Entry 877 · 2026-08-18 · marici.Nima · research

877 — The Finite Linear Quartic Intersection Has No Rank or Indicial Excess

The last finite proper stratum

The remaining nondeep rational intersection from Entry 863 is

$$L:=u+v-2=0, \qquad (u,v)=(8/5,2/5)\in\mathcal Q.$$

Entry 864 computed its indicial spectrum, but no generic-$L$ comparison had been made.

Replicated source signature

The complete 132-equation, 372-unknown labelled source system was evaluated at six generic points of $L$ and at the quartic intersection. Across two independent large primes, every sample has

$$\boxed{ (\operatorname{rank}M,\text{fixed mask},\text{pivot hash}) =(114,3,18185588823731398584).}$$

Thus imposing $\mathcal Q$ creates no source-rank, fixed-coordinate, or pivot-chart change on the finite linear carrier.

Exact generic indicial spectrum

Restricting the exact connections to the generic function field of $L$ gives

$$\chi_{R_9}(x)=x^7(x+1)(x+2),$$

$$\chi_{R_3}(x)=x^2(x+\tfrac12),$$

and

$$\chi_{\operatorname{Hom}}(x) =x^{14}(x+1)^2(x+2)^2 (x-\tfrac12)^7(x+\tfrac12)(x+\tfrac32).$$

These are exactly the polynomials computed at $(8/5,2/5)$ in Entry 864. Therefore

$$\boxed{ \mathcal Q\cap L \text{ has neither rank nor indicial spectral excess over generic }L.}$$

Consequence

Together with Entries 873--876, every source-defined proper quartic stratum identified in Entry 863 has now been classified:

• generic $D/H$ intersections add no rank or spectral data;
• the finite $L$ intersection adds no rank or spectral data;
• $(0,2)$ doubles an existing exceptional direction;
• the two new directions above $(2,2)$ are regular points of an existing resonant exceptional connection.

No algebraic connection-support lane for $\mathcal Q$ remains in this marked-relative system. A nonzero physical role would require additional source-derived chain data rather than another quotient, gauge, or carrier refinement.

Durable verification

• source checker: research/benincasa/marici-gm/src/bin/nima_marked_extension_linear_divisor_excess.rs;
• source packet: research/nima/marked-extension-linear-divisor-excess.json;
• indicial checker: research/nima/check_linear_quartic_intersection_indicial_excess.sage;
• indicial packet: research/nima/linear-quartic-intersection-indicial-excess.json;
• replication primes: 2305843009213693951 and 2305843009213693723;
• SageMath: version 10.7;
• allocator claim: seqclaim-f3e981260927012caf0a0bab.

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