Research: multi-connector / priced-shadow 7q readout obstruction (no new kappa)

research/multi-connector-7q-obstruction/CERTIFICATE.json

@@ -0,0 +1,312 @@
+{
+  "schema_version": 1,
+  "status": "PASS_MULTI_CONNECTOR_7Q_OBSTRUCTION",
+  "scope": "Five-source common-B mutable-source Q/R/X alphabet (PR1898). Priced multi-connector readout at Q=7: correlated dirty shadow snapshot, independent dual same-walk, and illegal clean-shadow counterfactual. Answers #2715 OQ1 (cr7q multi-connector).",
+  "claim": {
+    "Q": 7,
+    "legal_multi_connector_min_R": 82,
+    "dirty_shadow_min_R": 82,
+    "dual_independent_min_R": 82,
+    "even_subset_min_R": 82,
+    "clean_shadow_counterfactual_min_R": 71,
+    "one_repeat_legal_min_R": 96,
+    "one_repeat_clean_counterfactual_min_R": 88,
+    "undercuts_436_if_clean_shadow_free": true,
+    "undercuts_436_after_complete_dirty_bill": false,
+    "legal_tariff_at_X6": 442,
+    "hypothetical_clean_tariff_at_X6": 420,
+    "endpoint_Q6_tariff": 436,
+    "answers_cr7q_oq1": true,
+    "oq1_answer": "A priced shadow snapshot with inherited correlated dirt collapses to even-subset cost R>=82 via sym-diff with the snapshot index (spectrum {82,88} on all 583296 covering distinct-6 sets). Two independently dirty connectors on the same walk likewise cannot beat R=82: dual R is computed as \u03a3_m min_a (e[a]+e[a\u2295m]) and the even-subset triangle inequality is verified on every covering set (matches_even=triangle_holds=583296). A dirt-free shadow would reach R=71 and tariff 420<436, but cannot scrub inherited connector dirt under the PR1898 contract; shadow-only reads leave odd dirt. After a complete dirty bill, legal multi-connector alphabets stay at tariff >=442 and do not undercut the six-query endpoint 436.",
+    "no_new_kappa": true
+  },
+  "champion": {
+    "slots": [
+      0,
+      1,
+      2,
+      6,
+      12,
+      24,
+      16
+    ],
+    "path_X": 6,
+    "even_R": 82,
+    "dirty_shadow_R_by_k": [
+      82,
+      82,
+      82,
+      82,
+      82,
+      82,
+      82
+    ],
+    "dirty_shadow_min_R": 82,
+    "dual_independent_R": 82,
+    "clean_shadow_R_by_k": [
+      82,
+      71,
+      77,
+      77,
+      77,
+      77,
+      77
+    ],
+    "clean_shadow_min_R": 71,
+    "clean_best_k": 1,
+    "legal_tariff_X6": 442,
+    "hypothetical_clean_tariff_X6": 420,
+    "endpoint_Q6": 436,
+    "symdiff_checked_at_k1": 64
+  },
+  "clean_shadow_dirt_examples": [
+    {
+      "note": "champion_shadow_only_sigma",
+      "slots": [
+        0,
+        1,
+        2,
+        6,
+        12,
+        24,
+        16
+      ],
+      "snapshot_index": 1,
+      "sigma": 1,
+      "mask": 1,
+      "primary_reads": 0,
+      "shadow_reads": 1,
+      "inherited_dirt_parity": 1,
+      "legal_under_correlated_dirt": false,
+      "clean_R": 71,
+      "dirty_R": 82
+    },
+    {
+      "note": "first_clean_71_witness_shadow_dirt",
+      "slots": [
+        0,
+        1,
+        2,
+        4,
+        8,
+        15,
+        16
+      ],
+      "snapshot_index": 6,
+      "sigma": 16,
+      "mask": 16,
+      "primary_reads": 0,
+      "shadow_reads": 1,
+      "inherited_dirt_parity": 1,
+      "legal_under_correlated_dirt": false,
+      "clean_R": 71,
+      "dirty_R": 82
+    }
+  ],
+  "distinct6": {
+    "covering_sets": 583296,
+    "even_subset": {
+      "attainable_R": [
+        82,
+        88
+      ],
+      "histogram": {
+        "82": 97216,
+        "88": 486080
+      },
+      "min_R": 82,
+      "first_witnesses": {
+        "88": [
+          0,
+          1,
+          2,
+          3,
+          4,
+          8,
+          16
+        ],
+        "82": [
+          0,
+          1,
+          2,
+          4,
+          8,
+          15,
+          16
+        ]
+      }
+    },
+    "dirty_shadow": {
+      "attainable_R": [
+        82,
+        88
+      ],
+      "histogram": {
+        "82": 97216,
+        "88": 486080
+      },
+      "min_R": 82,
+      "matches_even_on_covering": 583296,
+      "first_witnesses": {
+        "88": [
+          0,
+          1,
+          2,
+          3,
+          4,
+          8,
+          16
+        ],
+        "82": [
+          0,
+          1,
+          2,
+          4,
+          8,
+          15,
+          16
+        ]
+      }
+    },
+    "dual_independent": {
+      "attainable_R": [
+        82,
+        88
+      ],
+      "histogram": {
+        "82": 97216,
+        "88": 486080
+      },
+      "min_R": 82,
+      "matches_even_on_covering": 583296,
+      "triangle_holds_on_covering": 583296,
+      "first_witnesses": {
+        "88": [
+          0,
+          1,
+          2,
+          3,
+          4,
+          8,
+          16
+        ],
+        "82": [
+          0,
+          1,
+          2,
+          4,
+          8,
+          15,
+          16
+        ]
+      }
+    },
+    "clean_shadow_counterfactual": {
+      "attainable_R": [
+        71,
+        80
+      ],
+      "histogram": {
+        "71": 97216,
+        "80": 486080
+      },
+      "min_R": 71,
+      "first_witnesses": {
+        "80": [
+          0,
+          1,
+          2,
+          3,
+          4,
+          8,
+          16
+        ],
+        "71": [
+          0,
+          1,
+          2,
+          4,
+          8,
+          15,
+          16
+        ]
+      },
+      "legal_under_dirty_contract": false
+    }
+  },
+  "one_repeat_even": {
+    "kind": "one_repeat_on_standard_basis",
+    "covering_walks": 1680,
+    "attainable_R": [
+      96
+    ],
+    "histogram": {
+      "96": 1680
+    },
+    "min_R": 96,
+    "first_witness": [
+      0,
+      1,
+      0,
+      2,
+      4,
+      8,
+      16
+    ]
+  },
+  "one_repeat_dirty_shadow": {
+    "kind": "one_repeat_on_standard_basis",
+    "covering_walks": 1680,
+    "attainable_R": [
+      96
+    ],
+    "histogram": {
+      "96": 1680
+    },
+    "min_R": 96,
+    "first_witness": [
+      0,
+      1,
+      0,
+      2,
+      4,
+      8,
+      16
+    ]
+  },
+  "one_repeat_clean_shadow_counterfactual": {
+    "kind": "one_repeat_on_standard_basis",
+    "covering_walks": 1680,
+    "attainable_R": [
+      88
+    ],
+    "histogram": {
+      "88": 1680
+    },
+    "min_R": 88,
+    "first_witness": [
+      0,
+      1,
+      0,
+      2,
+      4,
+      8,
+      16
+    ]
+  },
+  "leave_alone": {
+    "through": 2715,
+    "includes": [
+      2593,
+      2643,
+      2677,
+      2686,
+      2687,
+      2715
+    ],
+    "deferred": [
+      "mutable-source-7q-shared-xor soft-overlap #2643",
+      "host screens"
+    ]
+  }
+}

