cyber hierarchy

how the cybergraph scales to Avogadro numbers — 10^23 particles, 10^15 neurons — not by designing shards in advance, but by reading the natural hierarchy from the tri-kernel's own output

the insight

the tri-kernel that computes focus also reveals the natural hierarchy. all three operators contribute:

springs provides the eigenvectors that define fold lines. heat controls the resolution — which level of the hierarchy you read. diffusion reveals the flow patterns that validate the folds. the three together give robust community detection that no single operator provides alone

no administrator assigns structure. the tri-kernel computes it as a side effect of computing focus. the same operators that rank particles also partition the graph for scaling

four dimensions

the cybergraph has four dimensions — the four primitives themselves. particles that are close in any dimension should share a cell

particles — semantic

particles with high mutual focus flow — many cyberlinks between them, strong axon weights — form semantic clusters. the tri-kernel reveals these through spectral decomposition (springs) and multi-scale smoothing (heat)

neurons — social

neurons who transact frequently form social clusters. UTXO movement patterns reveal who sends to whom. co-locate frequent transactors in the same cell to minimize cross-cell transfers. social locality often correlates with semantic locality but not always

tokens — economic

each token naturally forms its own cluster. particles priced in $CYB cluster in $CYB cells. trading $CYB for $H is a cross-cell hop in the token dimension. a new token creates a new cluster. the number of token cells scales with the number of live tokens

locations — geographic

latency matters for interactive use. neurons in the same physical region want low-latency access to their neighborhood. location proof provides this dimension. validators in a region preferentially serve that region's cells

the 4×4 matrix

each dimension has four scales. a particle has a coordinate in each dimension at each scale

cells are the base operational level — they hold state, process transactions, run the tri-kernel. zones, domains, and global emerge from the cell topology at different heat kernel temperatures. they are not passive observations — each level holds stakes and coordinates consensus. validators stake at the level they serve

a particle's cell = the intersection of its coordinates across all four dimensions. two particles sharing more coordinates → cheaper to move tokens between them. sharing all four → same cell, zero cross-cell cost

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 cyber/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:

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 cyber/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:

$$\|\pi^*_{\text{folded}} - \pi^*_{\text{global}}\| \leq C \cdot e^{-\alpha h}$$

more communication → smaller error → closer to global focus

timescales

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:

most of the 4D space is empty — dimensions correlate. cells exist only where particles actually cluster

comparison

address space:

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 cyber/architecture for the five-primitive resource model. see tri-kernel architecture for the locality filter. see cyber/state for the bbg world state. see cyber/network for the narrowcast relay protocol. see forgetting for the hot/cold tier separation