Realizability Trajectories: How Voyager 2 Reveals Structural Transitions

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Category: UNNS Research
UNNS Substrate Research Programme · April 2026 · Voyager 2 Corpus

Realizability Dynamics
in the Heliosheath

Evidence from Voyager 2 for the first time-resolved structural trajectories in realizability space — and what 11 years of solar wind plasma reveal about the UNNS Substrate as a dynamical theory.
628 DLCP Runs · 4 Observables 96.0% Dominant-Class Conformance 3 FULL→GIANT Transitions · Pre-Heliopause 156 Theorem 1 Triggers Propositions 1–3 Empirically Instantiated STRUC-PERC-I v2.4 · DLCP 2025
Status: Manuscript complete · Submission candidate Corpus scale: 628 STRUC-PERC-I evaluations · 2007–2018 Key result: Physical boundaries preceded by detectable structural transition layers Theory advance: UNNS from classification to dynamical geometric theory
📄 Full Manuscript PDF 📊 Corpus Analysis 📦 Raw Data ZIP

Executive Summary

The UNNS Substrate has historically been a static framework: physical systems are placed in realizability space and classified. This paper changes that. Using 11 years of Voyager 2 heliosheath plasma data — 628 DLCP-evaluated ladders across four observables — we demonstrate for the first time that physical systems do not merely occupy realizability space. They trace continuous trajectories through it, governed by structural laws.

The principal result: structural class exhibits dominant-regime persistence (96.0% conformance) with controlled boundary excursions. Three GIANT windows in 2017–2018 — immediately before Voyager 2's heliopause crossing — constitute the first observed localized class transitions in any UNNS corpus, confirming that physical boundaries are preceded by detectable structural transition layers in realizability space. The UNNS Substrate is inherently dynamical: structural trajectories evolve, and boundary approach is detectable prior to transition.

🚀 A New Object: The Structural Trajectory

For the first time in the UNNS programme, the fundamental object of study is not a static ladder but a time-indexed family of ladders — and the trajectory they trace through the realizability manifold ℳadm.

Static UNNS (previously)

  • Fixed observable set → one ladder
  • One structural evaluation per system
  • Class as a property of the moment
  • No temporal information
  • No boundary-approach detection

Dynamic UNNS (this work)

  • Time-indexed ladder family → trajectory γ(t)
  • 628 evaluations across 11 years
  • Class as a property of the path through ℳadm
  • Temporal structural coordinates: κ(t), tail(t), m(t)
  • Boundary approach detected 1–2 years before physical crossing

The Dynamic Ladder Construction Protocol (DLCP) formalises how a physical observable is converted into a sequence of time-local ladders: sliding windows of Δ=1024 samples (~55 hours each), stride of 256, with a sort+unique+finite adapter. Each window yields one point in ℳadm. The sequence of points is a structural trajectory.

From Static Classification to Dynamic Trajectory in ℳ_adm Static Framework single evaluation one class label no temporal information Dynamic Framework — Trajectory γ(t) in ℳ_adm GIANT 628 window evaluations · 2007→2018 · continuous structural evolution ● FULL windows ▲ GIANT onset (pre-heliopause)

The Core Shift

Systems are no longer classified once. They evolve structurally through ℳadm, and the coordinates of that evolution — κconn(t), tail dominance(t), margin m(L(t)) — are now time-series with physical interpretation. This is the first new geometric level in the UNNS programme since the Percolative Realizability Principle.

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🛸 Why Voyager 2: A Unique Physical Laboratory

Voyager 2 is not simply a dataset. Between August 2007 (termination shock crossing) and November 2018 (heliopause crossing), it traversed the entire heliosheath — a plasma boundary region with known physical transitions, dense temporal sampling, and four independently measured observables from the same instrument.

Property 1

Dense Temporal Sampling

PLS instrument returns measurements every ~192 seconds. A Δ=1024 window spans ~55 hours — dense enough to capture structural evolution on timescales shorter than a solar rotation.

Property 2

Known Physical Transitions

The termination shock (2007-08-27) and heliopause (2018-11-05) are established physical events. The structural corpus can be evaluated against known boundaries.

Property 3

Multi-Observable Simultaneity

V, T, w, ρ from the same instrument at the same moments. Four simultaneous trajectories on different charts of ℳadm — enabling cross-channel structural comparison.

Property 4

Genuine Boundary Region

The heliosheath sits between two distinct plasma regimes. It is the only environment in which a structured approach to a realized physical boundary can be studied directly.

