Voyager 1 MAG → DLCP Multi-Scale Robustness Results

Figure-ready HTML developed from STRUC-PERC-I batch outputs in the given multi-scale results archive. Window scales: W512/S128, W1024/S256, W2048/S512. Years: 2011–2017.

Result summary

t* = 2012 is stable across all three window scales. The annual mean κ_conn minimum occurs in 2012 for W512/S128, W1024/S256, and W2048/S512. This supports the claim that the Voyager 1 MAG structural boundary estimator is not an artifact of the baseline 1024-sample DLCP window.

Robustness3 / 3 scales

All scales identify 2012 as the κ minimum.

Coverage10,500 runs

7 years × 3 scales × 500 windows.

Main diagnosticκ minimum

Boundary estimator remains fixed under window-size variation.

1. Robustness table

The table below summarizes the boundary estimator at each scale. The post/crossing ratio is computed as mean κ_conn over 2013–2017 divided by the 2012 minimum.

scale	tstar	min_kappa	post_mean	jump_2012_2013	post_to_crossing_ratio	exc_2011	exc_2012	exc_post_mean
W512_S128	2012	5,872.3224	13,984.3353	2.6280	2.3814	0.0360	0.0200	0.0152
W1024_S256	2012	14,685.6109	31,775.5210	2.1148	2.1637	0.0740	0.0520	0.0112
W2048_S512	2012	47,561.9957	78,113.4832	1.4587	1.6424	0.1200	0.1000	0.0084

2. Figures

Line chart of annual mean kappa across three window scales showing minimum in 2012 for all scales. — **Figure 1.** Annual mean κ_conn across window scales. Every scale reaches its minimum in 2012, confirming scale-stability of the structural boundary estimator.

Line chart of normalized kappa boundary coordinate across years and window scales. — **Figure 2.** Normalized boundary coordinate B_κ. The crossing year is normalized to zero at each scale; post-2012 values rise into a distinct post-crossing range.

Line chart of excursion density across years and window scales. — **Figure 3.** Excursion density across scales. The strongest boundary-adjacent enrichment occurs in 2011–2012 for the baseline and coarse windows. The fine window reduces amplitude but preserves the pre/crossing emphasis.

Line chart of FULL dominance percentage across years and window scales. — **Figure 4.** FULL dominance. All scales remain overwhelmingly FULL, while boundary information appears as localized deviations rather than global class collapse.

Line chart of mean tail dominance across years and window scales. — **Figure 5.** Mean tail dominance. Post-2012 tail dominance is elevated across all scales, supporting separation between heliosheath/crossing and ISM-side structural regimes.

Phase plane plot of annual mean kappa versus tail dominance labeled by year. — **Figure 6.** Phase plane, κ_conn vs tail dominance. The trajectory relocates from low-κ boundary-side coordinates into a higher-κ post-crossing region.

Bar chart showing minimum annual mean kappa for each scale, annotated t*=2012. — **Figure 7.** Window-scale robustness of t*. The κ minimum is 2012 for every tested DLCP scale.

3. Complete annual summary

Each row aggregates 500 STRUC-PERC-I batch outputs for one year and one window scale.

scale	year	windows	mean_kappa	median_kappa	full	giant	tail	hard	exc_density	full_pct	mean_tailDom	B_kappa
W512_S128	2011	500	6,303.2422	2,349.3555	482	8	8	2	0.0360	0.9640	0.7853	0.0531
W512_S128	2012	500	5,872.3224	2,113.5061	490	0	10	0	0.0200	0.9800	0.7713	0.0000
W512_S128	2013	500	15,432.2217	13,081.8604	492	2	6	0	0.0160	0.9840	0.9494	1.1785
W512_S128	2014	500	13,895.0917	11,487.3057	492	2	6	0	0.0160	0.9840	0.9417	0.9890
W512_S128	2015	500	12,438.9709	11,247.0268	492	0	8	0	0.0160	0.9840	0.9398	0.8095
W512_S128	2016	500	13,403.7220	9,431.0240	488	6	6	0	0.0240	0.9760	0.9323	0.9284
W512_S128	2017	500	14,751.6699	12,412.0779	498	0	2	0	0.0040	0.9960	0.9461	1.0946
W1024_S256	2011	500	18,186.9842	5,186.6817	463	26	10	1	0.0740	0.9260	0.7809	0.2049
W1024_S256	2012	500	14,685.6109	5,019.0908	474	16	10	0	0.0520	0.9480	0.7758	0.0000
W1024_S256	2013	500	31,056.6130	24,233.6773	500	0	0	0	0.0000	1.0000	0.9469	0.9579
W1024_S256	2014	500	28,747.7051	21,020.5233	495	4	1	0	0.0100	0.9900	0.9382	0.8228
W1024_S256	2015	500	27,282.2705	20,612.4959	489	5	6	0	0.0220	0.9780	0.9363	0.7371
W1024_S256	2016	500	35,805.5652	18,635.2213	488	10	2	0	0.0240	0.9760	0.9324	1.2358
W1024_S256	2017	500	35,985.4509	23,484.4689	500	0	0	0	0.0000	1.0000	0.9459	1.2463
W2048_S512	2011	500	49,503.7184	7,632.7189	440	48	12	0	0.1200	0.8800	0.7607	0.0636
W2048_S512	2012	500	47,561.9957	15,404.6969	450	46	4	0	0.1000	0.9000	0.8136	0.0000
W2048_S512	2013	500	69,379.5275	44,151.7813	498	2	0	0	0.0040	0.9960	0.9454	0.7141
W2048_S512	2014	500	81,291.7662	40,258.8520	499	1	0	0	0.0020	0.9980	0.9415	1.1040
W2048_S512	2015	500	73,038.2210	36,632.7601	496	4	0	0	0.0080	0.9920	0.9332	0.8339
W2048_S512	2016	500	84,474.7127	37,476.4042	488	12	0	0	0.0240	0.9760	0.9372	1.2082
W2048_S512	2017	500	82,383.1885	45,531.7980	498	2	0	0	0.0040	0.9960	0.9467	1.1398

4. Manuscript-ready conclusion

Across DLCP window scales W512/S128, W1024/S256, and W2048/S512, the annual mean κ_conn minimum remains fixed at 2012. The result is therefore stable under a fourfold change in window duration, from approximately 6.8 hours to 27.3 hours per window. The multi-scale test supports the interpretation of 2012 as a structural boundary estimator t* and weakens the objection that the heliopause signature is an artifact of the baseline 1024-sample window.

5. Caveat

The robustness result validates the annual-scale boundary estimator under the three tested DLCP scales. It does not by itself establish coordinate-invariant geometry, nor does it replace the need for additional physical-domain controls. It directly addresses the segmentation-artifact objection for Voyager 1 MAG.