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.

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This is a kernel-space namespace in the Define stage of the PRISM pipeline. It provides the immutable algebraic substrate — ring structure, schema vocabulary, and operation algebra.

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Class hierarchy
Class hierarchy for UOR Convergence Tower namespace ConvergenceLev HopfFiber ConvergenceRes CommutativeSub AssociativeSub

Imports

Classes

NameSubclass OfDisjoint WithComment
ConvergenceLevelThingA level in the convergence tower. Four instances: R (dim 1), C (dim 2), H (dim 4), O (dim 8).
HopfFiberThingThe fiber of the Hopf fibration at a convergence level. Four instances: S⁰, S¹, S³, S⁷.
ConvergenceResidualThingThe unresolved structure at a convergence level. The β_{2^k−1} = 1 Betti number that persists.
CommutativeSubspaceThingThe subspace U(1) ⊂ SU(2) selected when pairwise interaction converges.
AssociativeSubalgebraThingThe subspace H ⊂ O selected when triple interaction converges.

Properties

NameKindFunctionalDomainRangeComment
algebraDimensionDatatypetrueConvergenceLevelnonNegativeIntegerThe dimension of the division algebra at this level (1, 2, 4, or 8).
bettiSignatureDatatypetrueConvergenceLevelstringThe Betti number signature at this convergence level.
fiberTypeObjecttrueConvergenceLevelHopfFiberThe Hopf fiber associated with this convergence level.
characteristicIdentityDatatypetrueConvergenceLevelstringThe characteristic identity at this convergence level (existence, feedback, choice, self-reference).
levelNameDatatypetrueConvergenceLevelstringHuman-readable name of this convergence level.
fiberDimensionDatatypetrueHopfFibernonNegativeIntegerThe dimension of the Hopf fiber sphere.
totalSpaceDatatypetrueHopfFiberstringThe total space of the Hopf fibration.
baseSpaceDatatypetrueHopfFiberstringThe base space of the Hopf fibration.
fiberSphereDatatypetrueHopfFiberstringThe fiber sphere designation (e.g. S⁰, S¹).
residualBettiDatatypetrueConvergenceResidualnonNegativeIntegerThe persistent Betti number at this residual.
residualDimensionDatatypetrueConvergenceResidualnonNegativeIntegerThe dimension at which the residual persists.
subspaceRefObjecttrueCommutativeSubspaceCommutativeSubspaceThe commutative subspace selected by pairwise convergence.
subalgebraRefObjecttrueAssociativeSubalgebraAssociativeSubalgebraThe associative subalgebra selected by triple convergence.
commutatorRefObjecttrueCommutativeSubspaceCommutatorReference to the commutator pair for this convergence.
associatorRefObjecttrueAssociativeSubalgebraAssociatorTripleReference to the associator triple for this convergence.

Named Individuals

NameTypeComment
L0_StateConvergenceLevelLevel 0: R (reals), dimension 1, existence.
  • algebraDimension: 1
  • bettiSignature: [1]
  • fiberType: hopf_S0
  • characteristicIdentity: existence
  • levelName: R
L1_MemoryConvergenceLevelLevel 1: C (complex), dimension 2, feedback.
  • algebraDimension: 2
  • bettiSignature: [1,1]
  • fiberType: hopf_S1
  • characteristicIdentity: feedback
  • levelName: C
L2_AgencyConvergenceLevelLevel 2: H (quaternions), dimension 4, choice.
  • algebraDimension: 4
  • bettiSignature: [1,0,0,1]
  • fiberType: hopf_S3
  • characteristicIdentity: choice
  • levelName: H
L3_SelfConvergenceLevelLevel 3: O (octonions), dimension 8, self-reference.
  • algebraDimension: 8
  • bettiSignature: [1,0,0,0,0,0,0,1]
  • fiberType: hopf_S7
  • characteristicIdentity: self-reference
  • levelName: O
hopf_S0HopfFiberHopf fiber S⁰: dimension 0, total space S¹, base pt.
  • fiberDimension: 0
  • totalSpace: S¹
  • baseSpace: pt
  • fiberSphere: S⁰
hopf_S1HopfFiberHopf fiber S¹: dimension 1, total space S³, base S².
  • fiberDimension: 1
  • totalSpace: S³
  • baseSpace: S²
  • fiberSphere: S¹
hopf_S3HopfFiberHopf fiber S³: dimension 3, total space S⁷, base S⁴.
  • fiberDimension: 3
  • totalSpace: S⁷
  • baseSpace: S⁴
  • fiberSphere: S³
hopf_S7HopfFiberHopf fiber S⁷: dimension 7, total space S¹⁵, base S⁸.
  • fiberDimension: 7
  • totalSpace: S¹⁵
  • baseSpace: S⁸
  • fiberSphere: S⁷