spectral cell division
Status: research proposal. The historical title preserves the biological metaphor and earlier links. The object being divided is a shard: a region of graph state under a validation and availability contract. Its open protocol questions must be resolved before automatic division can become a consensus rule.
the mechanism
When a shard approaches its declared capacity, spectral analysis can propose a split boundary. Under a chosen weighting and normalization, the Laplacian describes connectivity; a small second eigenvalue λ₂ can indicate weakly joined communities. The Fiedler vector assigns each particle a coordinate. A sign cut or threshold sweep proposes a partition, evaluated against edge-cut cost, balance, data locality and capacity constraints. The spectral relaxation needs an explicit cut objective and acceptance rule; its sign cut has no general guarantee of being the exact minimum cut.
The proposed handoff replaces one serving region with two authenticated regions. Particles, links, routing coverage and spending-state obligations acquire explicit new owners at the partition layer; boundary focus state is exchanged with coverage proofs. A spending commitment or pending cross-region operation retains its protocol identity and conservation rules. Any mutator set or nullifier representation must define how witnesses and uniqueness survive the boundary.
Repeated partitioning could produce the hierarchy of shards → zones → domains, with the heat kernel suggesting resolution scales. Neuron keys and prog identities remain independent of these partitions. Moving a prog's retained state requires its runtime migration and writer-fencing contract in addition to graph placement; spectral analysis supplies no permission to dispatch work.
why it is not ready
open questions that keep this a proposal:
- Atomic handoff. Which checkpoint closes the old region, who serves queries during migration, and what proves complete, disjoint new coverage? The protocol must preserve availability, spend uniqueness, open conditions and historical proofs while preventing both old and new writers from accepting conflicting work.
- Validator economics. Who serves each new shard immediately, what stake and authority policy applies, and how does finality remain valid during reassignment? Graph partitions alone do not determine how validator stake should move.
- Trigger and adversarial cost. Which capacity and spectral thresholds authorize division, who pays for measurement, and how are forced split/merge cycles or manipulated boundaries bounded? An eigengap supplies evidence for a decision.
- Merging. Two under-used regions may benefit from reunion. The reverse handoff needs its own coverage, witness, routing and finality rules, including pending operations that refer to either former region.
- Scale evidence. bostrom supplies an unpartitioned bootloader reference. A decision threshold requires a reproducible workload and measurements of capacity, boundary traffic and proof cost. A particle-count estimate alone cannot establish that division is necessary or economically beneficial.
relation to oikos
oikos describes a token's complete home book under its issuer's rules. Book creation registers an economic domain; shard division changes graph coverage and serving responsibility. The operations have separate authorization and proof requirements. A book can retain its name and full obligations through storage repartitioning. This proposal owns graph partitioning; the domain model defines its relationship to neurons, progs, books and services. The old cell ladder remains a historical link.
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