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Registration Theory
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Research

Research map

A conceptual map of the research program, not a decorative diagram. Each node carries its own status badge; arrows are labeled with the relationship they represent, and none imply a completed derivation unless the node's status says so.

Primary conceptual flow

The program's explanatory direction, not a completed proof chain -- see each node's status badge.

  1. Primitive TrinityAxiom
  2. motivates
    RegistrationAxiom
  3. motivates
    Persistent consequence / retained structureExact Model Result
  4. motivates
    Host-resolved relational structureComputational
  5. motivates
    Geometry / dimensionality / dynamicsExact Theorem
  6. opens
    Operational reconstructionOpen Problem

    Registration order, operational time, and relative distance are kept distinct; a universal cross-host calibration remains open.

  7. opens
    Physical spacetime and observable physicsOpen Problem

ACRF-4 current/retention branch and the present frontier

One source paper states the first four results together; the last step is the open reconstruction problem.

  1. H4: rank-three registration sectorExact Theorem
  2. extends
    Rank-three reciprocal retained sector EExact Model Result
  3. derives from
    Normalized current/retained conjugacy (𝒥² = I)Exact Model Result
  4. motivates
    Finite local consequence supportConditional Result

    Conditional on faithful one-step locality of the native ACRF-4 update.

  5. Strict retained-edge densification and node-block nonautonomyExact Model Result

    Exact within canonical ACRF-4; constrains, rather than establishes, a sparse-locality interpretation.

  6. constrains
    Unresolved shared-event transfer (Hᵢ → Bᵢⱼ → Hⱼ)Open Problem

    The forward-generated inter-host transfer carrier and boundary-growth dynamics required for physical propagation.

A withdrawn interpretation and its replacement

  1. Direct physical identification of ACRF-4 sectors (v1.0 interpretation)Superseded
  2. superseded by
    Host axes + conjugate brokerage (current interpretation, v2.0)Conditional

What supports the current interpretation

  1. Brokerage generator: hyperbolic (1,1) structureExact Theorem
  2. supports
    Host axes + conjugate brokerage (current interpretation, v2.0)Conditional

Rank-three geometry lineage

  1. Minimal Robust Relational Closure
  2. motivates
    Rank-Three Invariant Relational Geometry
  3. extends
    Isotropic Tangent Geometry → Discrete Nonlinear Channels

A supplementary finite theorem package for dimensionality

A supplement, not a derivation or replacement -- the official Zenodo record for the second paper declares isSupplementTo the first.

  1. System-Relative Dimensionality
  2. extends
    Finite resolved-operator existence and stabilityExact Model Result

For the full claim-by-claim ledger, see Status. For an interactive view of published papers and their sources, open the knowledge graph. For what remains unresolved, see the current frontier.