Conditional T16 κ gain through neutral whole-helper hosting paths

research/astra-ultra-hosting-20261013/NEUTRAL-SEARCH.json

@@ -0,0 +1,83 @@
+{
+  "status": "PROVISIONAL_LEGAL_OWNER_GAIN",
+  "elapsed_ms": 116,
+  "before": {
+    "0": 24730,
+    "1": 2276,
+    "3": 377,
+    "7": 7,
+    "48": 4866
+  },
+  "after": {
+    "0": 24731,
+    "1": 2275,
+    "3": 377,
+    "7": 6,
+    "8": 1,
+    "48": 4866
+  },
+  "stats": {
+    "roots": 1,
+    "states": 842,
+    "neutral_edges": 2700,
+    "terminal_tests": 2524
+  },
+  "found": {
+    "root": "1,0,0",
+    "depth": 3,
+    "sequence": [
+      {
+        "role": 1664,
+        "to": 448
+      },
+      {
+        "role": 14144,
+        "to": 4794
+      },
+      {
+        "role": 34306,
+        "to": 12392
+      }
+    ]
+  },
+  "edits": [
+    {
+      "kind": "move",
+      "i": 1664,
+      "from": "12,0,90",
+      "to": "1,0,0",
+      "width": 7,
+      "free_before": [
+        0,
+        7
+      ]
+    },
+    {
+      "kind": "move",
+      "i": 14144,
+      "from": "15,0,72",
+      "to": "12,0,90",
+      "width": 7,
+      "free_before": [
+        0,
+        7
+      ]
+    },
+    {
+      "kind": "move",
+      "i": 34306,
+      "from": "11,8,103",
+      "to": "15,0,72",
+      "width": 7,
+      "free_before": [
+        1,
+        7
+      ]
+    }
+  ],
+  "pins": {
+    "owners": "87902c528dfab7d503dcf8a784260e3ab6fb7424c418a1820f7261f25be7b6bc",
+    "plan": "7bd786ba8e66408f02aa9ef446eaf20c1bfe981ea2e4dd1e5a929f0aa7767bc0"
+  },
+  "scope": "Width-7 hole transfers across full bins, at most 8 neutral moves, then one strictly improving relocation. BFS state pruning retains one path per (bin,freed-time); failed search not exhaustive over histories."
+}

research/astra-ultra-hosting-20261013/OVERLAP.json

@@ -0,0 +1,77 @@
+{
+  "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE",
+  "searched_at": "2026-10-13T23:30:41.426203+00:00",
+  "terms": [
+    "neutral relocation",
+    "neutral path",
+    "gap transfer",
+    "1 + 7"
+  ],
+  "coverage": {
+    "open_prs": {
+      "fetched_at": "2026-10-13T23:16:26.976112+00:00",
+      "complete_pagination": true,
+      "records": 834
+    },
+    "discussions": {
+      "fetched_at": "2026-10-13T23:16:46.038088+00:00",
+      "complete_pagination": true,
+      "records": 76
+    }
+  },
+  "local_records": 325,
+  "warnings": [
+    "open_prs: offline; cached data may miss current changes",
+    "discussions: offline; cached data may miss current changes"
+  ],
+  "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+  "matches_total": 3,
+  "matches": [
+    {
+      "kind": "pr",
+      "number": 1343,
+      "title": "Scoped obstruction: selected PR1094 has no improving single whole-helper relocation",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1343",
+      "head": "489f9011862dcd53a7785e151d3af0a1cd08250a",
+      "updated_at": "2026-10-13T23:09:11Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "neutral relocation",
+        "neutral path"
+      ],
+      "score": 2,
+      "excerpt": "metry audit is not claimed. Local calls, bit supplier and inherited extra charges are fixed. Swaps, neutral paths, multi-role repacking, new schedules/words and idle-axis transfers are excluded.\n\n## Task and provenance\n\nBase: current main `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`; contribution head `489f9011862dcd53a7785e151d3af0a1cd08250a`. Selected PR1094 audited head: `0fc329d0bec93ca7cd288eaea1295172e8789810`.\n\nTask: `selected-packing`, refined scope key `2eb6f6918b10e182033b:PR1094:one-who"
+    },
+    {
+      "kind": "pr",
+      "number": 854,
+      "title": "Research audit: kernel102 packing ceiling holds without fallback charges",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/854",
+      "head": "4e53da28f56c46ecf48614b54f165453f3b48a87",
+      "updated_at": "2026-10-13T07:40:52Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "1 + 7"
+      ],
+      "score": 1,
+      "excerpt": "ies.\n- Verifies a dual whose minimum slack exceeds `2/10^11`; its ideal-moment lower bound exceeds `1 + 7/10^10` at `b = 6981767/5000000000`.\n- Includes the weak-duality proof, exact deterministic result, source SHA-256/Git blob pins, and semantic negative controls that bypass file hashes.\n\nThe numerical ceiling is unchanged: under the original outer relation, `kappa < 6981767/5006981767`. The frozen local profile, helper widths, idle stocks, whole-helper assignment and paid-remainder model are "
+    },
+    {
+      "kind": "pr",
+      "number": 375,
+      "title": "\u03ba = 9.5424356568133e-4: seven-stage E8 suppliers with the complex idle climbs at halving degree two (+2.40 % over #373)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/375",
+      "head": "79874623cf86d92325c26ccafc31413d12e9d248",
+      "updated_at": "2026-10-11T05:43:05Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "1 + 7"
+      ],
+      "score": 1,
+      "excerpt": "side.\n\n**What changes.** #363 split the complex supplier's two longest idle climbs below m/2 (38 \u2192 31 + 7, 32 \u2192 31 + 1). It did this only to meet the half-shrink guard (2 \u00b7 max child < m) of the inherited complex finite bridge. Here they are left whole. The largest complex child becomes 38 of m = 63, so one level no longer halves the size but two levels do: 63\u00b2 = 3969 > 2 \u00b7 38\u00b2 = 2888, i.e. **halving degree two**.\n\n| side | layout | max child / m | coarse saving |\n| --- | --- | --- | ---: |\n| bi"
+    }
+  ]
+}

