Empirical Study: bank/multi-send Gas Surcharge in Gaia v27.0.0

TL;DR We ran 5 real transactions on the `provider` testnet to empirically verify the `multi-send` gas surcharge introduced in Gaia v27.0.0 (PR #3961 ). We confirmed the quadratic curve and found an additional linear component of ~8,628 gas per recipient from SDK store I/O. Complete empirical formula: `gas_total ≈ 95,302 + 8,628 × n + 300 × n²` Background Gaia v27.0.0 introduced a quadratic gas surcharge on `MsgMultiSend` to mitigate spam: ``` gas_surcharge = 300 × n² ``` We wanted to verify this in practice, so during Testnet Tuesday (March 2026) we ran transactions with 1, 10, 20, 49, and 100 recipients on the `provider` testnet, recording the actual `gas_used` from the public REST API. Results n | gas_used (real) | Theoretical 300n² | Ratio | 1 (base) | 103,963 | - | - | 10 | 211,587 | 30,000 | 3.59x | 20 | 387,909 | 120,000 | 2.37x | 49 | 1,238,130 | 720,300 | 1.57x | 100 | 3,958,152 | 3,000,000 | 1.28x | The ratio converges toward 1x as n grows, confirming the quadratic term dominates at scale. Key Finding Beyond the documented `300 × n²` surcharge, there is a…

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