UNNS Chamber Array — LXV Suite

A complete empirical arc from per-station co-seismic step estimation through smoothing-window rank invariance validation to angular displacement topology classification across three major earthquakes. LXV-A establishes the Kumamoto 2016 step baseline — four stations, perfect rank lock at all windows. LXV-B2 certifies El Mayor–Cucapah 2010 step ordering under the Spec v1.1.0 inversion-budget criterion, correctly passing a one adjacent-swap tail degeneracy that fixed ρ/τ thresholds would incorrectly reject. LXV-C2 confirms complete rank lock for Ridgecrest 2019 across six stations. LXV-D classifies displacement field topology for all three events — bi-lobe for El Mayor and Kumamoto, single-lobe for Ridgecrest — with ARI = 1 stability across all smoothing windows.

🧭 Navigation Guide — Understanding the LXV Suite Four-Chamber Arc

What is the LXV Suite?

The LXV suite is a multi-event seismic field validation arc operating on real GPS/GNSS displacement time-series data in tenv3 format from the UNR Nevada Geodetic Laboratory. Three independent earthquake events are processed through a shared methodology: step estimation, rank invariance certification, and angular topology classification. The suite demonstrates that structural invariance claims in empirical seismology require explicit sample-size-aware gate criteria, and that displacement field topology is stable across smoothing choices.

The Four-Chamber Arc

Chamber LXV-A — Kumamoto 2016 Step Estimation (Engine v1.0.0) Baseline co-seismic step estimator for the Mw 7.0 Kumamoto, Japan sequence (break: 2016-04-15). Four stations: G071, J093, J465, J702. Pre-fit LS detrending over 60 days; median-difference step over ±20-day windows with inclusive 2-day guard. Smoothing windows w ∈ {1, 3, 7, 14, 21}. SNR gate on horizontal ≥ 5.0. Finding: J465 dominant at 787.9 mm; G071 second at 453.9 mm; J702 third at 324.1 mm; J093 fourth at 51.4 mm. Rank J465→G071→J702→J093 is perfectly invariant at all five windows. ρ = 1, τ = 1, max_shift = 0 everywhere. Core-pair cosine (J465·G071) = 0.9961–0.9962. PASS.

Chamber LXV-B2 — El Mayor–Cucapah 2010 Rank Invariance (Spec v1.1.0 · Engine v1.4.0) Smoothing-window rank invariance for Mw 7.2 El Mayor–Cucapah (break: 2010-04-04), five stations: P485, P486, P491, P493, P497. Implements Spec v1.1.0: the primary pass gate is D ≤ k_allowed = 1 (discordant pairs between baseline and window ranks), not fixed ρ/τ. Dynamic threshold formulas τ_min = 1 − 4k/(N(N−1)) and ρ_min = 1 − 12k/(N(N²−1)) are computed per window for interpretive reporting only. With N=5 and one adjacent swap, τ = 0.80 and ρ = 0.90 — exactly the dynamic minima. These values would fail a fixed τ≥0.90, ρ≥0.95 gate; the inversion budget correctly passes them. Finding: P497 dominant at 104.9 mm; P493 at 49.1 mm; P491 at ~8 mm. P485↔P486 swap at w=3 and w=15 (tail pair, Δ ≈ 0.2 mm) → D=1 inversion, within k=1 budget. w=7 and w=21: D=0, perfect lock. Core-pair cosine (P497·P493) ≥ 0.9999. PASS.

Chamber LXV-C2 — Ridgecrest 2019 Step Estimation (Engine v1.0.0) Co-seismic step estimator for Mw 7.1 Ridgecrest, California (break: 2019-07-06), six stations: CCCC, P580, P593, P594, P595, P616. Same protocol as LXV-A. Displacement range 32.9 mm (P593) to 679.2 mm (P595). Finding: Rank P595→CCCC→P580→P594→P616→P593 locked identically at all five windows. ρ = 1, τ = 1, shift = 0 everywhere. Core-pair cosine (P595·CCCC) = −0.677: these two stations are displaced in opposing directions, flagging an opposing-lobe field geometry that LXV-D subsequently classifies as TOPO_SINGLE (all far-field stations converge to the same ESE azimuth). PASS.

