Conditional κ = 0.001674340686401949: rank-seven helper ends with T37 owner packing

.github/workflows/t37-ends7-owners.yml

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+name: Rank-seven-end T37 whole-owner composition
+
+on:
+  workflow_dispatch:
+  pull_request:
+    paths:
+      - 'research/complex-t37-ends7-owners/**'
+      - '.github/workflows/t37-ends7-owners.yml'
+  push:
+    branches: [main, codex/ends7-t37-20261013]
+    paths:
+      - 'research/complex-t37-ends7-owners/**'
+      - '.github/workflows/t37-ends7-owners.yml'
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 90
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7, retained repository pin
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7, retained repository pin
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Install retained cold-replay dependencies
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y --no-install-recommends g++ libboost-dev
+          python -m pip install -r research/e8-bit-p111-tuned/requirements.txt
+      - name: Fresh ancestry, supplier, owner construction and strict admission
+        env:
+          CXX: g++
+          BOOST_INCLUDE: /usr/include
+        run: >-
+          python -B research/complex-t37-ends7-owners/verify.py
+          --work "$RUNNER_TEMP/ends7-t37-cold"
+      - name: Require committed sources unchanged
+        if: always()
+        run: git diff --exit-code
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: ends7-t37-python-${{ matrix.python }}
+          path: |
+            ${{ runner.temp }}/ends7-t37-cold/*.json
+            ${{ runner.temp }}/ends7-t37-cold/*.log
+            ${{ runner.temp }}/ends7-t37-cold/t37/strict/*.json
+            ${{ runner.temp }}/ends7-t37-cold/t37/strict/*.log
+            ${{ runner.temp }}/ends7-t37-cold/t37/strict/global/audit/*.json

research/complex-t37-ends7-owners/CLAIM.json

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+{"T":37,"bit_lower":"1733427039589844234749/1000000000000000000000000","calls":333,"charged_prefix_bits":1024,"comparison":{"independently_replayed_pr1050":"0.001672241870811633","selected_pr1042":"0.001672188119205421","selected_pr942":"0.001661960547713947","seven_slot_t37_predecessor":"0.001674097969905390"},"complex_lower":"419287201220779036669/250000000000000000000000","complex_profile":{"1":806622,"2":143856,"3":141192,"4":47286,"48":11320,"5":27306,"8":2664},"deficit":11840,"idle":{"1":5424,"48":11320},"kappa":"1674340686401949/1000000000000000000","kappa_decimal":"0.001674340686401949","live":33152,"local_profile":{"1":2406,"2":432,"3":424,"4":142,"5":82,"8":8},"physical":33642,"physical_row_coefficient":17495,"prefix_bits":775,"rank_mass":2408256,"roles":159840,"scope":"Finite conditional construction under the retained compiler, whole-call hosting, common-label/mutable-source realization, precision/tape, analytic-transfer and bitH1-H5 hypotheses. No unconditional theorem or kappa=1 claim.","width_inventory":{"4":56,"5":32,"7":32,"8":120,"9":240}}