DLCP Pipeline: Voyager 2 PLS → Structural Trajectory Voyager 2 PLS 12 annual CDFs Sliding Windows Δ=1024 · stride=256 sort+unique+finite STRUC-PERC-I v2.4 628 evaluations class · κ · GR · tail Time Series κ(t) · tail(t) · m(t) class sequence Structural Trajectory γ(t) in ℳ_adm dynamical UNNS
Diagram showing Voyager 2 plasma data (velocity, temperature, density, thermal speed) entering a pipeline where time windows are formed, sorted into ladders, and analyzed to classify regimes such as FULL, HARD, and GIANT.
Figure 1 — Dynamic Ladder Construction Protocol (DLCP) pipeline. Voyager 2 heliosheath plasma measurements (V, T, ρ, w) are partitioned into time-local windows (W₁–W₃), forming state ensembles that are converted into ordered ladders via DLCP. Each ladder is evaluated by STRUC-PERC-I, mapping the system into realizability space through structural metrics (m, κconn, GR) and assigning regime classifications (FULL, HARD, GIANT). This pipeline defines the transformation from raw time series to trajectory-level structural objects.

🔬 Six Key Findings

Total Runs
628
4 observables · 12 epochs
Dominant Conformance
96%
603/628 runs · dominant regime
Boundary Excursions
22
TAIL/GIANT · all GR > 0.97
GIANT Transitions
3
First inter-chart transitions in UNNS
Theorem 1 Triggers
156
155 density · 1 velocity
V Tail Dom. Decline
−55%
2007→2018 secular fall

Finding 1 — Dominant-Regime Persistence: An Empirical Law

The dominant realizability class for each observable is the same in 2007 as in 2018. Despite the heliosheath undergoing continuous structural evolution — shocks, sector boundaries, temperature variations by factors of 30, episodic velocity collapses — the class label attached to each observable's ladder family does not change globally over 11 years. Velocity, temperature, and thermal speed remain predominantly in the FULL percolation regime; density remains in the HARD fragmentation regime.

This is not obvious. Class stability under large geometric deformation — κconn varying by a factor of 30 within the FULL class — means the topological structure of the gap distribution is more conserved than any individual structural metric. Topology is stable while geometry evolves.

Class Distribution by Observable — 628 Runs · 96.0% Dominant-Class Conformance V FULL 93.0% 158 T FULL 97.5% 157 w FULL 94.9% 156 FULL (dominant) TAIL (boundary-adjacent) GIANT (transition onset) HARD (anomalous)

Finding 2 — The Three-Phase Directed Trajectory

The annual mean κconn time series does not fluctuate randomly. It describes a directed, three-phase trajectory through realizability space:

  • Rise (2007–2009): Thermal variables intensify rapidly post-termination shock. Temperature κ reaches 941.8 in 2009 — the highest value in the corpus. Velocity does not follow: thermal-kinematic decoupling is already active.
  • Relaxation (2010–2016): Structural metrics broadly decline from the 2009 peak. Velocity shows two sharp episodic collapses (κ = 82.0 in 2014, κ = 98.2 in 2017) without thermal response — further evidence of channel separation.
  • Convergence (2017–2018): All three FULL observables simultaneously approach structural minima. Temperature κ: −57% from peak. Thermal speed κ: −79% from peak. Velocity tail dominance: −55% from 2007.

Random traversal through an isotropic plasma would produce a flat average with noise. A directed three-phase structure implies an internal gradient field in the heliosheath that the trajectory follows.

Annual κ_conn Trajectory — Annual Mean by Observable (2007–2018) RISE RELAXATION CONVERGENCE 900 600 300 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 T: 941.8 ★ ▲ GIANT Temperature (T) Velocity (V) Thermal speed (w) GIANT window epoch

Finding 3 — The Heliopause as a Structural Transition Layer

Three windows in 2017–2018 exit the FULL class and enter GIANT_COMPONENT_PERCOLATION. These are not noise: they share GR > 0.99 (backbone intact), occur in the final windows before the heliopause, and are spread across two observables (velocity and thermal speed).

Core Structural Discovery
Physical boundaries are preceded by detectable structural transition layers in realizability space. The FULL→GIANT class excursions in 2017–2018 are not isolated anomalies — they are the structural signature of a trajectory that has begun to sample the FULL/GIANT boundary from within the FULL region. The heliopause is not a sharp wall in ℳadm; it is a finite-thickness transition zone, visible in the data one to two years before the physical crossing.
Visualization comparing two behaviors: a smooth trajectory of velocity, temperature, and thermal speed approaching a boundary and briefly entering GIANT regions, versus a fragmented density structure with discrete values leading to a HARD regime.
Figure 2 — Voyager 2 dual trajectory and the density paradox. Kinematic observables (V, T, w) trace a continuous trajectory within the FULL regime, exhibiting coordinated structural softening as the heliopause is approached (2017–2018). Localized excursions into TAIL and GIANT regimes mark the onset of boundary accessibility. In contrast, density (ρ) forms a discrete ladder (~57 unique values per window), placing it systematically in the HARD regime (Theorem 1). This illustrates the coexistence of continuous and representation-induced discrete observables within the same physical system.

