Derivations
What Registration Theory has actually derived
A claim-disciplined ledger of published results. Every row separates the exact mathematical statement from the assumptions that make it valid and from the stronger physical claims that remain open.
Restricted-model proofs are genuine derivations of those models, but they are not automatically universal physical theorems of Registration Theory. DOI links point to the published source used for each entry.
Governing status rule: exact result, assumptions, and physical interpretation are tracked separately.
| Result | Exact statement | Assumptions / model | Physical status |
|---|---|---|---|
Closed-event consequence completeness exact theoremDOI 10.5281/zenodo.21909679 | A sufficient consequence representation factors later consequence through a closed event representation; minimal completion and the boundary to conservation are characterized. | Defined closed-event representation and consequence map. | Exact factorization theorem; it does not identify the conserved object with physical energy or momentum. |
Persistent Registration Lineage Theorem conditional theoremDOI 10.5281/zenodo.21969529 | Sufficient conditions preserve organizational identity through a successor chain under invariant persistence, consequence sufficiency, closed successor determination, commuting transport, and non-decomposition. | Finite-regime successor chain satisfying the stated hypotheses. | Exact/conditional persistence theorem; it characterizes continuity given succession and does not derive succession itself. |
Exact Trinity–ACRF-4 structural correspondence exact model resultDOI 10.5281/zenodo.22103700 | Canonical ACRF-4 decomposes into one common mode plus a three-dimensional relative-distinction quotient. | Canonical finite ACRF-4 and the stated quotient symmetry. | Exact structural model result; it does not identify ACRF coordinates with primitive space-, time-, or energy-facing roles. |
Persistent individuation and stable comparison conditional theoremDOI 10.5281/zenodo.22553227 | Under the paper's definitions, a stable operand-sensitive physical comparator requires persistence-bearing re-identification/equivalence. | Defined stable comparator and persistence-bearing equivalence. | Conditional formal result; arithmetic, scalar/vector structure, and geometry remain downstream reconstruction problems. |
Bilateral participatory registration exact model resultDOI 10.5281/zenodo.22654282 | Joint consequence sufficiency is equivalent to both participant consequences factoring through one common representation; canonical ACRF-4 realizes a common carrier, exchange covariance, a generic fibered decomposition, and global quotient reconstruction. | Bilateral principle for the abstract theorem; canonical finite ACRF-4 for the exact model realization. | Exact conditional theorem plus exact model theorems; the participant-relative records are not identified with primitive Trinity conjugates. |
Invariant three-dimensional closure and SU(3) automorphisms conditional theoremDOI 10.5281/zenodo.22243901 | Under a fixed paired-sector identification, conjugate doubling gives complex dimension three and normalized alternating triadic closure has automorphism group SU(3). | ACRF-4 rank-three carrier plus the stated complexification and closure assumptions. | Exact mathematics under stated assumptions; it is not a derivation of QCD color, gauge dynamics, or physical confinement. |
Cross-registration consequence networks model constructionDOI 10.5281/zenodo.22310077 | Canonical consequence data define receiver-conditioned consequential edges and a finite-type cross-registration reproduction operator. | Canonical ACRF-4 plus a consequence-incidence approximation. | Exact canonical inputs and a defined model construction; full dynamic propagation and the percolation claim remain open. |
Closure-induced complex structure conditional theoremDOI 10.6084/m9.figshare.33514537 | Two anticommuting involutions on one common closed sector imply J² = −I and therefore a 2π-periodic compact action. | Common closed-sector assumption with the specified involutions. | Exact conditional algebraic theorem; physical sector selection and phase succession remain open. |
Compact closure / noncompact conjugate escape exact model resultDOI 10.6084/m9.figshare.33649111 | Hyperbolic and compact invariants cannot both be preserved by a nonconstant continuous trajectory; exact boundary-kernel conditions, a zero-field non-invariance counterexample, and a successor-invariant internally active zero-field sector are derived in ACRF-4. | Canonical ACRF-4 and the stated closed-sector constructions. | Exact theorem package and model result; it is not a derivation of Navier–Stokes dynamics. |
