Test coupled returns through two query consumers and price a compressed exit

research/coupled-query-transport/.gitattributes

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research/coupled-query-transport/PROOF.md

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+# Coupled returns at two actual thin-query contacts
+
+New scoped work by zxv with substantial OpenAI Codex assistance. Apache-2.0.
+No subagents. This proof assumes the pinned PR5402 native endpoint. Its native
+word, compiler, all-width physical implementation and source admission are not
+proved again here. The new finite physical calculation uses an independent
+literal monomial evaluator, including absolute phases.
+
+## 1. Source contract and the compressed exit observation
+
+Use Dillon's PR5402 at `3348fccea855082786d5f0fc5558b73d4974e745`:
+
+\[
+ X=Dx-Ry+RW h,\quad Y=Dy,\quad H=D(h-Zy),\quad R=DQ.
+\]
+
+The eight mode inputs h are arbitrary and independent of all main and other
+helper inputs. The other 400 autonomous helpers and all nine zero owned returns
+are retained. W and Z are ordinary scalar/monomial maps,
+
+\[
+ W=K_p^{-1} M K_m/2,\qquad Z=K_m^{-1}M^T K_p/2,
+ \qquad ZW=14I.
+\]
+
+All K maps are unitary monomials, so Z=W*. The appropriate full Gaussians
+intertwine W and Z: R_main W=W R_mode and R_mode Z=Z R_main. Separate
+commutation with Q or D is not used.
+
+Suppose the caller supplies the **versioned eight-field observation**
+
+\[
+ b=ZQY=ZRy.
+\]
+
+At the native return, apply Q to H and perform
+
+\[
+ H_o=QH+b=Rh,\qquad X_o=X-WH_o=Dx-Ry,\qquad Y_o=Y.
+\]
+
+These are ordered identities. They restore all original mode directions as
+ordinary rank-nine jobs; they do not allocate independent credit to b. They
+hold at every positive fiber width under the source contract, with the scalar
+owner coefficients applied once outside the address tensor product.
+
+The observation may be borrowed: every operation on it below is undone, and
+it is returned unchanged. Source Y is unchanged. There is no erasure of a
+persistent input. The provider's nine owned fields already return zero.
+
+### Exact local operation bill
+
+M has 448 nonzero entries. Once b is supplied, the exit uses:
+
+1. Eight positive rank-one calls on H, then eight ADDs H+=b.
+2. Apply K_m to eight H fields and K_p to 112 X fields.
+3. The 448 ADDs X_i-=M_ik H_k/2.
+4. Undo both monomial banks.
+
+This costs **8 H1, 456 ADDs, 240 monomial field maps**, no new owned fields,
+and no new target credit except restoration of the original eight H9 jobs.
+The generator emits the literal field programs for these three contracts and the checker replays every adapter input, borrowed observation and dirty owned entry, checks every owned zero return, and recounts all instructions. Each ADD coefficient is an exterior dyadic scalar. A monomial field map is
+charged ordinary work, not a zero-cost operation or a single tape step.
+
+If a preserved full V=QY is supplied instead, fuse the common K_m pass:
+apply K_m to QH and K_p to V, perform 448 ADDs into H, restore V, apply
+K_p to X, perform another 448 ADDs, restore X and H. This costs **8 H1,
+896 ADDs, 464 monomial maps**, with V unchanged and no extra owned fields.
+
+If no observation is supplied, an explicit upper bound creates V by clearing
+112 owned fields, copying Y, applying 112 positive H1 calls, and clearing the
+observation bank after use. The resulting bill is **120 H1, 896 ADDs,
+464 monomial maps, 112 COPYs, 224 CLEARs and 112 additional owned fields**.
+All original helpers and targets are preserved. This is a constructive local
+upper bound, not a minimum decoder tariff.
+
+### Accuracy boundary
+
+Let the returned provider errors be e_X,e_Y,e_H. If V=Q(Y+e_Y)+e_V and
+the additional mode calls return Q(H+e_H)+e_J, then, writing e_A,e_B for
+aggregate ordinary-operation residuals in the two updates,
+
+\[
+ E_H=Qe_H+e_J+ZQe_Y+Ze_V+e_A,\qquad E_X=e_X-WE_H+e_B.
+\]
+
+Since ||W||=||Z||=sqrt(14),
+
+\[
+ ||E_H||\le ||e_H||+||e_J||+\sqrt{14}(||e_Y||+||e_V||)+||e_A||,
+ \quad ||E_X||\le ||e_X||+\sqrt{14}||E_H||+||e_B||.
