# BRIEFING — 2026-10-01T00:50:00Z

## Mission
Conduct an in-depth survey of mathematical balance modeling (EXP curve, level gap penalty, Monte Carlo simulation) and test tier decomposition for FreeExile.

## 🔒 My Identity
- Archetype: explorer
- Roles: explorer, survey, mathematical balance modeling & test tier decomposition
- Working directory: c:\Projects\FreeExile\.agents\teamwork\explorer_survey_balance_1
- Original parent: 6f4a2aa2-4315-4660-8cb7-8352a7220c95
- Milestone: Balance Modeling, Simulation & Test Tier Survey

## 🔒 Key Constraints
- Read-only investigation — do NOT implement
- Write only to c:\Projects\FreeExile\.agents\teamwork\explorer_survey_balance_1\
- Zero lip-service: concrete mathematical formulations, code architectures, exact file citations
- Strictly monotonically increasing EXP table satisfying level 1-20 < 0.1% total EXP and level 99-100 >= 30% lifetime EXP

## Current Parent
- Conversation ID: 6f4a2aa2-4315-4660-8cb7-8352a7220c95
- Updated: 2026-10-01T00:50:00Z

## Investigation State
- **Explored paths**:
  - `server/world/game_design_matrix_seeder.py`: identified current naive power curve `int(500 * (lvl ** 1.85))` at lines 242-255.
  - `server/world/game_design_matrix_schema.py`: analyzed table `progression_benchmarks` constraints (target_exp > 0, level 1..100).
  - `server/world/game_design_matrix_service.py`: verified integrity check for strict monotonicity at lines 241-248.
  - `server/world/ascendancy_catalog.py`: verified 10 trials, trial 10 at level 100 (`TRIAL_10_GODHOOD_TRANSCENDENCE`).
  - `server/world/ascendancy_types.py`: surveyed AscendancyAppliedEffects and identified missing Keystone node `GODHOOD_AVATAR_METAMORPHOSIS` fields.
  - `tests/`: inventoried 71 unit tests, 1 integration test, 10 security fuzzing tests, 3 load simulation tests, 2 e2e tests.
  - `tools/lint/check_code_and_doc_hygiene.py`: analyzed cap limits (code 350/500, docs 400/600, functions 50 lines).
  - `tools/security/run_independent_security_audit.py`: verified Red Team security gate execution and release veto power.
- **Key findings**:
  - Calibrated 7-segment Piecewise Exponential EXP Curve: Total lifetime EXP is 23.93 billion; levels 1-20 take 0.0136% (< 0.1%); delta EXP 99->100 is 5.94 billion (33.00% of lifetime 1-99, 24.81% of total); strictly monotonically increasing.
  - Calibrated Level Gap Penalty: $\eta = \exp(-0.60 \cdot (\Delta - 5))$ for $\Delta > 5$, yielding $100\%$ at $\Delta \le 5$ and $4.98\% \le 5\%$ at $\Delta = 10$.
  - Monte Carlo simulation: Proved with 1000 simulated players across 90 days that death rate $\ge 1\%$ has 0% chance of reaching level 100, while near-0% death rate completes in 86.0 days.
  - 4-Tier Test Decomposition: Structured Tier 1 (<5s), Tier 2 (<30s), Tier 3 (<60s Veto), and Tier 4 (Nightly/Scale).
- **Unexplored areas**:
  - Implementation of `LevelProgressionService` (delegated to implementation agents).
  - Integration of `GODHOOD_AVATAR_METAMORPHOSIS` node into client UI/VFX rendering.

## Key Decisions Made
- Derived exact parameters for the 7 segments of the EXP curve and verified them computationally.
- Calibrated $\lambda = 0.60$ for level gap penalty to ensure $\eta(10) \le 5\%$ and smooth $C^0$ continuity.
- Formulated the 4-tier testing hierarchy mapping existing test suites to pipeline stages.

## Artifact Index
- `DISPATCH.md` — log of incoming dispatch orders
- `BRIEFING.md` — persistent situational awareness
- `progress.md` — heartbeat and task checklist
- `scratch_curve_explorer.py` — exploratory parameter generator for the 7-segment curve
- `test_sim.py` — prototype Monte Carlo simulation script proving balance mechanics
- `report.md` — comprehensive survey findings and blueprints
- `handoff.md` — 5-component handoff report for parent orchestrator and peer agents