research/complex-t37-ends7-owners/NOTICE.md

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+# Attribution and source boundary
+
+Prepared for Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0.
+
+The new contribution is the 37-replica wave order, its frozen integral
+pattern-flow assignment, deterministic matching reconstruction, and strict
+composition with the rank-seven-end seven-slot k8 supplier. The PR1107 local
+word is unchanged. The preceding seven-slot T37 wave construction is retained
+as the direct source of the owner-flow and public reconstruction method.
+
+- Jeremy Kothe (`jeremykothe2`): PR1005 mutable-leaver k8 construction,
+  PR1018 seven-slot construction (following PR987), and PR1022's supplier and
+  sixteen-replica composition. The complete `gauge44-leaver8` and
+  `gauge44-slots` packages are copied unchanged from PR1022's pinned head.
+  Their original notices and attribution chains remain intact, including the
+  earlier gauge, pivot, cold-end, promotion, frame and hybrid constructions.
+- Jeremy Kothe: PR1107's rank-seven-end supplier and its frozen source package.
+  All 197 files are copied unchanged. Alexander Schwartzman (`AlexS-scale`):
+  PR1030's two rank-seven helper-end mechanism. `thakrarsagar`: PR1049's
+  independent leaver-premise checker, included unchanged in that supplier.
+- `jon314159`: PR942's T37 bank envelope, finite prefix reserve, explicit
+  source adaptations and all-replica signed-price argument.
+- Chafik Boukhalfa: PR890's variable-replica composition and independent
+  checker, the retained earlier gauge/owner work, and the prior local
+  pattern-flow/matching formulation used to nominate this assignment.
+- Hao Yan (`FanPUYen`): PR858's direct-sum parent construction, strict physical
+  source-event windows and independent owner audit.
+- Jeremy Kothe: PR799's paired-read-exchange supplier.
+- `DreamingOfClouds`: the retained PR589 tuned P111 bit supplier, with its
+  complete upstream notices.
+- The original source notices credit the PR514/484/507 controller lineage,
+  PR558/552/531 exact phase machinery, the signed-price antecedents, exact
+  moment engines and outer reduction. They are retained rather than replaced
+  by this list.
+
+PR635's required source subtree is retained at its constructor-pinned commit.
+`SOURCE-PINS.json` records each vendored file's original Git blob and SHA-256;
+`DEPENDENCY-PINS.json` pins repository dependencies. No author optimizer is
+needed to reconstruct the new frozen owner map.

research/complex-t37-ends7-owners/PROOF.md

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+# Finite construction and fixed-family ceiling
+
+Use the unchanged PR1107 local supplier. Its independently recounted paid
+profile is `(2406,432,424,142,82,8)` at ranks `(1,2,3,4,5,8)`; its 480 helper
+widths have multiplicities `(56,32,32,120,240)` at `(4,5,7,8,9)`.
+
+For `0 ≤ s < 9`, `0 ≤ r < 37`, order calls by `(37s+8r,s,r)`.
+Each replica retains the original stage order and hence all thirty original
+physical source events, including its nine bridges. PR858's event expansion
+reconstructs strict idle intervals. The independent PR890 checker reconstructs
+them separately from the original event stream.
+
+The frozen flow groups together only identical capacity/interval pairs. Each
+group retains the complete list of physical `(replica,child)` windows, with
+112 distinct port families per window. A pattern with multiplicity `N` has
+`N` bins. For every width `w`, its integer time flow totals `N` times the
+pattern multiplicity of `w`; at each invocation the total flow is at most `N`.
+
+Split each width's flow among that many left vertices of degree `N`. Add
+dummy left vertices to fill the unused capacity of the time vertices. This
+gives a regular bipartite multigraph of degree `N`. Successive perfect
+matchings decompose it into `N` bins. Every matching is checked to be a
+permutation using positive edges, and every used edge is removed. Consequently
+each bin has its exact pattern and receives at most one helper per invocation.
+`construct.py` performs the entire decomposition with exact integers and
+checks its reconstructed flow against the frozen one.
+
+Assign bins to their listed physical windows and port numbers in order; lay
+their helper slices consecutively. The independent audit checks all 159,840
+roles for strict bridge-aware timing, whole widths, complete per-call helper
+coverage, distinct physical families, disjoint prefix slices, and literal
+orthogonal 73-axis charts. These checks also detect aliasing between different
+idle children of the same physical family. The residual idle profile is
+`{1:5424,48:11320}`. Adding 333 local profiles gives the profile in CLAIM.json.
+
+The retained PR942 parent lift has bank groups `(8,8,8,8,5)` and shared restored
+private workspace. Its independent parent checker is unchanged. The emitted
+controller removes the dedicated banks and uses the frozen whole-owner map.
+The strict invoice charges the enlarged 1,024-bit prefix reserve. It derives
+prefix 775 and row coefficient 17,495, and binds every provider artifact to
+the fresh native replay. Both moment engines certify the same root bracket:
+
+```
+0.001677148804883116146676 < b < 0.001677148804883116146677.
+```
+
+The retained bit endpoint is `1733427039589844234749 / 10^24`. All 47 strict
+outer constraints hold at `κ = 1674340686401949 / 10^18`.
+
+For the fixed-family ceiling, retain PR795/890/942's signed helper prices
+`(-1,-20,-8,-2,4)` and bin bonuses `(2,4,8,-13)` for capacities
+`(8,16,32,48)`. There are `(672,448,448,448)` bins per replica. The new word
+leaves idle mass 14,832 and signed budget −1,192 per replica. The retained
+supporting-inequality proof therefore gives rank-one credit
+`48*(-1192)+13*14832 = 135600`. At 37 replicas, the attained rank-one count
+is `37*135600/925 = 5424`, with the remaining mass in rank 48.
+
+`price.py` re-enumerates all 1,163 bin patterns by two methods, checks the
+supporting inequalities with both exact arithmetic engines, and evaluates
+the outer reduction at both ends of the root bracket. Both yield the same
+`10^-18` grid tick. Thus this construction attains that fixed-family grid
+ceiling, even when other call orders and replica counts are admitted in the
+relaxation. This statement does not bound different local words, capacity
+families, helper interfaces or bit suppliers.
+
+All retained all-size and realization hypotheses are unchanged; this proof
+and its executable evidence establish the finite conditional composition.

