("assumption_shifts", r"\bassuming\b|\bwhat if\b|\badjust(?:ed|ment)\b|\bchange in\b", 1.5),
            ("if_then", r"\bif\b.{0,35}\bthen\b", 1.6),
        ],
        "Strategy Recommendations": [
            ("recommend_term", r"\brecommend(?:ation|ed)?\b|\bshould proceed\b|\bgo/no-go\b", 4.8),
            ("strategic_option", r"\bstrategic option\b|\brecommended path\b|\bdecision score\b", 2.8),
        ],
        "Survey / Interview Analysis": [
            ("survey_term", r"\bsurvey\b|\bquestionnaire\b|\brespondents?\b|\bresponse dataset\b", 4.0),
            ("interview_term", r"\binterview\b|\bcall summary\b|\bcohort\b|\bsentiment\b", 3.0),
            ("satisfaction_intent", r"\bsatisfaction\b|\bintent\b|\bpreferences?\b", 1.7),
        ],
        "Variance / Performance Analysis": [
            ("variance_term", r"\bvariance\b|\bperformance analysis\b", 4.2),
            ("gap_delta", r"\bgap\b|\bdelta\b|\bdifference\b|\bvs\.?\b|\brelative to\b", 2.4),
            ("target_attainment", r"\btarget\b|\bover[- ]?perform\b|\bunder[- ]?perform\b|\battainment\b", 2.2),
            ("pp_change", r"\bpercentage points?\b|\b% change\b", 2.0),
        ],
    },
    "Law": {
        "Compliance Program Review": [
            ("compliance_review", r"\bcompliance review\b", 4.0),
            ("compliance_program", r"\bcompliance program\b", 3.0),
            ("policy_or_procedure", r"\bpolic(?:y|ies)\b|\bprocedures?\b|\bprotocols?\b", 1.9),
            ("regulatory_compliance", r"\bregulatory compliance\b|\bin compliance with\b", 2.0),
            ("framework_or_controls", r"\bframework\b|\bcontrols?\b", 1.6),
            ("audit_or_supervision", r"\baudit\b|\bmra\b|\bcfpb\b|\bsupervision and examination\b", 1.8),
            ("notice_obligation", r"\bnotification requirements?\b|\bbreach and incident response policy\b", 1.4),
            ("sec_disclosure_controls", r"\b8-k\b|\bform 8-k\b|\bsec\b|\breg fd\b|\brule 10b-5\b", 2.1),
            ("facility_fire_safety", r"\bfire safety\b|\binspection report\b|\bexit signage\b", 1.7),
        ],
        "Contract Review": [
            ("agreement_or_contract", r"\bagreement\b|\bcontract\b|\bclause\b|\bterms?\b", 1.5),
            ("specific_agreement_type", r"\bmaster supply agreement\b|\bmsa\b|\blease\b|\boperating agreement\b|\bcharter party\b|\bjv agreement\b", 2.3),
            ("force_majeure", r"\bforce majeure\b", 2.8),
            ("execution_or_amendment", r"\bexecuted\b|\bamend(?:ed|ment)\b|\brevise\b|\bredline\b", 1.3),
            ("validity_or_notice", r"\bvalid\b.{0,35}\bnotice\b|\bcommencement date\b", 1.6),
            ("section_by_section", r"\barticles?\b\s+\d|\bsection[s]?\b\s+\d", 1.2),
        ],
        "Due Diligence": [
            ("due_diligence_phrase", r"\bdue diligence\b|\bdiligence file\b|\bdiligence memo\b", 4.8),
            ("transaction_context", r"\bacquisition\b|\btransaction\b|\bpurchaser\b|\bseller\b|\bpost-?closing\b|\bpre-?closing\b", 2.4),
            ("deal_docs", r"\bshare purchase agreement\b|\bstock purchase agreement\b|\bspa\b|\bindemnities?\b|\brepresentations?\b", 2.0),
            ("diligence_review", r"\breview\b.{0,35}\bdiligence\b|\bdiligence\b.{0,35}\breview\b", 2.5),
            ("closing_checklist", r"\bclosing checklist\b|\bchecklist\b", 1.4),
