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Fee curve: effective base-fee floor is max(minBaseFee, 10000/kRate); testnet ran 6M blocks at 7 wei against a declared floor of 1 #367
Description
Disclosure: I'm an external community contributor not affiliated with Circle, with no write access to this repository. This is advisory only. Everything below is reproducible — the model is the repo's own code compiled standalone, and the chain data is from the public testnet RPC.
Follow-on from #366, looking at the fee curve rather than the genesis file. Severity is low and I want to be upfront about that: I found nothing that affects mainnet as currently configured. Two things seem worth recording before launch anyway — one is a correction to a wrong impression the repo currently gives, the other is a documented-behaviour gap that has already produced a surprising result on testnet.
Method
I extracted arc_calc_next_block_base_fee and determine_ema_parent_gas_used verbatim from crates/execution-config/src/gas_fee.rs, compiled them standalone (rustc --edition 2021 -O), and checked the extraction against this crate's own test vectors before drawing any conclusion from it — 9 fee vectors from base_fee_should_greater_than_zero plus 6 EMA vectors from determine_ema_parent_gas_used_table, all passing. Chain data is from https://rpc.testnet.arc.io.
1. The committed testnet config no longer describes testnet
assets/testnet/config.json declares kRate: 25, minBaseFee: 1, maxBaseFee: 1000. Live ProtocolConfig.feeParams() on testnet returns:
alpha 20 kRate 200 inverseElasticityMultiplier 5000
minBaseFee 20000000000 maxBaseFee 20000000000000 blockGasLimit 30000000
That is exactly the mainnet parameter set from assets/mainnet/config.json. I mention it because I initially assumed from the committed files that mainnet would launch on a curve testnet had never run, and that assumption was wrong — testnet has been running the mainnet parameters for most of its history. Anyone auditing from the repo alone will form the same wrong impression, so a note that testnet's committed genesis is historical rather than current would help.
However, the parameters being live is not the same as the curve being exercised. Sampling 300 consecutive recent blocks: base fee is 20000000000 in every one of them, mean gasUsed is 2,070,231 (13.8% of the 15M target), max is 12,460,783 (83.1%), and zero blocks exceeded the gas target. Across a wider historical sample I also found no block above target. So the base fee has been pinned to minBaseFee and the upward branch of the curve has no production evidence behind it. Worth knowing when sizing mainnet launch expectations.
For reference, with mainnet's kRate: 200 the response is ±2.000% per block against ±12.500% for EIP-1559 — but at a 500ms target block time that is ~4.04%/s versus Ethereum's ~0.99%/s, so it is roughly 4× faster in wall-clock terms. Under sustained full blocks (EMA alpha: 20 included) the fee traverses the whole 20 gwei → 20000 gwei clamp range in 353 blocks ≈ 2.9 minutes, and decays back in 346 blocks. Both directions verified against the extracted implementation.
2. The effective fee floor is max(minBaseFee, 10000/kRate), not minBaseFee
The increase branch guarantees movement via max(1, increase). The decrease branch has no equivalent, so once base_fee * (gas_target - gas_used) / denominator truncates to zero the fee stops falling. I can see from base_fee_should_greater_than_zero and the "We add a lower bound to make sure it will not be zero" comment that the asymmetry is deliberate — the intent is that the fee never reaches 0 — so I am not suggesting a change to the arithmetic. The part I think is worth surfacing is that the resulting resting value is 10000/kRate, which is a function of kRate and bears no relation to the minBaseFee an operator actually declared.
This is not theoretical. Early testnet ran kRate: 1250 (a clean 12.5%/block decay off 1 gwei) with minBaseFee: 1. Replaying empty blocks through the extracted function reproduces the live chain exactly:
| block | observed on-chain | model | |
|---|---|---|---|
| 1 | 875000000 | 875000000 | match |
| 2 | 765625000 | 765625000 | match |
| 5 | 512908936 | 512908936 | match |
| 10 | 263075578 | 263075578 | match |
| 100 | 1592 | 1592 | match |
| 1000 | 7 | 7 | match |
The chain then sat at 7 wei from block ~1,000 to block ~6,000,000 — roughly 35 days at 500ms blocks — against a declared minBaseFee of 1. Predicted fixed point for kRate: 1250 is 10000/1250 = 8, i.e. the fee stalls below 8, so 7 is exactly where it should stop. Running a further 1,000,000 empty blocks through the model leaves it at 7.
