# Lifecycle-Aware Fee Optimization for `pump.fun`:
Revenue Optimization Through Cost Reallocation

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## Abstract
We propose a lifecycle modeling framework for `pump.fun` that
1. Segments tokens by market capitalization (MC) within each lifecycle phase — **Bonding Curve** (pre-graduation) and **PumpSwap** (post-graduation),
2. Measures the **total cost to traders** as the sum of protocol fee, creator fee, LP fee, and effective slippage, and
3. **Holds total cost per MC segment constant** while **reallocating the cost composition** to increase protocol revenue subject to guardrails on user, creator, and LP outcomes.

**Central thesis:**
**MC buckets with larger total cost provide more “wiggle room” to shift the cost pie toward protocol without harming user experience**, provided elasticity and leakage constraints are respected.

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## Motivation & Objectives
- **Business goal:** Maximize sustainable protocol revenue while preserving (or improving) user experience, creator supply, LP depth, and graduation dynamics.
- **Insight:** Traders primarily react to **total cost** of execution; they are less sensitive to the internal split across protocol/creator/LP/slippage if the **total** remains unchanged and UX is stable.
- **Approach:** Identify MC segments with high total cost, then **re-slice** that cost (hold total constant) to increase the protocol share where it is least likely to reduce volume.

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## Lifecycle Phases & Cost Components
**Phases:**
- **Bonding Curve (BC):** Tokens mint along a deterministic curve. Fees visible to traders: protocol fee $p$ and curve progression (perceived as slippage but not revenue).
- **PumpSwap (PS):** Post-graduation AMM trading. Fees/costs visible to traders: protocol fee $p$, LP fee $\ell$, creator fee $k$, and AMM slippage $\sigma$.

**Per-trade total cost (USD):**

$$
c_i = p_i + \ell_i + k_i + \sigma_i
$$

with

$$
\begin{cases}
\ell_i = 0,\; k_i = 0 & \text{in BC (pre-grad)} \\
\ell_i \ge 0,\; k_i \ge 0 & \text{in PS (post-grad)}
\end{cases}
$$

where $(p_i,\ell_i,k_i)$ are directly observed from columns (in USD), and $\sigma_i$ is an **effective slippage proxy** (see Data & Measurement).

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## Segmentation by Market Cap (MC)
- **Within Bonding Curve:** bucket trades by token's instantaneous MC percentile relative to the 69k graduation threshold (e.g., 0–25th, 25–50th, 50–75th, 75–100th of 69k).
- **Within PumpSwap:** bucket by post-graduation MC percentiles (e.g., quartiles of observed post-grad MC distribution).
- Tokens contribute to the MC bin corresponding to their **trade-time** \(MC\).

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## Data
**Minimum required fields:**
- `project` ∈ {`bonding_curve`, `pump_swap`}
- `mint_address` (token id), `trade_time`
- `amount_usd` (notional), `market_cap`
- `protocol_fee_usd`, `lp_fee_usd`, `creator_fee_usd`
- Optional price signals: `price_usd`, `price_base_per_quote`

**Effective slippage proxy per trade \(i\):**

$$
\sigma_i \approx (\text{execution price}_i - \text{reference price}_i) \times \text{qty}_i
$$

where reference price may be last-trade price, a short lookback mid-price, or quoted price (if available).
- In BC: $\sigma_i$ captures **curve progression** between quote and execution.
- In PS: $\sigma_i$ captures **AMM price impact & timing**.
- If unavailable, set $\sigma_i = 0$ and report separately (conservative).

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## Aggregation within MC Bins
For bucket $b$ (defined by phase $s \in \{\text{BC}, \text{PS}\}$ and MC range:

$$
C_b \equiv \sum_{i\in b} c_i = P_b + L_b + K_b + \Sigma_b
$$

with

$$
P_b = \sum p_i,\;\; L_b = \sum \ell_i,\;\; K_b = \sum k_i,\;\; \Sigma_b = \sum \sigma_i
$$

and

$$
V_b \equiv \sum_{i\in b} \text{amount_usd}_i
$$

**Cost density (bps):**

$$
\Gamma_b \equiv 10^4 \cdot \frac{C_b}{V_b}
$$

**Interpretation:**
- $C_b$: total cost paid by traders in bin $b$.
- $\Gamma_b$: highlights bins where traders bear the largest effective cost per \$ traded.

