---
tags: cyber, core
alias: particle space, cyber space, address space
crystal-type: entity
crystal-domain: cyber
---
the set of all possible particles β bounded by two limits
## hashing limit
the Hemera hash function outputs 256 bits. the total address space is 2^256 β 10^77 possible particles. this is the hard ceiling β no more unique particles can exist than unique hashes
at Avogadro scale (10^23 particles) the space is barely occupied: 10^23 / 10^77 = 10^-54 occupancy. the address space is large enough for every atom in the observable universe to have its own particle with room for 10^-30 of the space filled
## connectivity limit
the address space is vast but cyberspace is not the address space β it is the connected subgraph. a particle exists in the cybergraph only when linked (axiom A4: entry). the practical limit is not how many hashes are possible but how many cyberlinks can be created and maintained
connectivity is bounded by:
- will β every cyberlink costs will to create
- neurons β each neuron has finite will budget
- computation β the tri-kernel must converge on the connected graph
at 10^15 neurons with ~10^8 cyberlinks each, the graph holds ~10^23 edges β Avogadro scale. the particles are fewer (each edge connects two), so the practical particle count is the same order
## the space is sparse
most of 2^256 is empty. the occupied region is a tiny cluster in the hash space, structured by cyberlinks into cyberspace. the hierarchy organizes this cluster into cells, zones, and domains. the hash provides identity. the links provide structure. the tri-kernel provides meaning
see cyberspace for the navigable semantic space. see hierarchy for how the occupied region scales. see Hemera for the hash function
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