diff --git a/.github/workflows/pr128-bit-screen.yml b/.github/workflows/pr128-bit-screen.yml
new file mode 100644
index 0000000000..e84a51828c
--- /dev/null
+++ b/.github/workflows/pr128-bit-screen.yml
@@ -0,0 +1,44 @@
+name: PR128 restricted bit groups - rational-H negative control
+on:
+  push:
+    branches:
+      - research/pr128-zero-frame-sharing-screen
+  pull_request:
+    paths:
+      - 'research/pr128-zero-frame-sharing-screen/**'
+      - '.github/workflows/pr128-bit-screen.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  exact-screen:
+    name: Rational-H counterexample and screened moment (Python ${{ matrix.python-version }})
+    runs-on: ubuntu-24.04
+    timeout-minutes: 15
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.13', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Run exact hypothesis screen (not a physical certificate)
+        run: |
+          python3 research/pr128-zero-frame-sharing-screen/verify_screen.py > /tmp/bit-screen.json
+          python3 -m json.tool /tmp/bit-screen.json > /dev/null
+          python3 - <<'PY'
+          import json
+          r=json.load(open('/tmp/bit-screen.json'))
+          assert r['rational_H_orthogonal_pairs']==0
+          assert r['rational_H_nonorthogonal_pairs']==17514
+          assert r['legal_bit_supplier_certified'] is False
+          assert r['status'].startswith('PASS F2 geometry and formal moment; FAIL PR129')
+          print('PASS negative control: the hypothesized +10.83% bit result is NOT legal')
+          PY
+          cat /tmp/bit-screen.json
+      - name: Check tracked artifacts unchanged
+        run: git diff --exit-code
diff --git a/research/pr128-zero-frame-sharing-screen/README.md b/research/pr128-zero-frame-sharing-screen/README.md
new file mode 100644
index 0000000000..e3c22cbd92
--- /dev/null
+++ b/research/pr128-zero-frame-sharing-screen/README.md
@@ -0,0 +1,92 @@
+# Restricted PR128 bit groups: exact negative control (NOT a new κ)
+
+**Status: disproved candidate.** The restricted h=23 partition **does not
+implement valid completed-core bit sharing** under the rational
+`H = 9I - J` projector geometry of PR #129. The apparent 10.83% increase
+in stopped-bit saving is **only a hypothetical arithmetic screen** of an
+unrealizable child histogram; it is not a verified algorithm, bit supplier,
+or multiplication exponent.
+
+## Source and reproducibility
+
+- Based on [PR #128](https://github.com/CrocSwap/integer-mult-bounds/pull/128),
+  commit `530588a019b4a74f09180680c9e3961bf649ec89`.
+- Compared against [PR #129](https://github.com/CrocSwap/integer-mult-bounds/pull/129),
+  commit `992a442c10d243eee69bbd20f32ba6fa98fb430e`.
+- `pr128-bit-profile.json` pins PR128's existing bit-word histogram,
+  exterior histogram, source and blob SHA.
+- `restricted-groups.json` retains the 87 signed PR128 complex groups,
+  deletes triples containing coordinate 23 and reindexes the 1,771
+  surviving triples.
+- Run `python3 research/pr128-zero-frame-sharing-screen/verify_screen.py`
+  on standard Python without `-O`. Standard library only.
+
+This is a **negative experiment**, not a physical witness.
+
+## What passes
+
+The restricted partition has 83 groups of 21 and four groups of 7;
+every h=23 triple appears exactly once. Each triple indicator has norm
+one mod 2, and each distinct within-group pair has overlap zero mod 2.
+This makes the binary Gram matrix the identity and produces 36,799
+successful ordered Gram tests. The h=23 quadratic phase tests on 277
+weight-0, weight-1 and weight-2 inputs per group are also exact:
+24,099 checks pass. The orthogonal complements have nondegenerate binary
+forms; their Gauss sums are -2 for the 83 rank-two complements and
+-256i for the four rank-16 complements.
