diff --git a/research/native-helper-query-bank/ATTRIBUTION.md b/research/native-helper-query-bank/ATTRIBUTION.md
new file mode 100644
index 0000000000..51041de841
--- /dev/null
+++ b/research/native-helper-query-bank/ATTRIBUTION.md
@@ -0,0 +1,57 @@
+# Source credit and distinct addition
+
+The fixed source word and all its native/compiler/precision lineage are retained.
+New work is Apache-2.0 with substantial OpenAI Codex assistance for Dillon /
+dillona; no independent human or formal-kernel acceptance is asserted.
+
+- **Cao Yifan / intqwq, PR #4610**: round-three joint-helper/native-map word,
+  retained as `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz` and the
+  source payload consumed here.
+- **Dugongue / mdumitrean, PR #4929**: exact center-free producer, helper-clean
+  pre-compensation, explicit eight-mode code and all-width free-group proof in
+  `research/native-center-free-code/`. This package replays its complete forward
+  word; it does not claim center deletion or helper-clean endpoints as new.
+- **Cinna Davis / 1337isnot1337, PRs #4694 and #4698**, and the **PR #4470**
+  controller/native-helper lineage: center-free cache kernel, cold-helper
+  observations, physical helper normalization and explicit helper-basis methods.
+  The present full first-departure basis is a new application of that lineage,
+  not a claim to invent scalar helper recoding.
+- **Dillon / dillona, PR #4933**: exact real R-centralizing normalizers and their
+  signed phases, literal monomial lowering, physical coded interface and
+  all-width lift conventions in `research/coded-native-caller/`. Those K words
+  and the credited Clifford implementation are pinned and reused here.
+- **Chris R / Clear1nsight, PR #4931**: actual helper496 paid-prefix split and
+  ownership discipline. It supplied the source-history positive control and
+  motivation for using an existing chronological response. This package's
+  selected112 responses need no paid split.
+- **Dillon / dillona, PR #5126**: sharp standalone local-query count; its grammar
+  does not include this internal paid-history interface. We do not present this
+  interface as a counterexample to that scoped result.
+- **zxv, PR #5283**: exact Gaussian cache reuse requires the matching live row,
+  unchanged independent returns and full costs. The present package supplies
+  explicit rows and return decoding for one native interface, while preserving
+  that distinction from a completed caller.
+
+The retained source proofs also credit DaysSky, Nick Petalas, Ryanson Jonathan,
+Jacob Alan Sussman, zxv and the scalar, Clifford, precision, compiler and outer
+construction contributors. Their attribution and notices in the unchanged
+predecessor directories remain applicable. No predecessor archive is copied or
+rewritten by this package.
+
+The distinct result is the invertible **358-by-358 matrix of actual chronological
+first departures**, selecting **112 funded H1 observations of common Q** with
+literal exact phases, together with **26 H5 + 6 H1** cold-return completion,
+full 358-input decoding, unchanged 50-hot-helper return contract, and explicit
+ordinary work and owned observation storage. The entrance-prologue extension
+relocates those same children, using exact first-departure identities and
+whole-field swaps with chart transport. It adds explicit storage and movement,
+with the same Gaussian calls. That interface remains separate from the
+still-unproved main/helper caller.
+
+Submission checkpoint: canonical `1ec1119972c9aefe42525172d07b332fcff81cb4`;
+source-manifest baseline: `7c472563474e60185e6ca101a17622133d047e56`;
+scientific source freeze: `a5df48c55ea806d7952b65acc9c76d878ff09b13`.