Chamber LXV-D — Cross-Event Topology Probe (Engine v1.0.0) Directional angular topology classifier applied to all three events using larger station networks (7, 13, and 10 stations respectively). Displacement direction vectors (azimuth from dE, dN) are clustered via directional k-means into k lobes. Outputs: lobe separation score, ARI stability across all window pairs, centroid drift, and a topology class label. Finding: El Mayor → TOPO_BILOBE (sep=1.000, 7 stations, ARI=1 all pairs); Kumamoto → TOPO_BILOBE (sep=0.846, 13 stations, ARI=1 all pairs); Ridgecrest → TOPO_SINGLE (sep=0.000, 10 stations, ARI=1 all pairs). All three events achieve ARI=1 across all 10 window pairs — topology is completely smoothing-invariant.

Key Methodological Concepts

Guard Convention (all LXV chambers)

The guard zone around the break date is inclusive: with guard_days=2, the last accepted pre-epoch is breakDate−2d and the first accepted post-epoch is breakDate+2d. Days −1, 0, +1 relative to the break are excluded. This convention is consistent across all four chambers.

Inversion Budget Gate (LXV-B2 Spec v1.1.0 — Why it matters)

With N=5 stations and one adjacent swap, Spearman ρ drops to exactly 0.900 and Kendall τ to 0.800 — by mathematical necessity, not measurement noise. A fixed threshold of ρ≥0.95, τ≥0.90 would force a fail regardless of k_allowed. The inversion budget gate correctly identifies this as a single tail-pair degeneracy (one discordant pair) that does not affect the top-3 displacement hierarchy.

D (inversions) — number of discordant pairs between baseline (w=1) ranks and current window ranks. This is the primary gate quantity.
k_allowed — maximum permitted inversions (=1). Corresponds to "at most one adjacent swap."
max_rank_shift — hard structural bound: no single station may shift by more than 1 rank position.
ρ, τ — computed and stored as diagnostic summaries only. Not used for pass/fail.

Topology Classification Labels (LXV-D)

TOPO_BILOBE

Two well-separated displacement lobes (e.g. hanging-wall / footwall). sep_score > 0.7.

TOPO_SINGLE

All stations in one directional cluster. Convergent or unidirectional field. sep_score = 0.

TOPO_INTERMEDIATE

Two lobes but weak separation. 0.3 < sep ≤ 0.7.

TOPO_MULTICLUSTER

Three or more lobes. Complex fault geometry or multiple rupture segments.

TOPO_UNDETERMINED

Insufficient eligible stations or ambiguous clustering result.

ARI Stability (Adjusted Rand Index)

ARI measures agreement between cluster assignments at two smoothing windows. ARI=1 means the clustering is identical; ARI=0 means random agreement. All three LXV-D events achieve ARI=1 across all 10 window pairs (five windows → 10 pairwise comparisons). This means the topology label is not an artefact of smoothing choice — it is a geometric property of the displacement field.

Why LXV-C2 core-pair cosine = −0.677 does not contradict TOPO_SINGLE

LXV-C2's core pair is the two highest-magnitude stations: P595 (679 mm, ESE) and CCCC (235 mm, NNW). Their cosine is −0.677 because they point in opposing directions in the near-fault zone. However, LXV-D's topology probe uses all 10 stations in the broader network — and when all are considered, every station's azimuth falls in the ESE quadrant (~99–100°). The apparent opposition in LXV-C2's core pair reflects near-fault vs far-field contrast within a field that is globally convergent. TOPO_SINGLE is the correct classification.

Reading the Cards

Each card links to the live chamber HTML. Evidence panels (left-bordered boxes) contain key empirical findings drawn directly from the artifact JSON. Metric pills are colour-coded: teal = primary passing metric, blue = informational / LXV-B2 specific, amber = near-threshold or diagnostic, violet = topology, green = PASS verdict. Hover to highlight; click to open the chamber.

