Research note: restoration coalescing across a recursion batch (read-free + composable-family boundary; no new kappa)

research/restoration-coalescing/CERTIFICATE.json

@@ -0,0 +1,94 @@
+{
+  "base": "ce7ad1b6ab09452c3478723a2e96ed5ff212dc08",
+  "cases": {
+    "hetero_negative": {
+      "children": 3,
+      "composed_form": "dense",
+      "composed_inverse_dense": true,
+      "composed_inverse_nnz": 64,
+      "deferred_dense_mults": 64,
+      "deferred_factorized_mults": 16,
+      "deferred_factorized_passes": 3,
+      "eager_structured_mults": 16,
+      "factorized_matches_dense": true,
+      "mult_elimination": false,
+      "observables_equal": true
+    },
+    "perm": {
+      "children": 3,
+      "composed_form": "perm",
+      "deferred_moves": 8,
+      "deferred_restoration_passes": 1,
+      "eager_moves": 24,
+      "eager_restoration_passes": 3,
+      "observables_equal": true
+    },
+    "phase": {
+      "children": 3,
+      "composed_form": "diag",
+      "deferred_mults": 8,
+      "deferred_restoration_passes": 1,
+      "eager_mults": 24,
+      "eager_restoration_passes": 3,
+      "mult_ratio": "3",
+      "observables_equal": true
+    },
+    "reader_cancellation": {
+      "children": 5,
+      "deferred_restoration_passes": 1,
+      "eager_restoration_passes": 5,
+      "observables_equal": true,
+      "reader_coefficients": [
+        "1",
+        "1",
+        "1",
+        "-1",
+        "1"
+      ],
+      "readers_nonzero": true,
+      "summed_defect_zero": true
+    },
+    "reader_negative": {
+      "discrepancy": [
+        [
+          "0",
+          "0"
+        ],
+        [
+          "3",
+          "-1"
+        ],
+        [
+          "4",
+          "0"
+        ],
+        [
+          "6",
+          "0"
+        ],
+        [
+          "3",
+          "-1"
+        ],
+        [
+          "6",
+          "4"
+        ],
+        [
+          "6",
+          "0"
+        ],
+        [
+          "3",
+          "5"
+        ]
+      ],
+      "discrepancy_nonzero": true,
+      "observables_equal": false,
+      "summed_defect_nonzero": true
+    }
+  },
+  "dimension_N": 8,
+  "e": 3,
+  "summary": "phase=PASS perm=PASS hetero_dense=CONFIRMED reader_diverges=CONFIRMED reader_cancels=CONFIRMED factorized_matches_dense=CONFIRMED"
+}