            ("regulatory_deal_filing", r"\bhsr\b|\bfiling submission\b|\bpremerger\b", 1.8),
        ],
        "Internal Investigations": [
            ("internal_investigation", r"\binternal investigation\b|\bincident investigation\b|\boutage investigation\b", 4.6),
            ("incident_postmortem", r"\bincident report\b|\bpostmortem\b|\broot cause\b|\btimeline\b|\bevent logs?\b", 3.4),
            ("email_chain", r"\bemail chain\b|\bemail exchange\b", 2.2),
            ("outage_findings", r"\boutage\b.{0,35}\binvestigation\b|\bindependent investigation\b", 2.4),
            ("forensic_review", r"\bforensic\b|\binterrogatories\b|\bcivil investigative demand\b", 1.6),
        ],
        "Legal Research": [
            ("law_or_statute_question", r"\bunder\b.{0,45}\b(?:law|code|act|rule|regulation|statute)\b", 2.1),
            ("citation_request", r"\bcite\b|\brelevant section\b|\bwhat (?:does|is)\b|\bwhich section\b", 1.7),
            ("authority_tokens", r"\b\d+\s*u\.?s\.?c\.?\b|\b\d+\s*c\.?f\.?r\.?\b|\bfrcp\b|\bgdpr\b|\barticle \d+\b|\bncac\b|\bplanning act\b", 2.3),
            ("cases_and_courts", r"\bcase law\b|\bcourt\b|\bprecedent\b|\bholding\b|\bopinion\b", 1.9),
            ("requirements_question", r"\bdoes\b.{0,40}\brequire\b|\bis .* legal\b", 1.4),
        ],
        "Litigation Strategy": [
            ("likelihood_success", r"\blikelihood of success\b|\bchance of success\b|\bsurviv(?:e|ing)\b.{0,40}\bsummary judgment\b", 4.2),
            ("claims_defenses", r"\bclaims?\b|\bdefenses?\b|\bcounterclaims?\b|\bstrongest argument\b", 2.3),
            ("forum_and_venue", r"\bvenue\b|\bjurisdiction\b|\barbitration\b|\bpre-?trial\b|\bsettlement\b", 1.9),
            ("dismissal_strategy", r"\bmotion to dismiss\b|\brule 12\b|\bstrategy\b", 1.9),
        ],
        "Motion Drafting": [
            ("draft_motion_material", r"\bdraft\b.{0,55}\b(?:motion|complaint|brief|memorandum|memo|outline)\b", 4.4),
            ("prepare_motion_material", r"\bprepare\b.{0,55}\b(?:motion|brief|memorandum|outline)\b", 3.9),
            ("new_doc_litigation", r"\bpre-?litigation legal memorandum\b|\bsummary judgment\b", 2.7),
            ("edit_litigation_doc", r"\bedit existing\b.{0,35}\b(?:agreement|complaint|motion)\b", 1.8),
        ],
        "Risk Assessment": [
            ("risk_or_exposure", r"\brisk\b|\bexposure\b|\bfinancial exposure\b", 2.0),
            ("liability_penalty", r"\bliability\b|\bfine\b|\bpenalty\b|\bdamages?\b|\brefund\b", 1.8),
            ("max_amount", r"\bmaximum\b.{0,35}\b(?:liability|fine|penalty|refund|exposure)\b", 2.4),
            ("amount_question", r"\bhow much\b|\bwhat amount\b|\bpotential\b", 1.2),
            ("risk_matrix", r"\bheat map\b|\bmitigation\b", 1.6),
            ("defect_or_fault", r"\bfaulty\b|\bdefect(?:ive)?\b|\boutage\b", 1.2),
        ],
        "Other": [
            ("spreadsheet_output", r"\bmake_new_sheet\b|\bedit_existing_sheet\b", 4.8),
            ("capital_account", r"\bcapital account\b|\bdistribution amounts?\b", 2.6),
            ("child_support_calc", r"\bchild support\b", 2.8),
            ("quant_membership", r"\bpart of the class\b|\bhistoric stock transactions\b|\bmaximum refund amount\b", 2.4),
            ("distribution_calc", r"\bdetermine\b.{0,35}\bamounts? to be distributed\b", 2.6),
        ],
    },
}