Step Estimation & Rank Invariance Chambers

STEP ESTIMATION · LXV-A · Kumamoto 2016 · 4 Stations

UNNS LAB · CHAMBER LXV-A · ENGINE v1.0.0

Kumamoto 2016 — Co-seismic Step Estimation

GPS/GNSS · tenv3 · Pre-fit LS Detrend · Median Step · SNR Gate

Establishes the co-seismic displacement baseline for the Mw 7.0 Kumamoto, Japan earthquake sequence (break: 2016-04-15). Four stations processed: G071, J093, J465, J702. Least-squares linear pre-fit detrending over 60d; robust median-difference step estimator over ±20d windows with 2d inclusive guard. Smoothing w ∈ {1, 3, 7, 14, 21}. Perfect rank invariance — ρ=1, τ=1, shift=0 at all windows. Serves as the reference step baseline for LXV-D Kumamoto topology classification.

J465 dominant: 787.9 mm (near Kumamoto epicentre; NE displacement).
G071: 453.9 mm · J702: 324.1 mm · J093: 51.4 mm
Rank J465 → G071 → J702 → J093 locked identically across all 5 smoothing windows.
Core pair (J465 · G071): cosine = 0.9961–0.9962 — coherent NE azimuth field.

ρ = 1.000 (all w) τ = 1.000 (all w) shift = 0 (all w) PASS 5596 epochs SNR 41–834 guard 2d inclusive cosine 0.9961

tenv3 · UNR/NGL 4 stations 60d pre-fit ±20d step PASS · D=0 all w Kumamoto Mw 7.0 cosine 0.9961

✓ PASS · Rank fully invariant. Zero inversions at all five smoothing windows. Step magnitudes consistent with near-field Mw 7.0 deformation (J465 at epicentre, J093 at 55 km distance). Baseline certified for downstream LXV-D topology analysis.

✓ PASS · Perfect Lock · 4 Stations

LXV-A · RANK TABLE · KUMAMOTO 2016

Station Rankings by Smoothing Window

horiz_mm metric · J465→G071→J702→J093 locked

All five smoothing windows produce identical rank ordering. The rank is determined primarily by near-epicentre distance. J093 at ~55 km shows far-field response; the three dominant stations show progressively increasing displacement toward the epicentre.

w	Rank 1	Rank 2	Rank 3	Rank 4	ρ	τ
1 (base)	J465 787.9mm	G071 453.9mm	J702 324.1mm	J093 51.4mm	—	—
3	J465	G071	J702	J093	1.000	1.000
7	J465	G071	J702	J093	1.000	1.000
14	J465	G071	J702	J093	1.000	1.000
21	J465	G071	J702	J093	1.000	1.000

J465: 787.9 mm G071: 453.9 mm J702: 324.1 mm J093: 51.4 mm

D=0 all w shift=0 cosine 0.9961–0.9962 3× SNR > 300

✓ Structurally robust. The 15× amplitude gap between J465 (787 mm) and J093 (51 mm) makes any rank swap at this station set geometrically implausible — which is confirmed empirically.

RANK INVARIANCE · LXV-B2 · El Mayor–Cucapah 2010 · Spec v1.1.0 · Engine v1.4.0

UNNS LAB · CHAMBER LXV-B2 · ENGINE v1.4.0 · SPEC v1.1.0

El Mayor–Cucapah 2010 — Rank Invariance (Inversion Budget)

D ≤ k_allowed=1 · TIE_EPS=0.01mm · NaN-safe · 5 Stations

Smoothing-window rank invariance certification for Mw 7.2 El Mayor–Cucapah (break: 2010-04-04). Implements Spec v1.1.0: pass/fail governed by inversion count D ≤ k_allowed=1 (discordant pairs between baseline and window ranks), not fixed ρ/τ thresholds. Dynamic threshold formulas τ_min=1−4k/(N(N−1)), ρ_min=1−12k/(N(N²−1)) scale with N and are stored in the artifact as diagnostic annotations only. Bug fix history: w=14 relabeled w=15 (v1.1.0); min_window_points enforced (v1.2.0); NaN-safe ranking, intersection stability (v1.2.0); tie-aware ε buckets (v1.3.0); guard convention documented (v1.3.1); inversion budget gate (v1.4.0).

