Construct paired centre gaps in original complex frames

research/original-paired-gap/MANIFEST.json

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research/original-paired-gap/NOTICE.md

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+# Source attribution and license
+
+New research, code, and verification used substantial OpenAI Codex
+assistance under the user's direction. Separate agents developed and
+reviewed the operator identities, scalar words, native phases, and owner
+composition. These are agent reviews. No independent human review is
+claimed. New material uses Apache-2.0; the [license](notices/LICENSE) is
+retained without changes.
+
+The original scalar programs and phase data come from the historical
+gauge44/t16 lineage at commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The following original notices
+are retained byte for byte:
+
+- [Gauge44 notice](notices/research/gauge44-slots-t16/NOTICE.md).
+- [Construction notice](notices/research/gauge44-slots-t16/construction/NOTICE.md).
+- [T16 integration notice](notices/research/gauge44-slots-t16/t16/NOTICE.md).
+- [Complete upstream notice](notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md).
+
+Those sources credit icekylinx for the source gauge and supplier
+pipeline; Hao Yan (@FanPUYen) for t16 construction and integration;
+Jeremy Kothe for the retained [PR #799](https://github.com/CrocSwap/integer-mult-bounds/pull/799)
+X4 word; Chafik Boukhalfa for the
+[PR #741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) frames
+and [PR #685](https://github.com/CrocSwap/integer-mult-bounds/pull/685)
+owner construction; and Rohan Arun for the
+native exact-complex recurrence correction. The retained notices give
+the full earlier lineage, licenses, and AI disclosures. This package
+does not claim those contributions as new work.
+
+The loader is unchanged from `research/native-source-codes/source_data.py`
+at commit `7649d9ceecec949541bec4bbde5929344166ba59`. The direct route
+calculation adapts `research/joint-query/verify_native.py` at commit
+`a6e6ad3936f67b8f63b5b68c5e75d540610a65e7`. The earlier example circuits
+are not runtime dependencies.
+
+Within the centre-encoding campaign, history-encoding supplied the
+full-mode core, exact sparse replay, and physical phase-gap graphs.
+Coherent-port supplied the complementary-gap argument and exact native
+review. The coordinating agent supplied the original-complex replica
+construction and its monomial-square abstraction. Residual-syndrome
+supplied the literal paired packet and proof. Its independent reviewer
+checked the operator order, routes, and corrected frame hypotheses.
+Encoded-controller supplied the prior arbitrary-mode decoder consequence;
+that conditional controller is not an executable dependency here.
+Source-domain supplied the separate owner binding, and circuit-interface
+reviewed its composition with the local pair.
+
+The portable pair checker adapts the history and residual-syndrome
+replay methods. The native checker adapts the coherent-port independent
+review, with the direct original-source route reconstruction described
+above. The general checker records the ordered proof identities and
+counterexamples. It does not replace the hypotheses by a numerical test.
+Exact source paths and hashes are recorded in [SOURCES.json](SOURCES.json).
+
+The result is a local typed mechanism and an enabling theorem. Full
+global closure, a complete supplier, and a kappa improvement are not
+claimed. The package does not change the selected frontier.