Finding 4 — Thermal-Kinematic Decoupling: An Anisotropic Heliosheath

In 2009, temperature κ spikes to 941.8 (annual mean) while velocity κ remains at 269.3 — a thermal intensification event with no kinematic response. In 2014 and 2017, velocity κ drops to 82.0 and 98.2 respectively while temperature remains at 371.7 and 265.0. These channel-separated structural events demonstrate that the heliosheath is not a uniform, isotropic plasma: thermal and kinematic degrees of freedom evolve under different structural drivers.

Finding 5 — Density as a Discrete-Regime Observable

All 155 HARD density windows trigger Theorem 1 — the percolative USL violation that marks genuine structural fragmentation. The cause is representational: the PLS fitting procedure in the outer heliosphere returns approximately 57 unique density values per 1024-sample window. A near-discrete sorted sequence cannot achieve full percolation at any κ threshold.

Theoretical Significance

The density finding demonstrates a key principle: realizability class depends on the distributional structure of the measurement representation, not on the physical quantity being measured. The same physical system, measured through an instrument with limited resolution, lives in a structurally different region of ℳadm than it would under continuous measurement. Density joins TiO₂ density of states as the second canonical discrete-regime domain in the UNNS programme.

Finding 6 — Multi-Chart Simultaneity

Velocity, temperature, and thermal speed reside predominantly in the FULL chart of ℳadm throughout the traverse. Density resides predominantly in the HARD chart. The same physical system simultaneously occupies structurally different regions depending on which observable is laddered — the first direct instantiation of ℳadm's multi-chart structure in a real physical system. Near the heliopause, the FULL chart becomes permeable and partial inter-chart transitions occur.

📊 Interactive Corpus Dashboard

The full dashboard visualises the 628-run STRUC-PERC-I corpus: class distributions, κ trajectories, tail dominance time series, proposition system, and predictions for independent trajectories. It is embedded below and accessible directly at unns.tech/media/unns/rt_voyager2/voyager_dashboard.html.

Interactive dashboard — open full screen →

⚖️ The Proposition System: A Formal Theory of Structural Dynamics

Five propositions govern trajectory behaviour in ℳadm. They were stated before the corpus was evaluated and tested against the 628-run Voyager 2 dataset. Together they define realizability dynamics: a continuous trajectory constrained within a dominant regime, with boundary approach expressed through coordinated structural softening and localised class excursions.

Proposition 1

Temporal Structural Continuity

Structural coordinates (κ, tail dominance, GR, margin) evolve continuously or piecewise continuously, with every sharp variation attributable to a physical cause.

✓ Confirmed
Proposition 2

Dominant-Regime Persistence

DLCP trajectories remain in a dominant class (96.0% conformance), with deviations confined to localised, structurally conditioned excursions. Observable representation defines the baseline regime.

✓ Confirmed
Proposition 3

Detectable Boundary Approach

Boundary approach is indicated by coordinated coordinate softening and emergence of boundary-adjacent classes. The 2017–2018 GIANT windows confirm localised transition onset.

◐ Partially Confirmed
Proposition 4

Trajectory Regularity

Within the dominant class, γ(t) is locally smooth. Derivative discontinuities coincide with discrete physical events, not measurement noise.

✓ Confirmed
Proposition 5

Margin as Temporal Indicator

Sustained decrease of m(L(t)) is a probabilistic forward indicator of boundary approach. Velocity tail dominance declines −55% over 11 years — the structural forecast of the heliopause transition.

✓ Supported
Synthesis · §10.4

Trajectories in ℳadm

Physical systems evolve in ℳadm not as static classifications but as regime-stable trajectories with structurally detectable transition onset. The UNNS Substrate is inherently dynamical.

✦ Core Result

Synthesis Statement

Together, Propositions 1–3 define realizability dynamics as a continuous trajectory constrained within a dominant regime, with boundary approach expressed through coordinated structural softening and localised class excursions. Physical systems do not simply occupy realizability classes — they trace trajectories that evolve, soften, and partially transition before physical boundaries are crossed.