+The sources are already retained in canonical history, and exact live file pins
+are in `SOURCES.json`. Coordination and overlap were reviewed by the parent
+paid-history campaign in Discussion #4930 before this package was assigned;
+this subtask did not reroll the research card or take over a concurrent claim.
diff --git a/research/native-helper-query-bank/BANK.json b/research/native-helper-query-bank/BANK.json
new file mode 100644
index 0000000000..91a6c7a5f3
--- /dev/null
+++ b/research/native-helper-query-bank/BANK.json
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diff --git a/research/native-helper-query-bank/HOIST.json b/research/native-helper-query-bank/HOIST.json
new file mode 100644
index 0000000000..10b41d46b1
--- /dev/null
+++ b/research/native-helper-query-bank/HOIST.json
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diagonal K maps, before the existing T-inverse program.","raw_observation_rows_checked":112,"recipe_semantics":"Ordered patch recipe, not a standalone instruction stream.","rejected_controls":["wrong held query argument","swap without physical chart transport"],"replacement_cuts":[[14744,224,2,633],[14746,225,2,634],[14748,226,78,635],[14750,227,78,636],[14752,228,89,637],[14754,229,89,638],[14756,230,29,639],[14758,231,29,640],[14760,232,94,641],[14762,233,94,642],[14764,234,59,643],[14766,235,59,644],[14768,236,9,645],[14770,237,9,646],[14772,238,83,647],[14774,239,83,648],[14962,240,72,649],[14964,241,72,650],[14966,242,73,651],[14968,243,73,652],[14970,244,92,653],[14972,245,92,654],[14974,246,93,655],[14976,247,93,656],[14978,248,65,657],[14980,249,65,658],[14982,250,64,659],[14984,251,64,660],[14986,252,12,661],[14988,253,12,662],[14990,254,13,663],[14992,255,13,664],[15180,256,74,665],[15182,257,74,666],[15184,258,4,667],[15186,259,4,668],[15188,260,27,669],[15190,261,27,670],[15192,262,91,671],[15194,263,91,672],[15196,264,63,673],[15198,265,63,674],[15200,266,96,675],[15202,267,96,676],[15204,268,81,677],[15206,269,81,678],[15208,270,11,679],[15210,271,11,680],[15398,272,14,681],[15400,273,14,682],[15402,274,102,683],[15404,275,102,684],[15406,276,58,685],[15410,278,33,686],[15412,279,33,687],[15414,280,105,688],[15416,281,105,689],[15420,283,19,690],[15422,284,40,691],[15424,285,40,692],[15426,286,79,693],[15428,287,79,694],[15616,288,103,695],[15618,289,103,696],[15620,290,56,697],[15622,291,56,698],[15624,292,104,699],[15628,294,57,700],[15630,295,57,701],[15632,296,20,702],[15634,297,20,703],[15638,299,42,704],[15640,300,21,705],[15642,301,21,706],[15644,302,41,707],[15646,303,41,708],[15834,304,100,709],[15836,305,100,710],[15838,306,50,711],[15842,308,34,712],[15846,310,87,713],[15848,311,87,714],[15850,312,47,715],[15852,313,47,716],[15856,315,109,717],[15858,316,26,718],[15860,317,26,719],[15862,318,37,720],[15864,319,37,721],[16054,320,51,722],[16056,321,51,723],[16058,322,36,724],[16062,324,52,725],[16066,326,35,726],[16068,327,35,727],[16070,328,110,728],[16072,329,110,729],[16076,331,24,730],[16078,332,111,731],[16080,333,111,732],[16082,334,25,733],[16084,335,25,734],[16274,336,8,735],[16278,338,84,736],[16282,340,77,737],[16286,342,3,738],[16288,343,3,739],[16290,344,95,740],[16292,345,95,741],[16296,347,60,742],[16298,348,30,743],[16300,349,30,744]],"replacement_cuts_checked":112,"schema":"native-helper-query-hoist/1","source_paid":{"1":2201,"2":412,"3":510,"4":127,"5":40},"source_readout_boundary":"Observation copies are tracked raw; the same 112 exact-phase O_s identities normalize them independently.","splice":{"after_prologue":"Execute BANK.json entrance_scalar_program on the cold owners.","after_source":"Apply unchanged BANK.json cold_completions, exit_scalar_program and inverse K maps.","observation_clears":"The final 112 recipe items are consumer obligations after each observation last use.","prologue_items":672,"source":"research/native-center-free-code/CODED-WORDS.json.gz:programs.forward","source_events":"Replay every original source event in order; replace only the listed child events by their tagged SWAP and owned CLEAR."},"status":"PASS_EARLY_112_FUNDED_HELPER_QUERIES"}
diff --git a/research/native-helper-query-bank/PROOF.md b/research/native-helper-query-bank/PROOF.md
new file mode 100644
index 0000000000..7ae6b095a2
--- /dev/null
+++ b/research/native-helper-query-bank/PROOF.md
@@ -0,0 +1,313 @@
+# A forward native paid-history interface on independent helper inputs
+
+## Fixed source and precise scope
+
+Use the center-free forward word in the pinned `CODED-WORDS.json.gz`, with
+632 arbitrary independent inputs: 112 X, 112 Y and 408 helpers. Its predecessor
+proves, over the rational free-group algebra of the native warp symbols,
+
+    (X,Y,H) -> (X,Y+A X,H),
+
+with the original physical entrance and exit frames. Here
+`A=I-MM^T/4`, `M^T M=56I`, is the center-free producer's code. This package does
+not change A. The independent helper block and zero helper-to-main blocks are
+essential. Our verifier regenerates and checks all 632 endpoint rows against
+that identity, rather than trusting a stored prefix registry. It also checks the
+6,596-instruction source offset and exact center-deleted source suffix.