research/restoration-coalescing/CLAIM.json

@@ -0,0 +1,47 @@
+{
+  "track": "recursive-interfaces",
+  "track_range": "50-59",
+  "assignment_seed": 53,
+  "seed_source": "operating-system randomness (Cryptographic RandomNumberGenerator), 0-99",
+  "contributor": "Navinor",
+  "ai_assistance": "with help from opencode",
+  "base_commit": "ce7ad1b6ab09452c3478723a2e96ed5ff212dc08",
+  "branch": "research/agent-13-recursive-seed53",
+  "object_investigated": "Elimination of per-child dirty-workspace restoration across one recursion batch by deferring it to a single composed restoration at the node exit.",
+  "proposed_method": "Exact Gaussian-rational operator algebra at N=8: eager (restore after every child) vs deferred (restore once at exit). Two questions decided exactly: the summed-defect criterion sum_i B_i (G_{i-1}...G_1 - I) = 0 for exact observables (read-free batches are SUFFICIENT, not necessary) and composable restoration family / retained factorization (cost).",
+  "parameter_range": "N=8 coefficient positions (e=3); r=3 children per node; restoration families: diagonal unit phases (a in {1,2,3} via i^(a*popcount)), cyclic permutations (shifts {1,2,4}), and a heterogeneous mix (phase+Walsh+permutation).",
+  "candidates_considered": [
+    "Coalesce per-child dirty-workspace restoration across a batch (chosen)",
+    "Defer compact-control exceptional-address repair charged at every node to the root",
+    "Eliminate the Walsh entrance/exit boundary between same-subset children"
+  ],
+  "overlap_check": {
+    "CrocSwap/integer-mult-bounds#1012": "concurrent, same track 50-59 (seed 57, thakrarsagar): prices restoration DEFERRAL of U8 helper rank/frame climbs at the ASSEMBLY level (hosted T37 recurrence, coverage identity, kappa ceilings), finds it mass-neutral. Distinct layer and cost unit from this note's OPERATOR-level coalescing of phase/routing restoration passes. Complementary; not duplicated; numbers not reproduced here.",
+    "CrocSwap/integer-mult-bounds#974": "concurrent, same track (avirazza): prices the same boundary classes with zero parent cost at the assembly level. Distinct method; not duplicated.",
+    "research/seed51-clean-residual-dilation": "seed 51, recursive-interface track; prices a spectral-split residual ENCODER and its per-stream dirty restoration. Different object (encoded hosting vs restoration coalescing), different boundary. No duplication.",
+    "kernel-frame-coalescing": "changes frame ranks (rank-1 to rank-2 climbs), not restoration passes. Different cost axis.",
+    "universal-connector-boundary": "query-path / dirty-connector census; supplies the restoration invariant this note prices, not the coalescing mechanism."
+  },
+  "expected_deliverable": "A research note with a complete restoration cost recurrence, a sharp correctness boundary (read-free), a sharp cost boundary (composable family), and an exact stdlib verifier with two positive cases and two negative controls. No new kappa.",
+  "pinned_coordination_issue": "none reachable; claim recorded locally",
+  "expected_finish": "same session; verification reserved for the final quarter",
+  "status": "completed",
+  "result": "Scoped research note: a complete restoration cost recurrence plus (corrected) the exact terminal-observation criterion sum_i B_i (G_{i-1}...G_1 - I) = 0 for the observables, with read-free batches as a sufficient, not necessary, condition, and a cost boundary (pass reduction r->1 when the restorations collapse under composition to one cheap pass, with composition charged r*c_desc under the succinct descriptor hypothesis (c_desc = O(1)) and Theta(r*N) for full-length descriptor tables; deferral costs more only when no cheap factorization is retained and the dense product is applied directly). Two positive cases (phase 3->1 passes / 24->8 mults; permutation 3->1 passes), one example where a single reader breaks deferral, one exact nonzero-reader cancellation case (5 reader children, coefficients [1,1,1,-1,1], summed defect exactly zero, restorations 5->1), and the heterogeneous example: composed product dense (64/64 nonzero) yet its retained factorization costs the eager sum 16 mults at N=8 (verified against the dense product on every basis column), against 64 mults for DIRECT dense application. No new kappa; selected frontier and upstream/ unchanged.",
+  "post_review_correction": {
+    "trigger": "Batch review follow-up on https://github.com/CrocSwap/integer-mult-bounds/pull/1155#issuecomment-6161612247 (record: https://github.com/CrocSwap/integer-mult-bounds/blob/main/docs/research/community-efficient300-review.md)",
+    "corrected_claims": [
+      "Correctness: read-free is SUFFICIENT, not necessary. The exact terminal-observation criterion is vanishing summed defect sum_i B_i (G_{i-1}...G_1 - I) = 0; nonzero-reader counterexamples: https://github.com/CrocSwap/integer-mult-bounds/pull/1199, https://github.com/CrocSwap/integer-mult-bounds/pull/1203, https://github.com/CrocSwap/integer-mult-bounds/pull/1205. Prefix/adaptive observation requires each prefix defect B_i (P_{i-1} - I) to vanish (https://github.com/CrocSwap/integer-mult-bounds/pull/1205).",
+      "Cost: matrix density of the composed product is not an application-cost statement. A dense phase/Walsh/permutation product retains its cheap factorization; sequential factor application costs the eager sum (verified 16 = 16 mults at N=8). Deferral costs more only when no cheap factorization is retained and the dense product must be applied directly; the 64 vs 16 numbers at N=8 are kept as a statement about DIRECT dense application only."
+    ],
+    "unchanged": "The original reader counterexample (one reader can break deferral) and the original heterogeneous direct-dense counts (64 vs 16 at N=8) still run unchanged; only their scope is corrected."
+  },
+  "post_review_correction_2": {
+    "trigger": "Second review follow-up on https://github.com/CrocSwap/integer-mult-bounds/pull/1155#issuecomment-6197859152 (record: https://github.com/CrocSwap/integer-mult-bounds/blob/main/docs/research/community-efficient1100-review.md)",
+    "corrected_claims": [
+      "Cost recurrence: the O(r) descriptor-composition and one-pass terms are charged under an explicit succinct descriptor hypothesis (fixed-size parameter tuples: phase G = diag(omega^(a*chi(x))) with one exponent a and per-node character chi (checker shape chi(x)=popcount(x), q=4); permutation x -> +-x + s (mod N) with one shift s). Composition is r*c_desc with c_desc = O(1) under the hypothesis; the general full-length-descriptor case is recorded at Theta(r*N) to form the composed table, not O(r).",
+      "Evidence scope: the N=8 checker (r=3 phase/rotation/heterogeneous, r=2 reader, r=5 cancellation, all composed as exact dense products) establishes exact observables and costs on those instances only; the general r,N recurrence is a priced hypothesis, not a tested identity."
+    ],
+    "unchanged": "All algebraic content and every cost number of the first correction and of the original cases stand unchanged; only the pricing scope of the composition/bookkeeping term changed."
+  },
+  "pr_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1155"
+}