Emit the physical raw dual of #4935 with independent verification and a scoped ceiling (no new κ)

research/involutory-producer-raw-dual/.gitattributes

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+# Frozen source and scientific evidence must retain their exact input bytes.
+inputs/** -text
+science/** -text
+independent/** -text

research/involutory-producer-raw-dual/BUDGET.md

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+# Complete local repair bill and unfunded caller obligations
+
+The repaired typed word and RESULT.paid are authoritative. The artifact's
+canonical.local_profile intentionally remains4929 baseline metadata.
+
+|Item|Exact local bill/status|
+|---|---|
+|4929 backward Gaussian profile|2201H1+412H2+510H3+127H4+40H5|
+|New suffix|8H1; no other recursive job|
+|Complete repaired profile|2209H1+412H2+510H3+127H4+40H5, matching4935 forward|
+|Productive helpers retained|28H4+7H7+47H8+326H9:408 original independent jobs, once each|
+|New independent reward|None|
+|New storage arrays|None; reuse already owned C0, reset to zero|
+|Literal suffix|456 events:8 COPY,16 CLEAR,8 lifts,424 weighted ADDs|
+|Scatter coefficients|-12×8,-6×268,+6×148|
+|Scalar-primitive ADD allowance|2976, distinct from424 weighted instructions and8 Gaussian calls|
+|Conservative added array passes|3064=2976+24 COPY/CLEAR+64 emitted monomial primitives, beyond8 paid H1|
+|Normalized prefix L1|258 backward,457 forward; not an error-amplification certificate|
+
+Relative to the older632 producer, eight H8 centres become eight H1 repairs,
+but the target transfer changed. This is not an unchanged-output saving.
+Every original helper remains an independent job; none is consumed or credited
+twice. Source X inputs are not mutated into the excluded UNIT-TRANSFER variant.
+
+Each new lift is a literal compiled phase-bound word. Array volume is the
+inherited supplier embedding volume, with normal columnwise O(f) index/phase
+work. Counting all emitted identity/phase primitives is deliberately conservative.
+
+The finite repair suffix can amplify error. A conservative maximum-fiber-field
+norm bound is13^8*7^416 for its weighted ADDs; multiply by the inherited suffix
+bound when allocating errors inside the old prefix. New Gaussian/local errors
+need an explicit allocation after that amplification. Entrywise norms also need
+the relevant square-root volume conversion. Fixed constants can permit
+logarithmic guard precision under the admitted convention, but no complete
+caller/compiler reserve or multiplier precision theorem is funded here.
+
+The separate one-bank price screen grants an explicitly UNREALIZED224H17+2H
+reward against two repaired profiles. Its margin at C=.0030217758 is in
+[150.262158203082210620506138658847,150.262158203082210620506138658848].
+The source-specific112H2 floor makes this
+[-73.269156882594712940928576503039,-73.269156882594712940928576503038],
+and it stays negative through C=.0034 by the written normalized-moment argument.
+The package independently regenerates these intervals. They are necessary
+price-only tests for the stated one-bank architecture, not a completed target
+or a universal caller ceiling. Finite costs cannot rescue that negative bill;
+a different caller remains an open contract with unknown costs.

