every commit recomputes every commitment — the native node's cost curve

Date: 2026-09-27. Scope: the main-line node (soft3 434244e + cybergraph feat/durable-applications 0eae7ae + bbg feat/atomic-application-storage ef149e5, the composition the four version PRs describe), exercised by NativeNode::import_legacy on the spacepussy-test signal log (39,060 signals, 9,977,600 bytes, source sha256 a588264f…). No code changed.

the finding in one paragraph

prepare_native_batch calls BbgState::refresh_root on every accepted operation, and refresh_root → root_leaves → commit_fields rebuilds the commitment of every dimension from its full record set (stack sampled with gdb on deimos, always inside cyber_hemera::permutation::permute_with_constants under bbg::dim::commit_fields ← root_leaves ← refresh_root ← prepare_native_batch ← accept_encoded ← import_legacy). The cost of accepting a batch is therefore linear in the state, and the cost of a chain is quadratic in its length. This is the live acceptance path, not an import-only path: every POST /v1/link on the new node pays the same full recommit.

measured

Import of a strict prefix of the log (M4 Max, one thread, release build, spt-import HOME LOG N):

Exponent ≈ 1.7 and rising toward 2 as the per-batch recommit dominates. Extrapolated to the full 39,060-signal log: ≈ 1.5–2 days on the M4 Max, longer on the 2-core cyberproxy. On deimos (x86_64, 8 cores, one used) the import ran 55 minutes and was committing one 64-event batch every ≈ 40 s when stopped, consistent with ≈ 150 of 610 batches done.

For the launch this means: the chaosnet log cannot be imported in an operational window, and the bostrom genesis replay (2,949,732 links, row 14) cannot run at all on this path — it would take years.

what has to change

1. the root is refreshed per block, not per operation. With blocks as ticks (the epoch design of 2026-09-27) a root is needed once per block; per-operation receipts bind to the block root. This removes the factor "operations per block" but leaves the recommit linear in state.
2. commitments are incremental. Each dimension's commitment must be updatable in O(log n) per changed record (a Merkle or tensor-Merkle tree with cached inner nodes), so a block costs O(changes · log n) rather than O(state). This is the actual fix and it is bbg's.
3. import is a bulk build. A legacy import should build the dimension tables first and commit once at the end, then write the per-batch history against the final root or a per-block root; the "exact prefix" resumability the current import guarantees can be kept by batching at block granularity.

Until 2 lands, the main-line node is not deployable on spacepussy-test at its current size, and the 0.10.0 node (signal log, no per-signal recommit) stays live. Tracker: cyber/launch.md rows 14 and 43.

reproduce

# build spt-import against the four PR branches (see cyber/launch.md decisions 2026-09-27)
spt-import HOME LOG 250 ; spt-import HOME LOG 500 ; spt-import HOME LOG 1000
# stack of a running import: gdb -p PID -batch -ex "bt 12"