+\]
+
+No independent-error assumption is needed for these triangle bounds. Actual
+precision, coordinate rounding, source version retention, tape movement,
+storage, compiler and outer funding remain obligations. These bounds do not
+supply them for free. If b arrives after consumers have changed X or Y, the
+consumer's propagated defect must also be repaired; the native-return identity
+is not a late decoder for an already executed thin query.
+
+## 2. Literal first and second consumer
+
+The authenticated selected p16 controller begins with the following relevant
+physical events (indices in its physical_events array):
+
+| Event | Source instruction |
+|---|---|
+| 1 | backward FULL stage 1 on pair 0 |
+| 2 | paid IDLE on pair 1, stages 0 and 1 |
+| 3,4 | X0+=X1; Y1-=Y0 |
+| 5 | lower thin shear Y0+=Q^-1 X0 |
+| 6,7 | X0-=X1; Y1+=Y0 |
+| 8 | backward FULL stage 3 on pair 1 |
+| 9 | paid IDLE on pair 2, stages 0,1,3 |
+| 10,11 | X1+=X2; Y2-=Y1 |
+| 12 | lower thin shear Y1+=Q^-1 X1 |
+| 13,14 | X1-=X2; Y2+=Y1 |
+
+These fourteen instructions are also exactly the PR5398 successor caller's events 5 through 18, checked against its pinned literal controller. The two wrapped endpoint calls do not alter this clip. We leave those other FULLs completed; no claim is made for additional coupled substitutions at the wrapped endpoints.
+
+Stage 0, the RIGHT boundary and all original inputs preceding this clip are
+unchanged. Compare main outputs with the ordinary uncoupled main interfaces,
+and let independent h1,h3 be the two new coupled mode input banks. Fresh D1,D3
+commute with Q; W1 and W3 need not commute with Q or their own D.
+
+After event 7, the main defects are
+
+\[
+ (\delta X_0,\delta Y_0,\delta X_1,\delta Y_1)
+ =(R_1W_1h_1,D_1W_1h_1,0,D_1W_1h_1).
+\]
+
+The actual paid observation at event 5 has additional response D1 W1 h1.
+It reads the version X0+X1, **not** Y0. A response cannot be relabelled Z1 QY0
+without an additional embedding/identity. No impossibility claim about all
+possible uses of that response is made here.
+
+After event 14 the six main-bank defects are
+
+\[
+\begin{split}
+ \delta X_0&=R_1W_1h_1,&\delta Y_0&=D_1W_1h_1,\\
+ \delta X_1&=-R_3D_1W_1h_1+R_3W_3h_3,
+ &\delta Y_1&=D_3W_3h_3,\\
+ \delta X_2&=0,&\delta Y_2&=-D_3D_1W_1h_1+D_3W_3h_3.
+\end{split}
+\]
+
+The second helper return additionally contains -D3 Z3 D1 W1 h1. Thus the
+first defect disappears from Y1 but survives in X1, Y2 and the helper bank.
+This is real two-generation transport, not loss of a dependency in the ledger.
+The checker executes all fourteen source events over exact noncommutative
+polynomial rows; reversing the query direction is rejected. The two FULLs,
+224 thin H1 calls, 224 H16 IDLE jobs and 224 H24 IDLE jobs remain paid. No
+coupled helper target credit is assigned by this experiment.
+
+## 3. An eight-mode-only feed into the next FULL fails
+
+Consider the specific proposed family that absorbs the incoming first-stage
+innovation by updating the next helper input h3 to h3+T h1, leaves the main
+inputs otherwise unchanged, and introduces no additional observations. To
+cancel the inherited h1 term in X1 at stage 3, it necessarily requires
+
+\[
+ W_3 T=D_1W_1. \tag{*}
+\]
+
+This condition already allows **arbitrary linear address operators T**, a
+larger class than ordinary scalar/monomial programs. It is not asserted as a
+necessary condition for other joint encoders, changed main feeds, extra retained
+observations, additional helper banks or arbitrary controllers.
+
+At fiber width one embed the two stages on 17 physical bits: shared central
+axis 0, first private axes 1..8, second private axes 9..16. The source literal
+K_p and K_m words specify W1 and W3 on these planes with their exact phases.
+Since Z3 W3=14I and Z3=W3*, the orthogonal projector onto im(W3) is
+P3=W3 Z3/14. Therefore (*) implies (I-P3)D1 W1=0.
+
+For each mode k, take the mode input with the shared central bit 1 and all
+sixteen private bits zero. Denote its image under D1 W1 by v_k. The exact
+calculation gives <v_i,v_j>=14 delta_ij. It evaluates Z3 v_k by sparse
+Gaussian-integer arithmetic with common denominators 512 and 1024, and forms
+
+\[
+ G_{ij}=14\delta_{ij}-\langle Z_3v_i,Z_3v_j\rangle/14.