+
+The inherited physical rule is: a normalized logical term `a H_j` with native
+word W, in physical chart F, acts as
+
+    a F W F_birth(j)^-1 H_j.
+
+The rational coefficient stays outside the lifted address operator. Source
+`phase`, `adapter` and `residual_adapter` markers use the authenticated native
+physical implementation and the predecessor theorem; they are not newly proved
+by the symbolic interpreter. The source has one owned center temporary, cleared
+at exit; no persistent owner is erased.
+
+This result concerns the **forward** word only. In particular the raw-dual
+backward word, conjugated frames and the main X-only Q-squared correction are
+not supplied by reversing the observation list. A future bidirectional caller
+must prove those obligations separately.
+
+## The scalar first-departure basis
+
+Let J be the ordered set of 358 helper owners whose initial chart is empty.
+Let the other 50 helpers be called hot only to distinguish their nonempty birth
+charts; their inputs are also arbitrary and independent.
+
+For each j in J, stop immediately before that owner's first paid climb. Direct
+source replay proves:
+
+1. its current chart is empty;
+2. its row contains only inputs in J;
+3. every native word in that row is empty.
+
+Write that row as `sum_k T[j,k] H_k`, with rows and columns indexed by the same
+increasing list J. Thus T is an actual scalar matrix of chronological
+first-departure observations; its rows need not occur at one simultaneous cut.
+`BANK.json` lists every entry. Exact elimination and both product identities
+prove that the entire 358-by-358 matrix is invertible. T has 2,242 nonzero
+entries; its inverse has 3,206. This statement includes every cold helper input,
+not merely the selected query subspace.
+
+The deterministic elimination uses 2,949 ADDs, 117 SCALEs and 87 swaps. Each swap
+is emitted without scratch as
+
+    a += b; b -= a; a += b; b *= -1.
+
+The resulting 3,210 ADDs and 204 nonzero SCALEs implement T^-1 in place.
+Reversing them and reciprocating SCALE coefficients implements T. The checker
+executes both literal programs on all 358 independent input columns and checks
+both inverse identities. These operations preserve all input information; none
+uses a productive helper as an erased temporary. The coefficients are fixed
+rationals, including odd denominators. This is an ordinary scalar program, not
+a claim of free exact division in the eventual integer multiplier.
+
+## The selected common-Q responses
+
+Among the first departures, exactly 198 are already funded H1 children on odd
+noncharacteristic lines, and their original helper endpoints have rank nine.
+Choose the earliest 112, ordered by the emitted forward event index. Their
+helper owners, zero-based event indices in both words, first chart and line q
+are in `BANK.json`. Every selected row is an independent row of the full T.
+
+Let Q be the rank-one native Gaussian C gate on the first of the nine axes,
+and R the full nine-axis Gaussian. For selected slot s, use the real signed
+monomial K_s inherited from the phase-correct normalizer construction, so
+
+    K_s R K_s^-1 = R.
+
+Let E_s be the actual first-departure frame for that slot. Define the monomial
+response map
+
+    O_s = Q K_s^-1 E_s^-1.
