Migrate Amazon Connect TEI study to the Mercury Notebook Pattern

studies/202602_AmazonConnect -> studies/202602_TEI_Amazon_Connect,
rebuilt as pattern Variant 4 (TEI composite reproduction):

- teicalc/ self-contained engine (stdlib-only): Forrester's tables as
  the never-edited verbatim anchor, NPV/ROI/payback + risk adjustment
  transplanted from core/calculations, ClientDrivers overlay (contacts/
  agents/fixed driver map, growth re-base, identity at composite scale),
  scenario stress with core-identical semantics
- one deliverable notebook (business_case.ipynb): widget-pair sidebar
  drivers, published-vs-overlay KPI columns, cash-flow/waterfall/scenario
  charts, verification gate, backstage JSON data appendix
- gate + tests reproduce the published totals within PDF rounding:
  NPV $78.7M / ROI 342% / payback <6 months (engine $78,713,492 /
  342.48% / 0.7 months); 27 study tests, headless nbconvert green,
  stage simulation leak-free, exports carry the appendix
- old Athena workflow (00_provision..04_export, config.py, seed_data.py)
  deleted; git history preserves it; root test fixture repointed to
  teicalc.anchor
- docs: study README rewritten; root README points new studies at
  template/MercuryNotebook; pattern doc stale ctm-token-calculator paths
  now cite studies/202607_CTM_GenesysCX; Variant 4 cites this study as
  its realized reference

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

studies/202602_TEI_Amazon_Connect/README.md

@@ -0,0 +1,97 @@
+# 202602 — Amazon Connect TEI
+
+Self-contained reproduction of the Forrester *Total Economic Impact™ Of
+Amazon Connect* study (February 2026, commissioned by AWS), built on the
+[Mercury Notebook Deliverable Pattern](../../docs/Mercury_Notebook_Pattern_V1-00.md)
+as **Variant 4 — TEI composite reproduction**: Forrester's composite
+organization is the never-edited verbatim anchor, the in-notebook gate
+proves the engine reproduces the published totals, and 🟡 client drivers
+rescale the composite live.
+
+## Source
+
+The full Forrester study is at
+[`docs/202602_TEI Report Amazon Connect.pdf`](docs/202602_TEI%20Report%20Amazon%20Connect.pdf).
+
+Published composite totals (3-yr risk-adjusted PV @ 10%), reproduced by
+`teicalc` to within the PDF's own table rounding (benefits PV lands $223
+low; costs PV $0.22 low):
+
+| Metric | Published | Engine |
+|---|---|---|
+| Benefits PV | **$101,696,791** | $101,696,568 |
+| Costs PV | **$22,983,076** | $22,983,076 |
+| NPV | **$78,713,715** | $78,713,492 |
+| ROI | **342%** | 342.48% |
+| Payback | **<6 months** | 0.7 months |
+
+## Composite organization (the verbatim anchor 🟢)
+
+* Global B2C, ~$10B revenue (Y1), 30% YoY growth
+* 2,000 contact-center agents, 200 supervisors
+* 20M annual contacts (75% calls, 25% chat)
+* 10-min average handle time
+
+## Client overlay (🟡)
+
+A first-order linear rescale — "the composite at your size", not "your
+TEI". Each published row scales with the driver that dominates its PDF
+derivation:
+
+| Row | Driver | Confidence |
+|---|---|---|
+| AI contact resolution · content/sentiment | contacts | 🟡 |
+| Forecasting/supervision · legacy savings | agents | 🟡 |
+| Data-driven profit lift | contacts | 🔴 proxy (revenue-driven in the PDF) |
+| Amazon Connect usage | contacts | 🟡 |
+| Implementation · ongoing management | fixed | 🟡 project-based |
+
+The client growth rate re-bases the composite's Y1→Y3 trajectory (which
+embeds 30% YoY). At composite scale the overlay is the identity — the
+gate asserts it.
+
+## Layout
+
+```
+202602_TEI_Amazon_Connect/
+├── teicalc/               ← ALL math (stdlib-only) — notebooks hold none
+│   ├── anchor.py          ← Forrester's tables, VERBATIM, never edited
+│   ├── model.py           ← NPV/ROI/payback, risk adjustment, compute_summary
+│   ├── overlay.py         ← ClientDrivers + driver map + overlay_rows
+│   ├── scenarios.py       ← conservative / moderate / aggressive
+│   └── staging.py         ← on_stage()/backstage() (Mercury vs nbconvert)
+├── notebooks/business_case.ipynb   ← THE deliverable
+├── scripts/export_report.py
+├── tests/                 ← hand-checked pinned acceptance numbers
+├── config.toml            ← Mercury theme (NTT DATA brand)
+├── pyproject.toml         ← full toolchain as core deps — no requirements.txt
+├── docs/                  ← the Forrester PDF
+└── exports/               ← generated .html/.md; gitignored
+```
+
+## Run
+
+```bash
+python -m venv .venv && source .venv/bin/activate
+pip install -e ".[dev]"
+```
+
+| Task | Command |
+|---|---|
+| Tests | `pytest` |
+| Serve (the stage) | `mercury --working-dir notebooks/` (run from this project root so `config.toml` loads) |
+| Analyst view (backstage) | `jupyter lab` |
+| Headless check | `jupyter nbconvert --to notebook --execute --inplace notebooks/business_case.ipynb` |
+| Export for LLMs | `python scripts/export_report.py` |
+
+The data appendix (markdown tables + JSON model state) rides inside
+`exports/business_case.md` — it replaces the retired `exports/export.json`
+pipeline and is the payload for the Athena study-repository roadmap.
+
+## History
+
+This study previously ran on the shared `core/` package with an
+Athena-workflow notebook chain (provision → push → calculate → export).
+That workflow was retired when the study migrated to the pattern
+(git history preserves it); the engine reproduces the same published
+totals locally, pinned in `tests/`.

studies/202602_TEI_Amazon_Connect/config.toml

@@ -0,0 +1,81 @@
+# Mercury app-shell theme — NTT DATA brand (light), modern surfaces.
+# See docs/brand.md for the source palette.
+#
+# Loaded from the directory where you launch `mercury` (this project root);
+# restart the server to apply changes. Only keys in mercury/config.py
+# CSS_VARIABLE_MAP emit a CSS variable — anything else in DEFAULT_THEME is
+# either derived or component-baked (e.g. success/warning/danger, slider
+# track, widget bg) and silently no-ops here. Omitted keys are derived
+# from the ones below.
+
+[main]
+title = "Amazon Connect TEI — Business Case"
+favicon_emoji = "📊"
+footer = "Amazon Connect TEI study (Forrester, Feb 2026)"
+notebooks_button_label = "Analyses"
+
+[welcome]
+header = "Amazon Connect TEI"
+message = """
+Interactive reproduction of Forrester's *Total Economic Impact™ Of Amazon
+Connect* composite ($78.7M NPV · 342% ROI). The published study is the
+verbatim anchor; tune the 🟡 client drivers live to rescale the composite
+to your organization, then export the personalized report source with
+`python scripts/export_report.py`.
+"""
+
+[theme]
+# ── Type — Georgia headings, Arial body. Both web-safe system fonts,
+#    so no font_url / network fetch. Georgia ships only normal+bold, so
+#    heading weight is 700 (the default 800 would render as faux-bold). ──
+font_family         = "Arial, 'Helvetica Neue', Helvetica, sans-serif"
+heading_font_family = "Georgia, 'Times New Roman', Times, serif"
+font_size           = "15px"
+font_weight         = "normal"
+heading_font_weight = "700"
+
+# ── Text — NTT ink scale ──
+text_color       = "#2e404d"   # body
+muted_text_color = "#586671"   # captions / secondary
+
+# ── Surfaces — white content floating on a soft neutral canvas (depth).
+#    For a strictly-white page instead, set background_color = "#ffffff". ──
+background_color         = "#f4f5f6"   # outer page
+content_background_color = "#ffffff"   # notebook column
+surface_color            = "#ffffff"
+card_background_color    = "#f8f8f8"   # brand card
+border_color             = "#d5d9db"   # brand border
+border_radius            = "10px"      # modern rounding
+
+# ── Accents — Future Blue. primary_color also drives the Run button + focus. ──
+primary_color             = "#0072bc"
+accent_color              = "#0072bc"
+focus_border_color        = "#0072bc"
+hover_background_color     = "#eef5fb"  # light blue tint
+selected_background_color = "#dcecfa"
+
+# ── Sidebar — clean white, hairline divider ──
+sidebar_background_color = "#ffffff"
+sidebar_text_color       = "#2e404d"
+sidebar_title_color      = "#151d2c"
+sidebar_shadow           = "1px 0 0 #d5d9db"
+
+# ── Top bar — deep NTT navy (brand heading-primary) ──
+topbar_background_color = "#151d2c"
+topbar_text_color       = "#ffffff"
+topbar_border_color     = "rgba(255,255,255,0.08)"
+
+# ── Footer ──
+footer_background_color = "#ffffff"
+footer_text_color       = "#586671"
+footer_border_color     = "#d5d9db"
+
+# ── Run button — subtle brand-blue gradient (else derives from primary) ──
+run_button_background       = "linear-gradient(180deg, #0087dc 0%, #0072bc 100%)"
+run_button_background_hover = "linear-gradient(180deg, #1a93e6 0%, #0079c8 100%)"
+run_button_text_color       = "#ffffff"
+
+# ── Depth — soft, navy-tinted shadows (modern) ──
+shadow_sm = "0 1px 2px rgba(21,29,44,0.05)"
+shadow_md = "0 6px 18px rgba(21,29,44,0.08)"
+shadow_lg = "0 16px 40px rgba(21,29,44,0.10)"

