diff --git a/research/kappa010-rank-cap-floor/README.md b/research/kappa010-rank-cap-floor/README.md
index 31422dfff3..0d1c555957 100644
--- a/research/kappa010-rank-cap-floor/README.md
+++ b/research/kappa010-rank-cap-floor/README.md
@@ -44,6 +44,8 @@ These passing threshold rows are **necessary budget openings only**. They place
 
 The all-mass-at-cap row can hide a large local-profile gap. I also evaluated the source-bound selected bit histogram `{1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19}` (rank mass 5,129) under the hypothetical `u=2` coverage law, with the best admitted idle cap `R=53`. At `a=1/9` its exact outward-rational moment is **1.365696** with the existing centre charge `c=63`, or **1.355508** after deleting that charge. So changing coverage alone does not rescue the selected bit word.
 
+There is a stronger fixed-word bound: the local histogram by itself, normalized by the pinned `w=296/3` families per call, has exact outward-rational moment **1.195680** at `a=1/9`. This omits the centre and every idle child. Any change that retains this local histogram and `w` can only add nonnegative child costs, so changing the unpaid-coordinate coverage law alone cannot make this selected word pass. This is specific to the pinned bit word and call width; a different local word or changed `w` remains open.
+
 For comparison, the necessary all-mass-at-cap floor with `u=2` and `c=63` is only **0.999452**. Holding the selected local rank mass at 5,129 and fractionally repacking it at one uniform local rank, the first passing rank is **53** with the centre retained; rank 52 gives 1.001209. If the centre is deleted, rank 48 first passes (0.998447), while rank 47 gives 1.000411. This quantifies the missing mechanism: a bit-side endpoint must both leave a second coordinate unpaid and replace the selected low-rank local profile with children near the maximum admitted rank. It is a scoped profile screen, not a universal obstruction or a constructed supplier.
 
 ## Reproduction
@@ -66,8 +68,8 @@ The verifier uses only the standard library. It binds the selected record and th
 
 This refines the `coverage-law-change` card for the user-set target κ > 0.1. It tests the cheapest possible aggregate moment under the pinned coverage laws before searching for a mechanism. It does not prove that changing coverage or depth is impossible, and it does not replace the card's complete-instance acceptance gate. Local overlap surfaced the earlier `kappa01-complex-target-screen`, several paired-plane coverage-law packages, and the concrete paired-plane identity fit; this result contributes the exact shared rank-cap floor and strict threshold table for the new 0.1 target.
 
-The bit-side predecessor is Sagar Thakrar's `bit-revision3-levers-seed03`, building on DreamingOfClouds' PR589 / `format-limits`, eumemic's PR555, and the PR510 / PR442 template lineage. The complex predecessor is Douglas Colkitt's `complex-local-word-ceiling`, building on PR1012, the selected #1094 construction, and the credited frame/ownership chain. No predecessor artifacts were modified. The task began on `d8e0f83f00191df62174b641e9fff055c357f641`; canonical main was refreshed at `18aacb215fc3717b06be8ceb9fca62aeca0d3e99` (priority revision 6) on 2026-10-17. The only relevant guidance change adds a P104 precision-map pointer; the selected record and quantitative predecessor receipts are unchanged; the used κ conversion is unchanged.
+The bit-side predecessor is Sagar Thakrar's `bit-revision3-levers-seed03`, building on DreamingOfClouds' PR589 / `format-limits`, eumemic's PR555, and the PR510 / PR442 template lineage. The complex predecessor is Douglas Colkitt's `complex-local-word-ceiling`, building on PR1012, the selected #1094 construction, and the credited frame/ownership chain. No predecessor artifacts were modified. The task began on `d8e0f83f00191df62174b641e9fff055c357f641`; canonical main was refreshed at `18aacb215fc3717b06be8ceb9fca62aeca0d3e99` (priority revision 6) on 2026-10-17. The P104 precision-map pointer remains the only earlier relevant change. Before this update, `origin/main` advanced to `997e6a9ca7b4f95d50e366f61412fd640d72a88a`; its relevant changes add sparse-checkout/path-cache notes and record exact-head PR intake including concurrent PR3107, without changing the selected record, priority, family status or quantitative inputs. The κ conversion is unchanged.
 
