Conjugate / Brokerage Structure
Can time, space, and energy be recovered as brokered aspects of registration rather than assumed as separate physical sectors?
An abstract brokerage-generator theorem yields hyperbolic (1,1) structure from conjugate-channel assumptions; a candidate relativistic brokerage law connects it to the energy–momentum relation. Both replace the withdrawn direct physical-sector identification.
Established
- The elementary conjugate brokerage generator is unique up to scale and yields the hyperbolic group with invariant form Q(y) = y0² − y1², under stated assumptions.
Open problems
Temporal asymmetry / Lorentzian signature
A non-circular derivation of a single time-facing sign, not assumed as input.
Related threads: Conjugate / Brokerage Structure, Consequence Propagation
Relevant claims
The elementary brokerage generator is unique up to scale and yields hyperbolic (1,1) structure
For an elementary conjugate brokerage channel C = [0 1; 1 0] (C² = I), under stated continuity, composition, role-symmetry, unimodularity, and nontrivial-coupling assumptions, the infinitesimal generator is proportional to C. This gives the one-parameter group Bη = [cosh η, sinh η; sinh η, cosh η] and a preserved nondegenerate quadratic form, unique up to scale, of signature (1,1): Q(y) = y₀² − y₁².
Scope: An abstract theorem about brokerage-channel mixing under the stated assumptions; not by itself a completed derivation of physical Lorentz spacetime.
- Does not establish that this structure governs general spacetime.
- The proposed extension to physical energy via latent/exchanged brokerage is proposed, not derived.
Last reviewed 2026-08-27
Relevant publications
A First-Principles Brokerage Generator Theorem in Registration Theory
Conjugate Symmetry, Unimodular Mixing, Hyperbolic Invariance, and a Multi-Registration Route to Field Structure.
- Registration Theory
- Trinity ontology
- conjugate brokerage
- unimodular mixing
- hyperbolic geometry
- Lorentzian signature
- rapidity
A Candidate Relativistic Brokerage Law in Registration Theory
Latent–Exchanged Conjugacy, Proper-Time Weight, and the Energy–Momentum Relation.