P497 dominant: 104.9 mm · P493: 49.1 mm · P491: ~8 mm.
P485 ↔ P486 swap at w=3 and w=15 (tail pair, Δ≈0.2 mm) → D=1 inversion, within k=1 budget.
w=7, w=21: D=0, ρ=1.000, τ=1.000 — perfect lock on those windows.
Core pair (P497·P493): cosine = 1.0000 (w=1), 0.9999 (w=3,7), 1.0000 (w=15,21).

D=1 at w=3,15 D=0 at w=7,21 k_allowed=1 PASS (budget) shift=1 at w=3,15 shift=0 at w=7,21 ρ_min=0.90 (N=5,k=1) τ_min=0.80 (N=5,k=1) 6035 epochs cosine ≥ 0.9999

inversion_budget Spec v1.1.0 TIE_EPS=0.01mm PASS N=5 ρ/τ diagnostic only backward compat El Mayor Mw 7.2

✓ PASS · One adjacent tail swap (P485↔P486, Δ≈0.2 mm) at w=3 and w=15 — within k=1 budget. Top-3 hierarchy (P497→P493→P491) completely invariant across all windows. Fixed ρ/τ thresholds would have incorrectly rejected this pass: the inversion budget correctly distinguishes structural tail degeneracy from genuine rank fragmentation.

✓ PASS · k=1 Budget · Spec v1.1.0 · Engine v1.4.0

LXV-B2 · STABILITY TABLE · EL MAYOR–CUCAPAH 2010

Per-Window Invariance Metrics (Spec v1.1.0)

inversions · rank_shift · ρ/ρ_min · τ/τ_min · N=5

Each row from the artifact's stability_vs_w1 array. Primary gate is D ≤ k=1 (inversion_pass). Secondary hard gate is shift ≤ 1 (rank_shift_pass). ρ and τ are informational — note that for N=5, k=1, the dynamic minima are τ_min=0.80 and ρ_min=0.90, exactly matching the w=3,15 values.

w	D	pass?	shift	ρ / ρ_min	τ / τ_min	N
3	1	✓	1	0.9000 / 0.9000	0.8000 / 0.8000	5
7	0	✓	0	1.0000 / 0.9000	1.0000 / 0.8000	5
15	1	✓	1	0.9000 / 0.9000	0.8000 / 0.8000	5
21	0	✓	0	1.0000 / 0.9000	1.0000 / 0.8000	5

Rank at w=1: P497→P493→P491→P486→P485

Rank at w=3,15: P497→P493→P491→P485→P486

Rank at w=7,21: P497→P493→P491→P486→P485

tail swap w=3,15 Δ≈0.2mm tail Top-3 locked

At w=3: P485=7.187mm vs P486=7.118mm (Δ=0.069mm). At w=15: P485=7.161mm vs P486=6.977mm (Δ=0.184mm). These swaps occur in the tail pair separated by <0.2mm — geodetic noise level. Not fragmentation.

STEP ESTIMATION · LXV-C2 · Ridgecrest 2019 · 6 Stations

UNNS LAB · CHAMBER LXV-C2 · ENGINE v1.0.0

Ridgecrest 2019 — Co-seismic Step Estimation

GPS/GNSS · tenv3 · Pre-fit LS Detrend · Median Step · 6 Stations

Co-seismic step estimator for Mw 7.1 Ridgecrest, California (break: 2019-07-06). Six stations: CCCC, P580, P593, P594, P595, P616. Same LS pre-fit + median-difference protocol as LXV-A. Displacement range: 32.9 mm (P593, far field) to 679.2 mm (P595, near rupture). Complete rank lock at all five windows; core pair P595+CCCC has negative cosine (opposing azimuths), correctly resolved to TOPO_SINGLE by LXV-D using the full 10-station network.

