Refresh R437/OQ4 adapter and bind actual rank26/COPY515 physical returns

research/r437-oq4-caller-binding/.gitattributes

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+inputs/** -text -diff
+R437-* -text -diff

research/r437-oq4-caller-binding/BINDING.md

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+# The current source-to-physical boundary
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+
+## 1. Exact source delta
+
+Let S_old be PR3690's R437 source at36ff441 and S_new be the a24f9ff/OQ4
+source. Both catalogues are compiled with the same canonical selected compiler,
+with its exact661-to659 role adaptation. The adapter retains the source checks;
+it does not accept a new catalogue merely because its matrices have equal rank.
+
+The complete ordered records differ exactly at
+
+    18189,18464,18920,19854,20212,27776,27777.
+
+The five MOVE records are stage6, helper role644, family209. Their host chart
+moves from axes22..29 to30..37. Their residual ranks and source event ordinals
+are unchanged. The IDLE records retain their source ordinals and native family
+charts, but change their unused-axis projectors from ranks34/34 to26/42.
+Thus they move32 paid children from34 to26 and32 from34 to42. Counts and rank
+mass are unchanged. This calculation includes owner routes: accepting only the
+new histogram would miss five actual source changes.
+
+All COPY records, their identity common charts, ERASE guards and source ordinals
+are unchanged. This statement concerns the complete ordered request records,
+not equality of incoming dirty payloads. The latter retain the all-function
+COPY contract proved in PR3936/3950. The selected source's original661-role
+Catalogue still rejects the new source; our adapted Catalogue authenticates
+the complete current word/template/profile/digest before use.
+
+The old-data positive control enforces its own exact old word/template/profile
+and ordered digest using the same retained compiler. It is not an independent
+implementation of that compiler. A discovery-only exploratory run determined
+the new digest; the committed adapter has no discovery or disabled-guard path.
+Replays recompute the catalogue against the frozen digest and reject the old
+digest on new data. SOURCES.json records complete source identities.
+
+## 2. The real two-level generated program
+
+Choose current native IDLE27776 and common COPY1603. The first is the actual
+new rank26 idle in window6/family209; the second is stage0/position22014,
+frame515/centre475. Each source code comes from the full current Specifications
+table, its actual chart and the canonical LowCodes scheme. No two-label
+replacement vocabulary or synthetic ancestor is used.
+
+For each request choose low matrix equal to the inverse of its actual
+preparation modulo3. Native preparation includes the family chart. Hence the
+compiled unweighted projector is the leading-coordinate projector of its
+stated rank. With w=1, zero high fields and root unit2, all incoming diagonal
+weights remain2. Diagonal scalar conjugation leaves the projector unchanged;
+every good pivot equals1. The required good child coefficients therefore equal
+2. Coordinates0 and90 in the second child test that independently stated
+identity through the actual generated callback.
+
+The exact generated steps are
+
+    ROOT width2048, unit2, depth0
+      -> (good, actual IDLE27776 code, rank26): width832, depth1
+      -> (good, actual COPY1603 code, rank7): width91, depth2.
+
+Indeed832=26 floor(2048/64), and91=7 floor(832/64). Both widths exceed the
+64 cutoff; neither step is merely a terminal descriptor example. The encoded
+program contains the two actual source codes, ranks, flags and parent/child
+widths. The current COPY prefix is appended after the frozen ancestor field.
+The old rank34 label paired with the current ancestor code rejects at
+`actual selected rank`; the other actual COPY label in the current prefix
+rejects at `original global raw-field code`.
+
+This is an admissible generated source *grammar* instance, not a claim that
+the root's native family209 is literally followed by a stage0 COPY in one
+flat global schedule. The outer IDLE central recursive child runs another
+selected node, which has its own local source vocabulary. We test this nested
+descriptor/caller boundary, while the complete recursive node body is not run.