def _build_task_file_index(task_files_root: Path) -> dict[str, str]:
    """Build task_id -> concatenated file-name hint string."""
    index: dict[str, str] = {}
    if not task_files_root.exists():
        return index

    for task_dir in sorted(task_files_root.glob("task_*")):
        if not task_dir.is_dir():
            continue
        file_tokens: list[str] = []
        for path in task_dir.rglob("*"):
            if path.is_file():
                file_tokens.append(path.relative_to(task_dir).as_posix())
        index[task_dir.name] = "\n".join(file_tokens)
    return index


def _task_text(task: dict, task_file_hints: str) -> str:
    rubric_text = "\n".join(item.get("criteria", "") for item in task.get("rubric", []))
    parts = [
        task.get("prompt", ""),
        rubric_text,
        task.get("gold_response", ""),
        task.get("expected_output", ""),
        task_file_hints,
    ]
    return "\n".join(parts)


def _score_task(task: dict, task_file_hints: str) -> tuple[dict[str, float], dict[str, list[str]]]:
    domain = task.get("domain")
    if domain not in DOMAIN_WORKFLOW_QUOTAS:
        return {}, {}

    workflows = list(DOMAIN_WORKFLOW_QUOTAS[domain].keys())
    priors = DOMAIN_BASE_PRIORS[domain]
    signals = DOMAIN_SIGNALS[domain]

    text = _task_text(task, task_file_hints).lower()
    scores: dict[str, float] = {workflow: priors.get(workflow, 0.0) for workflow in workflows}
    reasons: DefaultDict[str, list[str]] = defaultdict(list)

    def add(workflow: str, amount: float, reason: str) -> None:
        scores[workflow] += amount
        reasons[workflow].append(f"{reason} (+{amount:.1f})")

    for workflow, rules in signals.items():
        for name, pattern, weight in rules:
            if re.search(pattern, text, flags=re.IGNORECASE):
                add(workflow, weight, name)

    expected_output = task.get("expected_output", "")

    if domain == "Investment Banking":
        if expected_output in {"make_new_sheet", "edit_existing_sheet"}:
            add("Sensitivity Analysis", 2.4, "sheet_output_sensitivity")
        if expected_output == "make_new_slide_deck":
            add("Valuation Analysis", 1.3, "slide_output_valuation")

        if re.search(r"\blbo\b", text) and re.search(r"\bscenario\b|\bsensitivity\b|\bshock\b|\bflex\b", text):
            add("Sensitivity Analysis", 1.5, "lbo_with_sensitivity")
        if re.search(r"\bdcf\b", text) and re.search(r"\bscenario\b|\bsensitivity\b|\bassum", text):
            add("Sensitivity Analysis", 1.2, "dcf_with_sensitivity")
        if re.search(r"\baccretion dilution model\b|\bmerger model\b", text):
            add("Merger Model", 2.0, "explicit_merger_model")
        if re.search(r"\bprecedent\b|\bpublic comparables?\b", text) and re.search(r"\bmultiple\b", text):
            add("Comparables", 1.4, "comparables_with_multiples")
        if re.search(r"\bimplied share price\b|\benterprise value\b", text) and not re.search(
            r"\blbo\b|\bmerger model\b", text
        ):
            add("Valuation Analysis", 1.2, "implied_value_focus")
        if re.search(r"\bdebt\b", text) and re.search(r"\bterm loan\b|\brevolver\b|\binterest coverage\b", text):
            add("Debt Model", 1.6, "debt_instrument_focus")

    if domain == "Management Consulting":
        if expected_output in {"make_new_slide_deck", "edit_existing_slide_deck"}:
            add("Benchmarking / Competitive Analysis", 0.9, "slide_output_benchmarking")
        if expected_output == "make_new_doc":
            add("Strategy Recommendations", 1.0, "doc_output_strategy")

        if re.search(r"\bsurvey\b", text) and re.search(r"\brecommend", text):
            add("Strategy Recommendations", 1.1, "survey_with_recommendation")
        if re.search(r"\bpayback period\b|\bone-time investment\b|\bannual savings\b", text):
            add("Cost Benefit Analysis", 2.2, "payback_investment_focus")
        if re.search(r"\bregression\b|\bcorrelat", text):
            add("Operations Analysis", 1.6, "regression_operations_focus")
        if re.search(r"\bgap\b|\bdelta\b|\bversus target\b|\brelative to\b", text):
            add("Variance / Performance Analysis", 1.3, "gap_vs_target")
        if re.search(r"\bscenario\b", text) and re.search(r"\bassum", text):
            add("Scenario/Sensitivity Analysis", 1.4, "scenario_with_assumptions")
        if re.search(r"\btam\b|\bsam\b|\bsom\b", text):
            add("Market Sizing, TAM, SAM", 1.7, "tam_sam_som_bonus")

    if domain == "Law":
        if expected_output in {"make_new_doc", "edit_existing_doc"}:
            if re.search(r"\bmotion\b|\bcomplaint\b|\bbrief\b|\bsummary judgment\b", text):
                add("Motion Drafting", 2.0, "doc_output_with_litigation_terms")
            elif re.search(r"\bagreement\b|\bcontract\b|\blease\b|\bmsa\b", text):
                add("Contract Review", 1.3, "doc_output_with_contract_terms")
            else:
                add("Motion Drafting", 0.8, "doc_output_default")