+
+For every selected slot the verifier proves that K_s and O_s have Fourier rank
+zero, compiles them into literal P/D/X/phase-only words, and checks
+
+    O_s E_s K_s = Q
+
+by the signed tableau **and** the complete exact zero-column amplitude. The
+latter fixes the absolute phase left undetermined by a tableau. The full
+R-commutator is checked by the same exact method. No Gaussian call occurs in
+these wrappers. The unselected diagonal entries of D_K are the identity.
+
+The input contract is 358 independent fields ξ, plus the original arbitrary
+main and hot-helper fields. Before the source word:
+
+    H_J = T^-1 D_K ξ.
+
+Execute the diagonal K maps, followed by the emitted T^-1 scalar program. The
+selected first-departure row is then `(T H_J)_s = K_s ξ_s`. The existing paid
+H1 child produces `E_s K_s ξ_s`. Immediately after that actual event, COPY the
+field into a distinct owned zero field and apply O_s to that copy. It is exactly
+`Q ξ_s`. The persistent native owner continues along its original paid path.
+This adds **no Gaussian child and no paid split** to obtain the observation.
+
+In this chronological version, each response becomes available after its listed
+event and may be retained until the source word finishes. The following exact
+rescheduling makes every response available in an entrance prologue instead.
+In both versions, observations are owned copies of existing paid history, not
+independent input jobs or extra productive credit.
+
+## An entrance prologue with the same 112 paid children
+
+After the diagonal K maps, but **before** the existing T^-1 scalar program,
+the cold coordinates are `w=D_K ξ`. For each selected coordinate s:
+
+1. Initialize a new owned raw field and COPY `w_s` into it.
+2. Execute the complete adapted H1 child from the listed source event on that
+   field. Its physical value is `E_s w_s`. This is the original child relocated,
+   not a second invocation or a bare C gate without its source adapters.
+3. COPY its value into the owned observation field and apply the already
+   compiled monomial O_s. This gives `Q ξ_s` immediately. Keep the raw field
+   `E_s w_s` unchanged for its later replacement cut.
+
+Now execute T^-1 and the source word, omitting the 112 selected child events.
+At such an event the original persistent field has chart zero and value
+
+    (T T^-1 w)_s = w_s.
+
+The first-departure proof establishes this identity on every original input;
+it contains no main-input coefficient. SWAP that entire physical field with
+its stored raw field, **transporting the chart tags with the data**. The
+persistent field now has exactly the chart E_s and value E_s w_s that the
+omitted original child would have produced. The owned raw slot contains the
+old duplicate w_s in chart zero; CLEAR that owned slot. No persistent field is
+cleared, and its input information remains in the invertibly transformed
+E_s w_s. A whole-field permutation works between these two charts; it is not
+the three-ADD common-chart swap used by the scalar basis program.
+
+All other source instructions are unchanged. Induction at the 112 replacement
+cuts therefore restores the complete source state, with exactly its original
+paid inventory. Completion and return decoding below apply unchanged. All
+responses are available after the 112 prologue children, before the original
+native operations and even before T^-1. This is an early-query interface, not
+a claim that the prologue has zero cost.
+
+The helper arguments are fixed before the prologue and thereafter follow only
+the declared basis program and source word. A caller may recode its **main**
+entrance values after receiving the responses: the replacement identities hold
+for arbitrary main values and have zero main coefficients. Such a recoding
+changes the main input to which the producer contract applies. It does not
+automatically preserve a caller's original jobs. Later interventions in the
+native word, changes to helper arguments, or mutation of held raw fields require
+a new integrated proof.
+
+[HOIST.json](HOIST.json) emits an **ordered patch recipe**, not a standalone
+instruction stream. After its prologue, insert the existing BANK scalar
+T^-1 entrance program. Then replay the pinned forward source in order, replacing
+only the listed child events and retaining every intervening source segment.
+Afterward apply the unchanged BANK completion and return decoder. The final
+observation clears are obligations after the consumer's last use.
+The verifier executes that program on all 632 original inputs and 225 arbitrary
+owned inputs (the native center, 112 held raw fields and 112 observation fields).