+
+## 3. What the physical protocol establishes
+
+For a complete source call of parent width n and child width c, the good
+chunks are the first c head atoms and their reflected tail partners. The
+existing Layout.child_extents emits
+
+    B'=B,  G'=G*A^(2(n-c)),  S'=S,
+
+with U in its separate row port. Thus
+
+    Z*U*B'*G'*S'*A^(2c) = Z*U*B*G*S*A^(2n).
+
+This is the whole-packet volume identity; it does not discard spectator
+addresses or replace U by U*B. The actual fixture checks the encoded grants
+
+    (prefixes,U,B,G,S) = (2,11,2,5*3^2432,3)
+    and then             (2,11,2,5*3^3914,3).
+
+Both equal prefixes are generated by the canonical directory producer with
+their separate ordinals. It is not a deduplicated header set.
+
+Machine.prepare_child checks that the event names the same parent Program
+object, current source code and active geometry code. It copies current,
+directory, extended program, prefix count, U and all three extents into fixed
+handoff ports. CALL writes the exact successor PC and numerical-role labels,
+parks the parent streams and numerical state, then installs the child grants.
+The tested current source codes use this unchanged path.
+
+On protected complete_return, the child frame is closed before inverse
+parking. The result stays in its distinct output port while numerical and
+stream parents restore; it is then transferred to current. Two nested returns
+recover the child-parent successor4 and root successor1, without replaying a
+prefix. Snapshot checks cover exact numerical objects/bytes/heads and every
+canonical role. Additional audits include erased-but-allocated numerical slots
+and template heads; clearing live content alone is insufficient.
+
+Within the child parent, the actual COPY dispatch preserves stage475, clones
+into copy_source, transfers the returned residual output to private stage659,
+and feeds all 63 actual literal XOR readers before clearing it. Each reader
+uses the unchanged physical XOR dispatcher on two complete reduced 23-bit
+prefix fibres. Source and private output remain immutable through all 65
+source events22014..22078. This tests ownership, actual private-result
+consumption and the physical disposal scan.
+
+There is also a uniform consumer implication, independent of the test bits.
+Let x be the borrowed source function and z the correctly completed residual
+result on the same complete packet. For arbitrary, possibly correlated target
+functions y_t, the63 literal readers produce y_t XOR z, preserve x and z,
+and leave every other staged role unchanged. This follows by induction over
+the actual65-event interval: the source/private roles never appear as XOR
+destinations, every target occurs once, and the last event is the matching
+ERASE. Thus a correct completed residual is consumed without another residual
+call or reversed uncompute. If X(V) is the completed physical XOR tariff,
+retain the full bill `C_residual +63*X(V)+C_copy/transfer(V)+C_disposal(V)+gamma_window`.
+Only under the retained linear XOR/copy/transfer contracts and admitted
+metadata bounds does the extra consumer work simplify to O_q(V). The probe
+tests this actual consumer using controlled z; it does not supply z's complete
+residual contract or erase its cost.
+The transported equality guard itself is checked over the complete literal
+controller census; the controlled bit transformation is not a claim that it
+equals the semantic COPY map. Three malformed physical gates reject before
+handoff mutation, followed by exact parent/scratch checks.
+
+These checks establish actual bound protocol execution at the finite stated
+context. **They do not establish a full residual body or global node.** The
+input is46 bits with an explicitly controlled fibre23, outputs are declared test stimuli, stock11 is a controlled
+fixture, and the receipt's global macro count is0. The complete volume at
+the encoded root would be660*3^4096 bits. Native gather/route, the adapter
+sweeps, complete primitive calls and the ordinary padded wrapper are not
+executed on that volume by this probe.
+
+## 4. Uniform caller substitution: the remaining hypotheses
+
+A complete production source binding would use the actual current topology,
+Specifications and SelectedBinding in macro_code.compile_node. Its loop order
+is schedule, replica, low class, literal event. That finite compiler accepts
+only q-dependent labels and emits the same fixed block vocabulary for every
+input width/precision; all 64-dimensional low classes are a fixed finite
+set for a fixed q. The full expansion is effective but enormous. This package
+does not pretend that a sampled class is that complete emitted tuple.