research/involutory-producer-raw-dual/CEILING.md

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+# Scoped one-parallel-bank ceiling for the source-restored involution
+
+This is a separate read/derive corollary for the actual source-restored F in
+PR4935 head `64c9f99693c92fb370096fb43dbc58a085b30e36`. It does not obstruct
+the newly constructed physical raw dual or an eventual direct coded consumer.
+Credit the parent for the projection/rank and determinant-lemma argument;
+this agent independently checked the actual matrix, grades and intervals.
+
+Let J={0,7,20,23,86,93,108,111} and D_J its diagonal selector. Exact source
+checks give F²=I, diag(F)=12D_J and F_JJ=12I8. Write G=F−12D_J. The matrix
+determinant lemma gives det(G)=det(F)det(I8−12F_JJ)=det(F)(−143)^8≠0;
+symmetry of F is not assumed. The checker additionally verifies the two-sided
+integer witness
+
+    G(143F−12F D_J F)=(143F−12F D_J F)G=143I.
+
+For the actual X entrance frames U_i, every nonzero off-diagonal F_ij has
+Fourier grade2 for U_i U_j*. There are 5,824 such supported pairs, all directly
+recomputed from the exact source Clifford library and checked by independent
+binary row reduction. The pure diagonal12D_J is monomial. Thus
+
+    pi2(U F U*)=U G U*,
+
+which is invertible. Since F^-1=F, the source-restored forward uncoding
+adapter is U F U*, with scalar exitF on the common-full X chart. The raw-dual
+adapter has entrance bar(U) F^T bar(U)* and scalar exitF^T; its projected
+matrix is likewise invertible. Fixed nonzero scalar rescaling preserves the
+same projected-rank argument. No free ordinary implementation of those exit
+matrices is asserted.
+
+Here is the exact all-width algebra boundary. Fix a finite-phase one-column
+Clifford group Gc on the declared address space and its central scalar subgroup
+Z. Impose the actual scalar character z=ζ^f at width f; the resulting twisted
+algebra A_f has one basis class per projective Clifford Gc/Z. Let H be the
+full admitted monomial-Clifford subgroup and B_f its subgroup algebra. Fourier
+grade is invariant under both left and right monomial multiplication, so
+projection pi2 onto pure grade2 basis classes is a B_f-bimodule map. Phases
+are retained, and no integral-domain or commuting-coefficient premise is used.
+
+The projective algebra faithfully evaluates into columnwise tensor action for
+all sufficiently large f. Indeed, choose nonproportional matrix representatives
+v_t for the finitely many projective classes. For each t, a product of linear
+forms vanishing on each other v_u but not v_t isolates v_t in homogeneous
+degree |Gc/Z|−1. Multiply by a linear form nonzero at v_t to obtain an isolating
+polynomial at every larger degree. Thus v_t^tensor(f) are linearly independent
+at those widths, with their scalar character retained. An exact identity at
+all positive widths must therefore hold in A_f at sufficiently large widths,
+even with width-dependent owner scalar coefficients. No operator sum is
+incorrectly tensor-powered.
+
+Grant arbitrary rectangular B_f-valued owner pre/post controls L,R, zero
+scratch, output selection, copies and a free identity bypass B0. A standalone
+ONE parallel bank D of pure Gaussian-Clifford channels satisfies
+
+    pi2(L D R+B0)=L pi2(D) R.
+
+If the bank has r grade-two channels, its right-hand side has regular-module
+rank at most r dim(A_f). All other pure grades project to zero; each grade-two
+channel is a group unit. The required adapter projection has rank 112dim(A_f).
+Consequently r≥112. This is the same restricted architecture ceiling even
+though the scalar port matrix F is now an involution.
+
+The explicitly UNREALIZED two-call grant 224H17+2H versus two copies of
+P={1:2209,2:412,3:510,4:127,5:40} has margin
+[150.262158203082210620506138658847,150.262158203082210620506138658848]
+at C=.0030217758. Subtracting the necessary 112H2 gives
+[−73.269156882594712940928576503039,−73.269156882594712940928576503038];
+at C=.0034 it gives
+[−80.401921647290247704383966403396,−80.401921647290247704383966403395].
+All negative coefficient ranks are ≤5 and all positive ranks ≥7. Therefore
+M(t)/5^t strictly increases in t=1−C, and negativity at the lower-C endpoint
+excludes this stated bill over the entire interval. All 816 inherited helper
+jobs are included exactly once. No productive Gaussian endpoint is supplied
+by this price grant, and finite scalar/storage/precision/outer costs cannot
+rescue its negative relaxation.
+
+Scope excludes chronological multibank circuits, native absorption or
+interleaving, source-prefix access, direct coded consumers, approximate/border
+endpoints, nonlinear operations, non-Clifford monomial gates and arbitrary
+noncolumnwise address controllers. The actual new raw-dual repair is not
+such an uncoding adapter and remains a positive local interface result.
+No caller, κ or universal producer ceiling follows.
+
+Reproduce normal/O with `check_ceiling.py`. This is a source-specific finite
+matrix/grade/interval verification supporting the written all-width proof,
+not a formal proof-kernel certificate. Apache-2.0; substantial OpenAI Codex
+assistance; upstream contributor credit is retained in REVIEW.md/SOURCES.json.