+\]
+
+This is the residual Gram matrix. In particular G00=173/14 and
+
+\[
+ \det G=1389039784345493055/26985857024>0.
+\]
+
+All eight exact elimination pivots are positive. Consequently all eight
+sampled innovations survive outside im(W3); no T in the stated enlarged class
+can satisfy (*). A width-one counterexample suffices to reject an all-width
+contract. It is not a theorem that eight whole-field Gaussian jobs are needed:
+these are eight independent complex directions, not a paid volume lower bound.
+
+An instructive positive control uses central bit 0 instead. Its entire
+residual Gram matrix is zero. Testing only the all-zero address would accept
+the wrong handoff. A phase-only mismatch at one stage, preserving all address
+permutations, is also rejected by the physical controls.
+
+## 4. Complete recursive screen for the explicit purchased-observation exit
+
+The selected native profile is rederived as PR5402's paid profile plus eight
+H1 and eight H8 calls. Its helper profile is the 400 autonomous helpers plus
+the original eight H9 jobs. Replaying controller event counts and target words
+reproduces the selected ARITHMETIC.json inventories, not the obsolete invoice
+embedded in the historical CONTROLLER.json.
+
+There are **16 backward FULLs**, not 18 applicable calls. At each, buying the
+missing observation and using the local exit changes the selected profile by
++112 H1 -8 H8, with original targets unchanged. The whole controller therefore
+changes by +1792 H1 -128 H8, retains all fifteen thin query blocks, and changes
+rank surplus 752 to **-16**. At saving a=1/250, a separate directed calculation
+of sum(target r^(249/250))-sum(paid r^(249/250)) is strictly negative.
+Each root enclosure is certified by exact 250th powers, with denominator 2^80.
+Ordinary costs would be additional. This rejects the explicitly purchased
+observation construction at the tested saving.
+
+If b were already supplied at the correct version and boundary, restoring the
+eight missing H1 calls would instead delete only the centers at these sixteen
+FULLs, giving rank surplus 1776 and a positive moment screen at .004. The
+observation's production, retention and consumer corrections are **unknown**,
+not zero; this is a conditional allowance rather than a supplier or new κ.
+The checker also reconstructs PR5413's declared economically neutral comparison profile: provider plus eight paid H8 and eight H8 mode targets at each of eighteen FULLs. Its 64,260 paid calls, 10,928 targets and masses 238,990/239,742 match the declared comparison. Replacing only the sixteen unwrapped calls with the purchased-response exit still gives surplus -16 and a strictly negative .004 signed moment. This is a conditional price comparison, not a replay or admission of PR5413's native completion, source application or compiler. No additional saving is claimed from its neutrality.
+
+## Open next questions
+
+1. Implement b=ZQY from already paid native observations on the correct version,
+   with all displaced helper targets, ownership and restoration charged. Test
+   one eight-field coefficient map before another full controller search.
+2. If using more retained modes, name the enlarged input/output type and carry
+   the full nonzero Gram residual through the next consumer. Its channel/volume
+   and ordinary exit cost need explicit bounds. Merely increasing a search seed
+   inside (*) does not change the rejection.
+3. An actual delayed exit must correct the already executed query responses as
+   well as the native return. The two-generation trace gives their exact maps.
+   Price those maps before treating the native-return exit as a late repair.

research/coupled-query-transport/README.md

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+# Coupled outputs through two real query consumers
+
+This package supplies a source-bound two-generation test of Dillon's coupled
+provider in PR5402. The first return survives the actual next paid query, but
+its defect cannot be absorbed solely by updating the following FULL's eight
+helper inputs: the necessary equation W3 T=D1 W1 fails even for arbitrary
+linear T. A 17-bit, phase-correct witness has residual rank eight. The zero
+address alone incorrectly passes; a nonzero central input exposes the defect.
+
+A constructive local exit identifies a smaller useful observation contract:
+**b=ZQY, eight versioned fields**. If supplied at the native return, it restores
+all original outputs with eight H1 calls, 456 ADDs and 240 monomial field maps,
+and preserves the borrowed observation. Buying a full QY response instead
+costs 120 H1 calls per replacement. On the selected controller's 16 backward
+FULLs that purchase changes rank surplus 752 to -16 and fails an exact .004
+moment screen. All existing queries remain paid. An already executed consumer
+needs its propagated defect repaired too; the local exit is not a free late
+repair.
