Assessment 213: when context codes fragment a complete cone

12 October 2026. A sustained failed aggregate extension, with an exact structural explanation. Native construction 70 remains unchanged.

Result and consequence

The argument resolves the next budget test negatively for creation-order coding. A complete clipped-cone row has one mixed prefix in its original fixed-width cube. Its immutable ordinal-code image has $2^D+6$ mixed coordinate occurrences, or $2^D-1$ after removing the shared stem. All rows are complete cones, greedy contexts are learned from literal input, and residuals have length two. Sharing equal records does not reduce the coordinate count used by the inherited splice argument.

This is not a contradiction to construction 70: the diagnostic allows its degree parameter and ordinal width to grow, explicitly outside one fixed machine. It tests the proposed aggregate replacement of that bound. It also does not concern theorem 66’s separate radial length-profile budget. The failure is a change of content geometry.

A finite-tree transfer criterion makes the gap precise. Charge each mixed output cylinder to the longest common prefix of its input preimage. If at most $g$ output cylinders charge any input prefix, mixed counts grow by at most $g$. Prefix-tree isomorphisms have $g=1$; the witness has $g=2^D-1$ and attains the bound. This is a conditional geometric argument, not a charged native implementation of the coordinate map.

Attack, failures and escape

The attempt first granted larger codes, separating semantic code existence from preservation of a cheap aggregate. The explicit producer order then refuted that preservation even without nested contexts or ownership holes. Replacing coordinate counts by shared-record counts would invalidate the existing coupling premise. A different shared-DAG or symbolic merge remains possible and requires its own proof.

Using literal-prefix codes preserves geometry in the witness, but gives length $D+4$ codes to length-two residuals and one-bit aliases. Query-prefix traversal may fund the reader. It does not pay the short-name selection’s pending installation, nor the disturbance of older jobs. The common-stem dispatcher failure from assessment 206 remains a control. A complete-cone validator and nested-context hole representation are separate remaining obligations.

Independent review and finite evidence

An independent adversarial reviewer reconstructed the ordinary-input family and exact mixed counts, and distinguished content-prefix geometry from radial depth profiles. Its separate scratch implementation checked the greedy producer for $D=1$ through 8, totaling 3,060 literal right records. No scratch copy is maintained as a second canonical checker.

The maintained finite audit uses independent prefix-count and canonical-tree computations. It confirms the witness, exact encoded right-block lengths, physical-sharing distinction, and literal-prefix control. It also passes 33,160 permutation/subset transfer checks and 32,904 rooted-tree-isomorphism/subset checks. All permutations are tested at depths one and two; depth three uses 128 reproducible sampled permutations and every subset. All rooted binary-tree isomorphisms through depth three are checked. Another 78 producer cases exhaust every balanced mask through depth three, with 3,528 additional ordinary records. The same complete literal rows realize each mask by changing only creator order. The independent reviewer also approved this generalization and the cut-congestion proof. Review caught an alias-one encoding typo in the checker; it was corrected and covered by a creator-alias-one smoke check before the final audit. Host strings, maps, sets and integers are semantic oracles, not native instructions. General statements rely on the written arguments.

The result adapts elementary prefix-tree counting to the Lab’s existing context-code and mixed-coordinate interfaces. Confidence is high in that classification; no external priority claim or fresh primary-paper review is counted. Last dedicated primary-proof review 210 remains current.

Handoff and accounting

Construct or refute a charged shared literal-prefix aggregate with source-specific pending selection, first for equal-depth contexts and sibling pairs. Test arbitrary creation order and many short-name selections under one long shared stem. Bound all truncated residual work including disturbance of older jobs; then restore nested ownership holes, clipped intervals and ordinary-input completeness. Arbitrary alias/residual scale ratios and independent-store joins remain separate.

Scheduled 117 to 118 once for the completed unsuccessful construction assessment. Mathematical 133, window five, reassessment 128 and native theorem 70 remain unchanged. Next 119 is research; scheduled 120 carries both primary-proof review and editorial duties. Root claims and existing SAT/scaffold frontiers remain unchanged.

Entry 129 remains an imported growing-alphabet state/port bound. No native lower bound, arbitrary coordinate conversion, independent-store join or unqualified PEG orientation follows. Replay, affine, causal and unary coherent controls retain their exact contracts. This work uses the Lab’s public constructions, not embargo material or an author-preprint response; no external messages.

Validation and publication boundary

The scoped research audit passed. Build, rendered-link/source inspection and repository verification results are recorded in the canonical integration receipt. Publication is complete only with the matching saved-version, terminal deployment and exact source-parity receipt. Browser viewport inspection remains unavailable in the supported managed Sites workflow; no visual layout claim is made. The previously recorded five full-suite failures are not treated as new successes.