+
+The source-relative structural implication is as follows. Suppose each emitted
+NODE, GATHER_ROUTE, RESIDUAL_BEGIN, ordered sweep/leaf, CHILD, route/scatter,
+XOR, bridge and exchange has its stated complete Boolean/ownership contract
+on admitted encoded inputs; suppose the numerical source callback supplies
+the actual source-bound coefficients at every frozen history; and suppose
+the existing parking codecs preserve the encoded parent at each matched cut.
+Then induction over the finite emitted word and decreasing-width recursive
+tree gives the current caller contract. COPY introduces an owned clone and
+the transported guard clears its owned result; it never projects arbitrary
+dirt away. At a recursive cut the capsule volume identity above supplies
+exactly the complete child input, and protected return supplies its one
+substitution. The five chart changes and two idle changes are consumed by
+the current authenticated bindings, rather than inferred from rank alone.
+
+This implication is not an independent proof of its primitive, callback,
+stock or source-level premises. The main physical-contract map still marks
+the inherited universal refinement partially reviewed. Its archival presence
+does not certify the all-width current program. A uniform source/native/router
+cohort must discharge or explicitly retain these premises and connect all
+constructors at one source; the bounded probe does neither by itself.
+
+## 5. Complete cost boundary
+
+Let T(j,w) be the inherited uniform completed-child cost per *complete payload
+bit*, including coefficients, owned output, restoration and head returns.
+PR3950 supplies the rank7 low-class bound
+
+    delta7 <= min(1,448*(q-1)/(q*(q-2))).
+
+Retaining its completed good/fallback contracts, the residual cover bill is
+
+    T(7f,w)+delta7*49911*max_(1<=j<=f)T(j,w)
+       + A_q*(f+leaf_toll(w)+1) + gamma_orig/(N*v).
+
+Here gamma_orig includes encoded source/history/Count preparation, transfer
+and cleanup not already charged by completed primitives. The initial clone,
+output commits and final disposal remain paid. Gather/route/scatter and the
+containing node's producer/wrapper work remain additional. Neither N low
+classes nor repeated high prefixes create an extra coarse-child factor;
+normalization is by the full complete cover volume N*v.
+
+At source-admitted q>2^80 the bad fraction fits10^-16. The familiar cheap
+local toll additionally needs the canonical root/history, numerical preparation
+and backend reserve arguments. This package does not supply them merely by
+changing the request digest. The fixture's q=3 is not an admitted exponent
+parameter and its finite parking instruction counts are not an asymptotic
+constant. No ordinary/native/router tariff is inferred from them.
+
+For storage retain the full logical frame envelope M_j, the fixed owned
+role/backend inventories, current and protected output, and the complete active
+parking stack. Only if the inherited admitted bounds prove
+
+    sum_j M_j <= C_q*V_root + F_q
+
+does the same fixed-role source lowering have O_q(V_root)+F_q visited cells.
+All physical inventories must include cleared-but-visited backing, markers and
+templates. A live-state snapshot or peak10 scratch leases does not prove
+this uniform bound, the sharp logical coefficient11, or a reserve of nine
+family packets. Interruption recovery is also outside this successful-return
+contract. These are precise remaining obligations, not costs set to zero.
+
+## 6. Attribution and next useful result
+
+The adapter comparison extends zxv/PR3690's exact source adaptation and
+controlled return. The physical protocol, source compiler and proofs remain
+David Arias/Jose Manuel/ywz65 and their retained lineage; R437/OQ4 remains
+ai-nanachi and credited predecessor work. PR3936/3950 supply the immediate
+all-function and conditional-cost boundary. Full notices are retained.
+
+The next substantive result is the complete production constructor/refinement
+join at this authenticated current catalogue, including actual native/router
+consumers, original-width stock and root/precision constraints. Another finite
+controlled return would add coverage, but would not discharge that join.