What exactly is bound in CSFS, IK+CSFS, and CHECKSIG?

Adding a fifth row to the binding framework, now that I have on-chain results for both ladder rebinding and APO rebinding side-by-side.

Pattern Binding target Cross-prevout reusable? Witness scaling
OP_CHECKSIGFROMSTACK Message (stack-supplied) Yes O(1)
OP_INTERNALKEY + OP_CHECKSIGFROMSTACK Identity (internal key) Yes (same key) O(1)
OP_CHECKSIG (default sighash) Full transaction sighash No O(1)
OP_CHECKSIG with APO (BIP-118) Sighash minus prevouts Yes (same script + amount) O(1)
CSFS rekey ladder Delegated key chain No (per-channel) O(n) in state count

A few observations from the empirical side, just from staring at TxIDs:

  1. APO and the CSFS ladder both achieve eltoo-style state replacement, but along different binding axes. APO loosens what the signature commits to; the ladder threads authority through fresh keys derived per state.
  2. The witness-scaling difference matters in practice. APO’s O(1) keeps a long-running channel cheap regardless of state count; the ladder’s O(n) makes it unattractive past roughly ten states. So the ladder is a “primitives-first” alternative for short state chains, not a structural replacement for APO in long-lived protocols.
  3. Cross-prevout reuse — APO’s distinguishing feature — is what lets the same signature spend a fee-bumped funding tx variant without re-signing. The ladder cannot do this because each ladder is anchored to one channel’s funding outpoint at script creation time. So if anything, the ladder strengthens the case for APO in the “long-running, fee-volatile channel” use case, while showing that short-state-chain eltoo can run today on already-activated opcodes.

References: Post :APO+CTV eltoo, 6 txs:

Post: CSFS+CTV ladder, 2 txs: