Lower the current selected quadratic Gaussian phase to a fixed tape table with complete owner return

research/literal-native-quadratic-phase/BINDING-OPTIMIZED.json

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+{
+  "basis_states": 512,
+  "frames": [
+    3,
+    99
+  ],
+  "native_event_index": 24472,
+  "negative_controls": [
+    "changed absolute phase"
+  ],
+  "note": "Retained exact compiler and independent interpreter, plus new XOR-parity phase oracle. No full native catalogue replay.",
+  "owner": 415,
+  "rank": 1,
+  "side": "right",
+  "source_files": 8,
+  "status": "PASS_CURRENT_SELECTED_QUADRATIC_RECIPE_BINDING"
+}

research/literal-native-quadratic-phase/BINDING.json

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+{
+  "basis_states": 512,
+  "frames": [
+    3,
+    99
+  ],
+  "native_event_index": 24472,
+  "negative_controls": [
+    "changed absolute phase"
+  ],
+  "note": "Retained exact compiler and independent interpreter, plus new XOR-parity phase oracle. No full native catalogue replay.",
+  "owner": 415,
+  "rank": 1,
+  "side": "right",
+  "source_files": 8,
+  "status": "PASS_CURRENT_SELECTED_QUADRATIC_RECIPE_BINDING"
+}

research/literal-native-quadratic-phase/ENVIRONMENT.json

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+{
+  "python": "3.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ]",
+  "platform": "linux",
+  "dependencies": "Python standard library only",
+  "normal_optimized_author_receipts_identical": true,
+  "relocated_independent_dense": "PASS, exact receipt equality",
+  "relocated_peer": "PASS_B3_INDEPENDENT_STRUCTURE",
+  "human_or_kernel_review": false
+}

research/literal-native-quadratic-phase/NOTICE

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+Prepared for Jerry Chen / CubeJerry with substantial OpenAI assistance.
+Apache-2.0. New contribution: literal local lowering, scoped proof and package.
+Ali Romman/#5375 supplies the incremental phase and repeated constant.
+The retained reference files preserve original source text.
+#7000 and its native/Gaussian lineage supply the selected source and engines;
+credit DreamingOfClouds, Ali Romman, Cinna Davis, zxv, unpaidmoon, icekylinx,
+CubeJerry and earlier authors named by the retained source.
+C2 literal-layer-phase supplies Gamma and signed staging/return. B1 literal-
+layer-egress supplies owner staging, and #7349 the retained literal machine.
+Exact original/copy source pins are in SOURCES.json. No predecessor identity,
+compiler, source construction or general monomial theorem is claimed as new.

research/literal-native-quadratic-phase/PR-DESCRIPTION.md

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+## Result and purpose
+
+This package lowers the diagonal phase of an actual current #7000 native
+monomial to a fixed local tape table. The source is MOVE index 24472, owner 415,
+frames 3→99, rank 1, right factor, at main
+`e54523517d0f03e58352e647c403a5af3e525a57`. Its nonzero constant, linear and
+quadratic terms are retained, including the constant once per column.
+
+The graph has **8,211 locations, 23 tapes and four symbols**, using only
+local reads, one-cell writes, unit moves, fixed jumps and halt. For every
+positive supplied five-Gamma `(f,r,P,S,w)` descriptor and complete packed
+`[P] × [2^f]^9 × [S]` payload, it phases every Gaussian field and commits to
+the original owner. Success restores every head and private window. Exact
+signed range rejection preserves the public payload; failure cleanup and
+reuse are not claimed.
+
+With `Q=2^(9f)`, `N=PQS r`, `V=2Nw` and descriptor length E, the proved bill
+is `65536[E+10f+r+P+S+w+100PQ+V+1]`, hence O(V) on this supplied interface.
+A separate historical bound retains prior backing K0.
+
+## Novelty and predecessors
+
+#5375 already proves the multicounter update and repeated constant phase.
+Structured physical Gaussian monomials and selected record lists remain
+predecessors. The new contribution is the current recipe's literal table
+and complete owner contract, not a phase identity or full monomial theorem.
+
+The [outer phase package](https://github.com/CubeJerry/integer-mult-bounds/tree/8b549ca6557ccbb3017b104b27ea35051f990416/research/literal-layer-phase)
+supplies Gamma and signed staging/return; the
+[egress package](https://github.com/CubeJerry/integer-mult-bounds/tree/51ab0539059214fcfa044938c36a0b6017232be5/research/literal-layer-egress)
+supplies whole-owner staging, and #7349 supplies the machine. Exact source
+pins and copied original notices are retained.
+
+## Reproduction and checks
+
+Python 3.11+ and standard library only, from the repository root:
+
+```sh
+python3 -I -W error -B research/literal-native-quadratic-phase/bind_selected.py
+python3 -I -W error -O -B research/literal-native-quadratic-phase/bind_selected.py
+python3 -I -W error -B research/literal-native-quadratic-phase/verify.py
+python3 -I -W error -O -B research/literal-native-quadratic-phase/verify.py
+```
+
+Normal/optimized receipts agree. Source binding checks the actual event,
+exact lowering, retained independent kernel, all 512 monomial basis inputs
+and a phase fault. The separate arithmetic/address oracle checks 376
+complete packets, 11,991,714 transitions, all 336 width 1–3 endpoint pairs,
+53 exact range rejections and four semantic controls. Four packets use
+actual m=9,f=1; smaller fixed dimensions cover multiple columns. The author
+replay does not claim a complete actual f=2 packet.
+
+## Independent verification
+
+The lead's separate dense CPU/XOR-popcount oracle passes 16 cases and
+6,428,358 transitions, including explicitly incomplete selected f=2,3,4
+prefixes; eight exact Git source bindings pass. A complementary reviewer
+accepts the universal proof and complete bill. Their separate interpreter
+checks 11 complete successes, 9,362 records and 6,786,145 transitions, plus
+three mutations. A functionally correct full-width rewind is rejected by
+an independently derived exact movement census. Copied sources, reviews
+and receipts are in `independent/`; the relocated copies also pass.
+
+## Limitations and kappa
+
+**No new kappa.** Descriptor/layout production, gapped-layout conversion,
+affine routing, exterior scalars, recursive C and joined lifetimes remain
+open. No complete native word, selected layer or multiplier is admitted.
+All five foundational assumptions remain in the full conditional theorem.
+The next obligations are the actual descriptor/layout bridge, affine/child
+composition, and complete caller grid/headroom admission.
+
+Prepared for **@CubeJerry (Jerry Chen)** with substantial OpenAI assistance.
+Credit Ali Romman/#5375, #7000's retained native/Gaussian authors and the
+B1/C2/#7349 predecessors. Independent AI checks are not human or formal
+kernel acceptance. Apache-2.0.

research/literal-native-quadratic-phase/PR-TITLE.txt

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+Lower the current selected quadratic Gaussian phase to a fixed tape table with complete owner return