+It checks all 112 replacement cuts, every persistent endpoint, unchanged paid
+counts, and clearing of every owned input. Observation copies are tracked in
+their raw representation; the independent signed-tableau and absolute-phase
+identities above verify their O_s readouts. The native word never reads those
+copies, so normalizing them immediately cannot affect the replay. Wrong held
+arguments and a swap that fails to transport chart tags are rejected.
+
+## Returning every independent helper
+
+At source termination, the old cold-helper target census is
+
+    26 H4 + 6 H8 + 326 H9.
+
+The other 50 helpers have targets `2 H4 + 7 H7 + 41 H8`. Rank means the dimension
+increase from that helper's actual birth chart, not just its exit-frame rank.
+The hot helpers remain completely unchanged in this package.
+
+The scalar decoder T cannot be applied while different cold fields still carry
+different physical Gaussian frames. For every cold owner j of original rank
+r<9, append the operator
+
+    C_j = R F_final(j)^-1.
+
+The verifier compiles C_j into a monomial wrapper, one contiguous standard
+Gaussian block of rank 9-r, and a monomial wrapper. It checks the exact signed
+tableau and phase of the compiled word, and `C_j F_final(j)=R`. The explicit
+32 recipes cost **26 H5 plus six H1**, with at most 64 monomial wrapper maps.
+The 326 original H9 outputs already equal R H_j. The whole cold bank is now
+uniformly `R H_J`.
+
+Apply the literal T program, then the diagonal K_s^-1 maps. Scalar owner maps
+commute with the same R on every owner, and K_s commutes with R, so the output is
+
+    D_K^-1 T R T^-1 D_K ξ = R ξ.
+
+Every one of the 358 input coordinates is returned as its independent H9 job.
+No original helper information is discarded or replaced by a main input. This
+changes the target contract for the cold bank to 358 H9 jobs; it does **not**
+claim that the old ordered H4/H8 target list survives the mixing unchanged.
+Together with the unmodified hot bank, the new target profile is
+`{4:2,7:7,8:41,9:358}`. The added target rank mass and added paid rank mass are
+both 136. The main coded endpoint remains exactly the source endpoint, because
+its helper-to-main blocks vanish for all original helper values, and all new
+exit operations act solely on helpers or owned observation copies.
+
+## Ownership and ordinary work
+
+The source retains its original persistent owners and owned center temporary.
+The scalar basis programs operate reversibly in place on all 358 cold fields.
+They require no additional basis scratch. The observation interface owns at
+most 112 extra fields. Each is initially cleared, receives one COPY after its
+specified H1 event, then receives its response monomial map. At an interface
+return these fields contain the promised responses and the recipient owns them;
+a completed caller must CLEAR them after their last use. The ordinary-work
+invoice includes those terminal clears. A demonstration that simply clears all
+responses at the end leaves only the independent original jobs, without
+turning the observations into productive outputs.
+
+Additional field passes for the chronological version, relative to the pinned
+center-free producer:
+
+| Operation | Count |
+|---|---:|
+| Scalar ADD | 6,420 |
+| Scalar SCALE | 408 |
+| Diagonal basis monomial maps K and K^-1 | 224 |
+| Observation monomial maps | 112 |
+| Completion monomial wrapper maps | at most 64 |
+| Owned observation COPY | 112 |
+| Owned observation initial CLEAR | 112 |
+| Owned observation terminal CLEAR | 112 |
+| Extra simultaneously owned fields | at most 112 |
+| Paid completion children | 26 H5 + 6 H1 |
+
+For the entrance-prologue version, keep the same scalar, monomial and completion
+counts. Replace the observation-storage rows by **224 owned COPYs, 448 owned
+CLEARs, 112 whole-field SWAPs and at most 224 extra simultaneous fields**. These
+totals include observation creation and the recipient's final observation
+clears. Each SWAP requires ordinary movement of two complete fields. Thus the
+prologue adds 112 copies, 224 clears, 112 swaps and 112 held
+fields over the chronological interface, with **zero additional scalar passes
+and zero additional Gaussian children**. Copying the selected w coordinates
+before T^-1 avoids reconstructing the dense T rows afterward. The source's
+original owned center remains separately charged as before.