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## Optimization Principle (Hold Total Cost, Re-Slice Pie)
**Key constraint (per MC bin):**

$$
\boxed{C_b' = C_b}
$$

but reallocate its composition:

$$
C_b' = P_b' + L_b' + K_b' + \Sigma_b'
$$

**Objective (first-order):**

$$
\max \sum_{b} P_b' \quad
\text{s.t.} \quad C_b' = C_b,\;\; \text{guardrails in each } b
$$

**Guardrails (per bin):**
- **User experience (volume/leakage):** predicted volume change $\Delta V_b \ge -\delta_b$; routing leakage ≤ $\lambda_b$.
- **Creators:** maintain creator share floor $K_b' \ge \underline{K}_b$.
- **LPs (PS only):** preserve LP APR floor/depth $L_b' \ge \underline{L}_b$.
- **Slippage:** $\Sigma_b'$ may decline via depth incentives; if large, creates **headroom** to raise $P_b'$.

**Highlighted main point:**
**MC buckets with larger $C_b$ (and higher $\Gamma_b$) provide more “wiggle room” to increase $P_b'$** because traders already tolerate higher total cost there.

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## Decision Logic by Phase
**Bonding Curve (BC):**
- $C_b = P_b + \Sigma_b$ (creator, LP fees = 0).
- If $\Sigma_b$ consistently high → increase $P_b'$ modestly while keeping $C_b' = C_b$.
- Messaging levers: micro-rebates for small orders, step-fee by trade size.

**PumpSwap (PS):**
- $C_b = P_b + L_b + K_b + \Sigma_b$.
- If $L_b$ dominates: shift slightly from $L_b \downarrow$ to $P_b \uparrow$.
- If $\Sigma_b$ dominates: reduce $\Sigma_b$ first, then raise $P_b$.
- Creator floor: taper $K_b$ with rising MC (early payoff, taper later).

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## Calculations & Outputs
1. **Baseline dashboards (per phase):**
- Stacked bars by MC bins: $P_b, L_b, K_b, \Sigma_b$.
- Overlay trade count or $V_b$.
- Cost density $\Gamma_b$ heatmap.

2. **Bin selection filters:**
- High $C_b$ and $\Gamma_b$.
- Favorable composition (adjustable $(L_b, K_b)$.
- Low elasticity/leakage risk.

3. **Counterfactual re-slicing:**
- Hold $C_b' = C_b$.
- Shift 5–15 bps from $L_b$ or $K_b$ to $P_b$.
- Reduce $\Sigma_b$ via LP incentives, allocate savings to $P_b$.

4. **Experiment design:**
- Cohort A/B by creation week within MC bins.
- SLA: daily refresh, 2–4 week readouts, kill-switch if guardrails breached.

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## Elasticity of Cost Composition (Laffer Curve)
Total cost in MC bin \(b\):

$$
C_b = P_b + L_b + K_b + \Sigma_b
$$

Constraint:

$$
C_b' = C_b
$$

**Component Elasticities:**

$$
$\eta^{(L)}_b = \frac{\Delta V_b / V_b}{\Delta L_b / L_b}, \quad
\eta^{(K)}_b = \frac{\Delta V_b / V_b}{\Delta K_b / K_b}, \quad
\eta^{(\Sigma)}_b = \frac{\Delta V_b / V_b}{\Delta \Sigma_b / \Sigma_b}
$$

- $\eta^{(L)}_b$: sensitivity of volume to LP revenue.
- $\eta^{(K)}_b$: sensitivity to creator rewards.
- $\eta^{(\Sigma)}_b$: sensitivity to slippage.

**Optimization View:**

$$
\max \sum_b P_b' \quad
\text{s.t.} \quad C_b' = C_b,\;\; \frac{\Delta V_b}{V_b} \geq -\delta_b
$$

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## Risks & Mitigations
- **LP flight risk (PS):** enforce APR floors; rollback if TVL declines.
- **Creator supply risk (BC/PS):** maintain creator share minimum; front-load payouts.
- **Slippage rebound:** if reducing $L_b$ increases $\Sigma_b$, net UX worsens.
- **Heterogeneous traders:** segment by trade size; protect small retail.

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## Deliverables
- Baseline lifecycle cost dashboards with $P,L,K,\Sigma$ and $\Gamma_b$.
- Opportunity shortlist: MC bins ranked by $C_b,\Gamma_b$, low risk.
- Counterfactual playbook: per-bin scenarios with $C_b'=C_b$.
- Experiment checklist: cohort selection, metrics, SLA, thresholds.

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## Summary (What We Will Prove/Disprove)
- **MC bins with larger $C_b$ (and higher $\Gamma_b$) allow more room to increase protocol share $P_b'$** while holding trader experience constant.
- **Re-slicing is phase-specific:**
- In BC: tradeoff is protocol vs curve tolerance.
- In PS: tradeoff is LP/creator splits and slippage reduction.
- With guardrails, **protocol revenue can increase** without harming volume, graduation, LP TVL/APR, or creator launches.

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