orionreed.com/public/stream/4.md

date
2023-05-11 00:00:00

multiple file formats

• heterogenous decentralisation
• cats is about objects which are processes, making them deployable as infrastructure
• processes are blocks. cats, like blocks, do not care what the objects being processed are
• RIDs for CARs? (is this RIDs for identity too?)
  • how to represent and deploy inter-systemic (Identity) relations
• are relations the same as blocks? are they a superset? subset?
• to Z: how would a non-process relation be represented as a block? i.e. relations
  • symmetric blocks?
• content-addressed files form a network of acyclical reference

portable relations & (RIDs for) content-addressed relations

RID[CID] -> {
	relation: RID (Identity)
	relata: set | (set, set)
}

Add -> {
	relation: AddBlock
	relata: [
		space_1,
		space_2
	]
}

ReduceDimensions -> {
	relation: ReduceDimensionsProcess
	relata: {...}
}

Isomorphic -> {
	relation: Isomorphism
	relata: {...}
}

Identity -> {
	relation: Identity
	relata: {O1, O2, ..., On}
}

Identity and symmetric functions

C(S, D) \land \forall O_1, O_2 \in \text{Identity}: S(O_1, O_2) \land (O_1 \neq O_2 \rightarrow D(O_1, O_2))

• S(f, g) \equiv \forall x \in \text{Domain}(f) \cap \text{Domain}(g): f(x) = g(x)

S((f_1, g_1), (f_2, g_2)) \equiv \forall a \in \text{Domain}(f_1) \cap \text{Domain}(f_2): g_1(f_1(a)) = a = g_2(f_2(a)) and \forall b \in \text{Domain}(g_1) \cap \text{Domain}(g_2): f_1(g_1(b)) = b = f_2(g_2(b)).