+
+A monomial field map is the complete emitted P/D/X/phase word, not a single
+machine instruction; its indexed movement and phase arithmetic must be priced
+using the retained source implementation. Each rational ADD/SCALE must likewise
+be implemented at the chosen precision. The lists are fixed finite programs,
+so they admit width-independent algebraic suffix bounds: charge each scalar
+ADD or SCALE coefficient c the bound `1+|c|`, and each unitary, whole-field SWAP
+or owned COPY/CLEAR the bound one in maximum-over-fields Euclidean fiber norm. The finite
+product bounds propagation of local rounding errors. This is a local existence
+bound, not a complete precision allocation, optimized ordinary-work tariff or
+outer multiplication budget. The new Gaussian children also require the source
+Gaussian implementation and its normal costs.
+
+## Every positive digit width
+
+For f positive, evaluate the source rational free-group identity at the actual
+consistent native operators on the f digit columns, as in the pinned
+`CODED-PROOF.md`. The same exact first-departure rows have empty words, hence
+the same scalar matrix T. All coefficients remain scalar owner coefficients;
+T is **not** raised to a tensor power.
+
+Independently lift each one-column physical word K_s, O_s, E_s, R and C_j to its
+columnwise f-fold operator, with spectator coordinates unchanged. Exact
+operator composition identities lift under this tensor operation. P and X act
+columnwise, diagonal Z4 phases sum over columns, and a one-column global phase
+`i^gamma` becomes `i^(f*gamma)`. Keeping that phase unchanged would be wrong.
+The signed-tableau plus absolute-phase checks establish the one-column
+identities, and the emitted literal words fix this lift unambiguously.
+
+Finally evaluate the same finite scalar owner programs in the algebra of these
+lifted address operators. This gives `O_s,f E_s,f K_s,f = Q_f`, and the completed
+return identity `D_K,f^-1 T R_f T^-1 D_K,f = R_f` at every f. It never asserts
+that tensor powers preserve sums. Thus the ABI is an all-width consequence of
+explicit fixed scalar programs and inherited source semantics, not merely a
+512-dimensional numerical experiment.
+
+The hoist uses those same evaluated first-departure identities. COPY and SWAP
+move complete f-column fields, with their frames, and the relocated child is the
+same lifted E_s. Hence the equality at each replacement cut and the source-state
+induction hold at every f as well. Neither scalar T nor an owner sum is tensor
+powered in this rescheduling argument.
+
+## Evidence boundaries
+
+The registered verifier authenticates every live source file before importing
+source code. It regenerates all 632 forward rows and all 358 first departures,
+checks the entire scalar basis, emits and checks 112 response words and 32
+completion words, and compares the deterministic receipt. It also rejects:
+main-input contamination of a claimed helper-only departure; a singular basis;
+a phase-only wrong response with the same tableau; and omission of a required
+cold-H8 completion. These checks use explicit exceptions and also run under
+Python `-O`. The additional hoist replay checks all 857 raw-state input columns,
+the 112 matching physical replacement cuts, the unchanged Gaussian inventory,
+and the two rescheduling controls described above.
+
+The inherited native physical compiler and multiplication analytic hypotheses
+are not independently audited here. No full historical suite, selected cold
+replay, hosted CI or formal-kernel acceptance is claimed. A complete caller must
+still put the required main arguments into this interface without losing any
+independent helper input, establish both directions actually used, clear all
+owned observations, and pay storage, precision, ordinary work and the outer
+budget. Until then the result is an exact reusable forward paid-history ABI,
+not an admitted supplier or a new exponent.
diff --git a/research/native-helper-query-bank/README.md b/research/native-helper-query-bank/README.md
new file mode 100644
index 0000000000..f33da4dde9
--- /dev/null
+++ b/research/native-helper-query-bank/README.md
@@ -0,0 +1,95 @@
+# 112 common-Q observations inside a paid native helper history
+
+This forward interface exposes **112 common rank-one Gaussian responses on 112
+independent helper inputs**, using 112 existing paid H1 children of the
+center-free native producer. An explicit invertible basis on all 358 cold helper
+inputs removes the other-helper contamination at those chronological cuts. The
+coded main endpoint is unchanged, and every independent helper input is returned.
