| tags | cyber, core, cip |
|---|---|
| crystal-type | entity |
| crystal-domain | cyber |
| crystal-size | article |
| alias | cyber hierarchy, folding, scaling, graph folding |
| status | draft |
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 [[tri-kernel]] that computes [[focus]] also reveals the natural hierarchy. all three operators contribute:
| Operator | What it reveals | Folding role |
|---|---|---|
| [[springs]] | [[Laplacian]] eigenvectors — structural communities | defines cluster boundaries via spectral decomposition |
| [[heat]] | multi-scale smoothing — communities at different resolutions | controls the scale: low τ = fine cells, high τ = coarse domains |
| [[diffusion]] | random walk communities — where [[probability]] flows | validates clusters via flow concentration |
[[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
the [[cybergraph]] has four dimensions — the four primitives themselves. [[particles]] that are close in any dimension should share a cell
[[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]] 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
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]]
the economic dimension is the only one of the four that is already a discrete label rather than a computed clustering — so it is realized explicitly first: a [[signal]] carries a network field (a [[card]] id), naming the network it is delivered to. a network is a [[card]] — unique, owned, transferable. the default is the neuron's private network,
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
each dimension has four scales. a [[particle]] has a coordinate in each dimension at each scale
| primitive | dimension | [[cell]] | zone | domain | global |
|---|---|---|---|---|---|
| [[particles]] | semantic | topic | field | continent | [[cybergraph]] |
| [[neurons]] | social | circle | community | network | humanity |
| [[tokens]] | economic | denomination | basket | economy | all [[tokens]] |
| locations | geographic | village | city | state | planetary |
[[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 is where all four dimensions meet at their global level — the origin (0,0,0,0)
it holds two things:
-
the [[crystal]] — the 5,040 [[particle]] seed that defines the foundational ontology. these [[particles]] are maximally general, referenced by everything, naturally highest [[focus]]
-
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
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
[[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
[[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 [[zheng]]. 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
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 [[zheng]] at each hop
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 [[zheng]] [[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]]
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:
more communication → smaller error → closer to global [[focus]]
| 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
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
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
| 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
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
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