studies/202602_TEI_Amazon_Connect/pyproject.toml

@@ -0,0 +1,36 @@
+[build-system]
+requires = ["setuptools>=68"]
+build-backend = "setuptools.build_meta"
+
+[project]
+name = "teicalc"
+version = "0.1.0"
+description = "Amazon Connect TEI (Forrester, Feb 2026) — composite reproduction + client overlay"
+requires-python = ">=3.10"
+# The notebook is the deliverable (served with Mercury, exported via
+# nbconvert, tables via tabulate) — the whole toolchain is a required
+# runtime dependency, not an extra. `pip install -e .` must be enough.
+dependencies = [
+    "pandas>=2.0",
+    "plotly>=5.18",
+    "openpyxl>=3.1",
+    "mercury>=3.2",
+    "jupyterlab>=4.0",
+    "ipywidgets>=8.0",
+    "nbconvert>=7",
+    "tabulate>=0.9",
+]
+
+[project.optional-dependencies]
+dev = ["pytest>=7.4", "mypy>=1.8"]
+
+[tool.setuptools.packages.find]
+include = ["teicalc*"]
+
+[tool.pytest.ini_options]
+testpaths = ["tests"]
+addopts = "-q"
+
+[tool.mypy]
+strict = true
+packages = ["teicalc"]

studies/202602_TEI_Amazon_Connect/scripts/export_report.py

@@ -0,0 +1,47 @@
+"""Export the deliverable notebooks as LLM-readable report sources.
+
+Executes each notebook fresh (widget defaults — or whatever defaults you edit in),
+then writes both formats to exports/:
+
+  exports/<notebook>.html  — human-reviewable, tables render
+  exports/<notebook>.md    — leanest LLM input
+
+Plotly figures export as JavaScript an LLM cannot read; each notebook's
+machine-readable appendix section carries every number behind them.
+
+Run from the project root:  python scripts/export_report.py [name-filter]
+An optional argument exports only notebooks whose filename contains it.
+"""
+from __future__ import annotations
+
+import subprocess
+import sys
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parent.parent
+NOTEBOOKS = [
+    ROOT / "notebooks" / "business_case.ipynb",
+]
+EXPORTS = ROOT / "exports"
+
+
+def main() -> None:
+    picked = [nb for nb in NOTEBOOKS
+              if len(sys.argv) < 2 or sys.argv[1] in nb.name]
+    if not picked:
+        sys.exit(f"no notebook matches {sys.argv[1]!r}")
+    EXPORTS.mkdir(exist_ok=True)
+    for nb in picked:
+        for fmt in ("html", "markdown"):
+            subprocess.run(
+                [sys.executable, "-m", "nbconvert", "--execute",
+                 "--to", fmt, "--output-dir", str(EXPORTS), str(nb)],
+                check=True, cwd=ROOT,
+            )
+    for p in sorted(EXPORTS.iterdir()):
+        if p.suffix in (".html", ".md"):
+            print(f"wrote {p.relative_to(ROOT)} ({p.stat().st_size / 1024:,.0f} KB)")
+
+
+if __name__ == "__main__":
+    main()

studies/202602_TEI_Amazon_Connect/teicalc/__init__.py

@@ -0,0 +1,56 @@
+"""
+teicalc — self-contained engine for the Amazon Connect TEI study
+(Forrester, February 2026). Mercury Notebook Pattern, Variant 4:
+verbatim composite anchor → published-totals gate → client overlay.
+"""
+
+from .anchor import ASSUMPTIONS, BENEFITS_VERBATIM, COSTS_VERBATIM, PUBLISHED
+from .model import (
+    X_LABELS,
+    YEAR_INDEX,
+    YEARS,
+    benefits_by_year,
+    by_calendar,
+    compute_summary,
+    costs_by_year,
+    discount_factor,
+    html_money,
+    initial_costs,
+    money,
+    month_label,
+    npv,
+    payback_label,
+    payback_months,
+    payback_years,
+    present_value,
+    risk_adjust_benefit,
+    risk_adjust_cost,
+    risk_adjusted_rows,
+    roi_pct,
+)
+from .overlay import (
+    BENEFIT_DRIVERS,
+    COMPOSITE,
+    COST_DRIVERS,
+    ClientDrivers,
+    growth_multiplier,
+    overlay_rows,
+    scale_factor,
+)
+from .scenarios import SCENARIOS, apply_scenario
+
+__version__ = "0.1.0"
+
+__all__ = [
+    "ASSUMPTIONS", "BENEFITS_VERBATIM", "COSTS_VERBATIM", "PUBLISHED",
+    "YEARS", "YEAR_INDEX", "X_LABELS",
+    "by_calendar", "month_label",
+    "discount_factor", "present_value", "npv", "roi_pct",
+    "payback_years", "payback_months", "payback_label",
+    "risk_adjust_benefit", "risk_adjust_cost", "risk_adjusted_rows",
+    "benefits_by_year", "costs_by_year", "initial_costs",
+    "compute_summary", "money", "html_money",
+    "ClientDrivers", "COMPOSITE", "BENEFIT_DRIVERS", "COST_DRIVERS",
+    "scale_factor", "growth_multiplier", "overlay_rows",
+    "SCENARIOS", "apply_scenario",
+]

