Mempool

The mempool is local, non-consensus state. It is a node’s current set of unconfirmed transactions that the node is willing to keep, relay, and consider for block-template construction. A transaction can be valid in a block and absent from a node’s mempool.

Let $U$ be the active UTXO set. A mempool is:

$$ Q = (M,G,I), $$

where $M$ is a finite map from transaction identifier to mempool entry, $G$ is the dependency graph induced by unconfirmed spends, and $I$ is the set of indexes needed to query entries by transaction identifier, witness transaction identifier, spent outpoint, created outpoint, feerate, and entry time. In equations, $t \in M$ ranges over transactions in the entry map, and $Q \cup \tx$ denotes the mempool obtained by adding $tx$ to $M$ and recomputing $G$ and $I$. For validation against mempool ancestors, define:

$$ \operatorname{View}(Q,U)=U \cup \bigcup_{t \in M}\operatorname{Out}(t). $$

Entry

The entry fields are logical fields: an implementation may derive, cache, or index them differently, but externally observable mempool behavior must be equivalent.

Graph Invariants

For a transaction $t$, let $In(t)$ be its spent outpoints and $Out(t)$ be its created outpoints. Direct mempool dependencies are:

$$ \begin{aligned} \operatorname{parents}{Q}(t) &= {u \in M : \operatorname{In}(t) \cap \operatorname{Out}(u) \ne \emptyset},\ \operatorname{children}{Q}(t) &= {u \in M : \operatorname{In}(u) \cap \operatorname{Out}(t) \ne \emptyset}. \end{aligned} $$

A mempool is well-formed relative to $U$ iff:

$$ \begin{aligned} \operatorname{TxAvailable}{Q}(t,U) \Longleftrightarrow;& \forall x \in \operatorname{In}(t): x \in U \cup \bigcup{u \in M \setminus {t}}\operatorname{Out}(u). \end{aligned} $$

$$ \begin{aligned} \operatorname{WellFormed}(Q,U) \Longleftrightarrow;& \forall t \in M:\neg\operatorname{Coinbase}(t) \wedge \operatorname{ContextFreeValid}(t) \wedge \operatorname{TxAvailable}{Q}(t,U) \wedge \ & \forall a,b \in M,\ a\ne b: \operatorname{In}(a) \cap \operatorname{In}(b)=\emptyset \wedge \ & G={(u,t):u \in \operatorname{parents}{Q}(t)} \wedge \operatorname{Acyclic}(G). \end{aligned} $$

The graph order is the spend order: a parent precedes every child. Any block template or package derived from $Q$ must include transactions in a topological order of $G$.

Admission

Admission is a local transition:

$$ Q \xrightarrow[P]{tx,U,H} Q’, $$

where $P$ is the node’s local policy parameter set and $H$ is the next-block height and median-time context. Write $H=(C,h,t)$, where $C$ is the active chain, $h$ is the next block height, and $t$ is the next block locktime cutoff. Let $V_Q=View(Q,U)$. A single transaction admission succeeds iff:

$$ \begin{aligned} \operatorname{Admit}{P}(Q,U,H,tx) \Longleftrightarrow;& tx \notin M \wedge \operatorname{WellFormed}(Q \cup {tx},U) \wedge \ & \operatorname{ConsensusValid}(V_Q,tx,H) \wedge \operatorname{AbsFinal}(tx,h,t) \wedge \operatorname{SeqFinal}(tx,C,V_Q,h) \wedge \ & \operatorname{Policy}{P}(Q,U,tx,H),\ Q’ = Q \cup {tx} \Longleftrightarrow;& \operatorname{Admit}_{P}(Q,U,H,tx). \end{aligned} $$

$Policy_P$ includes node-local standardness, feerate, resource, replacement, package, and denial-of-service rules. Those rules do not define consensus validity; when they are specified, they belong with the transaction, script, package, or relay behavior they constrain.

A package $\pi$ is admitted atomically by applying the same transition to a topologically sorted sequence of transactions. If any member fails, the package transition fails and $Q$ is unchanged.

Removal

Let $B$ be a connected block and $U’$ the UTXO set after connecting it. Let $H’$ be the next-block context after connecting $B$. Connecting $B$ removes every included transaction and every mempool transaction that conflicts with the block:

$$ \begin{aligned} \operatorname{ConnectBlock}(Q,B,U’) = {t \in M:;&t \notin B.\text{\code{txs}} \wedge \ &\operatorname{In}(t) \cap \operatorname{Spent}(B)=\emptyset \wedge \ &\operatorname{ConsensusValid}(\operatorname{View}(Q,U’),t,H’)}. \end{aligned} $$

After removal, all entry indexes and dependency edges are recomputed so that $WellFormed(Q,U’)$ holds.

Disconnecting a block does not automatically restore its transactions to the mempool. The disconnected transactions become admission candidates and may reenter only through the current admission relation under the post-disconnect chain state.

Orphans and Relay View

A transaction with unavailable inputs is not a mempool entry. A node may keep an orphan cache $O$ of such transactions and retry admission when parents become available, but $O$ is local resource state and has no consensus meaning.

Transaction relay announces transactions from $Q$ by txid or wtxid, serves requested transactions if still present, and may filter, delay, or suppress announcements according to local policy. Relay choices do not change the definition of $Q$ (sources: bitcoin-core-v31).