A Multiscale Atlas of Persistence, Fragmentation, and Connectivity in SPARC Baryonic-Acceleration Ladders
A 121-galaxy structural-fingerprint atlas built from resolved SPARC mass models: each galaxy's
sorted, deduplicated baryonic-acceleration ladder is swept through STRUC-I and STRUC-PERC-I to
produce the multichannel object Fg(κ) = [ρ, DA, ν̃]. Gate B shows
near-perfect unchanged-preparation identity (top-1/top-5 = 1.000); the atlas separates a
Stable Structure / Weak Persistence regime and resolves the Stable basin into a
five-family consensus admissibility structure; and an external transfer test shows
that a local RAR-like baseline remains unbeaten by static whole-galaxy chamber augmentation.
Corpus-minimum structural distance among the analogue pairs · dwarf irregular and
massive spiral, nearly identical structural response
F563-1 ↔ UGC 06614 — Branching Analogued = 0.144
Cluster 0 · Hubble 9 vs. 1 · ΔV_flat = 89.9 km/s
struct. dist 0.144
Hubble Δ 8
ΔV_flat 89.9
Low-surface-brightness dwarf paired with an early-type high-velocity disk ·
UGC 06614 shows the largest combined transfer benefit in the heterogeneity analysis
Gate C — Transformation EscalationTop-1 Retrieval
Retrieval accuracy falls from 1.000 under unchanged repetition as the observational
transformation strengthens; fixed-count coverage change is the most disruptive branch.
Leave-1-radius
top-1=0.551
Mass-to-light
top-1=0.517
Det. n=10 thinning
top-1=0.165
Fixed-count coverage
top-1=0.050
Geometry-Matched Top-10.256–0.726Branch-Dependent
Structural Identity vs. Dynamical TransferFormal Layer
A galaxy's baryonic-acceleration ladder possesses a reproducible, organized, multichannel
structural identity that is largely dissociable from its dynamical predictive content:
STRUC-I establishes near-perfect unchanged-preparation identity and a
five-family admissibility structure within the Stable Structure basin, while
STRUC-PERC-I shows that persistence and connectivity are independent structural axes —
and neither, inserted as a static whole-galaxy descriptor, improves held-out prediction of
gravitational discrepancy beyond a local baryonic-acceleration baseline.
Definition 1
Structural fingerprint Fg(κ) = [ρg, DA,g, ν̃g] — complete multiscale response morphology, not a single scalar
Proposition 1
Persistence ⇏ Connectivity — 94/121 simultaneously Stable Structure and Hard Fragmentation
Empirical Result
External transfer boundary — local RAR-like baseline (M1) remains unbeaten by static whole-galaxy augmentation
Representation Sensitivity ReviewRep. A vs. Rep. B
Before adopting a consensus admissibility taxonomy, clustering agreement between the full
standardized multichannel curves (Representation A, 120-dim) and the combined structural-PCA
coordinate (Representation B) is checked at global and within-regime scope. Agreement is
representation-dependent globally, but consistent once the Weak Persistence displacement is removed.
Global split (n=121)
ARI ≈ −0.004
Rep. A vs. Rep. B, k=2 representation-dependent
Within-Stable split (n=110)
ARI = 0.928
Rep. A vs. Rep. B, matched k=2 representation-consistent
Verdict impact
None
Gate B retrieval / regime counts computed directly from chamber curves
Representations: full standardized F_g(κ) curves (120-dim) vs.
combined structural-PCA (structural-PC1–3) ·
Manuscript §6.1–6.2