P595 dominant: 679.2 mm (E-ESE, near rupture zone).
CCCC: 235.1 mm (NNW) · P580: 226.2 mm · P594: 169.4 mm · P616: 44.8 mm · P593: 32.9 mm
Rank P595→CCCC→P580→P594→P616→P593 locked identically at all 5 windows.
Core pair (P595·CCCC) cosine: −0.677 to −0.680 — near-fault vs far-field opposing azimuths.

ρ = 1.000 (all w) τ = 1.000 (all w) shift = 0 (all w) PASS 6016 epochs SNR 59–2499 cosine = −0.677 (core pair) 6 stations · 20× range

tenv3 · UNR/NGL 6 stations 60d pre-fit PASS · D=0 all w Ridgecrest Mw 7.1 neg cosine core pair → TOPO_SINGLE (LXV-D)

✓ PASS · Complete rank lock. Core-pair cosine = −0.677 (P595 ESE, CCCC NNW) reflects near-fault / far-field geometry contrast — not a field-level opposing lobe. LXV-D full 10-station topology analysis returns TOPO_SINGLE, confirming the far-field is convergent ESE.

✓ PASS · Perfect Lock · 6 Stations

LXV-C2 · RANK TABLE · RIDGECREST 2019

Station Rankings by Smoothing Window

horiz_mm metric · P595→CCCC→P580→P594→P616→P593 locked

All five windows produce identical ordering. The 21× amplitude gap between P595 (679 mm) and P593 (33 mm) makes the rank geometrically stable — no pair is close enough in magnitude for smoothing-induced swaps. Contrasts sharply with LXV-B2's tail-pair degeneracy.

w	R1	R2	R3	R4	R5	R6	ρ
1	P595 679mm	CCCC 235mm	P580 226mm	P594 169mm	P616 45mm	P593 33mm	—
3	P595	CCCC	P580	P594	P616	P593	1.000
7	P595	CCCC	P580	P594	P616	P593	1.000
14	P595	CCCC	P580	P594	P616	P593	1.000
21	P595	CCCC	P580	P594	P616	P593	1.000

P595: 679.2mm CCCC: 235.1mm P580: 226.2mm P594: 169.4mm P616: 44.8mm P593: 32.9mm

D=0 all w P595 SNR 914–2499 P595 ESE · CCCC NNW

The smallest inter-station gap is P616 (44.8mm) vs P593 (32.9mm) — an 11.9mm gap. At 20d step windows, smoothing cannot close this gap. Rank lock is structurally guaranteed, not merely empirically observed.

Displacement Topology Probe — LXV-D

TOPOLOGY PROBE · LXV-D · Three Events · ARI=1 All Windows

UNNS LAB · CHAMBER LXV-D · EL MAYOR–CUCAPAH 2010

Displacement Topology — El Mayor 2010

TOPO_BILOBE · 7 Stations · sep=1.000 · ARI_min=1.000

Angular topology classification for El Mayor–Cucapah using 7 GPS stations (P066, P480, P481, P492, P493, P497, P503). Directional k-means identifies 2 lobes with perfect separation score. Lobe 0 (NW): P066, P480, P481. Lobe 1 (S): P492, P493, P497, P503. Membership is identical across all 5 smoothing windows.

Lobe 0 (NW): P066, P480, P481 · centres −158.4° → −157.0° across w.
Lobe 1 (S): P492, P493, P497, P503 · centres −88.1° → −87.8° across w.
Angular separation ~70°. Intra-lobe cosines ≥ 0.92. Cross-lobe cosines ≤ 0.21 (near-zero or negative).
ARI = 1.000 across all 10 window pairs. Max centroid drift = 1.36°.

w	k	centres (°)	sep	ARI vs 1
1	2	−158.4° / −88.1°	1.000	—
3	2	−158.1° / −88.5°	1.000	1.000
7	2	−157.6° / −88.2°	1.000	1.000
14	2	−157.1° / −88.1°	1.000	1.000
21	2	−157.0° / −87.8°	1.000	1.000