research/involutory-producer-raw-dual/HANDOFF.md

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+HANDOFF
+
+Research discussion / PR / artifact:
+LOCAL-ONLY `research/involutory-producer-raw-dual`, branch `research/involutory-producer-raw-dual-20261023`; final public artifact pending parent publication. One fixed physical raw-dual repair plus a separately scoped one-parallel-bank price/ceiling obligation. No complete caller, source-mutating UNIT-TRANSFER dual or new kappa. Existing green modules remain unchanged.
+
+Exact commit:
+Scientific base/fresh main `cef4b52f2a59009865bf8eabde1be3f159063703`; exact source-retention ancestor `984e02db73bc2d814e20cbe3830b26ff0c3b09fe`. Consumed source heads are4935 `64c9f99693c92fb370096fb43dbc58a085b30e36`,4929 `361f5d4100640177d6a983dd2f336021c75bfd5e` and native `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`. The4935 head is not claimed ancestral: its exact raw bytes, Git blob/SHA and original path/head metadata are retained in our real publication ancestry, and SOURCES binds those actual retained paths. Final publication commit remains pending.
+
+What is established:
+The actual4929 backward typed prefix plus8 owned H1 lifts and424 ADDs returns X'=X-F^T Y,Y'=Y for the actual4935 source-restored F, retaining all408 independent helper jobs and clearing existing ownedC0 with no new array. All632 original rows,12544 transpose coefficients and complete paid bill are checked. RESULT.paid and the replayed word are authoritative2209H1+412H2+510H3+127H4+40H5; canonical.local_profile is stale retained4929 baseline metadata. B independently reconstructs F, interprets all632 normalized owner rows without A/native_core, checks all4096NEWlift phase columns and7 semantic controls. The separate self-contained one-bank proof rechecks F premises, exact off-diagonal inverse witness,5824 grade2 supports and interval prices; its112H2 floor makes even the unrealized224H17+2H grant negative on the stated C interval.
+
+What remains uncertain:
+Inherited original physical warp semantics remain source premises; new-lift phases were freshly independently expanded. This is a physical producer dual, not a complete profitable caller or full multiplier theorem. No source-mutating variant, caller capacity, native absorption, chronological multibank construction, precision/compiler reserve, stock or outer recovery is supplied. The one-bank ceiling is restricted to a fixed finite columnwise Clifford alphabet with pure Gaussian channels and admitted monomial controls; it does not cover excluded chronological, approximate or noncolumnwise architectures. The positive pre-adapter price grant has no realized224H17 endpoint.
+
+Smallest useful next task:
+Write a complete direct chronological coded caller for the actual forward/raw-dual source pair, with every arbitrary owner, helper return, paid call, scalar/storage cost and precision obligation. Derive the full bill before downstream optimization or capacity expansion. The present package stops at the fixed repaired interface and its separate one-bank obligation; no additional family search is included.
+
+Reproduction command and expected runtime:
+Run `python3 scripts/research_package.py --package research/involutory-producer-raw-dual` for all8 registered normal/O commands. Direct launchers are `python3 -I -W error -B research/involutory-producer-raw-dual/verify.py` and `verify_independent.py derive`, `audit`, or `ceiling` under the same package path, then with `-O`; expected individual times are roughly5/25/36/2 seconds with90/120/180/60-second bounds respectively. Launchers authenticate frozen bytes, run read-only/private-scratch, compare scientific receipts and support Git-free export replay. Exact runtime/source/coverage qualifications are in VALIDATION.md and BUDGET.md.
+
+Predecessor credit:
+Credit Dugongue4935/4929; Rohan Arun1931; Ali Romman1862; Cinna Davis /1337isnot1337's4694/4698 and retained4470 lineage; Cao Yifan /intqwq native source beyond4610; zxv, Jacob Alan Sussman and retained E8/scalar/Clifford/compiler/precision/outer contributors. The parent proposed the physical repair and one-bank transfer, A emitted the word, B independently audited it and packaging preserved their science. Prepared for Chris R / Clear1nsight with substantial OpenAI Codex gpt-6.1-sol/high assistance. Apache-2.0; no independent human or proof-kernel acceptance claimed.