Mister-Meeseeks · Oct 20, 2026 · Oct 20, 2026
diff --git a/research/qq16-paired-precision/COST.json b/research/qq16-paired-precision/COST.json
@@ -0,0 +1,70 @@
+{
+  "N": "2^(73 lambda) complex payload coordinates per owner, lambda positive integer",
+  "baseline": {
+    "CLEAR": 416,
+    "H1": 224,
+    "cover_maps": 352,
+    "cover_numeric_ops_per_N": 1408,
+    "monomial_wrappers": 448,
+    "native_numeric_ops_per_lambda_N": 2240,
+    "numeric_constant_per_N": 12352,
+    "private_peak": 16,
+    "quarter_ADD": 896,
+    "scalar_allowance": 26944,
+    "scalar_numeric_ops_per_N": 8256,
+    "unit_ADD": 1920,
+    "wrapper_numeric_ops_per_N": 2688
+  },
+  "candidate": {
+    "CLEAR": 416,
+    "H1": 224,
+    "cover_maps": 352,
+    "cover_numeric_ops_per_N": 1408,
+    "monomial_wrappers": 448,
+    "native_numeric_ops_per_lambda_N": 2240,
+    "numeric_constant_per_N": 12152,
+    "private_peak": 16,
+    "quarter_ADD": 896,
+    "scalar_allowance": 26144,
+    "scalar_numeric_ops_per_N": 8056,
+    "unit_ADD": 1820,
+    "wrapper_numeric_ops_per_N": 2688
+  },
+  "common_width_tariff": "For each reference primitive priced at any common positive tau(W), candidate prescribed bill is200N tau(W) smaller; logical allowance model separately gives800 tau_L(W). These are comparisons of prescribed bounds, not lower bounds on optimal implementations.",
+  "logical_allowance_difference": "800 allowance units; distinct from200N numeric operations",
+  "numeric_bound_per_owner": {
+    "baseline": "(12352+2240 lambda)N",
+    "candidate": "(12152+2240 lambda)N",
+    "difference": "200N numeric word operations"
+  },
+  "numeric_storage_bound": "(930N+12) signed W-bit component slots, including448 persistent complexfields,16 privatefields,one complex permutation buffer,and12 scalar native temporaries",
+  "premises": [
+    "Common sufficient range/grid certificate for every numerical reference interior.",
+    "Exact dyadic divisions and no overflow/underflow at the stated common W.",
+    "Pair-first coordinate Gaussian reference is permitted for this numerical bill; it is not inferred to implement a paid recursive child tariff."
+  ],
+  "reference_lowering": {
+    "CLEAR": "2N zero stores",
+    "buffer_protocol": "Two-leg out-of-place permutation returns to its fixed external bank; address/control work is outside numeric count.",
+    "cover": "2N outward copies plus2N copies back to the fixed destination bank",
+    "quarter_ADD": "2N exact binary shifts by two (one W-bit shift primitive per component) plus 2N additions/subtractions",
+    "signed_H1": "lambda coordinate Gaussian lines; each at most4N additions,2N exact halves,4N copies",
+    "unit_ADD": "2N real-component additions or subtractions",
+    "wrapper": "2N component sign operations plus2N outward copies and2N copies back to the fixed destination bank"
+  },
+  "status": "PASS_CONDITIONAL_COMMON_WIDTH_NUMERIC_REFERENCE_COMPARISON",
+  "unpriced": [
+    "Owner/payload address generation and control",
+    "physical movement and placement tariffs",
+    "actual recursive native child error/width/cost contract",
+    "native workspace exclusivity in a recursive implementation",
+    "caller entry-format conversion",
+    "recursive usage and supplier caps"
+  ],
+  "width_mismatch_break_even": {
+    "equal_width": "Delta=0 satisfies bothstrictinequalities for everylambda>=1 andW>0",
+    "general": "tau(W_candidate)/tau(W_baseline) < (12352+2240 lambda)/(12152+2240 lambda)",
+    "linear_tau_W": "Delta < 200 W_baseline/(12152+2240 lambda), forW_candidate=W_baseline+Delta",
+    "logical_allowance_only": "tau_L(W_candidate)/tau_L(W_baseline) < 26944/26144"
+  }
+}
diff --git a/research/qq16-paired-precision/POLYNOMIAL.json b/research/qq16-paired-precision/POLYNOMIAL.json
@@ -0,0 +1,95 @@
+{
+  "baseline": {
+    "envelope_coefficients": [
+      "445",
+      "28230",
+      "96",
+      "142272"
+    ],
+    "observation_sha256": "d08d4039097f4e20f423bbcd432272759853e4cd86116b76dda02258f14ab6f0",