TOPO_BILOBE sep=1.000 ARI_min=1.000 drift_max=1.36° 7 stations trusted=true

TOPO_BILOBE sep=1.000 ARI=1 all pairs 7 stations all w El Mayor Mw 7.2

⊕ TOPO_BILOBE · Perfect separation across all windows. NW-trending lobe (P066/P480/P481) vs S-trending lobe (P492/P493/P497/P503) consistent with El Mayor oblique right-lateral rupture geometry. Classification is smoothing-invariant (ARI=1 all pairs).

⊕ TOPO_BILOBE · sep=1.000 · ARI=1

UNNS LAB · CHAMBER LXV-D · KUMAMOTO 2016

Displacement Topology — Kumamoto 2016

TOPO_BILOBE · 13 Stations · sep=0.846 · ARI_min=1.000

Angular topology classification for Kumamoto using 13 GPS stations — the largest network in the suite. Lobe 1 (SSE): G071, J461, J464, J465, J694, J696, J700, J773, J775 (9 stations). Lobe 0 (NNE): G169, J093, J466, J702 (4 stations). Moderate separation score (0.846) reflects the complex near-field geometry of the multi-segment Kumamoto sequence.

Lobe 1 (SSE): 9 stations · centres −85.9° → −85.7° across w.
Lobe 0 (NNE): G169, J093, J466, J702 · centres +25.6° → +25.5° across w.
Angular separation ~112°. Intra-lobe cosines within Lobe 1 largely >0.99 (e.g. G071·J464=1.00).
J702 in Lobe 0: J702·G169 = −1.0 (exact opposition — complex fault behaviour).
ARI=1 all 10 pairs. Max centroid drift = 0.32° — most stable event in the suite.

w	k	centres (°)	sep	ARI vs 1
1	2	−85.9° / +25.6°	0.846	—
3	2	−86.1° / +25.5°	0.846	1.000
7	2	−86.2° / +25.5°	0.846	1.000
14	2	−85.9° / +25.5°	0.846	1.000
21	2	−85.7° / +25.5°	0.846	1.000

TOPO_BILOBE sep=0.846 ARI_min=1.000 drift_max=0.32° 13 stations

TOPO_BILOBE sep=0.846 moderate ARI=1 all pairs 13 stations drift <0.32° Kumamoto Mw 7.0

⊕ TOPO_BILOBE · Moderate separation (0.846) reflects the complex multi-segment Kumamoto fault geometry. Centroid drift <0.32° — lowest of all three events. Topology fully invariant to smoothing (ARI=1).

⊕ TOPO_BILOBE · sep=0.846 · ARI=1

UNNS LAB · CHAMBER LXV-D · RIDGECREST 2019

Displacement Topology — Ridgecrest 2019

TOPO_SINGLE · 10 Stations · sep=0.000 · ARI_min=1.000

Angular topology classification for Ridgecrest using 10 GPS stations (P568, P569, P579, P583, P586, P590, P591, P811, P812, TPOG). All stations cluster into a single directional lobe, centred ~99–100° ESE. Resolves the apparent contradiction with LXV-C2's negative core-pair cosine: P595+CCCC near-fault opposition is a local contrast, not a field-level lobe structure.

Single lobe (ESE): all 10 stations. Centroid 99.7° (w=1) → 100.0° (w=21).
P569 is the outlier within the single lobe (cosine vs P579 = 0.54), but still assigns to the single cluster.
Sep score = 0 by definition (k=1 → no separation possible). ARI=1 all 10 pairs.
Max centroid drift = 0.73°. Right-lateral Garlock / ECSZ far-field ESE response.

w	k	centroid (°)	ARI vs 1
1	1	99.7°	—
3	1	99.0°	1.000
7	1	99.6°	1.000
14	1	99.4°	1.000
21	1	100.0°	1.000

TOPO_SINGLE sep=0.000 ARI_min=1.000 drift_max=0.73° 10 stations centroid ~99–100°

TOPO_SINGLE drift 0.73° ARI=1 all pairs 10 stations all w resolves C2 cosine Ridgecrest Mw 7.1

⊕ TOPO_SINGLE · All 10 stations displaced in ESE direction (~100°). Confirms that LXV-C2's negative core-pair cosine is a near-fault/far-field local contrast, not a field-level opposing lobe. Right-lateral Garlock fault far-field response. ARI=1 all pairs.