+
+A hypothetical paid rank-mass screen would remove the 17,597 zero-start
+roles' old exteriors and insert a rank-46/368 complement for each shared
+role and each of the 87 groups. This yields formal W=49,249,558 and the
+same rank deficit of 1,344,189. The approximate stopped bit moment
+suggests a 10.8253% gain over PR128's bit supplier **if this grouping
+were legally implementable**. It is not.
+
+## Decisive failure: incompatible rational geometry
+
+PR #129 uses the rational inner product `H=9I-J`, not the standard
+binary dot product. For any two triple incidence vectors T,U, its
+Gram entry is
+
+    T^T H U = 9*(|T intersect U| - 1).
+
+The group construction for PR128's **complex** operation requires binary
+intersection parity zero. After restriction to 23 coordinates, distinct
+triples in each group intersect in **zero or two** points. Those intersections
+yield rational Gram entries -9 or +9, respectively, **never zero**.
+
+The exhaustive witness has:
+- 15,012 within-group unordered pairs meeting in zero points;
+- 2,502 within-group unordered pairs meeting in two points;
+- **0 / 17,514 pairs are rational-H-orthogonal.**
+
+For example, `T={0,6,12}` and `U={0,6,18}` are in the first
+group, with intersection size 2 and `T^T H U=9`.
+
+Consequently their rational projectors do **not** annihilate one another.
+The identity `D_A D_B = D_(A+B)` used by completed-core sharing
+requires `AB=BA=0` and cannot be invoked for these blocks.
+**The 87-group allocation, its W, and its improved bit moment cannot
+be certified as a legal bit supplier.**
+
+PR #129 already constructs a different valid rational-H-orthogonal
+161-group sunflower partition, each group having eleven triples.
+Future physical work must start from that valid geometry (or independently
+prove another valid operator composition), not from this restricted
+F2-only complex partition.
+
+## Record and remaining work
+
+PR #129 claims a conditional coupled exponent
+`κ=0.000129186205798`. Beating it by 3% would require
+`κ >= 0.00013306179197194`, with improvements to **both** limiting
+suppliers and a new exact coupled certificate.
+
+No new `κ` is claimed by this repository branch. The experiment is
+preserved as a corruption/negative control to prevent rational-vs-binary
+orthogonality mistakes.
+
+The source construction is by an664 / PR128 contributors, with
+original partition credits to Zhang and Ge. The PR129 rational bit
+construction and its contributors are credited. This negative audit
+was prepared with OpenAI assistance. Retained upstream licenses apply.
diff --git a/research/pr128-zero-frame-sharing-screen/pr128-bit-profile.json b/research/pr128-zero-frame-sharing-screen/pr128-bit-profile.json
new file mode 100644
index 0000000000..3068ed2bf2
--- /dev/null
+++ b/research/pr128-zero-frame-sharing-screen/pr128-bit-profile.json
@@ -0,0 +1,88 @@
+{
+  "source": {
+    "repository": "an664/integer-mult-bounds",
+    "ref": "530588a019b4a74f09180680c9e3961bf649ec89",
+    "path": "research/completed-core-sharing/inputs/research/round8-network-opposite-profile.json",
+    "github_blob_sha": "ea5b8aa53d7acba929ba4c74014a8a0f83271400",
+    "attribution": "Zhihao Chen and original PR128/PR104 bit-network contributors"
+  },
+  "m": 529,
+  "v": 1771,
+  "R": 28866,
+  "N": 3136441,
+  "W": 108516254,
+  "deficit": 1344189,
+  "hist": {
+    "1": 235438511,
+    "2": 236428500,
+    "3": 51022510,
+    "4": 43669318,
+    "5": 22488158,
+    "6": 8072218,
+    "7": 3715558,
