The mempool-admission rules being layered onto frame transactions share a single implicit classifier: whether a validity check reads order-dependent state. This note names that classifier, grounds it in the CALM theorem and the Herlihy consensus hierarchy, and derives the irreducible core it implies.
1. Problem
A node currently establishes a transaction’s validity by executing it. In a public mempool this cost is asymmetric: admission-time evaluation is unpaid, and under account abstraction (EIP-8141) the validation code is arbitrary, so a cheap-to-send transaction can impose unbounded validation work on every node that considers it. The mechanisms in Table 1 each exist to bound that unpaid work.
2. Five mechanisms, one dimension
Three contention classes are used throughout and derived formally in sections 3 and 4; they are stated here so Table 1 reads cleanly.
- Class 0, single-writer: only the sender can change it (nonce, own balance-debit).
- Class 1, recent-root-bound: a shared value read against a saved root, where a stale value is acceptable (keystore authority).
- Class 2, live-contended: many writers within the block, the live value is required (AMM price, a first-come slot).
Classes 0 and 2 restate the standard single-writer versus shared split (for example Sui’s owned and shared objects); class 1 is the recent-root tier that split lacks, provided by EIP-8272. Framing it as a distinct class is this note’s contribution.
Table 1.
| Mechanism | What it bounds | Reading under contention |
|---|---|---|
| MAX_VERIFY_GAS (EIP-8141) | work a VERIFY prefix may do | admit only class 0 to 1 |
| VOPS profiles (EIP-8369) | which txs are cheap to FOCIL-enforce (EIP-7805) | VOPS-eligible = class 0 |
| recent roots (EIP-8272) | check against a saved root, not live state | the class-1 discharge |
| 2D gas (EIP-8037) | prices state access as a dimension | true split is contended versus not |
| validity proofs (ethereum/EIPs#12075) | verify a STARK instead of running the prefix | sender-local = class 0 only |
Read together, these are not five independent rules but five thresholds on one dimension.
3. Formal basis
The dimension behind those thresholds can be made precise. A read is order-independent within a block if and only if it commutes with the block’s other transactions, so order-independence coincides with commutativity (Shapiro et al., 2011). A sender’s own nonce commutes, being single-writer; a shared AMM price does not, since its value depends on which swap is ordered first. By the CALM theorem a computation admits a coordination-free implementation if and only if it is monotone (Hellerstein and Alvaro, 2019; proved by Ameloot, Neven and Van den Bussche, 2013), so order-free validity is exactly the monotone, commutative fragment. The “sender-local” restriction of the Transaction Validity Proofs draft (Harvey-Hill) is the common single-writer case of that fragment.
4. The classifying dimension
The classifying dimension is therefore order-dependence, not the volume of state read. Volume misranks these cases: a single-writer datum stays cheap to check however often it is rewritten, while a single contended slot is expensive, the same nonce-versus-price contrast of section 3 read off the correct dimension. Indexed by contention, the mechanisms of Table 1 collapse to thresholds on classes {0: single-writer, 1: recent-root-bound and stale-acceptable, 2: live-contended}.
5. The irreducible floor
This reduction has a floor. An assertion of the form “this nullifier is unspent” or “this slot is free” is anti-monotone, since a concurrent transaction can falsify it, so no proof against a past root settles it. By CALM such an assertion requires coordination; by the Herlihy hierarchy a consume-once object has consensus number at least two, hence is itself a consensus primitive and cannot be built from coordination-free registers. The irreducible, sequenced core of any ledger is thus exactly its exactly-once assertions; every other validity check can in principle be order-free, proof-carried admission.
6. Relation to prior work
This reframing rests on existing work, which the note credits explicitly. The distinction between cheap- and expensive-to-enforce validity, and the sender-local storage restriction of Profile 2, are due to EIP-8369 (Thiery) and are not claimed here. Relative to it, this note contributes three things: it identifies the dimension behind that boundary (order-dependence) and grounds it in existing theory (CALM; Herlihy; Shapiro et al.); it argues the correct ruler is contention, not state-volume, since a single-writer datum is cheap regardless of how often it is written; and it states the floor, exactly-once, that no admission scheme can cross. Prior systems use contention only for execution scheduling and fees, for instance Sui’s owned and shared split, Solana’s account model, and Block-STM, not for validity or admission; the middle class (a contended object read against a recent root, stale-acceptable) has no analogue in Sui’s binary split and is exactly what EIP-8272 already provides.
7. Conclusions
Order-dependence, not the volume of state a check reads, is the property that decides whether a validity check can be settled without a total order; a single-writer datum is cheap however often it is written, and a contended one is not. This both unifies the existing admission mechanisms as thresholds on one dimension and fixes their limit: proof-carrying admission can in principle cover the entire commutative fragment, while the exactly-once core is irreducibly sequenced and no admission scheme can cross it.