Research: audit native transport and helper-300 successor boundaries

research/helper-transport-contract/BOUNDARY.md

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+# One nominated helper-300 successor interface
+
+This is a bounded source-bound decision, not a new productive supplier or a global
+no-handoff theorem. It checks the backward interval [9044,9137) only, the exact
+twenty-field closure already studied, and one additional arbitrary successor S.
+The only two nominated birth frames are plane430 and line21. No helper census,
+larger window, or synthesis search was run.
+
+## Common local contract
+
+Let x_i denote the twenty independent values at the event9044 entry cut. The
+retained matrix is T. The proposed continuing outputs equal T with the input
+symbol x300 replaced by s; the old output role300 is instead restored to x300,
+and the old continuing output300 is assigned to S. This is the explicit
+relabel-and-retire interface suggested by the successor pattern. It is a sufficient
+handoff boundary, not a claim to characterize every possible changed suffix.
+
+All other field paths and the eight disjoint interval events stay unchanged.
+Allowed operations are coframed rational ADD/nonzero SCALE and monotone climbs;
+there are no new warps, descents, extra fields, or changed output charts.
+
+## Plane430 birth: excluded
+
+The successor starts at F430=span(273,85). Old H300 follows 0→21→430 and retires;
+S follows 430→437. This splits the original path 0→21→430→437 and retains38 H1.
+
+The exact retained rows are
+
+    output301 = x19 - x40 - x300 - x301
+    output299 = (x19 + x40 - x300 - x301)/2.
+
+Thus the declared successor interface requires coefficient−1 of s in output301
+and coefficient−1/2 in output299. Both outputs end at F419=span(273,51), which
+does not contain85. Every coefficient of s can only move to frames containing
+its birth space under the allowed operations. Consequently neither demanded
+coefficient can be delivered. This endpoint-inclusion argument already holds
+with arbitrary scalar refactoring and chronology; the optimistic station graph
+also confirms the disconnection.
+
+This excludes this plane430 boundary. It does not exclude different output
+charts, extra native transport, an earlier successor birth, or a changed suffix.
+
+## Line21 birth: exact local positive control
+
+If S starts at F21=span(273) and old H300 retires at that same line, the following
+literal local construction works:
+
+1. Keep the original first climb H300:0→21 at event9044.
+2. Retire H300 with its cut value x300.
+3. Redirect every remaining reference to H300 in this interval to S. In
+   particular event9045 now subtracts S from field19.
+
+S follows21→430→437; every other instruction is unchanged. The complete21-input
+row identity and all final frames hold exactly, with 38 H1. No other successor
+coefficient is blocked. This is the entrance-pure pattern already identified by
+PR5472, not a new gadget or an admitted productive split.
+
+If old H300 is instead required to retire at plane430 while S still starts at
+line21, an additional H300:21→430 climb gives the same exact row identity at
+39 H1. The local monotone rank mass itself increases by one: no scalar rewrite
+can make that duplicated ascent free. Its target benefit must not be booked
+without the producer/consumer ledger, and one extra H1 exceeds a single split's
+moment allowance near the selected endpoint.
+
+## Actual producer boundary: cut value is not the original helper
+
+The independent source slice contains 98 scalar instructions on41 dependency
+roles and no warp. It gives
+
+    x300 = h300
+      + (L113 - L123 + L128 - L135 - L140 - L145 - L162 + L163
+         - L174 - L183 + L190 + L194 - L203 - L205 + L216 - L221)/2,
+
+where h300 and all L terms are original input coordinates. The32 preload ADDs
+at events2343–2374 consume rows that were already mixed; calling these 32 original
+input terms would be incorrect. Retiring x300 at line21 returns a mixed
+original-input value and does not by itself certify the productive H1 image of
+the original h300. This is not an algebraic-dependence objection: the prefix is
+invertible, so x300 remains one of the independent cut coordinates. A change to
+that coordinate basis can be valid, but its effect on the original target and
+full caller must be certified.
+
+The separately propagated original-h300 column has exact event9044 support:
+
+| Role | Coefficient | Entry frame |
+|---:|---:|---:|
+|18|−1/2|20|
+|40|−1/2|42|
+|288|1/2|103|
+|289|−1/2|103|
+|290|−1/2|56|
+|291|1/2|56|
+|297|1/2|20|
+|299|1/2|42|
+|300|1|0|
+|301|−1/2|0|
+|303|1/2|0|
+|505|−1/4|0|
+
+No warp touches this nonzero column before the cut. Role505 is outside the
+twenty-field local closure and still lies at frame0. Hence a literal global
+input-transposed cut state would require coefficient−1/4 of the successor in
+that frame0 role. A successor born at line21 cannot supply this under monotone
+transport. Keeping the original prefix and merely renaming the nominated local
+suffix does not repair the producer boundary. This is an explicit obstruction
+to that claimed interface, not to every modified prefix/suffix construction.
+
+The next interface must supply an original-target and caller intertwining
+certificate that accounts for the full coordinate change, including the external
+role, together with its paid ledger. The obstruction above is limited to the
+unchanged-prefix, literal input-transposition contract; it does not rule out a
+zero-frame entrance basis shear or another modified producer. A feasible entrance
+change alone does not settle the exit restoration and caller obligations. The
+local positive control alone earns no new target credit.
+
+## Evidence
+
+check_split_boundary.py is standard-library code, imports no discovery or other
+worker functions, defaults repository root to two parents above its package,
+and accepts --repo and --json. Its --json output contains the exact source pins,
+matrix-defined target rows, modified frame paths, literal line21 program,
+preload/spread source events, entry-row backward slice, and original-input column.
+
+Normal and optimized runs produce identical JSON. The checker admits only the
+local scalar/climb language, proves that the eight untouched source events use
+disjoint roles, and requires them to remain byte-for-byte unchanged and in order.
+Six active controls reject a missing successor coefficient, a retained old-helper
+consumer subtraction, a false retirement frame, a missing first paid climb, a
+free duplicated ascent, and an unsupported warp on the original helper.
+
+Credit PR5472 at ce96fe9747ea0643bd8c30d448c1ba8e2b30ac30 for the successor pattern,
+its prior entrance-pure screen, and the gadget. Retain the selected native word,
+provider, controller and compiler lineage. Prepared by apoursh with substantial
+OpenAI Codex assistance. No native all-width, compiler, full-caller or new kappa
+claim is made.