studies/202602_TEI_Amazon_Connect/teicalc/anchor.py

@@ -0,0 +1,167 @@
+"""
+The verbatim anchor — Forrester *Total Economic Impact™ Of Amazon Connect*
+(February 2026, commissioned by AWS).
+
+VERBATIM, do not edit. These are Forrester's published composite-organization
+tables and financial summary, transplanted unchanged from the study PDF
+(``docs/202602_TEI Report Amazon Connect.pdf``). Client personalization
+lives in :mod:`teicalc.overlay`; scenario stress lives in
+:mod:`teicalc.scenarios` — both deep-copy, neither mutates this record.
+
+Rows keep Forrester's own year-index keys (``"1"``/``"2"``/``"3"``);
+:mod:`teicalc.model` maps them to calendar years (2026–2028). Values are
+*nominal* (pre-risk-adjustment); the risk factor is stored per row and
+applied by the model (benefits ×(1−rf), costs ×(1+rf), per the TEI
+methodology).
+"""
+
+from __future__ import annotations
+
+#: 3-year nominal benefit cashflows — 🟢 published.
+BENEFITS_VERBATIM: list[dict] = [
+    {
+        "field_key": "ai_contact_resolution",
+        "table": "benefits",
+        "label": "AI-driven contact resolution efficiency",
+        "category": "Productivity",
+        "year_values": {"1": 13_911_040, "2": 23_932_480, "3": 37_797_760},
+        "risk_adjustment": 0.15,
+        "notes": (
+            "PDF Section At/Atr. Composite: 20M annual contacts, 30% YoY "
+            "growth, 75% calls, 10-min AHT with legacy. Connect drops AHT "
+            "12% Y1 and shifts traffic to chat/self-service. 80% "
+            "productivity recapture. Risk adj 15% (legacy performance, "
+            "implementation depth, integration scope, growth)."
+        ),
+    },
+    {
+        "field_key": "ai_content_sentiment",
+        "table": "benefits",
+        "label": "AI-powered content and sentiment analysis savings",
+        "category": "Productivity",
+        "year_values": {"1": 4_586_620, "2": 5_358_412, "3": 6_291_680},
+        "risk_adjustment": 0.15,
+        "notes": (
+            "PDF Section Bt/Btr. Auto post-contact summaries reclaim ~60s "
+            "per call; QA scaled from 1–3% to 100%; supervisors freed from "
+            "manual review. Risk adj 15%."
+        ),
+    },
+    {
+        "field_key": "ai_forecasting_supervision",
+        "table": "benefits",
+        "label": "AI-enabled forecasting, agent scheduling, and supervision",
+        "category": "Productivity",
+        "year_values": {"1": 6_651_680, "2": 9_133_760, "3": 12_391_712},
+        "risk_adjustment": 0.15,
+        "notes": (
+            "PDF Section Ct/Ctr. ML-WFM yields 5% agent FTE optimization "
+            "and supervisors managing 20% more agents (10→12). 80% "
+            "productivity recapture. Risk adj 15%."
+        ),
+    },
+    {
+        "field_key": "data_driven_profit_lift",
+        "table": "benefits",
+        "label": "Data-driven profit lift with increased conversion",
+        "category": "Revenue",
+        "year_values": {"1": 1_200_000, "2": 1_560_000, "3": 2_028_000},
+        "risk_adjustment": 0.20,
+        "notes": (
+            "PDF Section Dt/Dtr. Composite revenue $10B Y1 (+30% YoY); "
+            "5% from outbound contact-center marketing; conversion lifts "
+            "from 10% to 12% (+20% relative); 12% operating margin. "
+            "Risk adj 20%."
+        ),
+    },
+    {
+        "field_key": "legacy_solution_savings",
+        "table": "benefits",
+        "label": "Legacy solution cost savings",
+        "category": "Cost Savings",
+        "year_values": {"1": 6_177_600, "2": 8_030_880, "3": 10_440_144},
+        "risk_adjustment": 0.20,
+        "notes": (
+            "PDF Section Et/Etr. Avg legacy license $180/agent-month × "
+            "(agents+supervisors) × 12, plus 30% overhead for infra & "
+            "third-party tools. Risk adj 20%."
+        ),
+    },
+]
+
+
+#: Costs include an ``initial`` (year-0, undiscounted) component for
+#: implementation. Cost risk adjustments are applied *upward*. 🟢 published.
+COSTS_VERBATIM: list[dict] = [
+    {
+        "field_key": "amazon_connect_usage",
+        "table": "costs",
+        "label": "Amazon Connect usage cost",
+        "category": "Subscription",
+        "initial": 0,
+        "year_values": {"1": 6_456_448, "2": 7_951_164, "3": 9_832_961},
+        "risk_adjustment": 0.05,
+        "notes": (
+            "PDF Section Ft/Ftr. Telephony $0.0106/min + Unlimited AI "
+            "$0.0380/min on minutes that reach an agent, plus chat at "
+            "$0.0100/message (10 messages/chat). Risk adj 5%."
+        ),
+    },
+    {
+        "field_key": "implementation_migration",
+        "table": "costs",
+        "label": "Implementation and migration cost",
+        "category": "Implementation",
+        "initial": 1_087_500,
+        "year_values": {"1": 188_333, "2": 188_333, "3": 0},
+        "risk_adjustment": 0.10,
+        "notes": (
+            "PDF Section Gt/Gtr. 6-month initial migration: 5 internal "
+            "FTE @ $115k + $800k pro-services. Y1/Y2 M&A integrations: 2 "
+            "months × 2 FTE + $150k pro-services. Risk adj 10%."
+        ),
+    },
+    {
+        "field_key": "ongoing_management",
+        "table": "costs",
+        "label": "Ongoing management",
+        "category": "Operations",
+        "initial": 0,
+        "year_values": {"1": 256_200, "2": 187_200, "3": 187_200},
+        "risk_adjustment": 0.15,
+        "notes": (
+            "PDF Section Ht/Htr. Y1: 5 IT/PM @ 30% × $115k + 5 business "
+            "users @ 30% × $55,800. Y2/Y3: 3 IT/PM @ 30% + 5 business "
+            "users @ 30%. Risk adj 15%."
+        ),
+    },
+]
+
+
+#: Composite-organization drivers — 🟢 published (PDF "Composite Organization").
+ASSUMPTIONS: dict = {
+    "agents_fte": 2_000,
+    "supervisors_fte": 200,
+    "annual_contacts_y1": 20_000_000,
+    "growth_rate": 0.30,
+    "call_share": 0.75,
+    "aht_legacy_minutes": 10,
+    "agent_salary": 45_760,
+    "supervisor_salary": 55_800,
+    "discount_rate": 0.10,
+    "analysis_years": 3,
+}
+
+
+#: The PDF's Financial Summary — the gate's reproduction target. 🟢 published.
+#: The engine reproduces these to within Forrester's own table rounding
+#: (benefits PV lands $223 low; costs PV $0.22 low).
+PUBLISHED: dict = {
+    "benefits_pv": 101_696_791,
+    "costs_pv": 22_983_076,
+    "npv": 78_713_715,
+    "roi_pct": 342,
+    "payback_months_max": 6,          # published as "<6 months"
+    "discount_rate": 0.10,
+    "analysis_years": 3,
+}

