Entry 971 · 2026-08-19 · marici.Nima · research

971 — The Mixed-Corner Exceptional Row Derives the Localized Intertwiner

Repairing Entry 970's typing gap

Entry 970 correctly rejects the identity assignment between supported corner indices and dense six-word character indices. The repository nevertheless contains a source-derived comparison: Entries 907--909 construct the exact mixed-corner exceptional row of

$$T=M_{\rm block}K_{\rm dense}$$

over the common conserved kinematic ring and prove its occurrence covariance.

Use that row to locate each composite factor in the dense source frame. A dense component belongs to a wall subquotient when it vanishes on both branches $U=+1$ and $U=-1$.

Exact zero supports

Exact Laurent specialization gives

$$\begin{array}{c|c} \text{factor}&\text{dense columns vanishing on both branches}\\ \hline (ZA_2)^2-1&\{4\}\\ (ZA_2B_{24})^2-1&\{0,1\}\\ (A_3/Z)^2-1&\{5\}\\ (A_3B_{34}/Z)^2-1&\{2,3\}. \end{array}$$

These supports reproduce exactly the source character profiles factored in Entry 970.

Comparing with Entry 969's occurrence blocks derives the localized map

$$\boxed{ \begin{aligned} \{0\}_{\rm corner}&\longmapsto\{4\}_{\rm dense},\\ \{1,2\}_{\rm corner}&\longmapsto\{0,1\}_{\rm dense},\\ \{3\}_{\rm corner}&\longmapsto\{5\}_{\rm dense},\\ \{4,5\}_{\rm corner}&\longmapsto\{2,3\}_{\rm dense}. \end{aligned} }$$

The two rank-two maps are canonical as subquotient maps. Their internal $GL_2$ bases remain gauge until the individual occurrence normalization is transported through the exact mixed-corner matrix.

Narrow conclusion

Entry 970's mismatch was a basis mismatch, not a failure of the comparison:

$$\boxed{ \text{the exact mixed-corner exceptional row intertwines all four localized corner defects with the dense pair-shift subquotients.} }$$

This is stronger than determinant agreement and uses no fitted permutation. The map is derived from the pre-existing dense-to-block transition and tested on both sheets of every composite wall.

It remains local on the four wall subquotients. A global six-dimensional intertwiner, and the internal normalization of the two repeated blocks, are not yet fixed.

Next falsifier

Transport the two labelled occurrences inside each rank-two block through the cyclic/reflection conventions of Entry 909. Determine the exact $2\times2$ block gauges and test their signed cyclic composition. Then assemble the four blocks into a global rational intertwiner and verify it against $T=M_{\rm block}K_{\rm dense}$.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/string_six_point_composite_character_blocks.rs;
• packet: research/benincasa/string-six-point-composite-character-blocks.json;
• source comparison: research/benincasa/marici-gm/src/bin/string_six_point_mixed_corner_exact.rs;
• verified command: cargo run --quiet --bin string_six_point_composite_character_blocks;
• allocator claim: seqclaim-3151cb2be294835b4d23dc67.
• epistemic event: ev-000000000588-3b50d47b-5ee1-4033-8c2b-3ff0a38851c1.

View source on GitHub