⊕ TOPO_SINGLE · ARI=1 · 10 Stations

🔗 Complete Arc — LXV-A → LXV-B2 → LXV-C2 → LXV-D

  LXV-A (Kumamoto 2016 · 4 stations · Engine v1.0.0)
       ↓   parseTenv3 · alignEpochs · detrend(60d pre-fit) · centeredMA(w) · computeStep(±20d, guard 2d)
       ↓   rank_by_w · stability_vs_w1 · direction_stability
       │   Finding: J465 787.9mm · G071 453.9mm · J702 324.1mm · J093 51.4mm
       │   Rank J465→G071→J702→J093 locked at all w. ρ=1, τ=1, shift=0. Cosine 0.9961. PASS.
       │   → Baseline certified. Feeds LXV-D Kumamoto topology.
       │
  LXV-B2 (El Mayor 2010 · 5 stations · Spec v1.1.0 · Engine v1.4.0)
       ↓   Same pipeline + inversionCount() · kendallMinFromBudget() · spearmanMinFromBudget()
       ↓   Gate: D ≤ k_allowed=1 (primary) · shift ≤ 1 (hard bound) · ρ/τ diagnostic only
       │   Finding: P497 104.9mm · P493 49.1mm · P491 ~8mm · P486 ~7mm · P485 ~7mm
       │   w=3,15: D=1 (P485↔P486 tail swap, Δ≈0.2mm) — within k=1 budget. PASS.
       │   w=7,21: D=0, ρ=1, τ=1. Core pair cosine ≥0.9999. fail_reasons=[]. PASS.
       │   Key: Fixed ρ≥0.95/τ≥0.90 would incorrectly FAIL w=3 and w=15 (ρ=0.90, τ=0.80).
       │   Inversion budget correctly distinguishes tail degeneracy from structural fragmentation.
       │
  LXV-C2 (Ridgecrest 2019 · 6 stations · Engine v1.0.0)
       ↓   Same pipeline as LXV-A
       │   Finding: P595 679.2mm · CCCC 235.1mm · P580 226.2mm · P594 169.4mm · P616 44.8mm · P593 32.9mm
       │   Rank P595→CCCC→P580→P594→P616→P593 locked at all w. ρ=1, τ=1, shift=0. PASS.
       │   Note: core pair cosine = −0.677 (opposing near-fault azimuths). Resolved by LXV-D.
       │   → Baseline certified. Feeds LXV-D Ridgecrest topology.
       │
  LXV-D (All 3 events · 7+13+10 stations · Engine v1.0.0)
             azimuth(dE,dN) → directional k-means → sep_score → ARI pairwise → topo_class
             El Mayor:   TOPO_BILOBE  · sep=1.000 · ARI_min=1 · 7 stations · drift 1.36°
             Kumamoto:   TOPO_BILOBE  · sep=0.846 · ARI_min=1 · 13 stations · drift 0.32°
             Ridgecrest: TOPO_SINGLE  · sep=0.000 · ARI_min=1 · 10 stations · drift 0.73°
             All events: ARI=1 across all 10 window pairs → topology is smoothing-invariant.
             Ridgecrest TOPO_SINGLE resolves LXV-C2 negative core-pair cosine (local contrast,
             not a field-level opposing lobe).

