This is an excellent, thought-provoking observation. You have genuinely discovered a clean numerical pattern using real atomic data. However, as requested, here is a brutally honest, scientific evaluation from the perspective of solid-state physics and atomic theory. 

The short answer is: **(c) trivially expected and (d) physically flawed.**

While your math is correct, the underlying physics involves a spurious correlation. Both your "core jump ratio" and the crystal structures are independently determined by the element's position in the periodic table (specifically, the number of valence electrons), but they do not physically cause one another.

Here is the detailed breakdown answering your specific questions:

### 1. Is this core jump ratio as a structure discriminator already known and published?
**No, it is not published or used as a discriminator.** 
Solid-state physicists and materials scientists use the number of valence electrons (often called the electron-to-atom ratio, $e/a$, or d-band filling) to predict transition metal crystal structures. Since your "core jump ratio" is simply a function that shrinks as the valence electron count increases, it acts as a **proxy variable**. It mathematically aligns with the structure boundaries, but physicists use the simpler, actual causal variable (d-band filling) instead of deep ionization ratios. 

### 2. Is the monotonic decrease trivially expected, or a non-obvious pattern?
**It is trivially expected from basic atomic physics.**
Your "core jump ratio" compares two very specific ionization events. Let's look at what is actually happening physically. 
*   **The denominator** (last valence electron) is the energy required to remove the single $3d$ electron from a $[Ar]3d^{1}$ ion (e.g., $Sc^{2+}$, $Ti^{3+}$). 
*   **The numerator** (first core electron) is the energy required to remove a $3p$ electron from a bare $[Ar]$ core.

You are examining an **isoelectronic sequence**. For a given period, you are comparing the energy of an $np$ orbital to an $nd$ orbital for the *exact same highly charged ion* under an increasing nuclear charge ($Z$). Because the core $p$-orbitals penetrate closer to the nucleus than the $d$-orbitals, they experience a higher effective nuclear charge ($Z_{eff}$). 

As $Z$ increases across the period, the bare nuclear charge begins to overwhelmingly dominate the constant electron-electron screening effect. Mathematically, the fractional difference between $Z_{eff}(p)$ and $Z_{eff}(d)$ shrinks. Therefore, the ratio of their ionization energies $\sim Z_{eff}(p)^2 / Z_{eff}(d)^2$ **must** decrease monotonically. 

### 3. Is our interpretation (well dimensionality → crystal structure) physically reasonable?
**No, the interpretation is flawed for two major reasons:**
1.  **Ionization vs. Solid State:** Your ratio utilizes the 4th to 12th ionization energies. These represent the potential well of a **highly charged bare ion** existing in a plasma or a vacuum. In a solid metal lattice, the atoms are neutral. The valence electrons do not experience that sharp "core jump" because they are smeared out into continuous energy bands and are heavily screened by conduction electrons.
2.  **The true driver of structure:** The crystal structure transitions (HCP → BCC → HCP → FCC) across the d-block are determined by the **filling of the d-band** (famously modeled by Friedel, and later by Pettifor's structural maps). BCC structures are stabilized when the d-band is roughly half-full because the specific geometry of the $d$-orbitals creates strong, directional bonding lobes that lower the band energy. As the band fills further, the system shifts to FCC to maximize close-packing while minimizing anti-bonding interactions.

### 4. Are there published studies correlating successive ionization energies with crystal structure?
**No.** While empirical structural maps (like Miedema's parameters or Pettifor maps) heavily utilize the *first* ionization energy, electronegativity, or atomic radius of neutral atoms, they do not use successive/deep core ionization energies. Deep core states are physically disconnected from the metallic bonding environment of the solid state.

### 5. What would a solid-state physicist say about this finding?
A solid-state physicist would say: *"You have correctly identified that crystal structure correlates with d-band filling. However, you've found a complex atomic property (the ratio of two deep, highly-ionized states) that is physically irrelevant to the solid state, but mathematically forced to vary smoothly across the periodic table due to hydrogenic scaling laws.* 

*Furthermore, your 'mismatches' in Period 4 (Mn, Fe, Co) actually prove this is a proxy correlation. The 4d (Period 5) and 5d (Period 6) metals follow the 'ideal' HCP → BCC → HCP → FCC structural sequence based perfectly on d-band filling. The anomalies in the 3d metals (like Fe being BCC instead of HCP) are famously known to be caused by strong **ferromagnetic and antiferromagnetic exchange interactions**, which alter their free energy and force different structures. Your 'core jump ratio' has no mechanism to account for these magnetic phase changes."*

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**Summary:** You found a beautiful mathematical artifact of isoelectronic scaling that reliably proxies the valence electron count. It is a great empirical observation, but the mechanism is atomic scaling, not potential well dimensionality driving the solid state.