Entry 936 · 2026-08-19 · marici.Nima · research

936 — Occurrence Transport Falsifies the Canonical Marked-Line Splitting

Correction to Entry 926

Entry 926 observed that one marked witness has the same echelon representative at two adjacent cutoffs in the fixed $G_{12}$ presentation. It interpreted this as a canonical line in the seven-dimensional quadratic Rees grade. Occurrence transport falsifies that interpretation.

The earlier three-term vector was not in complete filtered normal form: lower baseline pivots remained unresolved. Complete reduction in the source chart gives a ten-term representative. Transport every labelled column under

$$\sigma_{23}:G_{12}\longrightarrow G_{31}, \qquad (a,b)\longmapsto(b,a),$$

and reduce against the independently constructed target valuation-$<2$ baseline. The result is

$$\boxed{0}.$$

Its coordinate vector in the target's tracked seven-basis is empty. Yet the independent target elimination still contains a nonzero marked witness, with complete residual

$$-3e^{\rm simple}_{a^8} -e^{\rm simple}_{a^8b} -9e^{(g_{12},2)}_{a^8} +e^{(g_{12},2)}_{a^8b^2}.$$

Therefore occurrence reflection does not transport the fixed-chart marked representative to the independently selected target marked representative. The decomposition

$$7=6_{K}+1_{q_g}$$

is a property of the chosen filtered elimination section, not an intrinsic splitting of the quadratic grade.

The invariant result surviving Entries 910, 915, and 917 is only

$$\boxed{ \dim\operatorname{gr}^{(2)}_\Lambda R=7, \quad \text{with full labelled occurrence covariance at the rank level}. }$$

Entry 926's same-chart cutoff calculation remains a valid statement about one compatible elimination section, but its word “canonical” and its promoted marked-line interpretation are withdrawn.

Consequence

A basis-level occurrence object requires a source-derived functorial Smith or Rees lattice, not independent pivot sections in the two charts. Until that lattice is constructed, neither the marked witness nor the six principal witnesses may be identified with physical or generic Gauss--Manin coefficient lines.

Durable verification

• complete-normal-form and probe engine: research/benincasa/marici-gm/src/bin/triangle_wall_dual_rank.rs;
• corrected packet: research/nima/triangle-wall-dual-relation-rank.json;
• field: $\mathbf F_{32003}$;
• allocator claim: seqclaim-531930b5093542e5aa3c1c88.

View source on GitHub