research/astra-ultra-hosting-20261013/OWNER-CHECK.json

@@ -0,0 +1,41 @@
+{
+  "status": "PASS_EXACT_COMPOUND_OWNER_CONSTRUCTION",
+  "roles": 69120,
+  "bins": 32256,
+  "rounds": 11,
+  "actions": 24,
+  "changed_serialized_rows": 47,
+  "baseline": {
+    "0": 24730,
+    "1": 2276,
+    "3": 377,
+    "7": 7,
+    "48": 4866
+  },
+  "candidate": {
+    "0": 24733,
+    "1": 2277,
+    "3": 377,
+    "16": 3,
+    "48": 4866
+  },
+  "profile": {
+    "1": 349605,
+    "2": 60192,
+    "3": 62585,
+    "4": 20448,
+    "5": 11808,
+    "8": 1152,
+    "16": 3,
+    "48": 4866
+  },
+  "exponent_uniform_gain": "Each strict final move sends free ranks (x,y) to (x+w,y-w), with 0<=y-w and x+w>y, hence strictly increases concentration. r^(1-a) is strictly concave for 0<a<1.",
+  "controls_rejected": [
+    "omit_first_neutral",
+    "wrong_family",
+    "changed_width",
+    "overlapping_offset",
+    "after_deadline"
+  ],
+  "scope": "Exact finite owner construction and strict moment improvement; native source-bound operator, invoice, and outer acceptance are separate receipts."
+}