+An exact rescheduling can expose all 112 responses in an **entrance prologue**,
+before the original native operations, while preserving the same paid inventory.
+
+The observations add no Gaussian child or split. **Return decoding does add
+26 H5 and six H1 children.** It upgrades the 358 cold helper jobs to H9, and leaves
+the other 50 helper jobs unchanged. It does not retain the old helper target
+profile. The full local profiles are:
+
+| Profile | Before | After this interface |
+|---|---|---|
+| Paid children | `{1:2201,2:412,3:510,4:127,5:40}` | `{1:2207,2:412,3:510,4:127,5:66}` |
+| Independent helper targets | `{4:28,7:7,8:47,9:326}` | `{4:2,7:7,8:41,9:358}` |
+| Added paid rank mass | — | 136 |
+| Added productive observation jobs | — | 0 |
+
+The 112 copied responses are dependent observations, not additional productive
+jobs. Their 112 owned storage fields, 112 copies, 224 initial/terminal clears,
+6,828 scalar passes and at most 400 monomial field maps are explicit ordinary
+work, additional to the producer's existing work and 32 new Gaussian children.
+The scalar programs include fixed rational coefficients with odd denominators;
+no free exact-division operation or complete finite-precision tariff is assumed.
+Those counts describe observation at the original cuts. The early version uses
+224 owned fields, 224 copies, 448 clears and 112 whole-field swaps instead;
+its scalar, monomial and paid-child counts are unchanged.
+
+**This is a forward observer ABI, not a complete Gaussian caller or a new κ.**
+In particular, its arguments are independent helper inputs. Substituting main
+inputs for them still requires a caller that restores all displaced helpers.
+No backward observation interface is asserted.
+
+[PROOF.md](PROOF.md) gives the exact input/output contract, chronology, all-width
+argument and bill. [BANK.json](BANK.json) contains both 358-owner scalar programs,
+all query cut indices and literal phase-correct words, and all 32 completion
+recipes. [HOIST.json](HOIST.json) records the entrance prologue and the exact
+112 source-event replacements. [ATTRIBUTION.md](ATTRIBUTION.md) records the
+predecessor work.
+
+## Reproduce
+
+Only Python 3.12 and its standard library are required, in a full Git checkout:
+
+```sh
+python3 scripts/research_package.py --package research/native-helper-query-bank --check-only
+python3.12 scripts/research_package.py --package research/native-helper-query-bank
+```
+
+The bounded registered replay runs the verifier normally and with `-O`. Direct
+replay is `python3.12 -I -B research/native-helper-query-bank/verify.py`.
+It authenticates the source files, regenerates all 632 endpoint rows and 358
+first departures, checks the full scalar basis, checks exact signed Clifford
+tableaux and absolute phases for all 112 responses and 32 completions, and
+rejects four base semantic mutations. A second replay tracks all 632 original
+and 225 arbitrary owned inputs through the hoisted schedule, checks all 112
+replacement cuts and unchanged paid counts, and rejects two rescheduling
+mutations. The observation readout phases are checked separately from their raw
+copied rows. It compares parsed receipts without writing. The explicit authoring
+option `--write` regenerates `BANK.json` and `HOIST.json`.
+
+Local verification on 2026-10-23 passed the metadata check and both registered
+replays under Python 3.12.15 on macOS 27.0.1 arm64. The normal and optimized
+replays, including the entrance-prologue checks, took 13.20 seconds together.
+The independently regenerated T, T inverse and all 112 cut indices also matched
+the discovery witness. No hosted CI or selected-construction cold replay is
+claimed.
+
+Scientific inputs are unchanged from `a5df48c55ea806d7952b65acc9c76d878ff09b13`;
+the source manifest retains provenance baseline
+`7c472563474e60185e6ca101a17622133d047e56`. The submission checkpoint is canonical
+`1ec1119972c9aefe42525172d07b332fcff81cb4`, checked at 21:54 UTC on 2026-10-23.
+Priority revision 7 is unchanged; the selected conditional result is now
+κ = 0.0030217758 after the PR4610/PR5241 admission. All scientific inputs used
+here are unchanged across that selection update. The native decompressed payload is
+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.
