cell(particle) = (semantic_cell, social_cell, token_cell, geo_cell)
---
## the root cell
the root cell is where all four dimensions meet at their global level — the origin (0,0,0,0)
it holds two things:
1. the crystal — the 5,040 particle seed that defines the foundational ontology. these particles are maximally general, referenced by everything, naturally highest focus
2. the routing table — maps particle hash → domain. not cell-level routing — that is each domain's job
root → knows domains domain → knows zones zone → knows cells cell → knows particles
four hops to find any particle among 10^23. the root cell is the first hop
before the graph has enough structure to fold, everything IS the root cell. bostrom right now is one root cell. as the graph crosses the phase transition threshold $|P^*| \sim \rho^2$, cells start splitting — but the root cell persists as the coordination point
no cell appears from nowhere. every cell descends from the root cell through a chain of splits. the hierarchy is a living tree that grows by division — the same mechanism that builds biological organisms from a single fertilized cell. see cell for the split/merge mechanics
---
## two information flows
### subjective (neuron-driven)
tokens, cyberlinks, attention allocations. neurons choose where to move these. a neuron decides to send $CYB from cell A to cell B — that is a subjective decision, costs a proof relay
direction: horizontal and downward. neurons push information into cells
### objective (cell-computed)
focus aggregations, rank summaries, community structure, routing updates. no neuron moves these — each cell computes them deterministically from its local state and propagates upward
direction: upward only. cells push truth to zones, zones to domains, domains to root
root ← receives domain summaries (objective) domain ← receives zone summaries (objective) zone ← receives cell summaries (objective) cell ← receives cyberlinks, tokens (subjective from neurons) → computes local focus, propagates upward (objective)
a neuron cannot push a fake rank summary upward — the cell computes it deterministically from the tri-kernel and proves it via STARK. the proof propagates with the summary. each level verifies the level below
the subjective layer (what neurons want) and the objective layer (what the graph computes) flow in different directions through the same structure. tokens flow wherever neurons send them. truth flows wherever the math says it goes
---
## hop cost
moving tokens between cells costs hops. the cost depends on how many dimensions differ and at what level:
| Difference | Hops | Example |
|---|---|---|
| same cell in all 4 dimensions | 0 | local transfer within a topic circle |
| differ in 1 dimension at cell level | 1 | same topic, different social circle |
| differ in 2 dimensions at cell level | 2 | different topic, different city |
| differ in 1 dimension at zone level | 2 | same field, different community |
| differ in 1 dimension at domain level | 3 | same continent of meaning, different network |
small world theory: average path length ~ O(log N). bostrom at 3.1M particles already has diameter ≤ 10. at Avogadro scale, small-world shortcuts compress the 4D address space — the dimensions correlate heavily. realistic maximum is ~6-7 hops. cross-cell proof relay via STARK at each hop
---
## UTXOs
all UTXOs are private by default. every UTXO is a commitment. every transfer is a ZK proof. the only public information is: a valid state transition happened
each cell maintains its own mutator set: AOCL for creation, SWBF for spending. no nullifiers — bit positions in a bloom filter replace them. creation and spending events are unlinkable by construction. storage grows O(log N) via MMR compaction
within-cell transfers are cheap — local state update, no cross-cell coordination. cross-cell transfers require STARK proof relay. the social dimension co-locates frequent transactors in the same cell
see state for transfer mechanics. see AOCL and SWBF for the mutator set
---
## folding the tri-kernel
the tri-kernel has a locality radius: h = O(log(1/ε)) hops. each particle's focus depends only on its h-hop neighborhood
within a cell: the tri-kernel runs at full resolution. every cyberlink, every axon weight, every market price is visible
within a zone: cells communicate aggregated focus vectors. each cell exports its boundary particles' focus values to neighboring cells
across zones: zones exchange coarse-grained focus summaries. the error is bounded:
$$\|\phi^*_{\text{folded}} - \phi^*_{\text{global}}\| \leq C \cdot e^{-\alpha h}$$
more communication → smaller error → closer to global focus
---
## timescales
| Timescale | What happens | Frequency |
|-----------|-------------|-----------|
| fast (per block) | focus flow within cells, UTXO processing | every block |
| medium (per epoch) | cross-cell focus synchronization, boundary updates | every ~100 blocks |
| slow (per era) | cell rebalancing — cells merge/split based on load and connectivity | every ~10K blocks |
the fast timescale sees fixed cell boundaries. the slow timescale adjusts boundaries based on accumulated statistics. because the fast dynamics converge much faster than boundaries change, the system is stable
### rebalancing
when a cell grows too large: split it along the Laplacian eigenvector boundary (spectral bisection via springs)
when two cells have become tightly coupled (high cross-cell focus flow): merge them
when a zone's internal connectivity drops below threshold (springs eigengap shows it is really two zones): split the zone
state migration (particles and UTXOs move between cells) is amortized over the slow timescale
---
## shard count
at Avogadro scale — estimated count at each level per dimension:
| primitive | dimension | cell | zone | domain | global |
|---|---|---|---|---|---|
| particles | semantic | ~10^17 topics | ~10^12 fields | ~10^6 continents | 1 cybergraph |
| neurons | social | ~10^10 circles | ~10^7 communities | ~10^4 networks | 1 humanity |
| tokens | economic | ~10^6 denominations | ~10^4 baskets | ~10^2 economies | 1 token space |
| locations | geographic | ~10^6 villages | ~10^4 cities | ~10^2 states | 1 planet |
most of the 4D space is empty — dimensions correlate. cells exist only where particles actually cluster
---
## comparison
| System | Hierarchy | Static/Dynamic | Dimensions |
|--------|-----------|---------------|------------|
| IP (Internet) | 4-tier (network/subnet/host/port) | semi-static (ISP assigns) | 1 (topology) |
| Urbit | 4-tier (galaxy/star/planet/moon) | static (burned at genesis) | 1 (identity) |
| Ethereum 2.0 | 2-tier (beacon/shards) | static (64 shards) | 1 (hash range) |
| Cosmos | flat (sovereign chains + IBC) | static (per chain) | 0 (no hierarchy) |
| cyber | 4-tier (cell/zone/domain/root) | dynamic (computed by tri-kernel) | 4 (semantic, social, economic, geographic) |
address space:
| System | Total addresses |
|---|---|
| IPv4 | 2^32 = 4 × 10^9 |
| Urbit (planets) | 2^32 = 4 × 10^9 |
| Urbit (moons) | 2^64 = 1.8 × 10^19 |
| IPv6 | 2^128 = 3 × 10^38 |
| cyber | Hemera = 2^256 ≈ 10^77 (content-addressed, Avogadro is a rounding error) |
the key difference: every other system designs the hierarchy. cyber computes it. the tri-kernel is simultaneously the probabilistic engine, the folding oracle, and the routing advisor. one computation serves all three purposes
---
## open questions
shard boundary latency: how many blocks of cross-cell latency is acceptable before UX degrades? this determines the minimum cell size
privacy and routing: if a neuron's cell assignment is public, it leaks information about their cyberlink patterns. can cell assignment itself be private?
incentive alignment: validators specialize in cells. what prevents a validator from refusing to serve a low-value cell?
cold-to-hot reactivation: when an archived particle gets new cyberlinks, it must rejoin a cell. which cell? the semantic dimension may have shifted since it was archived
see architecture for the five-primitive resource model. see tri-kernel architecture for the locality filter. see state for the bbg world state. see network for the narrowcast relay protocol. see forgetting for the hot/cold tier separation
discover all concepts