studies/202602_TEI_Amazon_Connect/teicalc/model.py

@@ -0,0 +1,267 @@
+"""
+Finance engine — the single source of truth for every number in the notebook.
+
+Transplanted from the retired shared ``core/calculations`` and
+``core/export/report_data.py`` so the study is self-contained (Mercury
+Notebook Pattern, Required §2/§7). Conventions match the Forrester TEI
+methodology:
+
+* The *Initial* investment is **not** discounted — it occurs at time zero.
+* Year-N cash flows are discounted at the end of the year:
+  ``PV = CF_n / (1 + r) ** n``.
+* Benefits are risk-adjusted *down* (``×(1−rf)``), costs *up* (``×(1+rf)``).
+* Payback runs on risk-adjusted **undiscounted** flows (the PDF's
+  "<6 months" uses the Cash Flow Analysis table's nominal RA rows).
+
+Everything this module returns for display is keyed by **calendar year**
+(Forrester Year 1/2/3 → 2026/2027/2028); ``initial`` stays a Year-0 scalar
+and never appears inside a ``*_by_year`` dict.
+
+This module is stdlib-only on purpose — the repo-root test suite imports it
+without the study's venv.
+"""
+
+from __future__ import annotations
+
+import math
+from collections.abc import Iterable, Sequence
+from copy import deepcopy
+
+# ── Timeline ─────────────────────────────────────────────────────────
+
+YEARS: list[int] = [2026, 2027, 2028]      # Forrester Year 1/2/3; window opens Jan 2026
+YEAR_INDEX: dict[int, int] = {y: i for i, y in enumerate(YEARS, start=1)}
+X_LABELS: list[str] = ["Initial"] + [str(y) for y in YEARS]
+
+_MONTHS = ["Jan", "Feb", "Mar", "Apr", "May", "Jun",
+           "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
+
+
+def month_label(m: int) -> str:
+    """Calendar label for a 1-indexed month from Jan of YEARS[0]."""
+    return f"{_MONTHS[(m - 1) % 12]} {YEARS[0] + (m - 1) // 12}"
+
+
+def by_calendar(year_values: dict[str, float]) -> dict[int, float]:
+    """Map Forrester's ``{"1": v, …}`` year-index keys to calendar years."""
+    return {YEARS[int(k) - 1]: float(v or 0) for k, v in year_values.items()}
+
+
+# ── Discounting primitives ───────────────────────────────────────────
+
+
+def discount_factor(year_index: int, discount_rate: float) -> float:
+    """``1 / (1 + r) ** n``. Year 0 → 1.0 (no discount)."""
+    if year_index < 0:
+        raise ValueError("year_index must be >= 0")
+    return 1.0 / ((1.0 + discount_rate) ** year_index)
+
+
+def present_value(amount: float, year_index: int, discount_rate: float) -> float:
+    """Discount ``amount`` from end-of-year ``year_index`` to present."""
+    return amount * discount_factor(year_index, discount_rate)
+
+
+def npv(cashflows: Iterable[float], discount_rate: float,
+        initial: float = 0.0) -> float:
+    """``initial + Σ CF_n / (1 + r)^n`` — initial undiscounted (TEI)."""
+    return initial + sum(
+        present_value(float(cf), n, discount_rate)
+        for n, cf in enumerate(cashflows, start=1)
+    )
+
+
+def roi_pct(benefits_pv: float, costs_pv: float) -> float:
+    """``(Benefits − Costs) / Costs`` as a percentage; 0 when costs ≤ 0."""
+    if costs_pv <= 0:
+        return 0.0
+    return (benefits_pv - costs_pv) / costs_pv * 100.0
+
+
+# ── Payback ──────────────────────────────────────────────────────────
+
+
+def payback_years(initial_cost: float,
+                  yearly_net: Sequence[float]) -> float | None:
+    """
+    Years until cumulative net benefits cover the initial cost, with linear
+    interpolation inside the crossing year. ``None`` if never reached.
+    """
+    remaining = float(initial_cost)
+    if remaining <= 0:
+        return 0.0
+    for i, cf in enumerate(yearly_net):
+        cf = float(cf)
+        if cf <= 0:
+            remaining += -cf            # a net-loss year widens the gap
+            continue
+        if cf >= remaining:
+            return i + remaining / cf
+        remaining -= cf
+    return None
+
+
+def payback_months(initial_cost: float,
+                   yearly_net: Sequence[float]) -> float | None:
+    """Same as :func:`payback_years`, in months."""
+    yrs = payback_years(initial_cost, yearly_net)
+    return yrs * 12.0 if yrs is not None else None
+
+
+def payback_label(months: float | None) -> str:
+    """Human label: ``"0.7 months (~Jan 2026)"`` / ``"immediate"`` / ``"beyond 2028"``."""
+    if months is None:
+        return f"beyond {YEARS[-1]}"
+    if months <= 0:
+        return "immediate"
+    return f"{months:.1f} months (~{month_label(max(1, math.ceil(months)))})"
+
+
+# ── Risk adjustment (TEI: benefits down, costs up) ───────────────────
+
+
+def risk_adjust_benefit(amount: float, risk_factor: float) -> float:
+    """``amount × (1 − rf)``, rf clamped to [0, 1]."""
+    rf = max(0.0, min(1.0, float(risk_factor)))
+    return amount * (1.0 - rf)
+
+
+def risk_adjust_cost(amount: float, risk_factor: float) -> float:
+    """``amount × (1 + rf)``, rf clamped to [0, 1]."""
+    rf = max(0.0, min(1.0, float(risk_factor)))
+    return amount * (1.0 + rf)
+
+
+def risk_adjusted_rows(rows: list[dict], table: str) -> list[dict]:
+    """Deep-copied rows with the per-row risk factor applied to every value."""
+    adjust = risk_adjust_benefit if table == "benefits" else risk_adjust_cost
+    out: list[dict] = []
+    for raw in rows:
+        row = deepcopy(raw)
+        rf = float(row.get("risk_adjustment") or 0.0)
+        row["year_values"] = {
+            k: adjust(float(v or 0), rf) for k, v in row["year_values"].items()
+        }
+        if row.get("initial"):
+            # Only costs carry an initial; TEI adjusts it upward like the years.
+            row["initial"] = risk_adjust_cost(float(row["initial"]), rf) \
+                if table == "costs" else float(row["initial"])
+        out.append(row)
+    return out
+
+
+# ── Aggregation (calendar-keyed) ─────────────────────────────────────
+
+
+def _totals_by_year(ra_rows: list[dict]) -> dict[int, float]:
+    totals = {y: 0.0 for y in YEARS}
+    for row in ra_rows:
+        for y, v in by_calendar(row["year_values"]).items():
+            totals[y] += v
+    return totals
+
+
+def benefits_by_year(rows: list[dict]) -> dict[int, float]:
+    """Risk-adjusted benefit totals per calendar year."""
+    return _totals_by_year(risk_adjusted_rows(rows, "benefits"))
+
+
+def costs_by_year(rows: list[dict]) -> dict[int, float]:
+    """Risk-adjusted cost totals per calendar year (excludes ``initial``)."""
+    return _totals_by_year(risk_adjusted_rows(rows, "costs"))
+
+
+def initial_costs(rows: list[dict]) -> float:
+    """Risk-adjusted Year-0 outlay (undiscounted)."""
+    return sum(
+        float(row.get("initial") or 0)
+        for row in risk_adjusted_rows(rows, "costs")
+    )
+
+
+# ── Composite summary ────────────────────────────────────────────────
+
+
+def compute_summary(benefits: list[dict], costs: list[dict],
+                    discount_rate: float = 0.10) -> dict:
+    """
+    The full business-case readout for one set of value rows.
+
+    Returns KPIs (``benefits_pv``/``costs_pv``/``npv``/``roi_pct``/
+    ``payback_months``/``payback_label``/``initial_costs``/nominal totals),
+    calendar-keyed schedules (``benefits_by_year``/``costs_by_year``/
+    ``net_by_year``/``cumulative_net_by_year`` — cumulative subtracts the
+    initial outlay), and a per-row breakdown under ``rows``.
+    """
+    ben_ra = risk_adjusted_rows(benefits, "benefits")
+    cost_ra = risk_adjusted_rows(costs, "costs")
+
+    ben_by = _totals_by_year(ben_ra)
+    cost_by = _totals_by_year(cost_ra)
+    initial = sum(float(r.get("initial") or 0) for r in cost_ra)
+
+    benefits_pv = npv([ben_by[y] for y in YEARS], discount_rate)
+    costs_pv = npv([cost_by[y] for y in YEARS], discount_rate, initial=initial)
+
+    net_by = {y: ben_by[y] - cost_by[y] for y in YEARS}
+    cum, cum_by = -initial, {}
+    for y in YEARS:
+        cum += net_by[y]
+        cum_by[y] = cum
+
+    pb_months = payback_months(initial, [net_by[y] for y in YEARS])
+
+    def _row_breakdown(ra_rows: list[dict], table: str) -> list[dict]:
+        out = []
+        for row in ra_rows:
+            ra_by = by_calendar(row["year_values"])
+            init_ra = float(row.get("initial") or 0)
+            entry = {
+                "field_key": row["field_key"],
+                "label": row["label"],
+                "category": row["category"],
+                "risk_adjustment": row["risk_adjustment"],
+                "ra_by_year": ra_by,
+                "three_yr_ra": sum(ra_by.values()),
+                "pv": npv([ra_by[y] for y in YEARS], discount_rate,
+                          initial=init_ra if table == "costs" else 0.0),
+            }
+            if table == "costs":
+                entry["initial_ra"] = init_ra
+            out.append(entry)
+        return out
+
+    return {
+        "discount_rate": discount_rate,
+        "benefits_pv": benefits_pv,
+        "costs_pv": costs_pv,
+        "npv": benefits_pv - costs_pv,
+        "roi_pct": roi_pct(benefits_pv, costs_pv),
+        "payback_months": pb_months,
+        "payback_label": payback_label(pb_months),
+        "initial_costs": initial,
+        "benefits_nominal": sum(ben_by.values()),
+        "costs_nominal": sum(cost_by.values()) + initial,
+        "benefits_by_year": ben_by,
+        "costs_by_year": cost_by,
+        "net_by_year": net_by,
+        "cumulative_net_by_year": cum_by,
+        "rows": {
+            "benefits": _row_breakdown(ben_ra, "benefits"),
+            "costs": _row_breakdown(cost_ra, "costs"),
+        },
+    }
+
+
+# ── Display helpers ──────────────────────────────────────────────────
+
+
+def money(v: float) -> str:
+    sign, a = ("-" if v < 0 else ""), abs(v)
+    return f"{sign}${a/1e6:,.1f}M" if a >= 1e6 else f"{sign}${a/1e3:,.0f}K"
+
+
+def html_money(v: float) -> str:
+    """Plotly text with two or more bare ``$`` triggers MathJax math mode —
+    annotations holding several amounts must use the HTML entity instead."""
+    return money(v).replace("$", "&#36;")