research/complex-t37-ends7-owners/README.md

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+# Rank-seven helper ends with 37-replica whole-owner packing
+
+Conditional **κ = 0.001674340686401949**. This improves the selected PR1042
+value `0.001672188119205421` and the preceding seven-slot T37 construction
+`0.001674097969905390` at the preparation snapshot.
+
+The local word is Jeremy Kothe's PR1107 rank-seven-end k8 supplier, unchanged,
+using Alexander Schwartzman's PR1030 helper-end mechanism.
+The new construction is a 333-call wave order and a frozen integer flow
+expanded into **159,840 whole-helper owners**. It leaves 5,424 rank-one and
+11,320 rank-48 idle children. With the retained PR589 bit supplier, it attains
+the outer-grid ceiling for this fixed local paid profile, helper inventory
+and source capacity stock over all positive replica counts.
+
+## Reproduce
+
+Python 3.11+, a C++17 compiler, Boost headers, and the retained baseline's
+NumPy/SymPy/SciPy requirements are needed. The new owner constructor uses
+only the standard library; the verification does not run the owner optimizer.
+
+```sh
+python -m pip install -r research/e8-bit-p111-tuned/requirements.txt
+CXX=g++ BOOST_INCLUDE=/usr/include python -B \
+  research/complex-t37-ends7-owners/verify.py \
+  --work /tmp/t37-seven-slot-fresh
+```
+
+Use a new output directory outside the checkout. On Homebrew macOS, use
+`CXX=clang++ BOOST_INCLUDE=/opt/homebrew/include`. The driver first runs the
+retained cold PR589/741/799 ancestry and its coverage checks. It then rebuilds
+the k8, seven-slot and rank-seven-end suppliers, reconstructs the frozen owners, checks the
+independent geometry and five-bank parent, and runs strict emitted-controller
+admission. Fresh and retained parent artifacts are compared exactly.
+Retained builders use writable staging copies because their output builders
+preserve input permissions. The source checkout stays unchanged; all staging
+source bytes are bound before and after execution.
+
+`RESULT.json` binds the completed stages and source manifests. `MATH.json`
+contains the portable mathematical receipt. `PRICE.json` records both exact
+moment engines, all 47 strict outer inequalities and the fixed-family ceiling.
+The driver also rejects eight flow mutations, six owner mutations, fifteen
+controller mutations, 69 admission mutations and twelve bit-supplier mutations,
+in addition to the unchanged ancestral and supplier controls.
+
+## Result and scope
+
+The complex profile is
+`{1:806622, 2:143856, 3:141192, 4:47286, 5:27306, 8:2664, 48:11320}`.
+There are 33,152 live families, 33,642 physical families and deficit 11,840.
+The prefix is 775 bits within the charged 1,024-bit reserve; the physical-row
+coefficient is 17,495, below the retained 20,161 limit.
+
+This is a finite conditional construction. The retained all-size compiler,
+common-label/mutable-source realization, whole-call hosting, precision/tape,
+analytic transfer and bit H1–H5 hypotheses remain. It is not an unconditional
+integer-multiplication theorem or a κ = 1 result.
+
+See [PROOF.md](PROOF.md), [NOTICE.md](NOTICE.md), [SOURCE-PINS.json](SOURCE-PINS.json)
+and [CLAIM.json](CLAIM.json). All source and data files are manifest-bound.