        if expected_output in {"make_new_sheet", "edit_existing_sheet"}:
            add("Other", 5.0, "sheet_output")

        if re.search(r"\bclass action\b|\bmotion to dismiss\b|\bsummary judgment\b", text):
            add("Litigation Strategy", 1.2, "litigation_posture")

        if re.search(r"\bcheck these (?:four )?faxes\b|\bfor each item\b|\bindicate whether\b", text):
            add("Compliance Program Review", 1.0, "compliance_checklist_style")

        if re.search(r"\b8-k\b|\bform 8-k\b|\bsec\b|\brule 10b-5\b|\breg fd\b", text):
            add("Compliance Program Review", 1.4, "sec_disclosure_context")
            add("Legal Research", 0.8, "sec_disclosure_context")

        if re.search(r"\breview\b.{0,30}\bagreement\b", text) and re.search(r"\bcan\b|\bmay\b|\bvalid\b", text):
            add("Contract Review", 1.1, "agreement_interpretation")

        if re.search(r"\bbreach\b|\boutage\b", text) and re.search(r"\bincident report\b|\bpostmortem\b", text):
            add("Internal Investigations", 1.5, "breach_incident_combo")

        if re.search(
            r"\bcapital account\b|\bamounts? to be distributed\b|\bchild support\b|\bmaximum refund amount\b",
            text,
        ):
            add("Other", 1.8, "quantitative_legal_calculation")

    return scores, reasons


def _quota_assign(
    task_ids: list[str],
    scores_by_task: dict[str, dict[str, float]],
    workflow_quotas: dict[str, int],
    domain: str,
) -> dict[str, str]:
    slots: list[str] = []
    for workflow, count in workflow_quotas.items():
        slots.extend([workflow] * count)

    if len(task_ids) != len(slots):
        raise ValueError(
            f"{domain} task count ({len(task_ids)}) does not match workflow quota total ({len(slots)})."
        )

    score_matrix = np.zeros((len(task_ids), len(slots)), dtype=np.float64)
    for row_idx, task_id in enumerate(task_ids):
        scores = scores_by_task[task_id]
        for col_idx, workflow in enumerate(slots):
            score_matrix[row_idx, col_idx] = scores[workflow]

    row_ind, col_ind = linear_sum_assignment(-score_matrix)
    assignments: dict[str, str] = {}
    for row_idx, col_idx in zip(row_ind, col_ind):
        assignments[task_ids[row_idx]] = slots[col_idx]
    return assignments


def _score_rank(scores: dict[str, float], assigned_workflow: str) -> int:
    sorted_items = sorted(scores.items(), key=lambda item: item[1], reverse=True)
    for idx, (workflow, _) in enumerate(sorted_items, start=1):
        if workflow == assigned_workflow:
            return idx
    return len(sorted_items)


def _confidence(scores: dict[str, float], assigned_workflow: str) -> float:
    vals = sorted(scores.values(), reverse=True)
    top = vals[0]
    second = vals[1] if len(vals) > 1 else vals[0]
    assigned = scores[assigned_workflow]
    margin = assigned - second if assigned == top else assigned - top
    spread = max(vals) - min(vals) + 1e-6
    scaled = margin / (spread / 2.0 + 1e-6)
    return 1.0 / (1.0 + math.exp(-scaled))


def _augment_tasks(tasks: list[dict], task_file_index: dict[str, str]) -> tuple[list[dict], list[dict]]:
    domain_scores: dict[str, dict[str, dict[str, float]]] = {}
    domain_reasons: dict[str, dict[str, dict[str, list[str]]]] = {}
    domain_assignments: dict[str, dict[str, str]] = {}

    for domain, quotas in DOMAIN_WORKFLOW_QUOTAS.items():
        domain_tasks = [task for task in tasks if task.get("domain") == domain]
        task_ids = [task["task_id"] for task in domain_tasks]

        scores_by_task: dict[str, dict[str, float]] = {}
        reasons_by_task: dict[str, dict[str, list[str]]] = {}
        for task in domain_tasks:
            task_id = task["task_id"]
            file_hints = task_file_index.get(task_id, "")
            scores, reasons = _score_task(task, file_hints)
            scores_by_task[task_id] = scores
            reasons_by_task[task_id] = reasons