+
+[PROOF.md](PROOF.md) gives the exact contracts, source chronology, physical
+Gram witness, local operation bills, residual-error bound and limits.
+[RESULT.json](RESULT.json) records the reproducible rational evidence.
+No complete coupled recursive family, compiler admission or new κ is claimed.
+The selected conditional κ remains 0.0030217758. This is an author-checked
+scoped result, not independent human or formal-kernel acceptance.
+
+The same fourteen consumer instructions are byte-equal in the newer PR5398 all-backward caller, at events 5 through 18. The checker also rejects the purchased-response price screen against PR5413's declared neutral profile; this comparison does not replay or admit that primary construction.
+
+## Reproduce
+
+```sh
+python3.12 -B scripts/research_package.py --package research/coupled-query-transport
+```
+
+The normal and isolated optimized commands use Python's standard library and
+explicit checks. They authenticate inputs, interpret all 120 monomial maps on
+all 512 addresses including phase, replay the two source consumers, reconstruct
+the selected whole invoice, calculate the exact residual Gram matrix, reject
+semantic mutations, and compare every result field. Expected token:
+`PASS_TWO_GENERATION_COUPLED_QUERY_TRANSPORT`. Runtime is a few seconds. All three literal exit programs are generated and replayed on every adapter input column; their exact operation counts and payload hashes are recorded. To inspect their instruction arrays, add `--emit-exits /tmp/coupled-exits.json` to a direct verifier call.
+
+The mathematical native endpoint and its uniform physical model are explicit
+pinned premises. No full native provider replay, selected cold replay, all-history
+suite, Lean, Docker or outer/compiler admission is run for this local result.
+
+## Scope and overlap
+
+Explicit donor task: let encoded or coupled outputs survive their next consumer
+and test a second generation with eventual conversion/restoration charged.
+Historical card `centre-path-sharing` is retained as provenance; scope is changed
+to the PR5402 interface and actual FULL1/QUERY2/FULL3/QUERY4 sequence. No old
+fixed-word ceiling is applied to the changed interface. The first working
+example is the source's first two backward FULLs, rather than a new seed.
+
+Canonical base is 1ec1119972c9aefe42525172d07b332fcff81cb4, priority revision 7.
+The live overlap check covers PR5402/5407/5411, PR5413's new economically neutral
+completion, its PR5414 verification companion, the active broader caller claim in Discussion4930, and the released
+120-owner involution handoff. This package does not repeat the three-call search,
+claim the inverse as new, or supply that handoff's missing decoder. Full remote
+pagination covered 362 open PRs and 4701 Discussion records at entry; sparse
+local notes and unpublished work remain coverage limits. Exact source origins
+are in [SOURCES.json](SOURCES.json). Each vendored file is pinned to the ancestor recorded in its source row; each origin records its separately fetched source commit, path, Git blob and byte hash. This makes the replay independent of fetching a pending side branch. Origin equality was checked at creation; the offline replay does not reauthenticate remote history.
+
+## Open next questions
+
+- Supply the eight-field observation ZQY from an actual paid source at the right
+  chronological version. First compare exact coefficient maps, and charge every
+  displaced helper, return and retained observation before extending the caller.
+- Carry a larger coupled state past this rank-eight residual with a declared
+  volume and eventual exit cost. The fixed eight-mode-only feed is rejected;
+  more seeds within its necessary equation cannot repair it.
+- Implement the propagated corrections if decoding is delayed past the thin
+  query. The trace retains both query observations and the second helper defect;
+  the native-return identity alone does not close this obligation.
+
+Structured first steps and blockers are in [TASK.json](TASK.json).
+
+## Credit
+
+Dillon Amburgey / dillona: PR5402 unrestricted provider, helper basis and literal
+physical mode maps; PR4933 physical normalizers and coded-caller lineage. Ali
+Romman: PR5383 cache identities, PR5411 native inverse, PR5398 caller and current
+caller investigation. Chris R / Clear1nsight: PR5407 independent provider audit,
+PR5400 successor audit and PR5413 neutral completion. Cao Yifan / intqwq: PR4610
+native word; Dugongue / mdumitrean: center-free code; Cinna Davis /1337isnot1337:
+helper/controller construction; Ryanson Jonathan, Jacob Alan Sussman, zxv and
+the complete native/Clifford/compiler/analytic lineage retain their source
+credit. The frozen [provider proof](inputs/PROVIDER-PROOF.md) retains its exact
+source text and [complete provider attribution](inputs/PROVIDER-ATTRIBUTION.md). New contracts, transport calculation and witness/checker by zxv
+with substantial OpenAI Codex assistance, no subagents; Apache-2.0.