+    "observations": 4032,
+    "peaks": [
+      [
+        3797,
+        "post W0"
+      ],
+      [
+        3798,
+        "post W7"
+      ],
+      [
+        3799,
+        "post W20"
+      ],
+      [
+        3800,
+        "post W27"
+      ],
+      [
+        3801,
+        "post W36"
+      ],
+      [
+        3802,
+        "post W46"
+      ],
+      [
+        3803,
+        "post W57"
+      ],
+      [
+        3804,
+        "post W111"
+      ]
+    ],
+    "proof": "Every F-observation has nonnegative coefficients after x=1+y; F(1)=171043 and degree3 give F(x)<=171043*x^3.",
+    "variable": "x=2^(lambda-1)>=1"
+  },
+  "candidate": {
+    "envelope_coefficients": [
+      "445",
+      "28230",
+      "96",
+      "142272"
+    ],
+    "observation_sha256": "d9b4d9bf395ced9ed19a4ed56086d85ce4115c0c7366ab8efd4fe0a47d190751",
+    "observations": 3932,
+    "peaks": [
+      [
+        3697,
+        "post W0"
+      ],
+      [
+        3698,
+        "post W7"
+      ],
+      [
+        3699,
+        "post W20"
+      ],
+      [
+        3700,
+        "post W27"
+      ],
+      [
+        3701,
+        "post W36"
+      ],
+      [
+        3702,
+        "post W46"
+      ],
+      [
+        3703,
+        "post W57"
+      ],
+      [
+        3704,
+        "post W111"
+      ]
+    ],
+    "proof": "Every F-observation has nonnegative coefficients after x=1+y; F(1)=171043 and degree3 give F(x)<=171043*x^3.",
+    "variable": "x=2^(lambda-1)>=1"
+  },
+  "negative_control": "Understate cubic coefficient142272 by1: both inductive certificates reject. Not a minimum-physical-width lower bound."
+}
diff --git a/research/qq16-paired-precision/PREDECESSORS.json b/research/qq16-paired-precision/PREDECESSORS.json
@@ -0,0 +1,46 @@
+{
+  "schema_version": 1,
+  "files": [
+    {
+      "pr": 4106,
+      "head": "48529915d50bb59b53db53686c4add1cf53429dd",
+      "path": "research/qq16-sequential-recovery/WORD.json",
+      "local": "vendor/PR4106-WORD.json",
+      "sha256": "b4f2b5662734178d02a5d620ebd071bc284abd4d9b6dbe11b5d9646455a0f021",
+      "git_blob": "6c6f726cd14010f9763155518f833862eb167263"
+    },
+    {
+      "pr": 4106,
+      "head": "48529915d50bb59b53db53686c4add1cf53429dd",
+      "path": "research/qq16-sequential-recovery/CONSTRUCTION.json",
+      "local": "vendor/PR4106-CONSTRUCTION.json",
+      "sha256": "dbf7b1d077b1b58262afe22aceeac02262c50c6597392676ea7a98e7d9cdd075",
+      "git_blob": "f4376037d5a574e56d46f95997b64a50eb86dcf2"
+    },
+    {
+      "pr": 4106,
+      "head": "48529915d50bb59b53db53686c4add1cf53429dd",
+      "path": "research/qq16-sequential-recovery/PROOF.md",
+      "local": "vendor/PR4106-PROOF.md",
+      "sha256": "5d79ac0fafa95c81f000f1da9802abfaac5adedd9017d0d5e651220bb682e2a7",
+      "git_blob": "4518e496f89f59b20562ebfef360a7b404b66d98"
+    },
+    {
+      "pr": 4015,
+      "head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e",
+      "path": "research/qq16-streaming-recovery/WORD.json",
+      "local": "vendor/PR4015-WORD.json",
+      "sha256": "272d8c1bd172c29044eb227ec6d67a882501250978234685e035158f4479aa58",
+      "git_blob": "9a57a6f9c2fd8cdc4e5934408d78ef54e5f266b6"
+    },
+    {
+      "pr": 4015,
+      "head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e",
+      "path": "research/qq16-streaming-recovery/PROOF.md",
+      "local": "vendor/PR4015-PROOF.md",
+      "sha256": "81f0fa19b19fa7302ba9c61f4f1b2e11758f973b964240ba48c16ae9b6997396",
+      "git_blob": "8fd64e85e3e595403fe3ae4ed60b9ff368c9a3f5"
+    }
+  ],
+  "credit": "PR3985 owns336-to224native reduction; PR4015 streaming/outputhosting; PR4106 scalarpairing; PR4003 residual. Native/decoder math ywz65/2707, Arham Tahir/2681, Ali Romman and retainedlineage. Producer-grid3303 NickPetalas, independent3652 ToikY. Tekalign/tekuuu4030 shared-framegate isdistinct. Newaudit ChrisR/Clear1nsight with substantialOpenAIassistance. No predecessor executable imported; endpoint identities inherited ratherthanrerun."
+}