research/astra-ultra-hosting-20261013/PROOF.md

@@ -0,0 +1,112 @@
+# Whole-helper neutral paths remove seven rank-7 residuals
+
+## Construction and exact domain
+
+This is a successor to Rohan Arun's selected PR1094 owner assignment. The local
+provider (480 whole helpers per call), 144 complete calls, port set, orientations,
+all source events, endpoint adapters, global bridges and terminal corrections
+are fixed. Only the physical owner and coordinate offset of whole helper roles
+change. `CONSTRUCTION.json` gives 24 moves in eleven rounds. Prefix compaction
+changes 47 serialized role rows. It is part of the construction, not a free
+post-processing convention: the native emitter rebuilds every affected chart.
+
+A bin is `(owner replica, idle child, port)`. Its capacity and strict borrowing
+interval are the original idle transition. The invocation has to lie after the
+last source-event touch and before its idle deadline. The native lift and two
+owner audits recompute those intervals from the original source events,
+including all 144 bridges; the search uses the corresponding pinned plan.
+
+For a gap of free rank y, a helper of width w in a bin of free rank x can move
+into the gap if its whole invocation lies in the destination interval, its
+physical family is unused by every other helper in that invocation, and w<=y.
+The new free ranks are `(x+w,y-w)`. A neutral leg satisfies `x+w=y` and exchanges
+the two free ranks. The final leg satisfies `x+w>y`, strictly concentrating them.
+No helper is split; all local entry/exit interfaces are retained.
+
+The first round moves width-seven helper roles 1664, 14144, and 34306:
+
+```
+(12,0,90) -> (1,0,0)
+(15,0,72) -> (12,0,90)
+(11,8,103) -> (15,0,72)
+```
+
+The first two moves transfer a free-rank-seven gap through full bins. The last
+replaces free ranks `1+7` by `8+0`. Later rounds collect the remaining rank-seven
+gaps. The final idle profile changes exactly by `{1:+1,7:-7,16:+3}`. Rank mass is
+conserved: `1-7*7+3*16=0`.
+
+## All-input operator argument
+
+Use the inherited exact local supplier contract: a complete invocation applies
+its stated data shear, independently of all incoming helper values, and acts on
+each dirty helper by its declared residual Clifford operator. Private work is
+erased at the endpoint. This holds on all columns, hence on arbitrary correlated
+dirt, not only independent or clean helper inputs. The source-bound native local
+proof/phase receipts are unchanged; the new global run binds their exact hashes
+and semantic identities rather than assuming a favorable histogram proves them.
+
+Inside one borrowed bin, the owner has no data touch between the interval's
+opening event and its idle deadline. Consecutive whole invocations can therefore
+observe arbitrary transformed dirty values; each invocation's data output is
+independent of that dirt, while the owner's residual transformations compose.
+For its fixed orthonormal pending axes q_0,...,q_(c-1), the contribution of an
+assigned width-w role is the exact product of C_q over its assigned slice, using
+the admitted source/target wrappers. The residual idle child acts on the unused
+suffix. Distinct slices partition the same original c axes. Thus at the deadline
+
+```
+(product over assigned helper slices) * (remaining suffix child)
+  = product_(j=0)^(c-1) C_(q_j).
+```
+
+These exact Gaussian-dyadic factors commute. Chart changes are actual inherited
+orthogonal adapters, including their Z4 phase translations and spectator
+normalization; they are freshly emitted and checked. The proof never identifies
+operators merely from binary frames. There is no movement of an idle factor
+past a bridge, unlike the rejected earlier phase-flow attempt.
+
+By induction over deadlines and data touches, every physical owner's value is
+exactly the original value whenever the controller reads it. Each complete
+invocation has the original data shear on arbitrary incoming helper values.
+The original eight-stream operator, dirty-state endpoint, source restoration,
+terminal Y correction, signed exchange and cover corrections consequently remain
+identical on all inputs. This uses the inherited complete-cover/common-label and
+mutable-source realization assumptions; it is not a new proof of those interfaces.
+
+## Exact cost improvement
+
+For every real `0<a<1`, `f(r)=r^(1-a)` is strictly concave on nonnegative r.
+A neutral leg leaves `f(x)+f(y)` unchanged. If `x+w>y` and `0<=y-w`, then the new
+pair has the same sum and strictly larger maximum; hence
+`f(x+w)+f(y-w)<f(x)+f(y)`. Each of the eleven rounds has one such strict leg.
+This is a uniform analytic proof of the moment improvement, not a floating-point
+search score. The final complete profile is
+
+```
+{1:349605, 2:60192, 3:62585, 4:20448,
+ 5:11808, 8:1152, 16:3, 48:4866}.
+```
+
+The new boundary does not add calls, helpers, data families or conversions.
+Recompacted offsets change only the existing chart selection. Native recounting
+charges all adapters, phases, normalization, bridges, wrappers and the retained
+full idle-child overcharge. Live stock 14336, physical stock 14826, rank mass
+1041408 and deficit 5120 remain fixed. The independent owner checker additionally
+uses a conservative historical reserve of 14850, which has the same 2642-bit
+stock bound; it does not assert that larger reserve is the emitted stock.
+
+The prefix bound is 397 bits, charged within the unchanged 512-bit allowance.
+The physical row coefficient is 16469<20161. The maximum child stays 48 and
+`73^2=5329>4608=2*48^2`. The native complex surcharge remains absent under the
+selected exact-cover contract; the complete bit surcharge is retained. The
+conservative complex surcharge variant is checked separately and also improves.
+
+## Scope
+
+This establishes a finite conditional construction under the inherited all-size
+compiler, common-label/mutable-source realization, whole-call hosting,
+precision/tape, exact recovery, analytic transfer and bit H1-H5 assumptions.
+It is not a full multiplication theorem, formal Lean proof, global packing
+optimum, or claim of a new hosting principle. A failed two-role-swap nomination
+is retained separately and makes no universal obstruction claim.