R12 Raw-260k Source-Scheduled Failure Taxonomy

Status: post-result analysis of the immutable 256-case confirmation. This document does not change the frozen evaluator, result, parser, gates, or claim.

Bottom line

Whole Problem/Work decoding scored 9/256, but the original-task prefix reached the correct final value in 45/256 cases. Continued generation and the last-integer parser destroyed 36 otherwise correct trajectories. Source scheduling scored 115/256; the all-atomic-steps-correct ceiling was 113/256 (two sequential chains diverged and accidentally recovered).

The scheduler's main contribution is therefore control: it owns the operation cursor, scalar state transfer, parse boundary, and truncation boundary. It does not repair the remainder primitive, which remains a genuine executor defect.

Exclusive whole-decode taxonomy

Classification precedence is scored correct, correct trajectory lost to tail/parser, wrong first operation, wrong first arithmetic, loop/replay before completion, then later arithmetic/controller failure.

Family	Depth	Wrong first op	Wrong first arithmetic	Loop/replay	Later failure	Correct then parser loss	Scored correct
Multiply-subtract	2	0	29	14	1	16	4
Modular update	2	0	6	52	0	3	3
Sequential state	3	44	2	5	6	7	0
Base conversion	4	52	0	0	0	10	2
Total		96	37	71	7	36	9

All 64 base-conversion responses failed to follow the frozen Horner schedule. Twelve base-10 cases nevertheless stated the correct value through an alternative decimal expansion; ten then lost it to continuation.

Correct leading scheduled transitions

Family	0	1	2	3	4
Multiply-subtract	29	15	20
Modular update	6	52	6
Sequential state	46	9	2	7
Base conversion	64	0	0	0	0

Family	Whole reaches answer	Whole scored	All atomic steps correct	Scheduled final correct
Multiply-subtract	20/64	4/64	29/64	29/64
Modular update	6/64	3/64	4/64	4/64
Sequential state	7/64	0/64	36/64	38/64
Base conversion	12/64	2/64	44/64	44/64
Total	45/256	9/256	113/256	115/256

Local execution and compounding

Successive chain-position counts, denominator 64 per position:

Family	Atomic, oracle input	Scheduled, local arithmetic	Scheduled, oracle state
Multiply-subtract	`[39,45]`	`[39,48]`	`[39,29]`
Modular update	`[56,4]`	`[56,7]`	`[56,4]`
Sequential state	`[57,49,51]`	`[57,49,52]`	`[57,43,38]`
Base conversion	`[64,62,52,55]`	`[64,62,52,58]`	`[64,62,50,44]`

Operation totals are atomic add 230/256, multiply 204/256, subtract 96/128, remainder 4/64; scheduled-local add 233/256, multiply 204/256, subtract 100/128, remainder 7/64.

Looping and termination

A conservative loop signature (new-question continuation, duplicate canonical equation, duplicate substantive line, repeated operation/operand chain, or three repeated additive operands) occurs in 214/256 whole responses:

multiply-subtract 63/64
modular update 64/64
sequential state 26/64
base conversion 61/64

Every call in every arm hit its cap: whole 256/256, atomic 704/704, and scheduled 704/704, for 1920/1920 cap stops and zero EOS stops. Scheduled execution survives only because the evaluator parses the first nonempty line of each isolated transition and externally starts the next call.

Controller implication

The minimum autonomous target is not a larger free-form chain. It is a typed controller carrying (state, next_operation, operand, cursor, done) with one operation per transition, one cursor advance, one fixed scalar-state write, consumed-operation suppression, and an explicit DONE/EOS policy. It must be evaluated with one uninterrupted model call. Remainder needs a separate executor intervention and cannot be used to rescue a failed controller gate.