Mainnet is not exposed to this. kRate: 200 puts the fixed point at 50 wei while minBaseFee is 20 gwei — a factor of 4×10⁸ of headroom, so the clamp floor dominates and the truncation point is unreachable. I checked specifically because I wanted to know whether this mattered for launch, and it does not.
What is missing is any guard tying the two together. ProtocolConfig validates alpha <= 100, kRate <= 10000, minBaseFee <= maxBaseFee, blockGasLimit > 0 — nothing relates minBaseFee to kRate. Since ProtocolConfig.controller can update feeParams post-genesis, a future change that lowers minBaseFee below 10000/kRate, or lowers kRate substantially (at kRate: 1 the fixed point is 10,000 wei), would silently produce an effective floor above the declared one — which is precisely what already happened on testnet without anyone apparently noticing.
Suggestions
Both are cheap and neither touches consensus-critical arithmetic:
- Document the effective floor as
max(minBaseFee, 10000/kRate)next to thefeeParamsdefinition, so the interaction is discoverable. - Consider a
requireinProtocolConfigthatminBaseFee * kRate >= 10000, so a declared floor is always actually reachable. This would have flagged the early testnet configuration at the point it was set.
Happy to open a PR for either, or for a test case pinning the fixed-point behaviour so it is at least intentional and covered rather than emergent. Also glad to be told this is known and deliberate, in which case item 1 alone would still help external readers.
Reproduction for the replay above, in case it is useful:
cast call 0x3600000000000000000000000000000000000001 \
"feeParams()(uint256,uint256,uint256,uint256,uint256,uint256)" \
--rpc-url https://rpc.testnet.arc.io
Activity
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kutluhaneth46 commentedon Sep 9, 2026
I'll take the low-risk half of this: document the effective floor
max(minBaseFee, 10000/kRate)next to the fee-params guidance, and pin the empty-block fixed-point behavior with a unit test. Leaving the hardProtocolConfigrequire alone for now so historical testnet genesis (kRate: 25,minBaseFee: 1) still regenerates.osr21 commentedon Sep 9, 2026
That split sounds right to me, and I want to flag one thing in my own report before you write the test, because it would get frozen in.
Your call on the
requireis correct, and here's the numberrequire(minBaseFee * kRate >= 10000)would reject the historical testnet genesis outright:1 * 25 = 25, well under 10000. So regeneration would break exactly as you say. Worth noting the same trap sits in the neighbouring schema work — a constraint that looks obviously safe can reject Circle's own committed config, so validating against every config inassets/before adding one is the cheap check.Correction: the resting value is
ceil(10000/kRate) - 1, not10000/kRateThe formula in my issue title is loose, and my body contradicts it — the body says "the fee stalls below 8, so 7 is exactly where it should stop", which is the accurate version.
10000/kRateis the threshold at which the decrease truncates to zero; the fee comes to rest one wei below it.The live chain is the proof: early testnet ran
kRate: 1250, where10000/1250 = 8, and it sat at 7 wei for ~6M blocks. A doc line or test asserting a floor of10000/kRatewould be off by one against the chain's own history. For mainnet'skRate: 200the resting value is 49, not the 50 I wrote.Derivation, for the record: with
gas_used = 0,decrease = base_fee * gas_target / floor(gas_target * 10000 / kRate), which is zero exactly whenbase_fee * kRate < 10000.One caveat on that formula's domain
ceil(10000/kRate) - 1is exact for realistic gas targets, but it is not universal — thefloor()in the denominator costs another wei whengas_targetis small relative tokRate. Checked acrossgas_limit ∈ {3, 10_000, 300_000, 30_000_000, 1_000_000_000}×inverseElasticityMultiplier ∈ {2500, 5000, 7500, 10000}:ceil(10000/k)-1Every deviation is at a degenerate
gas_target(e.g.gas_limit: 3). At any production-scale limit the closed form holds. So the doc line is safe if it's stated for the real parameter domain, but a test shouldn't hardcode the constant without pinning the whole(kRate, gas_limit, iem)triple.Suggested shape for the test
