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Source-query encoder support tradeoff and fixed-frame obstruction - #1877
Mister-Meeseeks merged 3 commits into
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Batch review at Merged to Reviewed scope: Field-independent full-query support proof, sharp112-port8+104 example and fixed-read Fourier commutant obstruction reviewed. Exact rank/minor and seven rejecting controls pass. The120 rowwise bill is conditional on its tariff; changed charts, paid transport and other boundary contracts are not excluded. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
An invertible source encoder that logs the complete eight-coordinate query cannot make both endpoints sparse: its changed source fields and required target corrections together cover all 112 ports. Each support has at least eight ports. An explicit algebraic encoder attains the cover with 8 changed source ports and 104 corrected target ports. This is a structural result for PR1862's clean-J input interface, not a new supplier or kappa.
For Delta=G-I and H=(I-KR)Delta, LG=R gives RDelta=(R-L)G. Its full row rank and nonzero K rows prove the cover, including for arbitrary finite address-linear encoders. Three counterexamples show why the premises are needed. The 112/120 rowwise prices in the report are conditional comparators, not universal native-child bounds; the sharp algebraic example has no complete native invoice.
The fixed selected read also forces G_T=L_T^-1 R for every logger, not only the fixed-Z family. A forced coefficient of 1/2 from input port 2 to output port 21 distinguishes their line operators at Fourier character 2, ruling out commutation with the unchanged line or specified output frames. The argument extends to positive tensor powers. In the fixed-Z family, LZ=I makes the logger unique; a separate two-minor rank test agrees. Changed query reads, conjugated operators, paid transitions and carrying work through later native operations remain open.
Validation at
6d455d2d71eb35ecf8e562711e5f719b994fe3f3:Only the new package and dedicated workflow change. No full native supplier, global routing, hosting/precision or multiplication-theorem audit is claimed. Upstream PR checks are separate from the completed fork matrix.
Credit aliromman's PR1862 for the valid local encoder and stated interface, plus the pinned PR1042/PR1094 archive and retained E8/gauge44/native lineage. New proof and checker prepared for Chafik Boukhalfa with substantial OpenAI Codex assistance; no independent human review or formal proof assistant.