UNNS SUBSTRATE RESEARCH PROGRAM · ATOMIC PHASE LANDSCAPE · 6 ELEMENTS · APRIL 2026
Atomic Structural Phase Landscape
16 runs · 6 elements (H, He, Li, Na, Fe, Ag, Au) · 2 representations (QM-I, Zeeman) · 5 structural regimes
6× FULL3× HARD 4× GIANT-corner2× GIANT-interior 1× TAIL F separator: 13/13 narrow zone Fe-ZEE confirms chart locality
ELEMENTS
6
H, He, Li, Na, Fe, Ag, Au
TOTAL RUNS
16
all measured
REGIMES
5
A B C D E
FULL (Reg A)
6
He·Li·Na QMI
HARD (Reg B)
3
H QMI all reps
GIANT-corner C
4
H·He·Na ZEE
GIANT-interior D
2
Fe·Ag ZEE
TAIL (Reg E)
1
Au ZEE
DIAGATOMIC PHASE DIAGRAM — (tailDom, GR) SPACE — ALL 16 RUNS
COMPLETE ATOMIC CORPUS IN DECISIVE CHART — 5 REGIMES VISIBLE
x₁ = TAIL DOMINANCE x₂ = GIANT RATIO 0.9400.950 0.9600.970 0.9800.990 1.000 0.790.85 0.900.95 1.00 A: FULL (GR=1.000) C: corner D: GIANT interior B: HARD ZONE (GR < 0.95) GR=1.000 (FULL edge) GR=0.95 (HARD threshold) tailDom=1.0 F=GR−tailDom=0 (He-zone boundary) Na-QMI-spec ★ CANONICAL FULL m=0.053 Na-QMI-pre He/Li ×4 H-QMI-spec GR=0.934 H-QMI-pre GR=0.850 H-QMI-gap GR=0.814 H QMI: all HARD C: corner H/He/Na ZEE tailDom>0.999 Fe-ZEE ★ D: GIANT-interior D=0.967 F>0 but GIANT → chart locality confirmed ✓ Ag-ZEE D=0.9978 Au-ZEE TAIL GR=0.994 A C/D B F-sep. valid zone tailDom > 0.995
REGFIVE STRUCTURAL REGIMES — COMPLETE CORPUS
RegimeNameSystems GR rangetailDom range Active branchPhysical signature
AFULL interior He,Li,Na QMI (6) 1.00000.947–0.999 G₁ and G₃=0Multi-electron atoms, QMI; GR saturated
BHARD H QMI ×3 0.814–0.9340.998 G₁ (tiny), G₃ dominantHydrogenic n⁻³ shell structure; catastrophic fragmentation
CGIANT corner H,He,Na ZEE (4) 0.995–0.9980.999–1.000 G₁ (near corner)Light atoms; Zeeman split creates rare outliers; near (1,1) corner
DGIANT interior Fe,Ag ZEE (2) 0.997–0.9980.967–0.998 G₁ or G₃ (varies)Complex fine-structure; tailDom lower than corner zone
ETAIL Au ZEE (1) 0.9940.998 G₁ active, G₃<0Heaviest tested; Zeeman TAIL; no percolation at any scale
KEYTHREE PRINCIPAL FINDINGS
FINDING 1 — HYDROGEN QMI IS HARD ACROSS ALL REPRESENTATIONS

All three hydrogen QM-I representations (preprocessed, gap structure, spectrum) return HARD with GR ∈ [0.814, 0.934] — the only QM-I family that fails the FULL class. The hydrogenic n⁻³ level spacing creates extreme gap heterogeneity (gaps grow without bound with quantum number) that no encoding can regularize. This is a representation-invariant HARD result: Theorem 1 is triggered regardless of how the hydrogen ladder is constructed. By contrast, Zeeman H (magnetically split, finer-scale gaps) returns GIANT near the corner.

FINDING 2 — Fe-ZEE CONFIRMS CHART LOCALITY (F-SEPARATOR VIOLATION)

Iron Zeeman has tailDom = 0.967 — far from the helium zone (tailDom > 0.995). The helium separator F = GR − tailDom = 0 gives F = +0.030 (FULL side) for Fe-ZEE, but Fe-ZEE is GIANT. This is not an anomaly: it confirms exactly what the local theory of the main manuscript requires. The separator F=0 is a local geometric object, valid only in the narrow (tailDom, GR) zone explored by the helium corpus. Outside that zone, different chart geometry applies. Fe-ZEE is the first corpus system to demonstrate this locality explicitly. Within the narrow zone (tailDom>0.995): 13/13 correct separation.

FINDING 3 — ZEEMAN tailDom DECREASES WITH ATOMIC COMPLEXITY

Light atoms (H, He, Na) have Zeeman tailDom > 0.999 (corner zone C); heavier/more complex atoms fall into the interior (Ag: 0.998, Fe: 0.967) or TAIL (Au: 0.998 but GR<1). The Fe outlier (Z=26 but tailDom=0.967) reflects iron's dense d-electron fine-structure: many moderate-scale magnetic gaps dilute the outlier fraction, unlike lighter elements with sparser Zeeman splitting. Au (Z=79, simpler s-valence structure) stays in the corner zone by tailDom but reaches TAIL by GR. This is the first cross-system structural trend in the corpus.

CROSS-ELEMENT CANON. — REGIME A (FULL)
RankSystemtailDomm_local
1 ★Na-QMI-spec0.94650.0535
2Na-QMI-pre0.98210.0179
3He-QMI-spec0.99780.0022
4He-QMI-pre0.99810.0019
5Li-QMI-pre0.99830.0017
6Li-QMI-spec0.99840.0016
SEPARATOR VALIDITY — ZONE ANALYSIS
ZoneSystemsCorrectF-gap
tailDom>0.99513 systems13/13 ✓0.003–0.24
tailDom<0.9953 systems2/3Fe violation
tailDom>0.94all 1615/161 violation (Fe)
Fe-ZEE: tailDom=0.967 → outside narrow zone → F=+0.030 but class=GIANT. Locality of helium chart confirmed.
UNNS SUBSTRATE RESEARCH PROGRAM · unns.tech ATOMIC PHASE LANDSCAPE · 6 ELEMENTS · STRUC-PERC-I v2.4.0 · APRIL 2026 v1.0