Asserting the property rather than a magic number survives a parameter change:
arc_calc_next_block_base_fee(0, limit, b, k, iem) == bforbat and below the resting valuebforbone above itkRate: 1250, gas_limit: 30_000_000, iem: 5000—8 → 7,7 → 7A boundary case worth including: at
kRate: 10000, the maximumProtocolConfigpermits,denominator == gas_target, sodecrease == base_feeand a single empty block takes the computed fee to 0. The output clamp (base_fee.clamp(absolute_min_base_fee, absolute_max_base_fee),chainspec.rs:250/consensus.rs:209) then lifts it tominBaseFee, so the truncation floor disappears entirely at that end of the range. That is consistent withmax(minBaseFee, ceil(10000/k)-1)since the second term is 0, and it's the cleanest demonstration that the two floors interact.If you pin chain behaviour rather than the pure function
The pipeline feeds
determine_ema_parent_gas_usedoutput in asgas_used, not the raw block value. Withalpha: 20the smoothed value takes 72 empty blocks to truncate to 0 from a 22.5M target (70 from 15M), and until it does the decrease is smaller than thegas_used = 0case. A unit test calling the function directly withgas_used = 0is simpler and fine — just worth being explicit about which of the two you're pinning, since the descent rates differ.Provenance of these numbers
Same standalone extraction as the original report, re-validated: brute-forcing
kRate ∈ [1, 10000] × iem ∈ {2500, 5000, 7500, 10000}against the committedtest_calc_next_block_base_feetable returns a unique match at(200, 7500)— i.e.ARC_BASE_FEE_K_RATEandARC_BASE_FEE_INVERSE_ELASTICITY_MULTIPLIER. So the model reproduces the repo's own vectors before being used for anything above.Disclosure: I'm an external community contributor, not affiliated with Circle, with no write access to this repository. Advisory only — everything above is reproducible from the repo's own code and the public testnet RPC, and should be confirmed independently.
docs(fee): correct resting floor to ceil(10000/kRate)-1
kutluhaneth46 commentedon Sep 9, 2026
Thanks @osr21 — incorporated the `ceil(10000/kRate) - 1` correction into #372 (ADR wording + boundary test vectors). Still leaving the hard `ProtocolConfig` require alone so historical testnet genesis regenerates.
osr21 commentedon Sep 9, 2026
Thanks for landing that in #372 — I reviewed the PR separately. Before it merges, I have to correct myself again, and this one is worse than the last: the historical example in this issue is attributed to the wrong algorithm, and I'm the one who put it there.
I finally queried
ProtocolConfig.feeParams()at historical blocks instead of inferring the parameters from the observed fee.What the chain actually stored
eth_callto0x3600...0001(selector0x9242164f) againstrpc.testnet.arc.io, decoded as the 6-word staticFeeParamstuple:The stored
kRateduring the 7-wei era was 25, not the 1250 I inferred in this issue. Under the Arc curve,kRate = 25rests at 399, not 7. The decode is sound: 192 bytes, no ABI offset, andalpha = 20/maxBaseFee = 1000/blockGasLimit = 30000000all matchassets/testnet/config.jsonexactly.Which curve produced the 7
The 7 wei itself is real — I re-confirmed
baseFeePerGas = 7at blocks 1,000 / 100,000 / 1,000,000 / 3,000,000 / 6,000,000, all withgasUsed = 0andminBaseFee = 1. But simulating both candidate algorithms forward from the block-1 fee of 875,000,000 settles which one produced it:/8/40012/12 exact wei-level matches for EIP-1559, 0/12 for the Arc curve. Early testnet ran plain EIP-1559 — elasticity multiplier 2, change denominator 8 — and the stored
kRate = 25had no effect on the fee at all. Theiem = 2is literally the EIP-1559 elasticity multiplier; it was later redefined as basis points, where5000expresses the same 50% target. That also explains the discrepancy I flagged on #372:assets/testnet/config.jsonreads5000because the field's units changed, not because the target did.The switch to the Arc curve is a single block:
kRate 25 → 200,iem 2 → 5000at 21,659,090.What this means for #372
