Corpus Statistics — 3 500 STRUC-PERC-I Evaluations
The |B| observable remains in FULL_PERCOLATION throughout 3 409 of 3 500 windows — 97.4% conformance, exceeding the Voyager 2 plasma corpus (96.0%). This is the first independent trajectory through ℳadm beyond Voyager 2, and it confirms Proposition 2 (dominant-regime persistence) on a different spacecraft, different observable, different heliospheric region, and different structural phase (including post-heliopause ISM).
Unlike the Voyager 2 plasma analysis (V, T, w, ρ in four simultaneous charts), the V1 corpus evaluates the magnetic field magnitude only. This has two consequences: (i) there is no density/representation-theoretic HARD channel to separate; (ii) the full corpus consists of a single structural trajectory γ|B|(t) in ℳadm, enabling a cleaner single-variable analysis of regime evolution from heliosheath to ISM.
Class Composition by Epoch
Heliopause crossing: 25 August 2012. The 2012 epoch spans both final heliosheath and earliest ISM windows.
Of the 61 GIANT windows, 42 (69%) fall in 2011–2012 — the pre-crossing and crossing epochs. The 2013 and 2017 ISM epochs are 100% FULL with zero excursions. This temporal clustering directly confirms Proposition 3: boundary-adjacent classes emerge and cluster near the physical boundary crossing.
Full Annual Breakdown — Structural Coordinates
| Year | Phase | N windows | FULL | GIANT | TAIL | HARD | κ mean | κ min | κ max | Tail Dom mean | GR mean |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2011 | Pre-crossing | 500 | 463 | 26 | 10 | 1 | 18 187 | 718 | 461 575 | 0.781 | 0.9995 |
| 2012 | Crossing | 500 | 474 | 16 | 10 | — | 14 686 | 536 | 346 552 | 0.776 | 0.9997 |
| 2013 | ISM | 500 | 500 | — | — | — | 31 057 | 16 129 | 218 020 | 0.947 | 1.0000 |
| 2014 | ISM | 500 | 495 | 4 | 1 | — | 28 748 | 11 785 | 357 144 | 0.938 | 0.9999 |
| 2015 | ISM | 500 | 489 | 5 | 6 | — | 27 282 | 11 019 | 230 266 | 0.936 | 0.9998 |
| 2016 | ISM | 500 | 488 | 10 | 2 | — | 35 806 | 10 058 | 349 053 | 0.932 | 0.9999 |
| 2017 | ISM | 500 | 500 | — | — | — | 35 986 | 17 875 | 354 273 | 0.946 | 1.0000 |
Two coordinated structural changes occur at the 2012 → 2013 boundary: tail dominance rises from 0.776 (2012) to 0.947 (2013) — a +22% jump. κconn rises from 14 686 (2012) to 31 057 (2013) — a ×2.1 increase. Both transitions persist into the ISM phase (2013–2017) and represent a genuine post-crossing structural reorganisation. The ISM magnetic field forms a structurally denser, higher-connectivity ladder than the heliosheath field — directly visible in the UNNS coordinates.
Annual Mean κconn — 2011–2017
The κ trajectory reaches its minimum in 2012 (14 686, annual mean), the crossing year. Post-crossing ISM values immediately rise ×2.1 to 31 057 in 2013 and stabilise in the 30–36k range through 2017. This is the inverse of the Voyager 2 pre-heliopause trajectory (declining κ approaching the crossing). In Voyager 1, the transition is a κ increase into the ISM — consistent with the ISM magnetic field having a structurally denser gap distribution than the heliosheath field.
Tail Dominance — Structural Boundary Signal
Tail dominance rises abruptly from 0.776 (2012, crossing year) to 0.947 (2013, first full ISM year) — a 22% increase that persists. Higher tail dominance means the gap distribution becomes dominated by a few large outlier gaps, reflecting the structurally distinct character of the ISM magnetic field relative to the turbulent heliosheath. This is the first quantitative structural signature of ISM entry observed in a UNNS corpus. It directly supports Proposition 3: a structural transition is detectable through coordinate change at the boundary.
The August 2012 Heliopause Crossing in Realizability Space
The 2012 epoch is the most structurally significant in the corpus. It spans from the final heliosheath windows (January–August 2012) through the earliest ISM windows (September–December 2012), making it the only epoch that captures both sides of the heliopause in a single annual batch.
