Improve T16 kappa by composing the 408-helper rank-seven supplier

research/t16-rank7-provider-composition/CREDITS.md

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+# Attribution and scope
+
+This construction combines the current rank-seven local supplier with a newly allocated sixteen-replica schedule. It does not invent the local word, native projector compiler, controller, moment engines, or outer argument.
+
+- [PR3413](https://github.com/CrocSwap/integer-mult-bounds/pull/3413), exact head `391d02ced8e620d8f06aeda1ebe02f099d37af92`, supplies the admitted T16 comparison and the literal call chronology retained in `PLAN-3413.json`.
+- [PR3403](https://github.com/CrocSwap/integer-mult-bounds/pull/3403), retained by PR3413, supplies deterministic regular bipartite edge coloring of pattern flows. `PREDECESSOR-COLORING.py` is its exact retained verifier; `coloring.py` extracts its three generic coloring functions and generalizes the width loop from five classes to the supplied count-vector length. The original verifier and upstream explanations remain unchanged.
+- [PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) and [PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148) supply both actual rank-seven words, their native interfaces, and the complete paid local profile. All previous source and research credits in that ancestry remain applicable.
+- `research/t16-owner-audit-seed67/verify.py` and `research/rank7-joint-endframes/allocation/vendor/independent_owners.py` supply independent literal owner and current-provider checks. Their code is loaded unchanged from authenticated inputs.
+- `research/frontier1094-idle-star-ceiling/analyze.py` and the retained multicold engines supply independent rational profile pricing. Its ancestral outer price is labeled separately from the changed physical/controller admission and modern outer result.
+
+New work is the six-width chronological allocation certificate, its source-bound deterministic reconstruction, compact-helper correspondence, and combination of these existing scientific interfaces. Solver discovery is not part of verification. No private optimizer, orchestration script, or research notebook is required for replay.

research/t16-rank7-provider-composition/DISPATCH-RULE.json

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+{
+  "rule": "extra on (stage,replica)=(0,0); gauge44 on all other143calls",
+  "reason": "Exercise both authenticated providers under unchanged upstream reconstructor; actual widths and local paid profiles identical."
+}

research/t16-rank7-provider-composition/EXPECTED-PROFILE-PRICE.json

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+{
+  "native": {
+    "endpoint": "69086128517542103751/40000000000000000000000",
+    "endpoint_decimal": "0.001727153212938552593775",
+    "kappa": "344835059606577/200000000000000000",
+    "kappa_decimal": "0.001724175298032885"
+  },
+  "conservative": {
+    "endpoint": "863576604972635276219/500000000000000000000000",
+    "endpoint_decimal": "0.001727153209945270552438",
+    "kappa": "431043823762479/250000000000000000",
+    "kappa_decimal": "0.001724175295049916"
+  }
+}

research/t16-rank7-provider-composition/EXPECTED.json

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+{
+  "owner_canonical_sha256": "b177136dfa0be42d6b54796e6ae45afb2151f72a9a1fd67821acefdf278011ad",
+  "idle": {
+    "1": 4376,
+    "3": 1090,
+    "5": 458,
+    "48": 6078
+  },
+  "profile": {
+    "1": 354728,
+    "2": 104256,
+    "3": 33922,
+    "4": 14688,
+    "5": 3338,
+    "8": 1152,
+    "48": 6078
+  },
+  "rank_mass": 1041408,
+  "deficit": 5120,
+  "roles": 58752,
+  "calls": 144
+}

research/t16-rank7-provider-composition/INPUT-PINS.json

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+{
+  "research/coupled-carrier-cap740/words/base.json.gz": "300a9b8ad1d554f0e6f84f43f3f5fd870a5b4e5f81ad856900b6e8999684892e",
+  "research/coupled-carrier-cap740/words/extra.json.gz": "495d030f1e03b90e954dad3043994f03293d41b9ed220a3beaef849df435d3f0",
+  "research/rank7-joint-endframes/vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044",
+  "research/t16-owner-audit-seed67/verify.py": "f6e27f76c9ccb87b3ce6c5e673588338a09847d22771da7b3f28579661c9404b",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/frontier1094-idle-star-ceiling/analyze.py": "d9768cff06d5e19e75b2ccc4d03ff5bc2d93098f3192c167d3f208c802877bbc",
+  "research/community-frontier1094-audit/ASSEMBLY.json": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/rank7-joint-endframes/allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461",
+  "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "research/coupled-carrier-cap740/vendor/PR3133-PROVIDERS.json": "52eb0d85caa7b2d4a93acdf5011f52b793f61ddca86235fb03cd9a09397ad4cd"
+}

research/t16-rank7-provider-composition/LOCAL-PINS.json

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+{
+  "coloring.py": "0e43ba559f0552001b2271ea2eb0be968a372f6643bf1d3d14cf4779b82d5642",
+  "PLAN-3413.json": "27d6a1886d3f42b7bcc3dbf10d4e669524383227fa5e19c3453ca2eb6953e2d8",
+  "CERTIFICATE.json": "ff0c0956ca52d7a5845bc8e12a97cadd1bd39e836e6674c363fcb3af087b188b",
+  "PREDECESSOR-COLORING.py": "200e8005b121acdf0a68589e73961a1e1120faf6041f500822c0eb9c1cf09f05",
+  "EXPECTED.json": "3108da49d4a97a430a2562eb73d11e5a51205350da8a2ba86575d3bcaf09c187",
+  "EXPECTED-PROFILE-PRICE.json": "b246012aef395f91c69c875c79503bc6961bc4121502e65f5e041d9d2a718463",
+  "DISPATCH-RULE.json": "5b1b0d94b867ad95f385b684cf936cdf5bb31ad92e37932d8b5254b53ca2a96b"
+}