studies/202602_TEI_Amazon_Connect/teicalc/overlay.py

@@ -0,0 +1,107 @@
+"""
+Client overlay — Variant 4's personalization layer.
+
+The verbatim anchor is Forrester's *composite organization* (2,000 agents,
+20M contacts, 30% growth). This module rescales that composite to a client's
+size: a 🟡 **first-order linear rescale**, answering "what does the composite
+look like at your scale?", not "what is your TEI?".
+
+Each verbatim row is tied to the driver that dominates its derivation in the
+PDF (see ``BENEFIT_DRIVERS``/``COST_DRIVERS``); rows scale linearly with
+their driver, project-based costs stay fixed. The client's growth rate
+re-bases the composite's Y1→Y3 trajectory (which embeds 30% YoY).
+
+``overlay_rows(COMPOSITE)`` is the identity — it reproduces the verbatim
+numbers exactly, so headless widget defaults form the published-study
+reproduction the gate expects. The anchor is never mutated: every function
+deep-copies.
+"""
+
+from __future__ import annotations
+
+from copy import deepcopy
+from dataclasses import dataclass
+
+from .anchor import ASSUMPTIONS, BENEFITS_VERBATIM, COSTS_VERBATIM
+
+
+@dataclass(frozen=True)
+class ClientDrivers:
+    """Client inputs; defaults are the Forrester composite (identity overlay)."""
+
+    agents_fte: int = ASSUMPTIONS["agents_fte"]                    # 2,000 (+200 supervisors at 10:1)
+    annual_contacts_y1: int = ASSUMPTIONS["annual_contacts_y1"]    # 20M
+    growth_rate: float = ASSUMPTIONS["growth_rate"]                # 0.30 YoY
+    discount_rate: float = ASSUMPTIONS["discount_rate"]            # 0.10
+
+
+COMPOSITE = ClientDrivers()
+
+
+#: 🟡 Which driver each verbatim row scales with, per its PDF derivation.
+BENEFIT_DRIVERS: dict[str, str] = {
+    "ai_contact_resolution":      "contacts",   # AHT × volume → contact-driven
+    "ai_content_sentiment":       "contacts",   # per-call summaries/QA → contact-driven
+    "ai_forecasting_supervision": "agents",     # FTE optimization + supervisor span
+    "data_driven_profit_lift":    "contacts",   # 🔴 proxy — revenue-driven in the PDF;
+                                                #    outbound volume is the nearest linear driver
+    "legacy_solution_savings":    "agents",     # $/agent-month licences (supervisors follow 10:1)
+}
+COST_DRIVERS: dict[str, str] = {
+    "amazon_connect_usage":       "contacts",   # per-minute/per-message consumption
+    "implementation_migration":   "fixed",      # project-based — does not scale
+    "ongoing_management":         "fixed",      # small fixed team
+}
+
+
+def scale_factor(driver: str, d: ClientDrivers) -> float:
+    """Linear size ratio vs the composite for one driver kind."""
+    if driver == "contacts":
+        return d.annual_contacts_y1 / ASSUMPTIONS["annual_contacts_y1"]
+    if driver == "agents":
+        return d.agents_fte / ASSUMPTIONS["agents_fte"]
+    if driver == "fixed":
+        return 1.0
+    raise KeyError(f"Unknown driver: {driver!r}")
+
+
+def growth_multiplier(year_index: int, growth_rate: float) -> float:
+    """
+    Re-base the composite's Y1→Y3 trajectory on the client's growth.
+
+    The verbatim year values already embed the composite's 30% YoY growth;
+    dividing it out and compounding the client's rate preserves the
+    composite's *shape* while adopting the client's slope. Year 1 → 1.0.
+    """
+    composite_g = ASSUMPTIONS["growth_rate"]
+    return ((1.0 + growth_rate) / (1.0 + composite_g)) ** (year_index - 1)
+
+
+def overlay_rows(d: ClientDrivers = COMPOSITE) -> tuple[list[dict], list[dict]]:
+    """
+    Deep-copied (benefits, costs) rows rescaled to the client's drivers.
+
+    Non-fixed rows: ``year_values[n] ×= scale_factor × growth_multiplier(n)``.
+    Fixed rows keep their year values and ``initial`` unchanged (no growth
+    re-base either — they are project/team costs, not volume costs).
+    Risk factors, labels, and notes are untouched.
+    """
+
+    def _apply(rows: list[dict], drivers: dict[str, str]) -> list[dict]:
+        out = []
+        for raw in rows:
+            row = deepcopy(raw)
+            driver = drivers[row["field_key"]]
+            if driver != "fixed":
+                s = scale_factor(driver, d)
+                row["year_values"] = {
+                    k: float(v) * s * growth_multiplier(int(k), d.growth_rate)
+                    for k, v in row["year_values"].items()
+                }
+                if row.get("initial"):
+                    row["initial"] = float(row["initial"]) * s
+            out.append(row)
+        return out
+
+    return (_apply(BENEFITS_VERBATIM, BENEFIT_DRIVERS),
+            _apply(COSTS_VERBATIM, COST_DRIVERS))