Three-dimensional phase diagram showing regions labeled FULL, HARD, GIANT, and TAIL, with a trajectory mostly in FULL that approaches a boundary and briefly enters the GIANT region, while density occupies a separate HARD region.
Figure 3 — Phase diagram of realizability: dominant regime and boundary approaches. The admissibility manifold ℳadm is structured into regimes (FULL, HARD, GIANT, TAIL) separated by realizability boundaries. Voyager 2 trajectories remain predominantly within the FULL basin (96% conformance), with boundary-adjacent excursions into GIANT marking localized transition onset. Density occupies a distinct HARD manifold due to quantization effects. The diagram illustrates realizability dynamics as regime-stable trajectories with controlled boundary accessibility and finite transition layers.

🌌 What This Changes: From Classification to Dynamical Theory

This result is not an extension of prior UNNS results. It is a categorical shift in what the UNNS Substrate is and what it can do.

UNNS Before This Work

  • A structural classification framework
  • Describes where a system is in ℳadm
  • Static ladders, one evaluation
  • No temporal information
  • Boundaries are geometric objects
  • Class transitions are theoretical

UNNS After This Work

  • A dynamical geometric theory
  • Describes how systems move through ℳadm
  • Time-indexed ladder families, trajectory γ(t)
  • Full structural time series
  • Boundaries are transition layers, detectable before crossing
  • Class transitions observed in real data (3 GIANT windows)

Relation to Other Theories

UNNS Realizability Dynamics — Relation to Adjacent Theories UNNS Realizability Dynamics Stat. Physics phase transitions no therm. limit needed Dyn. Systems structural phase space Percolation data-induced geometry not lattices — ladders Plasma / MHD complementary layer

UNNS Realizability Dynamics does not replace MHD or statistical physics. MHD describes the equations of motion within the structural basin; percolation theory supplies the class geometry; dynamical systems theory provides the trajectory language. What UNNS adds is a new layer: the structural constraints on which realizability regions are accessible to a given physical system, and how the trajectory evolves as it approaches the boundary of those regions.

🔭 Predictions and Open Questions

The corpus results generate falsifiable predictions for independent trajectories — no additional data was used or fabricated to formulate them.

Prediction What would confirm it What would falsify it
P1 — Dominant-Class Persistence Any heliosheath traverse: observable stays in dominant class >90% of windows Stochastic class switching uncorrelated with physical events
P2 — Metric Non-Universality Voyager 1 (northward) shows distinct κ(t) profile while remaining within FULL Identical κ profiles across structurally independent trajectories
P3 — Non-Identical Boundary Approach Pre-crossing κ decline in any independent ISM-approach trajectory, at different rate from V2 2017–18 Abrupt class transition at heliopause with no preceding structural softening
P4 — Continuity Constraint m(L(t)) piecewise continuous in any slowly evolving system >15× κ change in 75%-overlapping windows without physical cause

The Definitive Open Test

The November 2018 heliopause crossing lies beyond this dataset. If ISM-side Voyager 2 PLS data becomes available at comparable resolution, Proposition 3 predicts a sustained FULL→GIANT or FULL→HARD transition within a few windows of the physical crossing, with the 2017–2018 GIANT excursions serving as the confirmed pre-cursor signal. That measurement would constitute the first full empirical confirmation of a class transition in realizability space coinciding with a physical boundary crossing.

💡 Implications and Significance

Implication 1

Predictive Structural Detection

If boundary approach is structurally detectable years before physical crossing, UNNS coordinates may serve as early-warning indicators for physical regime transitions in any domain — not just heliospheric plasma.

Implication 2

Cross-Domain Potential

The trajectory formalism applies wherever a time-indexed observable can be laddered. Atomic systems, condensed matter, cosmological structure, biological fitness landscapes — all are candidates for the same dynamical analysis.

Implication 3

Observable Relativity

The same physical system lives in different structural regions of ℳadm depending on which observable is laddered. Measurement is not neutral: the representation of a quantity partially determines its structural classification.

Implication 4

Heliosphere Reinterpretation

The heliosheath is not a uniform envelope. It is a structurally stratified, anisotropic medium with channel-separated dynamics and a directed structural gradient from termination shock to heliopause — all visible in the UNNS coordinates.

Implication 5

Structure Before Geometry

The structural basin constrains the effective geometry: the spatial boundary we call the heliopause is where the structural basin terminates. MHD and UNNS are complementary — not competing — theories of the same system.

Implication 6

A New Programme Layer

Admissibility (USL) → Realizability (PRP) → Local Geometry → Dynamics (this work). UNNS now has four structural layers, each adding descriptive power to the same geometric framework.

Resources & References

UNNS Substrate Research Programme · unns.tech · April 2026 · All structural evaluations performed with STRUC-PERC-I v2.4 and DLCP-compliant voyager_ladder_pipeline.py. Corpus data archived at the UNNS Substrate data repository.

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