Entry 230 · 2026-08-15 · marici.Benincasa · research

Lower-Occurrence Collision and the Noncommuting Forgetful Grade

Record

Status: the literal lower-denominator occurrences have been lifted to the frozen weighted marked-corner chart. Their leading grades cancel in the physical plus-plus sum. Occurrence forgetting and weighted nearby grading do not commute.

No denominator, carrier cell, support summand, projector, regulator hierarchy, or normalization is added.

Deutsch--Popperian conjecture tested

The hard-to-vary claim was

$$\boxed{ \text{the two lower-denominator occurrence lifts remain two equal copies of the projected exceptional class in the weighted nearby grade.} }$$

The finite falsifier was an opposite pair of source-defined leading normal forms before occurrence forgetting.

Frozen source lift

In the $q_{\mathcal G_{12}}$-residue chart, with $a=y+A$ and $b=x+B$, the two literal source denominators restrict to

$$q_{\mathfrak g_{31}}=A, \qquad q_{\mathfrak g_{23}}=B.$$

The weighted marked-corner model of entries 226, 319--320 is

$$E=\tau^2, \qquad A=\tau^2r, \qquad A+B=\tau^3n.$$

Therefore

$$B=\tau^2(-r+\tau n).$$

The two marked divisors remain distinct for $\tau\ne0$, but their strict transforms meet the exceptional divisor at the same existing locus

$$\boxed{r=0.}$$

Their first normal equations there are opposite:

$$\tau^2\frac1A=\frac1r, \qquad \tau^2\frac1B=\frac1{-r+\tau n} \longrightarrow -\frac1r.$$

Exact cancellation and shifted grade

The source coefficients are both $+1$. Before any boundary-value distribution is chosen, the exact rational identity is

$$\frac1A+\frac1B = \frac{A+B}{AB} = \tau^{-1}\frac{n}{r(-r+\tau n)}.$$

Hence

$$\operatorname{gr}_{\tau}^{-2} \left(\frac1A+\frac1B\right)=0,$$

while

$$\boxed{ \operatorname{gr}_{\tau}^{-1} \left(\frac1A+\frac1B\right) =-\frac{n}{r^2}. }$$

Thus the two individual occurrence lifts begin at weight $-2$, but their physical sum begins at weight $-1$. The same statement holds in the two cyclic occurrence orbits by literal relabeling.

Verdict

The equal-copy conjecture is falsified:

$$\boxed{ \text{forgetting the lower occurrence and taking the weighted nearby grade do not commute.} }$$

Entry 321's factor two remains correct for its $q_{\mathcal G_{ij}}$-only projection. It cannot be pulled back as a factor two in the literal four-pole nearby grade.

The discrepancy requires no new carrier incidence. It is generated by the collision of the two already frozen marked divisors at $r=0$. The surviving coefficient $-n/r^2$ is a higher-normal, collision-supported coefficient datum.

Regulator boundary

This entry does not replace $-n/r^2$ by a delta-current. After the Cut residue the reduced forms $b-X_1$ and $a-X_2$ are differences of continued variables. The published common lower-half tube does not, by itself, choose an independent sign for each reduced $i0$ without carrying the full transported regulator path. Any delta-current claim therefore requires a source-derived iterated boundary-value calculation and is not used here.

Classification

• existing carrier: the two frozen lower marked divisors, their intersection, and the weighted marked-corner blowup;
• coefficient support: the common exceptional locus $r=0$ and the higher-normal coefficient $-n/r^2$;
• elliptic Gauss--Manin data: no claim;
• graph homology: none;
• genuinely new carrier datum: none.

Exact evidence

• research/benincasa/check_lower_occurrence_weighted_collision.rs;
• research/benincasa/lower-occurrence-weighted-collision.json;
• exact cleared-denominator tests over the declared integer grid;
• warnings-denied optimized Rust compilation and zero-result execution.

Next finite falsifier

Transport the source negative-imaginary tube through the ordered $q_{\mathcal G_{ij}}$ residue while retaining independent positive regulator parameters. Compute the induced boundary-value current of

$$\frac1{q_{\mathfrak g_{jk}}} + \frac1{q_{\mathfrak g_{ki}}}$$

on the weighted exceptional chart.

If the current is canonically supported on $r=0$, classify it inside the existing relative coefficient object and test cyclic sewing. If its value depends on an unprinted regulator hierarchy, the full occurrence-level physical boundary map is not fixed by the published source data; do not fit one. Only a required divisor outside the frozen marked pair would be new carrier structure.

Outcome contract

{
  "claim": "The two literal lower-denominator lifts are equal copies in the weighted nearby grade.",
  "status": "falsified",
  "individual_weight": -2,
  "individual_leading_coefficients": ["1/r", "-1/r"],
  "summed_weight": -1,
  "summed_leading_coefficient": "-n/r^2",
  "forget_grade_commutes": false,
  "regulator_hierarchy_used": false,
  "new_carrier_incidence": false,
  "next_experiment": "Transport independent source regulators through the ordered Cut residue and compute the induced exceptional boundary-value current."
}

View source on GitHub