        assignments = _quota_assign(task_ids, scores_by_task, quotas, domain)
        domain_scores[domain] = scores_by_task
        domain_reasons[domain] = reasons_by_task
        domain_assignments[domain] = assignments

    augmented: list[dict] = []
    audit_rows: list[dict] = []

    for task in tasks:
        task_copy = dict(task)
        domain = task_copy.get("domain")
        if domain in DOMAIN_WORKFLOW_QUOTAS:
            task_id = task_copy["task_id"]
            workflow = domain_assignments[domain][task_id]
            scores = domain_scores[domain][task_id]
            conf = _confidence(scores, workflow)
            rank = _score_rank(scores, workflow)

            task_copy["workflow"] = workflow
            task_copy["workflow_inference"] = {
                "source": "heuristic_quota_constrained_v2_all_domains",
                "confidence": round(conf, 4),
                "assigned_score_rank": rank,
                "reason_signals": domain_reasons[domain][task_id].get(workflow, [])[:6],
                "paper_domain_quota_aligned": True,
            }

            sorted_scores = sorted(scores.items(), key=lambda item: item[1], reverse=True)
            audit_rows.append(
                {
                    "domain": domain,
                    "task_id": task_id,
                    "task_name": task_copy.get("task_name", ""),
                    "workflow": workflow,
                    "confidence": f"{conf:.4f}",
                    "assigned_score_rank": rank,
                    "top1_workflow": sorted_scores[0][0],
                    "top1_score": f"{sorted_scores[0][1]:.3f}",
                    "top2_workflow": sorted_scores[1][0],
                    "top2_score": f"{sorted_scores[1][1]:.3f}",
                    "top3_workflow": sorted_scores[2][0],
                    "top3_score": f"{sorted_scores[2][1]:.3f}",
                    "assigned_signals": " | ".join(domain_reasons[domain][task_id].get(workflow, [])[:6]),
                }
            )

        augmented.append(task_copy)

    return augmented, audit_rows


def _write_audit_csv(rows: list[dict], path: Path) -> None:
    fieldnames = [
        "domain",
        "task_id",
        "task_name",
        "workflow",
        "confidence",
        "assigned_score_rank",
        "top1_workflow",
        "top1_score",
        "top2_workflow",
        "top2_score",
        "top3_workflow",
        "top3_score",
        "assigned_signals",
    ]
    with path.open("w", encoding="utf-8", newline="") as fp:
        writer = csv.DictWriter(fp, fieldnames=fieldnames)
        writer.writeheader()
        writer.writerows(rows)


def parse_args() -> argparse.Namespace:
    parser = argparse.ArgumentParser(description=__doc__)
    parser.add_argument(
        "--input",
        type=Path,
        default=Path("tasks_and_rubrics.json"),
        help="Input task JSON file.",
    )
    parser.add_argument(
        "--output",
        type=Path,
        default=Path("tasks_and_rubrics_with_workflow.json"),
        help="Output JSON file with inferred `workflow` labels.",
    )
    parser.add_argument(
        "--task-files-root",
        type=Path,
        default=Path("task_files"),
        help="Root folder containing `task_<id>` subfolders.",
    )
    parser.add_argument(
        "--audit-output",
        type=Path,
        default=Path("workflow_inference_audit.csv"),
        help="CSV path for per-task assignment diagnostics.",
    )
    return parser.parse_args()


def main() -> None:
    args = parse_args()
    tasks = json.loads(args.input.read_text(encoding="utf-8"))
    if not isinstance(tasks, list):
        raise ValueError("Input JSON must be an array of task objects.")

    task_file_index = _build_task_file_index(args.task_files_root)
    augmented_tasks, audit_rows = _augment_tasks(tasks, task_file_index)

    args.output.write_text(json.dumps(augmented_tasks, indent=2, ensure_ascii=False), encoding="utf-8")
    _write_audit_csv(audit_rows, args.audit_output)

    print(f"Wrote {args.output} ({len(augmented_tasks)} tasks)")
    print(f"Wrote {args.audit_output} ({len(audit_rows)} labeled tasks)")
    for domain, quotas in DOMAIN_WORKFLOW_QUOTAS.items():
        distribution = Counter(
            task.get("workflow")
            for task in augmented_tasks
            if task.get("domain") == domain
        )
        print(f"Inferred {domain} workflow distribution:")
        for workflow in quotas:
            print(f"  {workflow}: {distribution.get(workflow, 0)}")


if __name__ == "__main__":
    main()