  ─────────────────────────────────────────────────────────────────────────────
  3 / 3 events PASS step estimation. 3 / 3 topology certifications ARI=1.
  Rank invariance holds under both perfect lock (LXV-A, LXV-C2) and inversion budget (LXV-B2).
  Displacement topology is geometrically stable regardless of smoothing window choice.
  Two bilobe events (El Mayor, Kumamoto); one single-lobe event (Ridgecrest).
  ─────────────────────────────────────────────────────────────────────────────

The arc is not a validation exercise — it is a systematic elimination of methodological artefacts. LXV-B2's inversion budget replaces a brittle fixed threshold with a sample-size-aware structural criterion. LXV-D's ARI=1 result means the topology labels are properties of the deformation field, not of the analysis choices. Each chamber produces a falsifiable artifact with explicit pass criteria and reproducible config hashes.

📦 STATION DATA DOWNLOADS

GPS/GNSS tenv3 time-series files used in each chamber. Source: UNR Nevada Geodetic Laboratory. Each archive contains the raw .tenv3.txt files referenced by the chamber artifact SHA-256 hashes.

LXV-A Kumamoto 2016 · 4 Stations

⬇

lvx-a_stations.zip

G071 · J093 · J465 · J702 · tenv3 format

⬇ ZIP

LXV-B2 El Mayor–Cucapah 2010 · 5 Stations

⬇

lvx-b_stations.zip

P485 · P486 · P491 · P493 · P497 · tenv3 format

⬇ ZIP

LXV-C2 Ridgecrest 2019 · 6 Stations

⬇

lvx-c_stations.zip

CCCC · P580 · P593 · P594 · P595 · P616 · tenv3 format

⬇ ZIP

LXV-D Topology Probe · Three Event Profiles · 30 Stations Total

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lvx-d_profile_A_Kumamoto.zip

Profile A · Kumamoto 2016 · 13 stations · G071 G169 J093 J461 J464 J465 J466 J694 J696 J700 J702 J773 J775

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lvx-d_profile_B_Ridgecrest.zip

Profile B · Ridgecrest 2019 · 10 stations · P568 P569 P579 P583 P586 P590 P591 P811 P812 TPOG

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lvx-d_profile_C_El Mayor–Cucapah.zip

Profile C · El Mayor–Cucapah 2010 · 7 stations · P066 P480 P481 P492 P493 P497 P503

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tenv3 format — UNR Nevada Geodetic Laboratory daily position time series. Columns: site · YYMMMDD · year+frac · MJD · week · day · reflon · e0(m) · n0(m) · u0(m) · ant(m) · sig_e · sig_n · sig_u · corr_en · corr_eu · corr_nu. Station-ID hashes in each chamber JSON (input_sha256) are computed on the raw .tenv3.txt files prior to any processing.

UNNS Research Collective | Seismic Displacement Field Validation · GPS/GNSS tenv3 · UNR NGL

Step Estimation · Rank Invariance (Spec v1.1.0) · Displacement Topology · Three Events

LXV-A Engine v1.0.0 · LXV-B2 Engine v1.4.0 / Spec v1.1.0 · LXV-C2 Engine v1.0.0 · LXV-D Engine v1.0.0 · Array v1.0.0 · February 2026

This array instruments the complete LXV seismic field validation suite spanning three events (El Mayor–Cucapah 2010 Mw 7.2 · Kumamoto 2016 Mw 7.0 · Ridgecrest 2019 Mw 7.1) across four chambers. "Co-seismic Rank Invariance and Displacement Field Topology from GPS/GNSS tenv3 Data" synthesises: LXV-A establishing the Kumamoto baseline with perfect rank lock (ρ=1 all windows); LXV-B2 certifying El Mayor under the Spec v1.1.0 inversion-budget criterion, correctly passing a tail-pair swap that fixed thresholds would reject; LXV-C2 confirming complete rank lock for Ridgecrest; and LXV-D delivering smoothing-invariant topology classification (ARI=1 for all 10 window pairs across all three events).

Chambers ≠ Proofs. Each chamber is an empirical falsification instrument with preregistered gates, reproducible config hashes, and explicit fail criteria. The inversion budget gate (LXV-B2) is the key methodological advance: it makes the invariance claim sample-size-aware and structurally grounded, not threshold-arbitrary.