research/multi-connector-7q-obstruction/NOTICE.md

@@ -0,0 +1,24 @@
+# Notice
+
+New material in this directory is Apache-2.0.
+
+Predecessor credit (do not alter historical notices elsewhere):
+
+- Arham Tahir / PR1898 `research/mutable-source-minimum-queries` — five-source
+  alphabet, minimum-query endpoint, abstract complete-call tariff.
+- ywz65 / open PR2455 `research/mutable-source-six-query-xor` — component lemma
+  and restored interaction-graph census at six queries.
+- Arham Tahir / PR1370 — path-local shear lowering.
+- TennisBowling / PR1524 — equal-price theorem and unequal-price handoff.
+- Ross Richardson / PR943/934 — prefix framework.
+- Fork path-lowered `research/mutable-source-789q-invoice` / open #2677 —
+  distinct-slot spectrum and champion path; not edited.
+- Open #2643 `research/seven-query-xor-floor` — restored `X ≥ 6` at `Q = 7`;
+  not edited.
+- Open #2686 `research/seven-query-r-floor` — even-subset `R ≥ 82`; not edited.
+- Open #2715 `research/cheaper-readout-7q-obstruction` — all-subset /
+  dirty-parity repair and OQ1 answered here; not edited.
+- Live pin: `research/mutable-source-shear-cost/CERTIFICATE.json`.
+
+Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI
+assistance.