-The overlap helper refreshed open PRs on 2026-10-17 at 02:00:46 UTC: 262 records with complete pagination, including PR #3093's fixed-profile screens and the present target work. Its complete 1,866-discussion snapshot was last fetched at 01:23:03 UTC and is stale for a new expansion. Earlier checks surfaced PRs #3064 and #3097 and Discussions #1163, #1166 and #1167. The fixed-bit-profile result extends this package's own aggregate screen; no novelty is claimed. Recheck active discussions before opening another research round.
+The overlap helper refreshed open PRs on 2026-10-17 at 02:03:00 UTC (237 records) and discussions at 02:03:33 UTC (1,872 records), both with complete pagination. It surfaced extensive possible overlap, including PR #3093's fixed-profile screens and the broader target work; the helper searches PR bodies and discussion claims, not arbitrary code diffs. Earlier checks also surfaced PRs #3064 and #3097 and Discussions #1163, #1166 and #1167. This fixed-bit-profile result extends the package's own aggregate screen; no novelty is claimed. Recheck relevant heads before opening another research round.
 
 Prepared by Codex with OpenAI assistance. New work is Apache-2.0.
diff --git a/research/kappa010-rank-cap-floor/RESULT.json b/research/kappa010-rank-cap-floor/RESULT.json
index 8015a60919..56fb37958a 100644
--- a/research/kappa010-rank-cap-floor/RESULT.json
+++ b/research/kappa010-rank-cap-floor/RESULT.json
@@ -100,6 +100,12 @@
       "7": "19"
     },
     "local_rank_mass": "5129",
+    "local_only_moment_interval_at_a_1_over_9": [
+      "1921383040434905601017631659884927637082654655778498244349731/1606938044258990275541962092341162602522202993782792835301376",
+      "960691520217452800508815829942463818541327327889249122174883/803469022129495137770981046170581301261101496891396417650688"
+    ],
+    "local_only_moment_approx": "1.195679601525",
+    "local_only_below_one": false,
     "actual_profile_at_u2_R53": {
       "0": {
         "unpaid_coordinates": 2,
@@ -166,7 +172,7 @@
         }
       }
     },
-    "scope": "Fixed selected bit local profile under a hypothetical u=2 law, with or without its centre; separate from the all-mass-at-cap necessary floor. No new bit endpoint or supplier is constructed."
+    "scope": "The pinned selected bit local histogram alone has moment above one at a=1/9, so any profile-preserving coverage-only change at the same families-per-call is insufficient; the u=2 and uniform-rank rows are narrower sensitivities. No new bit endpoint or supplier is constructed."
   },
   "complex": {
     "supplier": "complex",
diff --git a/research/kappa010-rank-cap-floor/TASK.json b/research/kappa010-rank-cap-floor/TASK.json
index 136d87124a..7d737fffe2 100644
--- a/research/kappa010-rank-cap-floor/TASK.json
+++ b/research/kappa010-rank-cap-floor/TASK.json
@@ -45,21 +45,21 @@
     ]
   },
   "scope_status": "refined",
-  "actual_scope": "For the donor-set target \u03ba > 0.1, certify aggregate moment floors under current bit and complex coverage/rank caps, exact unpaid/depth thresholds, and the fixed selected bit profile under a hypothetical two-unpaid-coordinate law.",
-  "scope_change_reason": "The user raised the target from the repository planning target \u03ba > 0.01 to \u03ba > 0.1. The initial exact target-level screen found that u=2 just opens the ideal bit floor. A bounded follow-up applies the pinned selected bit histogram to that changed law to measure how far the actual profile remains from the aggregate floor before pursuing any new endpoint.",
-  "bottleneck_link": "A fixed rank-mass budget and child-rank cap impose a lower bound on the recursive moment. This proves whether either supplier can reach a=1/9 even after granting perfect high-rank repacking and deleting centre cost.",
+  "actual_scope": "For the donor-set target \u03ba > 0.1, certify aggregate moment floors under current bit and complex coverage/rank caps, exact unpaid/depth thresholds, and the selected bit word's local-only cost under profile-preserving coverage changes.",
+  "scope_change_reason": "The user raised the target from the repository planning target \u03ba > 0.01 to \u03ba > 0.1. The initial exact target-level screen found that u=2 just opens the ideal bit floor. A bounded follow-up applies the pinned selected bit histogram to that changed law, then prices the local histogram alone to determine whether any coverage-only change at the same call width can cross the target.",
+  "bottleneck_link": "The aggregate rank-cap floor tests ideal high-rank repacking. The pinned selected bit local histogram alone has moment 1.195680 at a=1/9, so profile-preserving coverage changes at the same families-per-call cannot reach the target even after every other charge is deleted.",
   "budget_minutes": 480,