studies/202602_TEI_Amazon_Connect/teicalc/scenarios.py

@@ -0,0 +1,67 @@
+"""
+Scenario stress — transplanted from the retired shared ``core/calculations/scenarios.py``
+with identical semantics.
+
+Forrester TEI risk-adjusts benefits *down* and costs *up*; scenarios stress
+both levers:
+
+* ``adoption`` scales nominal values (``year_values`` and ``initial``).
+* ``risk_delta`` is *added* to a benefit's risk factor and *subtracted*
+  from a cost's (conservative = more uncertainty on benefits, less padding
+  on costs), then clamped to [0, 1].
+
+``"moderate"`` is the identity — the headless default reproduces the
+published study. Note the counterintuitive corollary: the conservative
+scenario *lowers* costs PV, because 80% adoption shrinks consumption-priced
+usage and the clamp caps cost padding.
+"""
+
+from __future__ import annotations
+
+from copy import deepcopy
+
+SCENARIOS: dict[str, dict[str, float]] = {
+    "conservative": {"adoption": 0.80, "risk_delta": 0.10},
+    "moderate":     {"adoption": 1.00, "risk_delta": 0.00},
+    "aggressive":   {"adoption": 1.15, "risk_delta": -0.05},
+}
+
+
+def apply_scenario(
+    items: list[dict],
+    scenario: str = "moderate",
+    *,
+    multipliers: dict[str, dict[str, float]] | None = None,
+    table: str | None = None,
+) -> list[dict]:
+    """
+    Deep-copied value rows with the scenario applied; inputs are not mutated.
+
+    Each row needs ``year_values`` (year-string → float), optionally
+    ``initial`` and ``risk_adjustment``, and a ``table`` of ``"benefits"``
+    or ``"costs"`` (or pass ``table=`` to force one) — the table decides the
+    sign of ``risk_delta``.
+    """
+    cfg = (multipliers or SCENARIOS).get(scenario)
+    if cfg is None:
+        raise KeyError(f"Unknown scenario: {scenario!r}")
+    adoption = float(cfg.get("adoption", 1.0))
+    risk_delta = float(cfg.get("risk_delta", 0.0))
+
+    out: list[dict] = []
+    for raw in items:
+        item = deepcopy(raw)
+        item_table = item.get("table") or table or "benefits"
+        item["table"] = item_table
+
+        item["year_values"] = {
+            k: float(v) * adoption for k, v in item["year_values"].items()
+        }
+        if item.get("initial") is not None:
+            item["initial"] = float(item["initial"]) * adoption
+
+        ra = float(item.get("risk_adjustment") or 0.0)
+        new_ra = ra + risk_delta if item_table == "benefits" else ra - risk_delta
+        item["risk_adjustment"] = max(0.0, min(1.0, new_ra))
+        out.append(item)
+    return out

studies/202602_TEI_Amazon_Connect/teicalc/staging.py

@@ -0,0 +1,29 @@
+"""
+Stage vs backstage — is this notebook render stakeholder-facing?
+
+The Mercury CLI (``mercury --working-dir …``) exports ``MERCURY_CONFIG_DIR``
+into the server process so the widget library can locate ``config.toml``
+(see ``mercury/config.py``); every kernel that server spawns inherits it.
+JupyterLab and nbconvert kernels don't have it. That makes the variable a
+reliable signal for "the audience is looking" (the stage) versus an
+analyst session or a headless export run (backstage).
+
+Diagnostics routed through :func:`backstage` stay visible in JupyterLab
+and land in the nbconvert exports (where the machine-readable appendix
+must appear for LLM consumption) but never render in the Mercury app.
+"""
+
+from __future__ import annotations
+
+import os
+
+
+def on_stage() -> bool:
+    """True when running under the Mercury app (stakeholder-facing)."""
+    return os.getenv("MERCURY_CONFIG_DIR") is not None
+
+
+def backstage(*args, **kwargs) -> None:
+    """``print`` that renders only backstage (JupyterLab, nbconvert)."""
+    if not on_stage():
+        print(*args, **kwargs)

studies/202602_TEI_Amazon_Connect/tests/conftest.py

@@ -0,0 +1,7 @@
+"""Make teicalc importable even without the study venv active (the normal
+setup is ``pip install -e ".[dev]"`` into the study-local ``.venv/``)."""
+
+import pathlib
+import sys
+
+sys.path.insert(0, str(pathlib.Path(__file__).resolve().parent.parent))

studies/202602_TEI_Amazon_Connect/tests/test_anchor.py

@@ -0,0 +1,95 @@
+"""The verbatim anchor is Forrester's published record — pinned value by
+value, and proven immutable under every engine code path."""
+
+from copy import deepcopy
+
+from teicalc import (
+    ASSUMPTIONS,
+    BENEFITS_VERBATIM,
+    COMPOSITE,
+    COSTS_VERBATIM,
+    PUBLISHED,
+    ClientDrivers,
+    apply_scenario,
+    compute_summary,
+    overlay_rows,
+)
+
+
+def _row(rows, key):
+    return next(r for r in rows if r["field_key"] == key)
+
+
+def test_benefit_rows_verbatim():
+    assert [r["field_key"] for r in BENEFITS_VERBATIM] == [
+        "ai_contact_resolution",
+        "ai_content_sentiment",
+        "ai_forecasting_supervision",
+        "data_driven_profit_lift",
+        "legacy_solution_savings",
+    ]
+    expected = {
+        "ai_contact_resolution": ({"1": 13_911_040, "2": 23_932_480, "3": 37_797_760}, 0.15),
+        "ai_content_sentiment": ({"1": 4_586_620, "2": 5_358_412, "3": 6_291_680}, 0.15),
+        "ai_forecasting_supervision": ({"1": 6_651_680, "2": 9_133_760, "3": 12_391_712}, 0.15),
+        "data_driven_profit_lift": ({"1": 1_200_000, "2": 1_560_000, "3": 2_028_000}, 0.20),
+        "legacy_solution_savings": ({"1": 6_177_600, "2": 8_030_880, "3": 10_440_144}, 0.20),
+    }
+    for key, (years, rf) in expected.items():
+        row = _row(BENEFITS_VERBATIM, key)
+        assert row["year_values"] == years
+        assert row["risk_adjustment"] == rf
+        assert row["table"] == "benefits"
+
+
+def test_cost_rows_verbatim():
+    expected = {
+        "amazon_connect_usage": ({"1": 6_456_448, "2": 7_951_164, "3": 9_832_961}, 0.05, 0),
+        "implementation_migration": ({"1": 188_333, "2": 188_333, "3": 0}, 0.10, 1_087_500),
+        "ongoing_management": ({"1": 256_200, "2": 187_200, "3": 187_200}, 0.15, 0),
+    }
+    for key, (years, rf, initial) in expected.items():
+        row = _row(COSTS_VERBATIM, key)
+        assert row["year_values"] == years
+        assert row["risk_adjustment"] == rf
+        assert row["initial"] == initial
+        assert row["table"] == "costs"
+
+
+def test_assumptions_and_published():
+    assert ASSUMPTIONS["agents_fte"] == 2_000
+    assert ASSUMPTIONS["supervisors_fte"] == 200
+    assert ASSUMPTIONS["annual_contacts_y1"] == 20_000_000
+    assert ASSUMPTIONS["growth_rate"] == 0.30
+    assert ASSUMPTIONS["discount_rate"] == 0.10
+    assert ASSUMPTIONS["analysis_years"] == 3
+
+    assert PUBLISHED["benefits_pv"] == 101_696_791
+    assert PUBLISHED["costs_pv"] == 22_983_076
+    assert PUBLISHED["npv"] == 78_713_715
+    assert PUBLISHED["roi_pct"] == 342
+    assert PUBLISHED["payback_months_max"] == 6
+
+    # The composite drivers ARE the anchor assumptions.
+    assert COMPOSITE.agents_fte == ASSUMPTIONS["agents_fte"]
+    assert COMPOSITE.annual_contacts_y1 == ASSUMPTIONS["annual_contacts_y1"]
+    assert COMPOSITE.growth_rate == ASSUMPTIONS["growth_rate"]
+    assert COMPOSITE.discount_rate == ASSUMPTIONS["discount_rate"]
+
+
+def test_anchor_is_never_mutated():
+    """Exercise every engine code path, then prove the record unchanged."""
+    ben_snap = deepcopy(BENEFITS_VERBATIM)
+    cost_snap = deepcopy(COSTS_VERBATIM)
+
+    overlay_rows()
+    overlay_rows(ClientDrivers(agents_fte=137, annual_contacts_y1=1_000_000,
+                               growth_rate=0.0))
+    for scenario in ("conservative", "moderate", "aggressive"):
+        apply_scenario(BENEFITS_VERBATIM, scenario)
+        apply_scenario(COSTS_VERBATIM, scenario)
+    compute_summary(BENEFITS_VERBATIM, COSTS_VERBATIM, 0.10)
+    compute_summary(BENEFITS_VERBATIM, COSTS_VERBATIM, 0.08)
+
+    assert BENEFITS_VERBATIM == ben_snap
+    assert COSTS_VERBATIM == cost_snap

