[aliromman]

This package gives scoped information bounds for the historical complex nine-stage word. It puts the proofs, exact certificates, independent agent reviews, and portable checks in one dependency closure. It does not improve the complete kappa calculation. The results restrict specific query and observation models; they do not price a native supplier or prove a universal circuit lower bound.

The proof map, independent publication review, and source manifest give the exact premises and checked files.

• Nine queries of one fixed arbitrary source on the full regular cover have first five moments 72, 120, 244, 1649/3, 47467/36. Their dimension is at least 15560/273 complete fields: at least 57 whole fields, or 64 in whole eight-field cohorts. This premise does not apply automatically to changing controller sources.
• The actual query row space has exact source-port support distance 53. For the specified snapshots of rank at least two, a common span for k query dimensions needs at least k+2 birth fields. Each of the 1,002 positive proper snapshot cones also fails to contain any nonzero completed query, even with all its snapshot times granted.
• For same-content monotone observation networks with the original core fixed, the general cut lemma gives the global floor 42. Separate contained-frame certificates give 9k for twelve rank-five spaces and 8k for cones 983 and 991, including direct FULL bypass edges. These results do not give a global floor of 64.
• The specified controller has exact residual rank 72|G|-d. With the separate cover bound d<=8|G|/183, one complete residual channel needs 72 whole arrays per replica, or 1,152 across 16 replicas. This does not bound peak workspace or a procedure that reads the source again. The local native lift and global endpoint normal form remain inherited application premises.

These bounds have separate models and cannot be added. No failed search or LP result is used as an impossibility proof. No new capture schedule, native phase audit, precision bound, tape cost, recursive invoice, or supplier admission is supplied.

The cache-path appendix adds an exact permitted-ring criterion for a fixed read path and an independently reviewed native-rank lower bound of eight for one nonzero query in the stated scalar monotone merge-tree model. The bound 64 applies only to eight separately paid trees. It does not establish a global 64 bound for a shared multi-output network. The unchanged support checker passes in normal Python and with -O; no native cache is constructed.

python3 -I -B research/actual-query-information-bounds/annexes/chronological-cache-paths/replay.py --out /tmp/chronological-cache-paths-replay

Expected final line:

PASS_SCOPED_SUPPORT_PROOF_REPLAY

The separate appendix review gives the proof argument and replay limits. Its manifest binds the unchanged source closure and new review.

The publication base is b58ad9ef4d4e861b0eaa5dba41742bdc072dca51. Its selected record names PR #4470, with conditional kappa 0.00302015. Transfer of these historical bounds to that changed construction is unproved. The consumed supplier remains pinned at bce54fb3f895cbe5cd4c0eb477c3afeed100190f; its selected replay archive supplied the exact native word, clean programs, phase data, and controller template. The source pins bind the four consumed members.

The original source notice credits @icekylinx for the Gauge44 construction and records its earlier supplier, compiler, frame, owner, and controller dependencies. The package notice preserves that ancestry, the @jeremykothe2, @chafreaky, @FanPUYen, and @rohanarun credits, and the source licenses. It also identifies the campaign lanes that supplied each new result and independent check. Substantial OpenAI Codex assistance was used. The independent reviews are agent reviews; no human review is claimed.

Use Python 3.11 or later, SymPy 1.14.0, and at least 3 GiB of free disk space. From the repository root:

python3 -I -O -B research/actual-query-information-bounds/replay.py --output /tmp/actual-query-information-bounds-replay

The output path must be new and outside the package. The replay uses one Python child at a time and needs no Git, network, or search solver. The expected final line is:

PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE

Both producer and independent relocated replays passed all 17 checks. They rebuilt the source matrix, all 712-input snapshot rows and 16,687 intervals, and all 194,400 fifth-order triples. They checked the support and cut certificates, the 73-axis cover traces, and the residual algebra. Complete typed JSON receipts matched their declared targets. The checks rejected wrong route order, changed snapshot data, invalid quartet bounds, wrong flag order, understated edge charges, a missing controller bridge, and a wrong triangular sign. See the validation record and independent cold replay. The optional sixth-moment extension, searches, and inherited native checks were not rerun. The open questions state the remaining obligations.

This PR also includes a source-geometry annex with four reviewed theorem families about source access. The results have different interface classes and must not be added as one cost invoice. They give no complete kappa improvement. The annex manifest, exact source closure, and executed checks are separate from the unchanged primary package and chronological-cache annex. The fresh independent publication review accepted the frozen annex after all seven checks passed from a relocated package.

• The eight actual centre rows have rank-seven binary support spaces in four equal-space pairs. Their shared-port graph is K_(2,2,2,2). If each unwarped source value has one carrier on an increasing subspace chain, and each complete row has one direct common-frame capture with no partial query, extra carrier, or operator-valued code, at most two captures can have rank seven. Their rank sum is at least 62. This is not a construction at 62. Pair coding violates the one-carrier premise. The proof and independent review state the exact geometry and capture model.