   "stop_rule": "Stop this aggregate screen once the strict a=1/9 obstruction and exact unpaid/rank boundaries are certified. Do not expand to another search unless one complete dirty endpoint or row-coefficient invoice can realize a passing boundary with margin.",
   "outcome": "partial",
-  "evidence": "Exact rational ninth-power comparisons prove that with one unpaid coordinate the centre-free minimum moment is >1 at bit R=53 and complex R=51. At the current caps, the ideal aggregate floor first drops below one at bit u=2 and complex u=3 centre-free / u=4 with centre retained. The pinned paired-plane identity-fit candidate (u=2,c=112) has floor approximately 1.02818 at a=1/9 and also needs u=4 to pass this aggregate budget. With one unpaid coordinate, deleting centre requires R=56 (bit) and R=65 (complex), first allowed by the halving guard at depths 6 and 6. This is a necessary-budget screen only; no supplier, replacement coverage identity, or higher-depth row invoice is constructed. For the pinned selected bit histogram, u=2 and R=53 still give moment 1.365696 with the centre and 1.355508 without it. If all 5,129 local rank mass is fractionally repacked at a uniform rank, first passing ranks are 53 with the centre (rank52 gives 1.001209) and 48 centre-free (rank47 gives 1.000411). This is a fixed-profile screen only.",
+  "evidence": "Exact rational ninth-power comparisons prove that with one unpaid coordinate the centre-free minimum moment is >1 at bit R=53 and complex R=51. At the current caps, the ideal aggregate floor first drops below one at bit u=2 and complex u=3 centre-free / u=4 with centre retained. The pinned paired-plane identity-fit candidate (u=2,c=112) has floor approximately 1.02818 at a=1/9 and also needs u=4 to pass this aggregate budget. With one unpaid coordinate, deleting centre requires R=56 (bit) and R=65 (complex), first allowed by the halving guard at depths 6 and 6. This is a necessary-budget screen only; no supplier, replacement coverage identity, or higher-depth row invoice is constructed. The pinned selected bit histogram alone has exact outward-rational moment 1.195680 at a=1/9 after deleting the centre and all idle children. Thus no profile-preserving coverage-only change at the same w=296/3 can pass. At u=2 and R=53 the full relaxed profile gives 1.365696 with the centre and 1.355508 without it. Fractionally repacking all 5,129 local rank mass at one uniform rank first passes at ranks 53 with the centre (rank52 gives 1.001209) and 48 centre-free (rank47 gives 1.000411). These are fixed-profile screens only.",
   "author": "Codex with OpenAI assistance",
   "ai_assistance": "Substantial OpenAI Codex assistance; exact arithmetic, verifier, and report prepared with AI assistance.",
   "open_questions": [
     {
-      "question": "Can one complete bit endpoint leave two coordinates unpaid and replace the selected local profile by high-rank children?",
-      "why_it_matters": "The aggregate floor passes at u=2 only narrowly with the centre (0.999452); the fixed selected bit histogram still costs 1.365696 at R=53.",
-      "first_step": "Trace one named two-coordinate candidate through a complete selected bit call, then price its local child-rank profile, source delivery, frame, consumer and restoration.",
-      "blocked_by": "No changed complete call or local high-rank consumer is source-bound."
+      "question": "Can a changed bit local word reduce the local-only moment below one while changing the complete endpoint or coverage contract?",
+      "why_it_matters": "The selected bit local histogram alone costs 1.195680 at a=1/9, so no change to unpaid-coordinate coverage can rescue it while w=296/3 and the local word stay fixed.",
+      "first_step": "Name one alternative local word and its exact dirty-input boundary; screen its local-only moment, then price source delivery, frame, consumer and restoration before a wider search.",
+      "blocked_by": "No candidate alternative local word with a source-bound complete consumer is available."
     },
     {
       "question": "Can the complex supplier leave four coordinates unpaid while retaining the current centre charge?",
@@ -75,9 +75,9 @@
     }
   ],
   "upstream_checkpoint": {
-    "commit": "18aacb215fc3717b06be8ceb9fca62aeca0d3e99",
+    "commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
     "priority_revision": 6,
-    "checked_utc": "2026-10-17T02:01:40Z",
-    "comparison": "Canonical origin/main was refreshed before this submission checkpoint and remains 18aacb215fc3717b06be8ceb9fca62aeca0d3e99. No changes appeared in the current-priorities, task-catalogue, family-status, selected-result, bottleneck-brief, or paired-plane contract-map files since the prior checkpoint. The P104 precision-contract pointer remains present; selected κ and quantitative predecessor receipts are unchanged."
