Assessment 187: fixed live slots for unbounded promotions

10 October 2026. Scheduled research completion 92. Written native theorem 59; mathematical result 122 and six-result reassessment. No root-ledger admission or priority claim.

For the latest result and next test, see the current composition checkpoint. The continuation and publication statements below record this assessment at completion.

Result and payoff

A written native construction reuses complete-level rows with any fixed number of arbitrary missing levels per row and no bound on maximum diversity. At most $r$ live hole slots and two envelope reader slots suffice. Covering witnesses retire obsolete candidates, and threshold progress pays reader handoffs without restarting unfinished repair.

The complete proof, section 17 removes the maximum-diversity hypothesis of theorem 58. The producer already exports each row’s exact bounded missing set. The advance is a consumer whose resource bound depends on live exceptional observations rather than the number of profiles or promotions seen during its lifetime.

When a new row raises the envelope, every surviving old hole and every new hole belongs to that row’s missing set. Retire covered candidates before creating new ones, so a fixed pool suffices. Survivors keep their partial comparisons; new occupants receive fresh copied-queue debt. Retirement is justified by permanent coverage, never by age or a need to free a slot.

For envelope access, one reader remains aligned while one replacement catches up. New promotions update a latest-root field but do not restart that repair. If the global queue remains unfinished after query position $t$, its maximum exceeds $4t$. A reader captured under that condition finishes well before its own maximum, leaving time for the next handoff. A reader captured after exhaustion is final and needs no successor.

Adversarial writing-agent review

The global job was enlarged to include comparisons of every live old hole against its row before committing. Without this work, the semantic bound on surviving holes would not supply a charged retirement operation. The proof absorbs these tests into $C(M)=O_r(\log(M+1))$ because old candidates are at most the old maximum. Birth tests still compare with the old maximum, even if the incoming maximum is much larger.

A partially executing job snapshots bounded candidate fields. Independent workers may delete those candidates but cannot repurpose slots before global commit. A prepared deletion mask is intersected with live flags before births; it cannot delete a new occupant. This avoids both stale results and hidden identity tests.

The two-reader proof treats the final maximum separately. After queue exhaustion its magnitude need not be four times the query position. No successor is needed in that case. On a same-symbol handoff, at most two repair batches are needed because the global batch has already finished and its latest root is fixed. Every copied prefix is replayed through actual cells, with fresh service.

The first-bit maximum $A=1$ is checked separately; the general ceiling inequality covers $A\ge2$. The query never waits for global exhaustion at its delimiter. Candidate comparison and equality-reader deadlines remain those of section 16, applied to each new incarnation. Old versions keep their own roots and cannot be modified by slot reuse.

Finite evidence

The readable Python audit imports the previous audit’s immutable row and hole primitives. It checked 142,851 query endpoints and progress alternatives across 2,588 retained query forks; 1,142 query-time births and 1,421 retirements; and 19,999 handoff inequalities. It observed 437 promotions while a repair was pending and two repair batches in a single symbol. A rising-maxima history produced 398 recorded births while its live pool stayed at two slots. Random histories tested up to three holes per row, duplicate names and retained old versions.

Python integers, tuples, history logs and direct membership tests are audit machinery. The checker validates the event schedule and semantics, not the runtime of a native compiler. The all-length proof supplies bounded local tests, allocation, immutable queue work and reader service. The global job duration uses the larger implementation constant from the proof, normalized to one in the model.

Six-result reassessment, results 117 through 122

The block gives a coherent sufficient criterion, not six independent answers to general composition. Ordinary input prepares query-readable descriptors; distinct names bound unfinished payload work; future target input funds repair before the first affected observation; and permanent witnesses retire obsolete obligations. The new construction removes an input-growing lane count, a material scope change rather than a constant improvement.

The entry129 matching and positive-path theorems retain their exact interface hypotheses. This native construction uses branching, shared immutable roots, bounded negative observations and charged pending work; it is not an extraction of a small matching diagram. Nor does it imply a native recognizer for arbitrary relation products. Complete binary levels and a fixed hole bound remain checked restrictions on the encoded input.

Earlier replay slices, affine-fragment joins, persistent causal algebra and unary coherent cubical algebra remain controls for paid preparation, shared interpretation and closure boundaries. The native SAT separations and sufficient classes are unchanged. None supplies a free independent-store join or a reversal-free PEG transfer here. Review 185’s primary queue comparison still pays queue maintenance rather than payload tests; the latter are charged explicitly in this block.

Decision: continue toward moving exceptional regions. One missing interval is the next decisive case: fixed endpoint description with unbounded hole cardinality. A semantic interval intersection alone does not pay endpoint export or reader replacement. General radial families and independent-store joins remain separate, and the support-omission frontier is preserved.

Integration and continuation

Custody: one maintained proof and new checker in GitLab, with generated Site projections. Claims: written theorem 59 in the reader; root CLAIMS.yaml unchanged. Evidence: retirement, threshold and handoff arguments plus a finite independent union oracle. Failure ledger: retiring merely to reclaim a slot is unsound; restarting every repair has no deadline proof; fresh births do not inherit past service. Frontier: moving intervals, unrestricted radial profiles and independent-store joins. Reader synthesis: existing program and proof, no new paper or publication-rank change. Site representation: styled proof/review and highlighted Python with line anchors and exact downloads; deployment and parity receipts remain in integration state.

Test one contiguous interval of missing positive levels per row, with arbitrary interval length and unbounded maxima. Supply a native ordinary-input endpoint export and a paid persistent interval-union readout, or isolate the precise deadline failure of moving endpoints. Keep general radial profiles and independent-store joins separate.

Scheduled 91 to 92 and mathematical 121 to 122 are counted once. The six-result window closes at 122 and resets to zero. Next scheduled 93 is research; dedicated review 95 and editorial 96 remain unchanged. Installed reverse-writer retirement remains a separate unverified follow-up.