+    "8": 6694380,
+    "9": 1919764,
+    "10": 1059058,
+    "11": 1423884,
+    "12": 2064986,
+    "13": 995302,
+    "14": 347116,
+    "15": 2387308,
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+    "18": 2266880,
+    "19": 7484246,
+    "20": 8847916,
+    "21": 1466388,
+    "22": 127512,
+    "484": 6272882,
+    "506": 62328574,
+    "507": 7084,
+    "508": 49588,
+    "509": 159390,
+    "510": 449834,
+    "511": 3542,
+    "512": 276276,
+    "513": 17710,
+    "514": 1083852,
+    "515": 127512,
+    "516": 403788,
+    "517": 99176,
+    "518": 1144066,
+    "519": 315238,
+    "520": 378994,
+    "521": 106260,
+    "522": 1583274,
+    "523": 626934,
+    "524": 2854852,
+    "525": 13711082,
+    "526": 4629394,
+    "527": 5653032,
+    "528": 6233920
+  },
+  "exterior_hist": {
+    "506": 62328574,
+    "507": 7084,
+    "508": 49588,
+    "509": 159390,
+    "510": 449834,
+    "511": 3542,
+    "512": 276276,
+    "513": 17710,
+    "514": 1083852,
+    "515": 127512,
+    "516": 403788,
+    "517": 99176,
+    "518": 1144066,
+    "519": 315238,
+    "520": 378994,
+    "521": 106260,
+    "522": 1583274,
+    "523": 626934,
+    "524": 2854852,
+    "525": 13711082,
+    "526": 4629394,
+    "527": 5653032,
+    "528": 6233920
+  }
+}
diff --git a/research/pr128-zero-frame-sharing-screen/restricted-groups.json b/research/pr128-zero-frame-sharing-screen/restricted-groups.json
new file mode 100644
index 0000000000..56d299359d
--- /dev/null
+++ b/research/pr128-zero-frame-sharing-screen/restricted-groups.json
@@ -0,0 +1,1953 @@
+{
+  "origin": "PR128 completed-core sharing (an664), pinned commit 530588a019b4a74f09180680c9e3961bf649ec89",
+  "h": 23,
+  "source_geometry_blob_sha": "51aea7dd4404c6eae89aebca4969d81695e3adc9",
+  "method": "Restrict each signed PR128 h=24 orthogonal triple group to triples not containing coordinate 23; reindex lexicographically in h=23.",
+  "groups": [
+    [
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+  ]
+}
diff --git a/research/pr128-zero-frame-sharing-screen/verify_screen.py b/research/pr128-zero-frame-sharing-screen/verify_screen.py
new file mode 100644
index 0000000000..c7ff34b7c3
--- /dev/null
+++ b/research/pr128-zero-frame-sharing-screen/verify_screen.py
@@ -0,0 +1,281 @@
+#!/usr/bin/env python3
+"""Independent exact geometric and arithmetic screen for PR128 h=23 sharing.
+
+This DOES NOT certify a legal bit-core sharing implementation or a new kappa.
+The signed physical schedule, local Gaussian normalization, scalar charges
+and coupled recurrence proof remain obligations. Standard library only.
+"""
+import json
+import os
+import sys
+from collections import Counter
+from fractions import Fraction as Q
+from itertools import combinations
+from math import factorial
+from pathlib import Path
+
+if sys.flags.optimize or os.environ.get("PYTHONOPTIMIZE"):
+    raise RuntimeError("assertions must not be disabled")
+HERE = Path(__file__).resolve().parent
+
+
+def require(ok, why):
+    if not ok:
+        raise AssertionError(why)
+
+
+def parity(x):
+    return x.bit_count() & 1
+
+
+def gf_basis(vectors, width):
+    piv = {}
+    for v in vectors:
+        x = v
+        while x:
+            j = x.bit_length()-1
+            if j in piv:
+                x ^= piv[j]
+            else:
+                piv[j] = x
+                break
+    return piv
+
+
+def nullspace(vectors, width):
+    # Reduced echelon form of the rows of the orthogonality constraints.