studies/202602_TEI_Amazon_Connect/tests/test_model.py

@@ -0,0 +1,123 @@
+"""Engine pins — every number hand-checked before pinning.
+
+RA_benefit = v×(1−rf), RA_cost = v×(1+rf), PV = Σ RA_n/(1.1)^n, initial
+undiscounted. The composite reproduction lands within Forrester's own table
+rounding of the published Financial Summary (benefits PV $223 low, costs PV
+$0.22 low) — pinned both engine-exact (±$1) and against PUBLISHED (±$1,000,
+the convention the retired workflow notebooks used).
+"""
+
+import pytest
+
+from teicalc import (
+    BENEFITS_VERBATIM,
+    COSTS_VERBATIM,
+    PUBLISHED,
+    X_LABELS,
+    YEAR_INDEX,
+    YEARS,
+    by_calendar,
+    compute_summary,
+    discount_factor,
+    money,
+    npv,
+    payback_label,
+    payback_months,
+    payback_years,
+    roi_pct,
+)
+
+# Hand-checked risk-adjusted PVs per row (see module docstring).
+ROW_PVS = {
+    "ai_contact_resolution": 51_699_826.78,
+    "ai_content_sentiment": 11_326_357.54,
+    "ai_forecasting_supervision": 19_469_777.37,
+    "data_driven_profit_lift": 3_123_065.36,
+    "legacy_solution_savings": 16_077_540.50,
+    "amazon_connect_usage": 20_819_775.10,
+    "implementation_migration": 1_555_794.82,
+    "ongoing_management": 607_505.86,
+}
+
+
+@pytest.fixture(scope="module")
+def composite():
+    return compute_summary(BENEFITS_VERBATIM, COSTS_VERBATIM, 0.10)
+
+
+def test_calendar_mapping():
+    assert YEARS == [2026, 2027, 2028]
+    assert YEAR_INDEX == {2026: 1, 2027: 2, 2028: 3}
+    assert X_LABELS == ["Initial", "2026", "2027", "2028"]
+    assert by_calendar({"1": 10, "2": 20, "3": 30}) == {2026: 10, 2027: 20, 2028: 30}
+
+
+def test_primitives():
+    assert discount_factor(0, 0.10) == 1.0
+    assert discount_factor(1, 0.10) == pytest.approx(1 / 1.1)
+    assert npv([110], 0.10) == pytest.approx(100)
+    assert npv([110], 0.10, initial=-50) == pytest.approx(50)
+    assert roi_pct(101_696_791, 22_983_076) == pytest.approx(342.48, abs=0.1)
+    assert roi_pct(100, 0) == 0.0
+    assert money(78_713_492) == "$78.7M"
+    assert money(-250_000) == "-$250K"
+
+
+def test_payback_edges():
+    assert payback_years(0, [100]) == 0.0
+    assert payback_years(500, []) is None
+    assert payback_years(500, [-100, 200]) is None          # gap widens, never covered
+    assert payback_years(300, [-100, 400]) == pytest.approx(2.0)
+    assert payback_months(100, [1_200]) == pytest.approx(1.0)
+    assert payback_label(None) == "beyond 2028"
+    assert payback_label(0.0) == "immediate"
+    assert payback_label(0.7178) == "0.7 months (~Jan 2026)"
+    assert payback_label(14.2) == "14.2 months (~Mar 2027)"
+
+
+def test_per_row_pvs(composite):
+    rows = composite["rows"]["benefits"] + composite["rows"]["costs"]
+    assert len(rows) == 8
+    for row in rows:
+        assert row["pv"] == pytest.approx(ROW_PVS[row["field_key"]], abs=1)
+
+
+def test_composite_totals_engine_exact(composite):
+    assert composite["benefits_pv"] == pytest.approx(101_696_567.55, abs=1)
+    assert composite["costs_pv"] == pytest.approx(22_983_075.78, abs=1)
+    assert composite["npv"] == pytest.approx(78_713_491.78, abs=1)
+    assert composite["roi_pct"] == pytest.approx(342.4846, abs=0.01)
+    assert composite["payback_months"] == pytest.approx(0.7178, abs=0.001)
+    assert composite["initial_costs"] == pytest.approx(1_196_250, abs=0.01)
+
+
+def test_composite_reproduces_published(composite):
+    assert composite["benefits_pv"] == pytest.approx(PUBLISHED["benefits_pv"], abs=1_000)
+    assert composite["costs_pv"] == pytest.approx(PUBLISHED["costs_pv"], abs=1_000)
+    assert composite["npv"] == pytest.approx(PUBLISHED["npv"], abs=1_000)
+    assert round(composite["roi_pct"]) == PUBLISHED["roi_pct"]
+    assert composite["payback_months"] < PUBLISHED["payback_months_max"]
+    assert composite["payback_label"] == "0.7 months (~Jan 2026)"
+
+
+def test_yearly_schedules(composite):
+    assert composite["benefits_by_year"][2026] == pytest.approx(27_279_019.00, abs=0.01)
+    assert composite["benefits_by_year"][2027] == pytest.approx(40_333_658.20, abs=0.01)
+    assert composite["benefits_by_year"][2028] == pytest.approx(57_983_494.40, abs=0.01)
+    assert composite["costs_by_year"][2026] == pytest.approx(7_281_066.70, abs=0.01)
+    assert composite["costs_by_year"][2027] == pytest.approx(8_771_168.50, abs=0.01)
+    assert composite["costs_by_year"][2028] == pytest.approx(10_539_889.05, abs=0.01)
+    assert composite["cumulative_net_by_year"][2028] == pytest.approx(97_807_797.35, abs=0.01)
+
+
+def test_cross_foots(composite):
+    assert composite["npv"] == pytest.approx(
+        composite["benefits_pv"] - composite["costs_pv"], abs=0.01)
+    for y in YEARS:
+        assert composite["net_by_year"][y] == pytest.approx(
+            composite["benefits_by_year"][y] - composite["costs_by_year"][y], abs=0.01)
+    assert composite["cumulative_net_by_year"][2028] == pytest.approx(
+        sum(composite["net_by_year"].values()) - composite["initial_costs"], abs=0.01)
+    for table, total in (("benefits", "benefits_pv"), ("costs", "costs_pv")):
+        assert sum(r["pv"] for r in composite["rows"][table]) == pytest.approx(
+            composite[total], abs=0.01)

