Rank-budget screens for orthogonal permutation codes and triple DAGs

[aliromman]

FINDING / RELEASED — 2026-10-23. No new kappa or admitted supplier.

Two changed-construction screens failed their recursive rank budgets. They
are discovery results. They do not rule out other center-free codes, other
side circuits, or a different controller. No scope remains reserved.

The base is canonical main 7c472563474e60185e6ca101a17622133d047e56, priority
revision 7. The selected conditional kappa remains 60403/20000000. I used
the actual p16 target and IDLE words in the
controller
and the typed caller.
The one-query-per-thin-shear invoice is retained. Nonrecursive costs were
granted free in these screens; those missing costs cannot repair a failed
recursive budget.

1. An orthogonal permutation code loses its apparent rank gain

Replace the dense center-free code by a permutation A whose edges join
binary-orthogonal ports. A deterministic bipartite matching supplies such a
permutation on all 112 ports. A proposed producer then needs only the two
rank-eight main paths per port and one side ADD per matched pair. Its code
is monomial after the inherited port normalizers.

This does not preserve the old main target invoice. In the inherited fresh
stage caller, a negative output is Q^-1 B D. The permutation code sends
the central vector into the first encountered fresh block, with zero
central coefficient. All later distinct blocks leave that vector fixed.
After removal of the output monomial, the Gaussian B block on the active
space is I + e e^T + v v^T, where e.v=0 and both vectors have odd norm.
Its rank is two less than the old target. The positive outputs keep their
old ranks.

Exact binary elimination checked all 3,584 proposed output jobs, using all
224 forward/inverse local maps from the
normalizers.
The paid profile below grants each main path one coalesced rank-eight
child, including a source path split by its side ADD. This is an optimistic
relaxation, not an emitted physical word. Splitting that child increases
its moment at a positive saving. The relaxed paid profile is

{1:1680, 8:4032, 16:448, 24:448, 32:448, 40:448,
 48:448, 56:448, 64:448, 72:224}

The new target mass is 173,824. The paid mass is 175,504. Thus the rank
surplus is -1,680, exactly the retained thin-query charge. At saving
0.00302015 the floating paid-minus-target moment is about 1,958.74.
There was no full phase/literal producer replay or supplier admission.
The failed budget was the stopping test. This result concerns the stated
orthogonal permutation construction and the distinct fresh-stage caller.

2. Current native frames remove an old local obstruction, but this DAG still costs too much

The historical parity-side circuit
was rejected under its nondegenerate frame interface. That restriction is
not a restriction on the current canonical Clifford frames.

For the five-point witness, use sources 21 and 26, targets 19 and 28, and
the degenerate span U=span(21,26) in five coordinates. The current
exact Clifford implementation
lowers both source-line-to-U transitions at rank one and both
U-to-target-hyperplane transitions at rank two, including its exact phase
checks. This changes the old interface premise; it does not contradict the
scoped historical obstruction.

I then regenerated the unchanged signed DAG and assigned each node its
binary source span. The proposed helper paths grow from zero to the full
space. I charged every path increment, all main paths, all h+1 center
queries at rank h, all p16 IDLEs and all thin queries. Each arbitrary side
input receives one rank-h target per FULL call. The exact rank surplus is

17*binomial(h,3) - 18*h*(h+1).

h	Ports	Side roles	Approximate raw moment root
8	56	724	No positive rank surplus
10	120	2,271	0.00010638
12	220	4,764	0.00069895
14	364	8,946	0.00086621
16	560	14,608	0.00091881
20	1,140	33,168	0.00087904
26	2,600	82,720	0.00076841

These are floating discovery roots of the proposed mixed rank bill, not
certified kappa values. No full scalar/native word, compiler, precision,
tape or outer admission was completed. The measured bill already misses
the selected threshold. A lower-cost side topology or a different helper
contract would be a new experiment; another frame repair of this fixed DAG
is not the missing step.

Credit Douglas Colkitt and the retained parity-side and Clifford authors;
Arnav's historical frame note;
Dugongue, Dillon, Cinna Davis, Cao Yifan, zxv, Jacob Alan Sussman and Ryanson
Jonathan for the source code, native interfaces and controller lineage in
the linked files. These screens do not claim those constructions as new.
Prepared for Ali Romman with substantial OpenAI Codex assistance. No
independent human or proof-kernel review is claimed.

The overlap refresh covered 329 open PR bodies, 4,666 Discussion records and
7,267 local README/TASK notes. Remote pagination was complete at
20:36–20:37 UTC. Arbitrary diffs and unpublished work remain outside that
coverage. No matching active claim was found for these two screens.