Canonical local complex structure exact model resultDOI 10.6084/m9.figshare.33823234 | Native reduced dynamics at a persistent closed ACRF-4 registration derive two anticommuting local tangent involutions whose product satisfies J² = −I. | Persistent closed ACRF-4 fixed registration and reciprocal-gain normalization. | Exact local/tangent ACRF-4 theorem; a global finite-amplitude complex structure and physical phase-succession bridge remain open. |
Complex orientation no-go no-go theoremDOI 10.6084/m9.figshare.33916978 | Gauge-equivalent participant-exchange lifts send J to +J or −J, so a unique complex orientation does not descend; only the class [J] = {J, −J} is canonical. | Canonical ACRF-4 internal-label quotient and participant exchange. | Exact finite-model no-go theorem; no identification with charge, time reversal, or particle–antiparticle conjugation is made. |
Unoriented phase connection and bilateral circle invariant exact model resultDOI 10.6084/m9.figshare.33946051 | The compact phase circle descends exactly despite orientation ambiguity; a gauge-invariant bilateral circle variable is derived with ζ_BA = ζ_AB⁻¹, and factorized local phases give trivial continuous triangle holonomy. | Canonical bilateral ACRF-4 quotient on the nondegenerate relational stratum. | Exact mathematical bridge; it does not derive electromagnetism, electric charge, spin, or a physical wavefunction. |
Deterministic quadratic projective weights conditional theoremDOI 10.6084/m9.figshare.33963466 | A deterministic preparation–measurement–reset construction reproduces binary quadratic projective weights in a controlled tangent/refinement limit. | Isotropic rank-three relational sector, deterministic cyclic fine-state successor, retained detector rule, and an explicit linear seed coupling. | Exact existence construction under an additional coupling assumption; canonical ACRF-4 has not thereby derived the Born rule. |
Conditional Born theorem and native quadratic invariants conditional theoremDOI 10.6084/m9.figshare.33970894 | Qubit Born weights follow under additive seed, spherical-shadow fine-state law, and angle locking; native quadratic invariants and obstructions are isolated. | Explicit bridge conditions C1–C3. | Conditional theorem; the preparation–measurement map remains the missing physical bridge. |
Near-critical Born-frequency limit conditional theoremDOI 10.6084/m9.figshare.33980422 | If a ready apparatus has smooth nonzero density near the native critical surface and weak canonical consequence shifts native stability linearly, newly committed fractions are linear in consequence and the two-channel weak-coupling capture ratio approaches cos²(Δ). | Canonical ACRF-4 plus the stated apparatus-ensemble, exchangeability, and linear-response assumptions. | Conditional theorem with numerical premise tests; the physical apparatus ensemble and general multi-channel extension remain open. |
Radial 1/r registration field conditional theoremDOI 10.6084/m9.figshare.33977947 | Conserved radial registration flux in an effectively massless three-dimensional exterior integrates to χ(R) = χ∞ + C/R and therefore a 1/R² gradient. | Conserved flux, effectively massless exterior balance mode, and an emergent three-dimensional propagation volume. | Conditional field derivation; source normalization, Newton's constant, dimensional derivation, and the microscopic flux law remain open. |
Emerging Registration Calculus foundational frameworkDOI 10.6084/m9.figshare.34003980 | Introduces host-relative equivalence, coarse-graining, relational zero, persistence, and residual distinction as a candidate native mathematical grammar for Registration Theory. | Foundational synthesis built from IRD, Trinity, persistent individuation, and the existing common-mode/distinction architecture. | Foundational framework proposal, not a completed universal calculus or a theorem deriving motion, spacetime, or classical dynamics. |
How to read this ledger
An exact model result can be mathematically complete while its interpretation as a law of nature remains open. A conditional theorem is exact once its listed premises are supplied. A no-go theorem is equally important: it records a route the theory has shown cannot work under the stated assumptions. The ledger will expand as additional corpus results are verified against their published sources.