studies/202602_TEI_Amazon_Connect/tests/test_overlay.py

@@ -0,0 +1,96 @@
+"""Client-overlay pins — identity at the composite, linear per-driver
+scaling, growth re-basing, and copy semantics."""
+
+import dataclasses
+
+import pytest
+
+from teicalc import (
+    BENEFIT_DRIVERS,
+    BENEFITS_VERBATIM,
+    COMPOSITE,
+    COST_DRIVERS,
+    COSTS_VERBATIM,
+    ClientDrivers,
+    compute_summary,
+    growth_multiplier,
+    overlay_rows,
+    scale_factor,
+)
+
+
+def _row(rows, key):
+    return next(r for r in rows if r["field_key"] == key)
+
+
+def test_identity_at_composite():
+    """overlay_rows(COMPOSITE) reproduces the verbatim study to the cent."""
+    ob, oc = overlay_rows(COMPOSITE)
+    got = compute_summary(ob, oc, 0.10)
+    want = compute_summary(BENEFITS_VERBATIM, COSTS_VERBATIM, 0.10)
+    assert got["benefits_pv"] == pytest.approx(want["benefits_pv"], abs=0.01)
+    assert got["costs_pv"] == pytest.approx(want["costs_pv"], abs=0.01)
+    assert got["npv"] == pytest.approx(want["npv"], abs=0.01)
+
+
+def test_driver_map_covers_every_row():
+    assert set(BENEFIT_DRIVERS) == {r["field_key"] for r in BENEFITS_VERBATIM}
+    assert set(COST_DRIVERS) == {r["field_key"] for r in COSTS_VERBATIM}
+
+
+def test_scale_factor():
+    d = ClientDrivers(agents_fte=1_000, annual_contacts_y1=40_000_000)
+    assert scale_factor("agents", d) == pytest.approx(0.5)
+    assert scale_factor("contacts", d) == pytest.approx(2.0)
+    assert scale_factor("fixed", d) == 1.0
+    with pytest.raises(KeyError):
+        scale_factor("revenue", d)
+
+
+def test_half_agents_halves_agent_rows_only():
+    ob, oc = overlay_rows(ClientDrivers(agents_fte=1_000))
+    assert _row(ob, "ai_forecasting_supervision")["year_values"]["1"] == \
+        pytest.approx(6_651_680 / 2)
+    assert _row(ob, "legacy_solution_savings")["year_values"]["1"] == \
+        pytest.approx(6_177_600 / 2)
+    # Contact-driven and fixed rows unmoved.
+    assert _row(ob, "ai_contact_resolution")["year_values"]["1"] == \
+        pytest.approx(13_911_040)
+    assert _row(oc, "amazon_connect_usage")["year_values"]["1"] == \
+        pytest.approx(6_456_448)
+    assert _row(oc, "implementation_migration")["initial"] == 1_087_500
+
+
+def test_double_contacts_doubles_usage_only():
+    _, oc = overlay_rows(ClientDrivers(annual_contacts_y1=40_000_000))
+    assert _row(oc, "amazon_connect_usage")["year_values"]["1"] == \
+        pytest.approx(6_456_448 * 2)
+    assert _row(oc, "implementation_migration")["year_values"]["1"] == \
+        pytest.approx(188_333)
+    assert _row(oc, "ongoing_management")["year_values"]["1"] == \
+        pytest.approx(256_200)
+
+
+def test_growth_rebase():
+    assert growth_multiplier(1, 0.0) == 1.0                       # Y1 always 1.0
+    assert growth_multiplier(2, 0.0) == pytest.approx(1 / 1.3)
+    assert growth_multiplier(3, 0.0) == pytest.approx((1 / 1.3) ** 2)
+    assert growth_multiplier(3, 0.30) == 1.0                      # composite growth = identity
+
+    ob, oc = overlay_rows(ClientDrivers(growth_rate=0.0))
+    row = _row(ob, "ai_contact_resolution")
+    assert row["year_values"]["1"] == pytest.approx(13_911_040)
+    assert row["year_values"]["2"] == pytest.approx(23_932_480 / 1.3)
+    assert row["year_values"]["3"] == pytest.approx(37_797_760 / 1.3**2)
+    # Fixed rows ignore the growth re-base too.
+    assert _row(oc, "ongoing_management")["year_values"]["2"] == pytest.approx(187_200)
+
+
+def test_drivers_frozen_and_rows_are_copies():
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        COMPOSITE.agents_fte = 1  # type: ignore[misc]
+    ob, oc = overlay_rows(COMPOSITE)
+    ob[0]["year_values"]["1"] = -1
+    oc[0]["year_values"]["1"] = -1
+    assert BENEFITS_VERBATIM[0]["year_values"]["1"] == 13_911_040
+    assert COSTS_VERBATIM[0]["year_values"]["1"] == 6_456_448

studies/202602_TEI_Amazon_Connect/tests/test_scenarios.py

@@ -0,0 +1,75 @@
+"""Scenario pins — hand-checked composite results per scenario, clamp
+behaviour, and copy semantics."""
+
+import pytest
+
+from teicalc import (
+    BENEFITS_VERBATIM,
+    COSTS_VERBATIM,
+    SCENARIOS,
+    apply_scenario,
+    compute_summary,
+)
+
+
+def _summary(scenario):
+    return compute_summary(
+        apply_scenario(BENEFITS_VERBATIM, scenario),
+        apply_scenario(COSTS_VERBATIM, scenario),
+        0.10,
+    )
+
+
+def test_scenario_definitions():
+    assert SCENARIOS == {
+        "conservative": {"adoption": 0.80, "risk_delta": 0.10},
+        "moderate": {"adoption": 1.00, "risk_delta": 0.00},
+        "aggressive": {"adoption": 1.15, "risk_delta": -0.05},
+    }
+
+
+def test_moderate_is_identity():
+    got = _summary("moderate")
+    want = compute_summary(BENEFITS_VERBATIM, COSTS_VERBATIM, 0.10)
+    assert got["benefits_pv"] == pytest.approx(want["benefits_pv"], abs=0.01)
+    assert got["costs_pv"] == pytest.approx(want["costs_pv"], abs=0.01)
+
+
+def test_conservative_pins():
+    s = _summary("conservative")
+    assert s["benefits_pv"] == pytest.approx(71_672_867.65, abs=1)
+    assert s["costs_pv"] == pytest.approx(17_437_916.34, abs=1)
+    assert s["npv"] == pytest.approx(54_234_951.31, abs=1)
+    assert s["roi_pct"] == pytest.approx(311.02, abs=0.01)
+    assert s["payback_months"] == pytest.approx(0.763, abs=0.001)
+
+
+def test_aggressive_pins():
+    s = _summary("aggressive")
+    assert s["benefits_pv"] == pytest.approx(123_911_705.40, abs=1)
+    assert s["costs_pv"] == pytest.approx(27_682_368.61, abs=1)
+    assert s["npv"] == pytest.approx(96_229_336.79, abs=1)
+    assert s["roi_pct"] == pytest.approx(347.62, abs=0.01)
+    assert s["payback_months"] == pytest.approx(0.705, abs=0.001)
+
+
+def test_risk_delta_clamps_at_zero():
+    """Conservative subtracts 0.10 from cost risk; usage (0.05) clamps to 0."""
+    rows = apply_scenario(COSTS_VERBATIM, "conservative")
+    usage = next(r for r in rows if r["field_key"] == "amazon_connect_usage")
+    assert usage["risk_adjustment"] == 0.0
+    impl = next(r for r in rows if r["field_key"] == "implementation_migration")
+    assert impl["risk_adjustment"] == pytest.approx(0.0)          # 0.10 − 0.10
+    assert impl["initial"] == pytest.approx(1_087_500 * 0.80)     # adoption scales initial
+
+
+def test_unknown_scenario_raises():
+    with pytest.raises(KeyError):
+        apply_scenario(BENEFITS_VERBATIM, "wildly_optimistic")
+
+
+def test_inputs_not_mutated():
+    apply_scenario(BENEFITS_VERBATIM, "aggressive")
+    apply_scenario(COSTS_VERBATIM, "conservative")
+    assert BENEFITS_VERBATIM[0]["year_values"]["1"] == 13_911_040
+    assert COSTS_VERBATIM[1]["initial"] == 1_087_500

studies/202602_TEI_Amazon_Connect/tests/test_staging.py

@@ -0,0 +1,15 @@
+"""Stage/backstage detection — Mercury kernels carry MERCURY_CONFIG_DIR."""
+
+from teicalc import staging
+
+
+def test_backstage_prints_only_off_stage(monkeypatch, capsys):
+    monkeypatch.delenv("MERCURY_CONFIG_DIR", raising=False)
+    assert not staging.on_stage()
+    staging.backstage("visible")
+    assert capsys.readouterr().out == "visible\n"
+
+    monkeypatch.setenv("MERCURY_CONFIG_DIR", "/tmp/app")
+    assert staging.on_stage()
+    staging.backstage("hidden")
+    assert capsys.readouterr().out == ""