Closure-Node Registration: Redox richness as the signature of where unresolved relational difference is registered relative to a closure node — and two regimes of one event in the d- and f-blocks

The spatial profile of redox accessibility around an electronic closure node differs systematically between the d-block and the lanthanide f-block — whether richness peaks at the node or in its neighbours. For 30 transition metals (3d, 4d, 5d; groups 3–12) under a curated representative-state protocol, the single d-octave descriptor d_balance = 1 − |N_d − 5|/5 predicts oxidation-state count with lower leave-one-series-out error than electron count, group, Z, or period + group (LOO-RMSE 1.23 vs. ≥ 1.64; R² = 0.55). The local contrast at the half-filled node is positive — mean count 5.00 at d⁵ (Cr, Mn, Mo, Tc, Re) versus 3.75 at the adjacent d⁴/d⁶ (Fe, Nb, W, Os), Δ = +1.25 — but its 95% bootstrap interval, [−0.35, 2.85], crosses zero (92.9% of replicates positive). For the oxidation span, Δ = +1.35 (90.7% positive, 95% interval [−0.60, 3.25]). Thus the d⁵ enrichment is suggestive, not independently validated. For the lanthanide f-block the pattern inverts: Gd (f⁷) is rigid (+3 only), while additional states appear in the neighbours of the closures f⁰ (Ce⁴⁺), f⁷ (Eu²⁺, Tb⁴⁺), and f¹⁴ (Yb²⁺). This qualitative inversion is consistent with standard lanthanide chemistry but remains quantitatively preliminary pending standardised oxidation-state lists. The two patterns are read — as a hypothesis, not a derivation — as two regimes of one mechanism: registration of unresolved relational difference relative to a closure node, selected by the node’s local resolution capacity (its hardness). Soft d‑nodes hold difference locally (centred profile); hard lanthanide f‑nodes project it to neighbours (peripheral profile). The mechanism is falsifiable: under the same protocol the early actinides (decisively U, Np, Pu), less shielded than the lanthanides, must show an intermediate, more node‑centred profile. The empirical anchor is the profile shape, not the RGM vocabulary, which does not validate the wider framework.