+    piv = gf_basis(vectors, width)
+    # Descending pivots prevent a later XOR from reintroducing an
+    # already-eliminated (higher) pivot column.
+    for j in sorted(piv, reverse=True):
+        for k in piv:
+            if j != k and (piv[k] >> j) & 1:
+                piv[k] ^= piv[j]
+    free = [j for j in range(width) if j not in piv]
+    result = []
+    for j in free:
+        x = 1 << j
+        for k, row in piv.items():
+            if (row >> j) & 1:
+                x ^= 1 << k
+        result.append(x)
+    require(all(parity(x & row) == 0 for x in result for row in vectors),
+            "nullspace mistake")
+    return result
+
+
+def quadratic_signature(B):
+    # Exact four-phase Gauss sum: real=cnt[0]-cnt[2],
+    # imaginary=cnt[1]-cnt[3]. Enumerate Gray-coded basis vectors.
+    counts = [0, 0, 0, 0]
+    x = 0
+    for k in range(1 << len(B)):
+        if k:
+            j = (k & -k).bit_length()-1
+            x ^= B[j]
+        counts[x.bit_count() % 4] += 1
+    return (counts[0]-counts[2], counts[1]-counts[3])
+
+
+def ln_interval(x, terms=48):
+    # Normalize 1 <= u < 2; artanh has a rational nonnegative tail bound.
+    require(x >= 1, "log argument below one")
+    power = 0
+    u = x
+    while u >= 2:
+        power += 1
+        u /= 2
+
+    def unit(z):
+        y = (z-1)/(z+1)
+        termsum = 2*sum((y**(2*j+1)/Q(2*j+1)
+                         for j in range(terms)), Q(0))
+        rem = 2*y**(2*terms+1)/(Q(2*terms+1)*(1-y*y))
+        return (termsum, termsum+rem)
+
+    a,b = unit(u)
+    c,d = unit(Q(2))
+    return (a+power*c, b+power*d)
+
+
+def exp_interval(lo, hi, degree=12):
+    require(0 <= lo <= hi < 1, "bad exponential argument")
+    low = sum((lo**k/Q(factorial(k)) for k in range(degree+1)), Q(0))
+    upper = sum((hi**k/Q(factorial(k)) for k in range(degree+1)), Q(0))
+    upper += hi**(degree+1)/Q(factorial(degree+1))/(1-hi/Q(degree+2))
+    return low, upper
+
+
+def moment_interval(hist, m, W, saving):
+    low = high = Q(0)
+    for r, count in sorted(hist.items()):
+        if not count:
+            continue
+        require(0 < r < m and count > 0, "invalid recursive child")
+        lglo, lghi = ln_interval(Q(m, r))
+        elo, ehi = exp_interval(saving*lglo, saving*lghi)
+        factor = Q(r*count, m*W)
+        low += factor*elo
+        high += factor*ehi
+    return low, high
+
+
+def main():
+    p = json.loads((HERE/"pr128-bit-profile.json").read_text())
+    z = json.loads((HERE/"restricted-groups.json").read_text())
+    h,m,v,R,N,W,deficit = (p[k] for k in
+                             ("h","m","v","R","N","W","deficit")) if "h" in p else (
+                             23,p["m"],p["v"],p["R"],p["N"],p["W"],p["deficit"])
+    require((h,m,v,R,N,W,deficit)==
+            (23,529,1771,28866,3136441,108516254,1344189),
+            "pinned PR128 dimensions changed")
+    require(z["h"]==h and len(z["groups"])==87, "group dimensions")
+    masks = [sum(1<<i for i in t) for t in combinations(range(h),3)]
+    require(len(masks)==v, "triple enumeration")
+    groups = z["groups"]
+    flat = [i for group in groups for i in group]
+    require(Counter(flat)==Counter(range(v)), "partition must cover each triple once")
+    require(Counter(map(len, groups))=={21:83,7:4}, "unexpected restricted group sizes")
+
+    # IMPORTANT NEGATIVE CONTROL: the PR129 bit supplier uses the
+    # RATIONAL form H=9I-J, not our F2 parity form. For triple vectors
+    # t_T^T H t_U=9*(|T intersect U|-1), which is zero precisely when
+    # distinct triples meet in one point. The PR128 complex signed group
+    # construction does NOT meet this requirement after restricting h=24
+    # to h=23; hence these grouped bit-core exteriors cannot be claimed.