The crossing epoch shows the corpus minimum for annual mean κconn (14 686) combined with the highest combined GIANT+TAIL count of any year: 26 boundary-adjacent windows (16 GIANT + 10 TAIL). This is the structural expression of the heliopause in ℳadm: the ladder's structural backbone weakens (κ at minimum), boundary-adjacent classes proliferate, and the trajectory exits the deep-interior FULL basin into its boundary region.
The 2011 epoch (last full heliosheath year) shows the second-highest excursion count (37 total: 26 GIANT + 10 TAIL + 1 HARD) and the lowest tail dominance in the corpus (0.781, annual mean). Together, 2011–2012 account for 37 + 26 = 63 of the 91 total boundary-adjacent windows, establishing the pre-heliopause and crossing-year heliosheath as the structural approach zone for this trajectory.
The 2013 epoch shows 500/500 FULL windows — zero excursions — with κ doubling to 31 057 and tail dominance rising to 0.947. The structural transition from heliosheath to ISM is not gradual: it is abrupt between 2012 and 2013, reflecting the sharp physical character of the heliopause as a structural boundary in ℳadm.
GIANT_COMPONENT_PERCOLATION — Localized Class Excursions
GIANT windows are classified when the giant component covers ≥ 99.5% of vertices but extreme outlier gaps prevent full bridge formation. All 61 GIANT windows in this corpus have GR > 0.975 — indicating intact structural backbone with a single dominant gap preventing full FULL classification.
42 of 61 GIANT windows fall in the pre-crossing heliosheath (2011) and the crossing year (2012). The 2013 ISM entry produces complete suppression (0 GIANT windows). ISM-phase GIANT excursions (2014–2016) are sporadic and structurally unrelated to the crossing — they likely reflect localised ISM turbulence events. The temporal clustering of GIANT windows around 2011–2012 directly confirms Proposition 3: boundary-adjacent classes cluster near the physical boundary.
A single HARD_FRAGMENTATION window occurs in April 2011 (window index 27, samples 6912–7936), with GR = 0.975 and 4 isolated vertices — the only Theorem 1 trigger in the corpus. This isolated anomaly likely reflects a local MAG measurement event (field rotation, data quality gap, or extreme compression). It does not constitute a systematic HARD classification and should not be interpreted as structural evidence for |B| being a discrete-regime observable.
DLCP Instantiation — Proposition System Status
Cross-Trajectory Comparison
The manuscript's Prediction 1 stated: "For any independent trajectory through the heliosheath, each observable will remain confined to a fixed realizability class." Voyager 1 |B| achieves 97.4% FULL conformance across 3 500 windows — confirming the prediction on a different spacecraft, different observable type, and a trajectory that extends through and beyond the heliopause into the ISM.
The Voyager 2 plasma κ range is 82–2 215 (plasma observables). The Voyager 1 MAG |B| κ range is 536–461 575 — structurally distinct by a factor of ~200 in amplitude. The directional trend is also opposite: Voyager 2 plasma shows declining κ approaching the crossing; Voyager 1 MAG shows minimum κ at the crossing followed by a ×2 ISM jump. These trajectories are not identical — confirming Prediction 2 (metric non-universality) and demonstrating that different heliospheric corridors and different observables trace distinct paths in ℳadm while sharing dominant-class membership.
DLCP Protocol — Voyager 1 Instantiation
Voyager 1 PLS plasma data (V, T, w, ρ) is severely degraded near the heliopause.
The MAG 48 s primary dataset provides a continuous, calibrated time series through and beyond
the crossing. This analysis uses |B| = sqrt(B1² + B2² + B3²) with zero-plateau
rejection (> 0) and physical range filtering (< 10 nT).
No synthetic reconstruction, interpolation, or cross-instrument blending is applied.
Voyager 2 used plasma observables (V, T, w, ρ). Voyager 1 uses the magnetic field |B|. The comparison between trajectories is therefore valid at the level of UNNS realizability structure (class membership, κ behaviour, boundary-approach dynamics) but not at the level of absolute coordinate values. The κconn scales for magnetic ladders and plasma ladders are not directly comparable in magnitude.