research/complex-t37-ends7-owners/audit.py

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+"""Independent PR890 owner audit, with exact T37/480-helper parameter edits."""
+import argparse
+from pathlib import Path
+from common import P,ROOT,read,dump,load,sha
+
+def check(base,local,owners_path,out):
+    source=ROOT/'research/complex-t21-owners/independent_check.py'
+    text=source.read_text()
+    edits=[('2 * 512','2 * 1024'),('prefix < 512','prefix < 1024'),
+      ('charged_prefix_bits=512','charged_prefix_bits=1024'),
+      ('{4: 80, 5: 32, 7: 54, 8: 122, 9: 216}','{4: 56, 5: 32, 7: 32, 8: 120, 9: 240}')]
+    for before,after in edits:
+        assert text.count(before)==1,(before,text.count(before));text=text.replace(before,after)
+    adapter=out.parent/'independent_owner_adapter.py';assert not adapter.exists();adapter.write_text(text)
+    ck=load(adapter,'independent_seven_slot_owner_checker');ck.T=37;ck.R=480;ck.EXPECTED_IDLE={1:5424,48:11320}
+    refs=[base/'split-centres/GLOBAL-TEMPLATE.json.gz',base/'work/complex-nine-native/DATA-PHASES.json',
+          base/'split-centres/CANONICAL-WORD.json.gz',local/'CANONICAL-WORD.json.gz',
+          local/'INDEPENDENT-LOCAL-REPLAY.json',owners_path]
+    parent,phases,canonical,word,receipt,owners=map(read,refs)
+    assert receipt['canonical_word_sha256']==sha(refs[3])
+    assert receipt['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert word['ports']==canonical['ports']
+    assert [ck.basis(word['frames'][f])for f in word['center_frames']]==[ck.basis(canonical['frames'][f])for f in canonical['center_frames']]
+    context=ck.make_context(parent,phases,word['ports'],word,receipt,owners)
+    result=ck.check_roles(context,owners);result['controls_rejected']=ck.controls(context,owners)
+    result.update(edits=edits,source_sha256=sha(source),adapter_sha256=sha(adapter),inputs={str(p):sha(p)for p in refs})
+    claim=read(P/'CLAIM.json')
+    for field in ('roles','calls','live','physical','rank_mass','deficit','prefix_bits','physical_row_coefficient'):
+        assert result[field]==claim[field],field
+    assert {str(r):n for r,n in result['profile'].items()}==claim['complex_profile']
+    dump(out,result);return result
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    for k in ('base','local','owners','out'):ap.add_argument('--'+k,type=Path,required=True)
+    a=ap.parse_args();out=a.out.resolve();assert not out.exists() and not out.is_relative_to(ROOT)
+    out.parent.mkdir(parents=True,exist_ok=True)
+    r=check(a.base,a.local,a.owners,out);print(r['status'],r['roles'],flush=True)
+if __name__=='__main__':main()

research/complex-t37-ends7-owners/common.py

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+"""Strict shared I/O; construction and independent audit remain separate."""
+import gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+P=Path(__file__).resolve().parent
+ROOT=P.parents[1]
+if not __debug__:raise RuntimeError('Assertions must remain enabled')
+def read(path):
+    path=Path(path);raw=path.read_bytes()
+    return json.loads(gzip.decompress(raw)if path.suffix=='.gz'else raw)
+def canonical(value):return json.dumps(value,sort_keys=True,separators=(',',':')).encode()
+def sha(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+def identity(value):return hashlib.sha256(canonical(value)).hexdigest()
+def dump(path,value):
+    raw=canonical(value)
+    if path.suffix=='.gz':
+        raw=bytearray(gzip.compress(raw,mtime=0));raw[9]=255
+    path.write_bytes(raw)
+def load(path,name):
+    previous=sys.modules.pop('common',None);sys.path.insert(0,str(path.parent))
+    try:
+        spec=importlib.util.spec_from_file_location(name,path)
+        module=importlib.util.module_from_spec(spec);sys.modules[name]=module;spec.loader.exec_module(module)
+        return module
+    finally:
+        sys.path.pop(0);sys.modules.pop('common',None)
+        if previous is not None:sys.modules['common']=previous