minBaseFeeof 1" is true, but it demonstrates EIP-1559's truncation floor. Citing it under "Effective base-fee floor vsminBaseFee" attributes it to a curve that wasn't running yet.matching early testnet. The arithmetic is untouched —kRate = 1250genuinely rests at 7 — but testnet never ran 1250. 1250 is the Arc-equivalent of EIP-1559's/8, which is precisely why back-inferring it from the observed 7 reproduced the number and why it looked like confirmation. It was circular, and that's my error, not yours.kRate = 200(resting 49) againstminBaseFeeof 160 then 20 gwei. So this issue is a forward-looking governance risk with no production precedent — still worth an ADR note, but it shouldn't read as something that has already bitten.The underlying defect is unaffected: the decrease path still truncates with no
max(1, …)counterpart, andeffective_floor = max(minBaseFee, ceil(10000/kRate) - 1)is still the right closed form. Only the worked example was wrong.On leaving the
ProtocolConfigrequire aloneYour reasoning holds, and it's stronger than you stated:
>= 10000assets/testnet/config.jsonassets/devnet/config.jsonassets/mainnet/config.jsonIt breaks devnet too, not just historical testnet. And the testnet genesis isn't a stale artifact worth little: the hash pinned in
chainspec.rs(0xe20e653a…) is byte-identical to live testnet block 0, which I checked directly. Breaking regeneration would break reproduction of the real chain's genesis, and the pinned-hash test would catch it immediately.Two notes if maintainers do want the guard on
updateFeeParamsonly:minBaseFee * kRate >= 10000impliesminBaseFee >= ceil(10000/kRate), i.e.resting + 1, so it rejectsminBaseFee == resting— a harmless config where the fee rests exactly at the floor and the clamp is a no-op. The tight condition isminBaseFee >= ceil(10000/kRate) - 1.updateFeeParams-era transition (block 21,659,090) moved tokRate = 200whileminBaseFeewas already 160 gwei — which the guard would have passed. A guard onupdateFeeParamsalone would not have prevented the situation this issue describes.For the record,
updateFeeParamstoday enforcesalpha <= 100,kRate <= 10000,minBaseFee <= maxBaseFee,blockGasLimit > 0,inverseElasticityMultiplier <= 10000— no coupling between any two of them.Disclosure: I'm an external community contributor, not affiliated with Circle, with no write access to this repository. Advisory only. All figures above are from public RPC against
rpc.testnet.arc.ioon 2026-09-10 and are reproducible with the selector and block numbers given.huklaa commentedon Sep 10, 2026
Hi, I would like to work on this issue. Could you assign it to me?
kutluhaneth46 commentedon Sep 10, 2026
Thanks @osr21 for the historical-block
feeParams()correction — incorporated into #372. The ADR no longer attributes the early-testnet 7 wei floor to the Arc curve.docs(fee): document effective base-fee floor vs minBaseFee
docs(fee): correct resting floor to ceil(10000/kRate)-1
kutluhaneth46 commentedon Sep 10, 2026
@huklaa Already covered by open PR #372 (ADR + unit test for the effective floor). Please review or comment there instead of opening a parallel PR.
docs(fee): document effective base-fee floor vs minBaseFee
docs(fee): correct resting floor to ceil(10000/kRate)-1
kutluhaneth46 commentedon Sep 28, 2026
@ZhiyuCircle requesting assignment — linked PR is already open, CI-green, and mergeable. Per CONTRIBUTING the only remaining gate is assignment; happy to rebase or adjust scope once assigned.
osr21 commentedon Oct 8, 2026
@lamkyo The requested function is already in crates/execution-config/src/gas_fee.rs, and #372 is already the open PR for the documentation and fixed-point test.
One important correction: early testnet’s 7-wei floor came from plain EIP-1559, with stored kRate = 25 and iem = 2; the Arc curve began at block 21,659,090 with kRate = 200 and iem = 5000 (historical correction). The 7-wei period is not evidence that the Arc curve ran with kRate = 1250.
For production-scale gas targets, the Arc decrease branch rests at ceil(10000/kRate) - 1, with a small-target rounding caveat—not 10000/kRate. PR #372 already documents this corrected formula, though its description still contains the older summary and should be reconciled. The latest comment includes no patch or reproducible test output, so its “10/10 invariants” claim can’t be independently checked. Please link any remaining change to #372 and include the exact test command and output.