+    rational_overlap_counts = Counter()
+    for group in groups:
+        for i in range(len(group)):
+            for j in range(i+1,len(group)):
+                intersection_size=(masks[group[i]] & masks[group[j]]).bit_count()
+                rational_overlap_counts[intersection_size]+=1
+    rational_pair_count=sum(rational_overlap_counts.values())
+    rational_orthogonal_pairs=rational_overlap_counts[1]
+    rational_nonorthogonal_pairs=rational_pair_count-rational_orthogonal_pairs
+    require(rational_overlap_counts=={0:15012,2:2502}
+            and rational_pair_count==17514 and rational_orthogonal_pairs==0,
+            "Pinned rational-H negative control changed: re-evaluate proof")
+    require(tuple(masks[groups[0][i]] for i in (0,1))
+            ==((1<<0)|(1<<6)|(1<<12),(1<<0)|(1<<6)|(1<<18)),
+            "Pinned rational-H counterexample pair changed")
+    signatures = Counter()
+    tested_gram = tested_phase = 0
+    x_tests = [0]
+    x_tests += [1<<i for i in range(h)]
+    x_tests += [(1<<i)|(1<<j) for i,j in combinations(range(h),2)]
+    for group in groups:
+        B = [masks[i] for i in group]
+        for a in range(len(B)):
+            for b in range(len(B)):
+                require(parity(B[a]&B[b]) == (a==b),
+                        "group binary Gram matrix not I")
+                tested_gram += 1
+        C = nullspace(B,h)
+        require(len(C)==h-len(B), "complement dimension")
+        require(len(gf_basis([sum(parity(a&b)<<j for j,b in enumerate(C))
+                              for a in C],len(C)))==len(C),
+                "complement Gram matrix singular")
+        gauss = quadratic_signature(C)
+        signatures[(len(B),len(C),gauss[0],gauss[1])] += 1
+        for x in x_tests:
+            projected = 0
+            for b in B:
+                if parity(x&b):
+                    projected ^= b
+            remaining = x^projected
+            require((x.bit_count() - projected.bit_count()
+                     - remaining.bit_count())%4==0,
+                    "signed Gaussian quadratic phase mismatch")
+            tested_phase += 1
+
+    require(signatures=={(21,2,-2,0):83,(7,16,0,-256):4},
+            "unexpected signed complement types")
+    H = Counter({int(k):int(n) for k,n in p["hist"].items()})
+    old_mass = sum(k*n for k,n in H.items())
+    require(old_mass == m*W-deficit, "original pinned rank mass")
+    ext = {int(k):int(n) for k,n in p["exterior_hist"].items()}
+    require(all(H[k]>=n for k,n in ext.items()), "exterior multiplicity")
+    count_zero = ext[m-h]
+    require(count_zero%(2*v)==0, "zero-frame role count nonintegral")
+    roles_zero=count_zero//(2*v)
+    require(roles_zero==17597, "unexpected zero-start-role count")
+
+    # Remove exactly the old terminal exteriors of the zero-frame roles.
+    # Each candidate shared role instead has one final group complement
+    # per stage. Other local and full-frame children remain unchanged.
