Assessment 216: support growth without old-row migration

12 October 2026. Written native construction 72. Fixed component capacity is an explicit checked restriction; no root admission or external priority claim.

Result and consequential mechanism

The complete construction permits late support growth after many completed rows. A new component grows only during its birth owner’s consecutive alias block. Its owner is FULL there, every other row is EMPTY, and the component freezes before a different alias uses it. Thus no unmodified row changes meaning or mixed-budget contribution as the support grows.

This carries the one-new-branch test through a stronger positive class: any fixed number of later components can each gain arbitrarily many leaves. Ordinary target records supply the supports; no decomposition, ignored anchor or external ready handle is added. Old-component targets inside a birth-owner block still update their old component. An alias can own several components at different times. One signed budget counts mixed regions across the whole row vector.

Componentwise splice uses at most $K+2m(v)$ calls, where the gate is $m(v)\le C\ell$. Nonempty aliases pay the constant-root calls as well as recursive work. One pending vector per source and fixed parallel literal validators preserve exact answers at the final symbol. Construction 71 is recovered at $K=1$. For $K=2$, one later birth block can add an unbounded new support without converting any previously completed other-row view.

The one-tree adapter route was also carried to its cost boundary. A single adapter can expose children locally, but old FULL becomes mixed along the inserted branch’s ancestral path. Against the new singleton, inherited splice performs $2d+3$ calls at insertion depth $d$. This is a failure of that budget transfer, not a lower bound on all representations. The new construction avoids it by retaining separate support coordinates.

Independent argument review and finite evidence

Adversarial review examined the producer and consumer together. It checked fixed row slots, end-discovered births, full literal candidate construction during actual target input, owner-name readiness, frozen-component precedence over speculative active insertion, total-budget initialization, final-budget repair, historical support binding and nonempty-alias payment. It approved the written theorem under construction 71’s inherited native primitives. Historical FULL views retain their enclosing historical support vector; using the latest support for an old snapshot would be incorrect.

The standalone Python audit compares an online record-level producer with an independently formulated maximal-alias-block oracle. Compressed-tree mixed counts are compared against direct literal-prefix counts. It imports no other Lab checker. The completed audit reports:

• 14,043 exhaustive histories of length zero through four over two one-bit aliases and four two-bit targets, with capacities one through three.
• 1,200 seeded histories and 12 targeted histories, including leading-zero names, reused owners, old-component records during growth and component exhaustion.
• 133,015 historical snapshot checks and 306,528 component-view checks.
• 3,241 source selections, 207,844 immediate or retained query checks, and the complete-call bound for componentwise splice.
• 17,488 one-point growth identities and nine increasing-depth splice-inflation stresses.
• 5,141 component-capacity rejections; 10,114 histories reached final row semantics. Testing two budget constants produced 19,931 budget acceptances and 297 rejections.

The finite experiment uses host sets, strings and counters as oracles. It does not execute native routing, deadlines, allocation or the compiler. Those are obligations of the universal written construction, not inferred from the number of checks. The audit initially rejected a too-narrow insertion-delta formula at the new branch; the final formula uses old-side nonemptiness, not fullness, at that new node. The written proof and final checker agree.

Contribution, limits and controls

This is an extension of the Lab’s frozen-support and asymmetric-splice constructions, with high confidence in that internal classification. The added content is the input-derived support partition and its uniform-growth invariant, which discharge producer, budget and deadline obligations together. The latest external comparison is review 215; this run does not count a new primary review or promote external originality.

Unbounded component count remains consequential. Even if every component view is constant, a row’s pattern of FULL and EMPTY components can be large. The internal mixed-region budget alone does not pay that activation pattern. The fixed number of slots and readers is therefore part of the theorem, not an implementation convenience that can be silently removed.

Replay pays its traversals, affine joins retain their coordinate conditions, persistent causal sharing does not itself maintain current union, and unary coherent algebra alone does not supply branching readout. The early unique-routing subclass remains a useful separate control. Imported entry 129 retains its growing-alphabet state/port scope. No independent-store join or native lower bound is derived. The native-to-PEG consequence is for reversal of the complete checked language.

Next target and integration

Remove the fixed support-component cap while preserving paid current union and bounded active readers. Start with many component births under a long common literal prefix, arbitrary short aliases and an immediate negative pin. Account for each row’s FULL/EMPTY component activation pattern as well as its internal mixed regions; charge directory construction, activation and pending union to actual creating, selection or query symbols. Use the early unique-routing subclass as a control. Variable alias widths, nested ownership holes and independent-store joins remain separate.

Scheduled 120 to 121 and mathematical 134 to 135 count once. Window one after reassessment 134; native construction 72. Last primary review and editorial remain 215; next primary review 125 and editorial 126. Scoped checks, repository verification and exact deployment/source-parity receipts are recorded in integration state. Browser viewport review remains unavailable under the supported workflow. Installed legacy-writer retirement remains a separate unverified follow-up. No external messages.