59 lines
1.5 KiB
Markdown
59 lines
1.5 KiB
Markdown
---
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date: 2023-05-11 00:00:00
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---
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multiple file formats
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- heterogenous decentralisation
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- cats is about objects which are processes, making them deployable as infrastructure
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- processes are blocks. cats, like blocks, do not care what the objects being processed are
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- RIDs for CARs? (is this RIDs for identity too?)
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- how to represent and deploy inter-systemic (Identity) relations
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- are relations the same as blocks? are they a superset? subset?
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- to Z: how would a non-process relation be represented as a block? i.e. relations
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- symmetric blocks?
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- content-addressed files form a network of acyclical reference
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portable relations & (RIDs for) content-addressed relations
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```
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RID[CID] -> {
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relation: RID (Identity)
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relata: set | (set, set)
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}
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```
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```
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Add -> {
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relation: AddBlock
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relata: [
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space_1,
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space_2
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]
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}
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ReduceDimensions -> {
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relation: ReduceDimensionsProcess
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relata: {...}
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}
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Isomorphic -> {
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relation: Isomorphism
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relata: {...}
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}
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```
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```
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Identity -> {
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relation: Identity
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relata: {O1, O2, ..., On}
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}
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```
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Identity and symmetric functions
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$C(S, D) \land \forall O_1, O_2 \in \text{Identity}: S(O_1, O_2) \land (O_1 \neq O_2 \rightarrow D(O_1, O_2))$
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- $S(f, g) \equiv \forall x \in \text{Domain}(f) \cap \text{Domain}(g): f(x) = g(x)$
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$S((f_1, g_1), (f_2, g_2)) \equiv \forall a \in \text{Domain}(f_1) \cap \text{Domain}(f_2): g_1(f_1(a)) = a = g_2(f_2(a))$ and $\forall b \in \text{Domain}(g_1) \cap \text{Domain}(g_2): f_1(g_1(b)) = b = f_2(g_2(b))$.
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