• For the actual BD=13I construction, every dyadic log M with dyadic two-sided unit MD has stack rank rank[B;M]=16. The full-null terminal family requires ker N to lie in ker B intersect ker M when fixed linear N is the only further observation of retired ordinary Y. Thus total observation rank is at least sixteen complete fields, even with nonlinear postprocessing. This is not simultaneous scratch or native-child cost. Over an integral coefficient domain that contains the dyadics, a unit log with fraction-field stack rank eight requires 13 to be invertible; under MD=I, that rank-eight log is uniquely M=B/13. The residue proof and independent review include the ordered full-null argument. The finite routed extension assumes the ordered identities and Gaussian-dyadic two-sided inverses after flattening. Its executed two-coordinate route test is only a fixture. Odd division, a cheap remaining query, scatter, and a complete decoder are not implemented here.

• Fixed native paths and equal physical views force a constant scalar centre matrix to be A=cI8 if E+KAR is a clean diagonal response, with K=R^T/4. All 64 centre entries may vary. A 63-row minor of the 6,608 forbidden-pair equations has determinant -2^71; the diagonal response then has the same scalar c at every port. A nonzero response cannot factor through seven constant scalar centre channels. The all-cut proof and physical support review cover the fixed source/Y-tail one-way insertion class and, separately, scalar rewiring inside canonical cuts 7502–17249 with a fixed exterior, fixed wrappers, and the stated support and endpoint conditions. The two-basis proof and peer check retain the connected overlap argument and bounded extension. Arbitrary wrapper edits, new native paths, changed query/scatter spaces, and operator-valued centre entries remain outside the theorem.

• With scalar gates B tensor I, scalar plain input/output interfaces, and queries I+uQv with scalar u,v, both simultaneous scalar source and response spans have dimension at most the counted query total. An r-direction block query counts r times. Every non-scalar payload map counts, including rank-zero address maps. The actual line-centre query and proposed matched-plane query have scalar source rank 112 at every positive tensor depth. A mixed-plane endpoint on n fields needs at least n payload queries without a common negative-eigenspace premise. These are payload-query counts, not added native invoices; prior port-dependent input encoding changes the contract. The theorem and independent source/certificate review contain the ordered factorizations, exact minors, tensor compression, and rank-zero-map limit.

Seven serial checks passed in normal and optimized Python with exact typed JSON comparisons. Of the eight output receipts, four are byte-equal to the frozen receipts. The other four differ only in checker_sha256, which is replaced by the verified portable checker hash. The independent mixing checker rebuilt both complete source/tail interval inventories and all 4,276 products, checked the physical-view conditions, and recomputed the determinant and two-basis certificate. It uses reverse operator order. The frozen producer's forward-order loop is valid only because the consumed X histories have length at most one; that limit is checked. The query-span review reconstructed R from 10,851 scalar events and checked 28,672 plane Fourier columns and 802,816 functional contributions. Controls show why the residue hypotheses and full-null correction are needed. They also check a failing dense rank-seven mixer, a zero determinant after row duplication, a disconnected overlap graph, and a changed plane orientation. The original mixing emitters/modular check, native recipe generator, plane routes, odd-grid implementation, parent/cache mathematics, and full supplier were not rerun by this annex.

Use Python 3.11 or later, its standard library, one process, and at least 3 GiB of free disk space. Keep the full parent package at its published paths and use a new output directory:

python3 -I -O -B research/actual-query-information-bounds/annexes/source-geometry/replay.py --out /tmp/source-geometry-replay

Expected final output:

PASS_SOURCE_GEOMETRY_ANNEX

The annex reuses three exact parent archive members. The whole-archive and unique-member check binds the older query-span archive to those bytes. Runtime checks require no archive download, Git, external tools, or solver. The portability diff changes source/output locations and replaces two archive reads with exact parent-member reads. All original proofs, checkers, and review receipts remain unchanged.

The publication base remains b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, whose selected PR #4470 result is conditional at kappa 60403/20000000. These theorems retain their historical source packets and the parent's bce54fb3f895cbe5cd4c0eb477c3afeed100190f source; transfer to the newer selected construction is unproved. A useful next construction must pay for physical queries, scatters, address operations, owners, restoration, recursive precision, and complete supplier costs under its own contract.

The source notice preserves lane credit, original notices, and Apache-2.0. The clean core consumes the retained source construction from PR #3133 at 51eb9c4ee9e4722010d308aa3309e039d3940cc2 and the byte-equal base and extra provider words from PR #3148 at f2927a4b8afcf0701a6b945e14f30de1d94f5176; the retained credit record credits @dcharb78 for the coupled folds, and the exact source README credits Jeremy Diviney (@jeremydiviney) for packing exchange and integration. The logical warp definition is from PR #2588 at 8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb, with its source notice retained. PR #1825 at d16fb8936795ff101e4d2f63cfdc6a25066ebabf supplied the 56-plane matching; its original credit text is retained, and no human author is inferred from its submitter. OpenAI Codex assisted the research and separate agent reviews. No independent human review is claimed.