The batched counting oracle (digit lifting into tensor slots) solves the oracle task

Procedure pOracle (number 84) of the program oProg solves the counting oracle task Light.Filter2.oracleTask within $T(n,U,s,p)=$ oTimeF 3000000 n U s p steps with need oNeed.

The task: for an Exact Triangle instance (three $n\times n$ weight matrices $AB,BC,AC$ with entries bounded by $U$), a block size $1\le s\le n$, a modulus $p\ge1$ and a place cnt, write the list cntList n s p AB BC AC of the $\lceil n/s\rceil n^2$ counts at cnt: for the candidate $i=jn^2+an+b$, the number of $c$ in $[js,\min((j+1)s,n))$ with $p\mid w(a,b)+w(b,c)+w(a,c)$; no other cell below the free pointer changes.

oProg is base58B, the procedures of Section 4.4 for $c=20$, $\theta=56569/500000$, and the oracle's procedures 74-84 (tables of residues and digits, writeSrc, the queries, the top procedure). oTimeF A is explicit: $A(n^2\log U+\dots)$ plus, per batch, one preprocessing tPreCoreP and the queries.

“Procedure $p$ of program $P$ solves the task within $T$ steps with need $\nu$” (SolvesN) means: in every program that begins with $P$, for every instance and every memory satisfying the task's precondition, and all limits (word size, cells, call depth) allowing $\nu$ of the instance's parameters, the call of $p$ with the instance's arguments ends within $T$ of the parameters steps and leaves a memory satisfying the postcondition.