+    "checked_utc": "2026-10-17T02:06:36Z",
+    "comparison": "Canonical origin/main advanced to 997e6a9ca7b4f95d50e366f61412fd640d72a88a. Priority revision 6, current priorities, task catalogue, family status, selected record, bottleneck brief and paired-plane contract map are unchanged. agent-procedure.md adds sparse-checkout and PR path/head-cache guidance; research-archive-intake.md records exact-head intake including concurrent PR3107, without replacing the retained source packages. No pinned quantitative input or selected κ changed."
   }
 }
diff --git a/research/kappa010-rank-cap-floor/VERIFY.json b/research/kappa010-rank-cap-floor/VERIFY.json
index 9d69dc91b7..48d8a4c088 100644
--- a/research/kappa010-rank-cap-floor/VERIFY.json
+++ b/research/kappa010-rank-cap-floor/VERIFY.json
@@ -24,7 +24,7 @@
         "{package}/verify.py"
       ],
       "timeout_seconds": 120,
-      "checks": "Binds the selected record and bit/complex predecessor receipts; checks the exact a=1/9 aggregate rank-cap floors, unpaid and required-depth boundaries, and the paired-plane identity-fit aggregate candidate. It additionally prices the pinned selected bit histogram under hypothetical u=2 for centre-free/retained cases and certifies adjacent uniform local-rank boundaries using the pinned outward-rational moment engine. Passing floors and fixed-profile failures are scoped budget results only, not supplier constructions."
+      "checks": "Binds the selected record and bit/complex predecessor receipts; checks the exact a=1/9 aggregate rank-cap floors, unpaid and required-depth boundaries, and the paired-plane identity-fit aggregate candidate. It additionally prices the pinned selected bit local histogram alone and under hypothetical u=2 for centre-free/retained cases, then certifies adjacent uniform local-rank boundaries using the pinned outward-rational moment engine. Passing floors and fixed-profile failures are scoped budget results only, not supplier constructions."
     }
   ]
 }
diff --git a/research/kappa010-rank-cap-floor/verify.py b/research/kappa010-rank-cap-floor/verify.py
index 2b90028816..4d7ed9c2e5 100644
--- a/research/kappa010-rank-cap-floor/verify.py
+++ b/research/kappa010-rank-cap-floor/verify.py
@@ -176,6 +176,9 @@ def main() -> None:
     bit_levers = load_bit_levers()
     bit_local = {int(r): Q(n) for r, n in bit_replay["local_histogram"].items()}
     bit_local_mass = Q(bit_replay["local_mass"])
+    bit_local_only_lo, bit_local_only_hi = bit_levers.bill(
+        bit_local, 64, Q(296, 3), Q(1, 9)
+    )
     bit_two_unpaid = {}
     for centre in (0, 63):
         H = bit_levers.relaxed(bit_local, 64, Q(296, 3), centre, 53, unpaid=2)
@@ -218,6 +221,8 @@ def first_uniform_bit_rank(centre: int) -> int:
         bit_uniform_rank_adjacent[label] = rows
     need(not bit_two_unpaid["0"]["below_one"] and not bit_two_unpaid["63"]["below_one"],
          "fixed selected bit profile with two unpaid coordinates unexpectedly passes")
+    need(bit_local_only_lo > 1,
+         "selected bit local profile alone unexpectedly reaches the target")
     need(bit_uniform_rank_boundary == {"centre_free": 48, "centre_retained": 53},
          "bit uniform local-rank target changed")
     need(not bit_uniform_rank_adjacent["centre_free"]["47"]["below_one"]
@@ -275,10 +280,17 @@ def first_uniform_bit_rank(centre: int) -> int:
             "source_result": BIT_RESULT,
             "selected_local_profile": {str(r): str(n) for r, n in sorted(bit_local.items())},
             "local_rank_mass": str(bit_local_mass),
+            "local_only_moment_interval_at_a_1_over_9": [
+                str(bit_local_only_lo), str(bit_local_only_hi)
+            ],
+            "local_only_moment_approx": format(
+                float((bit_local_only_lo + bit_local_only_hi) / 2), ".12f"
+            ),
+            "local_only_below_one": bit_local_only_hi < 1,
             "actual_profile_at_u2_R53": bit_two_unpaid,
             "first_uniform_local_rank_at_u2_R53": bit_uniform_rank_boundary,
             "adjacent_uniform_rank_checks": bit_uniform_rank_adjacent,
-            "scope": "Fixed selected bit local profile under a hypothetical u=2 law, with or without its centre; separate from the all-mass-at-cap necessary floor. No new bit endpoint or supplier is constructed.",
+            "scope": "The pinned selected bit local histogram alone has moment above one at a=1/9, so any profile-preserving coverage-only change at the same families-per-call is insufficient; the u=2 and uniform-rank rows are narrower sensitivities. No new bit endpoint or supplier is constructed.",
         },
         "complex": complex_screen,
         "paired_plane_identity_fit_candidate": {