design principles

the three laws that govern every design decision in bbg.

law 1: bounded locality

no global recompute for local change. every operation's cost is proportional to what it touches, not to the total graph size.

at 10^15 nodes, global operations are physically impossible. light-speed delays across Earth exceed any acceptable latency bound. a PageRank recomputation over the full graph would take longer than the time between blocks.

this eliminates most graph algorithms. what survives: operators with provable decay guarantees — diffusion (geometric via teleport), springs (exponential via screening), heat kernel (Gaussian tail). the tri-kernel is the complete set of local operators. see nox for the computation model.

bbg separates operations into two classes with distinct locality profiles:

graph operations (cyberlinks)

a cyberlink creates a private record and updates public aggregates — bounded-local by construction:

private record: append to cyberlinks.root AOCL, O(1) amortized
axon update: update aggregate weight in particles.root, O(log n)
directional indexes: update axons_out.root and axons_in.root, O(log n) each
neuron focus: deduct focus in neurons.root, O(log n)
particle energy: update energy in particles.root, O(log n)
LogUp cross-index: O(k log k) proportional to axons touched, not |G|
sync: O(|my_namespace|) data transfer, not O(|all_data|)

focus is public — it must be visible for cyberank computation. a cyberlink deducts focus proportional to weight, updates the axon aggregate (weight, market state, meta-score), updates neuron focus and particle energy, and recomputes O(log n) NMT paths in the affected sub-roots. no global structure is touched. individual cyberlinks remain private — only aggregates are committed publicly.

economic operations (private transfers)

touch the global mutator set — O(log N) where N is total UTXO count:

AOCL append: O(1) amortized (MMR peak merge)
SWBF bit set: O(1) per index in active window
SWBF inactive proof: O(log N) MMR membership path
proof maintenance: O(log L · log N) per UTXO lifetime

the mutator set (AOCL + SWBF) is a global structure. private transfers touch it. this is the cost of privacy — unlinkability requires a shared accumulator. the bound is logarithmic, not linear, so it scales to 10^9 UTXOs.

bridge operations (coin → focus)

explicit conversion crosses the private→public boundary:

spend coin UTXO via mutator set (economic, O(log N))
credit focus NMT leaf (graph, O(log n))

this is the only operation that touches both layers. it is explicit — a neuron chooses when to convert private coins into public focus. the two worlds do not leak into each other otherwise.

law 2: constant-cost verification

verification cost is O(1) — bounded by a constant independent of computation size.

any computation, regardless of how many steps it takes, produces a proof verifiable in 10-50 μs. this is stronger than proportional verification (cost ≤ c × computation). with zheng-2 folding, verification cost does not grow at all:

N computation steps → fold into 1 constant-size accumulator → 1 decider (~6K constraints) → 1 proof (1-5 KiB)
verification: 10-50 μs whether N = 100 or N = 10^9
hemera-2 tree hashing: 1 permutation call per node (32-byte children fit in one rate block)

this enables planetary-scale delegation: any node can verify any other node's computation at fixed cost. the verifier's work is independent of the prover's work.

law 3: structural security

security guarantees emerge from data structure invariants, not from protocol correctness.

a protocol can have bugs. a tree whose internal nodes carry min/max namespace labels cannot lie about completeness — the structure itself prevents it.

examples in bbg:

NMT sorting invariant: misordered leaves produce an invalid root (structural)
SWBF double-spend: second spend sets already-set bits → rejection (structural)
content addressing: H(e) → e means identity IS hash (structural)
AOCL append-only: MMR structure physically prevents modification of past entries (structural)

the ZK circuit enforces the privacy boundary (see privacy). but the completeness guarantees come from the tree, not the circuit.

bbg/docs/explanation/design-principles.md