Assessment 228: current activation under independent reindexings

12 October 2026. Supporting argument and sustained unsuccessful extension. No new native construction or substantive-result count.

Subsequent progress: construction 80 supplies growing-delay envelopes and bounded speculative readout. This dated review retains its original scope and evidence. Current research target.

Outcome and useful failure

The complete argument tests shared foreign predicates without local omissions or arbitrary graph topology. There are K primary namespaces and h foreign stores; each target has exactly two owners, with an independently input-built permutation selecting its foreign owner. Foreign-only selections ask whether that permuted coordinate belongs to one current activation set.

The first attempted extension, spelling both owners in each query, already follows the earlier section 14.6 fixed-decoder theorem. The identity-permutation control follows the same theorem. Every fixed K also follows construction 77 with foreign packet bound K. None is counted again.

For growing K, literal enumeration and independently materialized answer cells require namespace-proportional work on short-source instances. Looking up a permutation before the current activation bit releases a second lookup too late unless a source-dependent continuation was prepared earlier. Sharing equal views, transporting a source-key search position and retaining pending rows were examined; none supplied the complete immutable producer, update and strict readout schedule for independent growing views. Shared predicates and input-built indices remain permitted. These failures do not give a native-language lower bound.

Independent adversarial review

The independent reviewer checked the full manuscript, exact record length, two-owner semantics, fixed-family diagonal quantifiers, literal mixed-prefix count, completed controls and representation restrictions. Review required fixing source length to one in the update-work bottlenecks, and recognizing every fixed namespace count as already covered by construction 77. Both corrections are incorporated. Separate-cell consequences expressly exclude shared indirection, lazy predicates and precomputed whole views; finite changed-coordinate counts alone are not native work bounds.

Independent finite evidence

The standalone audit independently compares explicit relation composition with forward Horn closure and retains immutable activation snapshots.

All pass. Growing families through 64 namespaces also check mixed-prefix counts and exactly K changed coordinates after one foreign activation. These are host semantic and representation diagnostics, not native parsing or timing simulation.

Next decisive test

Construct shared current activation access through a growing number of independently input-built namespace permutations. The source pin and actual primary prefix must initialize a residual predicate; every subsequent suffix bit and activation record must pay bounded local work, with final-symbol output. Charge initial preparation, old-storage observations, allocation, name routing, consumed-prefix replay and retained versions. Fix one finite-label, fixed-degree/radius machine and exclude identity, address, metadata and timing channels. The test family is explicitly serialized; no free checker for permutation completeness is granted.

Keep fixed K and fixed query decoders as completed controls. Preserve arbitrary-name routing, heterogeneous service, entry 129’s conditional state/port scope, replay, affine, causal, unary and native SAT controls. A future native theorem supplies a PEG for the reversal of its complete checked language.

Integration and accounting

One maintained GitLab source supplies the argument, audit and handoff. Styled HTML/KaTeX readings and highlighted source with line anchors and exact raw downloads are generated projections. The homepage date and paper ordering are unchanged: this is a sharpened unsuccessful extension, not a newly completed advance. Integration state records actual builds, rendered checks and publication parity. Browser viewport inspection is unavailable in the supported workflow; responsive layout and clipping are unverified.

Scheduled completion advances 132 to 133 exactly once. Mathematical count 140, window zero, reassessment 140 and native construction 77 remain unchanged. Last primary review 225 and editorial 227 remain; next 134 is research, 135 primary review and 138 editorial. Installed reverse-writer retirement remains a separate unverified follow-up.