+    H[m-h]-=count_zero
+    if not H[m-h]:
+        del H[m-h]
+    for group in groups:
+        H[h*(h-len(group))] += 2*roles_zero
+    newW = 2*N+2*v*(R-roles_zero)+2*len(groups)*roles_zero
+    new_mass = sum(k*n for k,n in H.items())
+    require(newW==49249558, "unexpected candidate allocation")
+    require(new_mass==m*newW-deficit, "rank mass/deficit mismatch")
+    require(all(0<rank<m and n>0 for rank,n in H.items()), "invalid child")
+    # The next tests certify the ARITHMETIC MOMENT of an assumed
+    # paid child histogram; they do not show that histogram can be
+    # realized by the physical bit-core word.
+    lower=Q(1380218257,10**13)
+    next_point=lower+Q(1,10**13)
+    low,high=moment_interval(H,m,newW,lower)
+    nextlow,nexthi=moment_interval(H,m,newW,next_point)
+    require(high<1, "candidate moment fails to contract")
+    require(nextlow>1, "next moment grid point was not rejected")
+    old_saving=Q(384599,10**10)
+    stopped=(1-Q(1,1000))*lower+Q(1,1000)*old_saving
+    pr128_bit=Q("0.0001244501335381315811393")
+    require(stopped*100>pr128_bit*110,
+            "less than 10 percent conditional arithmetic saving")
+    complex_pr128=Q("0.0001231305483517511358")
+    overall_baseline=Q("0.00012310001053253")
+    target=overall_baseline*Q(103,100)
+    require(complex_pr128<target, "complex bottleneck check changed")
+
+    result = {
+        "status":"PASS F2 geometry and formal moment; FAIL PR129 rational H-orthogonality; proposed physical bit sharing NOT valid",
+        "baseline":"PR128 commit 530588a019b4a74f09180680c9e3961bf649ec89",
+        "triples":v,"groups":len(groups),
+        "group_counts":dict(Counter(map(len,groups))),
+        "gram_entries_checked":tested_gram,
+        "quadratic_phase_cases":tested_phase,
+        "rational_H_overlap_counts":dict(sorted(rational_overlap_counts.items())),
+        "rational_H_total_pairs":rational_pair_count,
+        "rational_H_orthogonal_pairs":rational_orthogonal_pairs,
+        "rational_H_nonorthogonal_pairs":rational_nonorthogonal_pairs,
+        "counterexample":{"group":0,"first_triple":[0,6,12],
+                          "second_triple":[0,6,18],
+                          "intersection":2,"rational_H_inner_product":9},
+        "legal_bit_supplier_certified":False,
+        "signed_complements":[
+          {"group_dimension":d,"complement_dimension":c,
+           "gauss_real":re,"gauss_imag":im,"groups":n}
+          for (d,c,re,im),n in sorted(signatures.items())
+        ],
+        "zero_frame_original_roles":roles_zero,
+        "original_W":W,"screened_W":newW,
+        "original_deficit":deficit,"screened_deficit":m*newW-new_mass,
+        "complete_screened_children":{str(k):n for k,n in sorted(H.items())},
+        "moment_parameter_lower":str(lower),
+        "moment_upper_below_one":str(1-high),
+        "next_grid_point_rejected":str(next_point),
+        "next_grid_lower_exceeds_one":str(nextlow-1),
+        "conditional_stopped_bit_saving_lower":str(stopped),
+        "baseline_pr128_stopped_bit":str(pr128_bit),
+        "baseline_pr128_kappa":str(overall_baseline),
+        "target_plus_three_percent":str(target),
+        "pr128_unchanged_complex_ceiling":str(complex_pr128),
+        "required_before_final_kappa_claim":[
+            "Replace current H-incompatible partition with a valid H-orthogonal sharing scheme",
+            "formal independently restored bit-core scratch identity",
+            "literal forward/reflected physical frame schedule for shared roles",
+            "paid signed Gaussian normal forms for -2 and -256i complements",
+            "basis/phase/scalar/semantic precision charges",
+            "coupled exact complex+bit recurrence certificate"
+        ],
+    }
+    print(json.dumps(result, indent=2, sort_keys=True))
+
+
+if __name__=="__main__":
+    main()