UOR Convergence Tower

IRI: https://uor.foundation/convergence/
Prefix: convergence:
Space: kernel
Comment: Hopf convergence tower: four levels R, C, H, O corresponding to the four normed division algebras of dimensions 1, 2, 4, 8. Each level carries a Hopf fibration fiber and Betti signature.

Imports

https://uor.foundation/op/
https://uor.foundation/reduction/
https://uor.foundation/observable/
https://uor.foundation/homology/

Classes

Name	IRI	Subclass Of	Disjoint With	Comment
ConvergenceLevel	`https://uor.foundation/convergence/ConvergenceLevel`	`http://www.w3.org/2002/07/owl#Thing`		A level in the convergence tower. Four instances: R (dim 1), C (dim 2), H (dim 4), O (dim 8).
HopfFiber	`https://uor.foundation/convergence/HopfFiber`	`http://www.w3.org/2002/07/owl#Thing`		The fiber of the Hopf fibration at a convergence level. Four instances: S⁰, S¹, S³, S⁷.
ConvergenceResidual	`https://uor.foundation/convergence/ConvergenceResidual`	`http://www.w3.org/2002/07/owl#Thing`		The unresolved structure at a convergence level. The β_{2^k−1} = 1 Betti number that persists.
CommutativeSubspace	`https://uor.foundation/convergence/CommutativeSubspace`	`http://www.w3.org/2002/07/owl#Thing`		The subspace U(1) ⊂ SU(2) selected when pairwise interaction converges.
AssociativeSubalgebra	`https://uor.foundation/convergence/AssociativeSubalgebra`	`http://www.w3.org/2002/07/owl#Thing`		The subspace H ⊂ O selected when triple interaction converges.

Properties

Name	Kind	Functional	Domain	Range	Comment
algebraDimension	Datatype	true	`https://uor.foundation/convergence/ConvergenceLevel`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The dimension of the division algebra at this level (1, 2, 4, or 8).
bettiSignature	Datatype	true	`https://uor.foundation/convergence/ConvergenceLevel`	`http://www.w3.org/2001/XMLSchema#string`	The Betti number signature at this convergence level.
fiberType	Object	true	`https://uor.foundation/convergence/ConvergenceLevel`	`https://uor.foundation/convergence/HopfFiber`	The Hopf fiber associated with this convergence level.
characteristicIdentity	Datatype	true	`https://uor.foundation/convergence/ConvergenceLevel`	`http://www.w3.org/2001/XMLSchema#string`	The characteristic identity at this convergence level (existence, feedback, choice, self-reference).
levelName	Datatype	true	`https://uor.foundation/convergence/ConvergenceLevel`	`http://www.w3.org/2001/XMLSchema#string`	Human-readable name of this convergence level.
fiberDimension	Datatype	true	`https://uor.foundation/convergence/HopfFiber`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The dimension of the Hopf fiber sphere.
totalSpace	Datatype	true	`https://uor.foundation/convergence/HopfFiber`	`http://www.w3.org/2001/XMLSchema#string`	The total space of the Hopf fibration.
baseSpace	Datatype	true	`https://uor.foundation/convergence/HopfFiber`	`http://www.w3.org/2001/XMLSchema#string`	The base space of the Hopf fibration.
fiberSphere	Datatype	true	`https://uor.foundation/convergence/HopfFiber`	`http://www.w3.org/2001/XMLSchema#string`	The fiber sphere designation (e.g. S⁰, S¹).
residualBetti	Datatype	true	`https://uor.foundation/convergence/ConvergenceResidual`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The persistent Betti number at this residual.
residualDimension	Datatype	true	`https://uor.foundation/convergence/ConvergenceResidual`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The dimension at which the residual persists.
subspaceRef	Object	true	`https://uor.foundation/convergence/CommutativeSubspace`	`https://uor.foundation/convergence/CommutativeSubspace`	The commutative subspace selected by pairwise convergence.
subalgebraRef	Object	true	`https://uor.foundation/convergence/AssociativeSubalgebra`	`https://uor.foundation/convergence/AssociativeSubalgebra`	The associative subalgebra selected by triple convergence.
commutatorRef	Object	true	`https://uor.foundation/convergence/CommutativeSubspace`	`https://uor.foundation/observable/Commutator`	Reference to the commutator pair for this convergence.
associatorRef	Object	true	`https://uor.foundation/convergence/AssociativeSubalgebra`	`https://uor.foundation/interaction/AssociatorTriple`	Reference to the associator triple for this convergence.

Named Individuals

Name	Type	Properties	Comment
L0_State	`https://uor.foundation/convergence/ConvergenceLevel`	`algebraDimension`: 1 `bettiSignature`: [1] `fiberType`: `https://uor.foundation/convergence/hopf_S0` `characteristicIdentity`: existence `levelName`: R	Level 0: R (reals), dimension 1, existence.
L1_Memory	`https://uor.foundation/convergence/ConvergenceLevel`	`algebraDimension`: 2 `bettiSignature`: [1,1] `fiberType`: `https://uor.foundation/convergence/hopf_S1` `characteristicIdentity`: feedback `levelName`: C	Level 1: C (complex), dimension 2, feedback.
L2_Agency	`https://uor.foundation/convergence/ConvergenceLevel`	`algebraDimension`: 4 `bettiSignature`: [1,0,0,1] `fiberType`: `https://uor.foundation/convergence/hopf_S3` `characteristicIdentity`: choice `levelName`: H	Level 2: H (quaternions), dimension 4, choice.
L3_Self	`https://uor.foundation/convergence/ConvergenceLevel`	`algebraDimension`: 8 `bettiSignature`: [1,0,0,0,0,0,0,1] `fiberType`: `https://uor.foundation/convergence/hopf_S7` `characteristicIdentity`: self-reference `levelName`: O	Level 3: O (octonions), dimension 8, self-reference.
hopf_S0	`https://uor.foundation/convergence/HopfFiber`	`fiberDimension`: 0 `totalSpace`: S¹ `baseSpace`: pt `fiberSphere`: S⁰	Hopf fiber S⁰: dimension 0, total space S¹, base pt.
hopf_S1	`https://uor.foundation/convergence/HopfFiber`	`fiberDimension`: 1 `totalSpace`: S³ `baseSpace`: S² `fiberSphere`: S¹	Hopf fiber S¹: dimension 1, total space S³, base S².
hopf_S3	`https://uor.foundation/convergence/HopfFiber`	`fiberDimension`: 3 `totalSpace`: S⁷ `baseSpace`: S⁴ `fiberSphere`: S³	Hopf fiber S³: dimension 3, total space S⁷, base S⁴.
hopf_S7	`https://uor.foundation/convergence/HopfFiber`	`fiberDimension`: 7 `totalSpace`: S¹⁵ `baseSpace`: S⁸ `fiberSphere`: S⁷	Hopf fiber S⁷: dimension 7, total space S¹⁵, base S⁸.