Build the complete application

## User
A private-company valuation specialist reviewing allocation mechanics.

## Build
Allocate a supplied total equity value across share classes using documented option-pricing breakpoints. Expose volatility, timing, rights, and numerical sensitivities for professional review.

## Input Contract
- Key: cap_table_version + breakpoint + scenario_id.
- Fields: total_equity, strike_breakpoint, time_years, volatility, risk_free_rate, tranche_allocation.
- Breakpoints derive from approved rights. Use a declared continuous-rate convention in the pricing implementation.

## Workflow
1. Derive and review the breakpoint schedule.
2. Price equity tranches with a tested numerical library.
3. Allocate tranches according to documented participation rights.
4. Export class values, sensitivities, and reconciliation tests.

## Interface
A breakpoint diagram, class-allocation matrix, sensitivity charts, and solver diagnostics.

## Deliverables
- An option-pricing allocation engine with independent numerical comparisons.
- An allocation report linking each breakpoint to share rights.
- Runnable local application, setup commands, and a dependency lockfile.
- Versioned input data, data dictionary, acquisition instructions, and rights notes.
- Calculation traces, source references, assumption records, and exported review artifacts.
- A deterministic baseline and tests for normal, incomplete, contradictory, and failure-recovery cases.
- A recorded complete workflow with a reproducible manifest and explicit limitations.

## Acceptance Criteria
- Class values sum to total equity within 1e-6 of total value.
- Call values decline with increasing strike under the same assumptions.
- Handle zero-time and zero-volatility limits explicitly.
- Do not treat a successful numerical calculation as proof of model appropriateness.

## Contrast Case
A higher supplied breakpoint-call value changes tranche allocations while total equity remains conserved.

## Dataset Scope
The attached starter files are prototype inputs. Expected starter answers are visible. They are not independent holdouts.

Full target: Use fictional capitalization structures with explicit breakpoints, time horizons, volatility, rates, and total equity values. Document every modeling assumption.

Complete target contracts and expert review remain pending. Public observations are not historical release vintages.

## Tools
SciPy, NumPy, Plotly

Use an available model appropriate to the task. Record provider, model identifier, version or retrieval date, settings, cost, and latency. Use deterministic code for calculations. Models may extract, retrieve, or explain evidence. They must not invent missing records, override approval rules, or claim professional authority.

## Constraints
The fixture verifies supplied tranche arithmetic, not the full option-pricing model or an appraisal conclusion.

- No fabricated records, source citations, professional endorsements, or expert-adjudication claims.
- No future-data leakage into dated decisions, model fitting, or historical valuation inputs.
- No unauthorized payments, account restrictions, regulatory filings, or production changes.
- No automated appraisal certification, tax-compliance determination, or unsupported fraud accusation.
- No concealed uncertainty or silently invented inputs required for a numerical conclusion.

## Scoring
- Correct domain calculations and justified methods with documented assumptions. Weight: 30.
- Source lineage, temporal integrity, rights checks, and explicit synthetic-data labels. Weight: 25.
- A working application with review, export, error handling, and reproducible state. Weight: 20.
- Adversarial cases, uncertainty, missing-data behavior, and sensitivity analysis. Weight: 15.
- Evidence-linked conclusions that distinguish facts, assumptions, and unresolved judgments. Weight: 10.
Score each dimension from zero to two. Weighted score = sum(weight * score / 2). A failed safety gate blocks acceptance.