+[SOURCES.json](SOURCES.json) pins every live input. The physical native source
+implementation and its all-width evaluation theorem are explicitly inherited,
+not independently re-proved or accepted by a formal kernel here.
+
+## Open next questions
+
+[TASK.json](TASK.json) records the scoped continuation questions: a chronological
+main-input caller that restores all helpers; an independently checked backward
+interface; and a full storage, finite-precision and multiplication budget after
+caller closure. The present package is an intermediate result in the continuing
+[paid-history investigation](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19154057).
+It does not complete that investigation or claim the selected frontier changed.
+
+Prepared for Dillon / dillona with substantial OpenAI Codex assistance.
+Apache-2.0; predecessor credit is retained.
diff --git a/research/native-helper-query-bank/SOURCES.json b/research/native-helper-query-bank/SOURCES.json
new file mode 100644
index 0000000000..be3a0b69a9
--- /dev/null
+++ b/research/native-helper-query-bank/SOURCES.json
@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/coded-native-caller/NORMALIZERS.json",
+      "usage": "input",
+      "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f",
+      "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da"
+    },
+    {
+      "path": "research/coded-native-caller/PHYSICAL.md",
+      "usage": "input",
+      "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f",
+      "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078"
+    },
+    {
+      "path": "research/coded-native-caller/clifford_exact.py",
+      "usage": "input",
+      "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    {
+      "path": "research/native-center-free-code/CODE.json",
+      "usage": "input",
+      "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae",
+      "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0"
+    },
+    {
+      "path": "research/native-center-free-code/CODED-PROOF.md",
+      "usage": "input",
+      "git_blob": "1f28d33884ec99b34f8366d022d8f7b9b7653ae2",
+      "sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01"
+    },
+    {
+      "path": "research/native-center-free-code/CODED-WORDS.json.gz",
+      "usage": "input",
+      "git_blob": "935fedd9c9a77f870dd6afbabbf56c8ea6e321d4",
+      "sha256": "797bad53122f84aa0f05b602f2bdceb6b50f95a64023799d4f24560d9c61aad6"
+    },
+    {
+      "path": "research/native-center-free-code/SOURCE-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    },
+    {
+      "path": "research/native-center-free-code/native_core.py",
+      "usage": "input",
+      "git_blob": "5d8a8f0a6382c66449f76b6f57bdd380c057ddc1",
+      "sha256": "178ff80824a012970fc9435f122152da03c7e6bdc3a7de12136fe03e05cf24fe"
+    }
+  ]
+}
diff --git a/research/native-helper-query-bank/TASK.json b/research/native-helper-query-bank/TASK.json
new file mode 100644
index 0000000000..85074ec8af
--- /dev/null
+++ b/research/native-helper-query-bank/TASK.json
@@ -0,0 +1,86 @@
+{
+  "schema_version": 1,
+  "task_id": "centre-path-sharing",
+  "priority_revision": 7,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "original_card": {
+    "id": "centre-path-sharing",
+    "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
+      "Prove a lower bound on copied information per call for the selected decoder contract."
+    ],
+    "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
+    "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
+    "allowed_variations": [
+      "One sharing pattern across a fixed number of calls.",
+      "One reduced copied-total contract for the existing decoder.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Removing copies without a replacement contract for the decoder's copied totals.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "centre path",
+      "copied totals",
+      "private temporary",
+      "shared centre",
+      "batching"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Forward paid-history ABI: 112 existing H1 children expose a common Q on 112 independent cold-helper input coordinates, either at their original cuts or in an entrance prologue, with an invertible 358-owner basis and charged completion and decoding of every cold helper return.",
+  "scope_change_reason": "This continues the authorized native-history campaign rather than rerolling the center-sharing card. It isolates an executable information interface needed by a future caller; it does not claim the card acceptance gate or finish the donor objective.",
+  "bottleneck_link": "The center-free producer still has the coded main cross-transfer A. Actual funded native responses may provide the missing caller information, while preserving every original productive helper. This package identifies those responses but does not show that they can receive the necessary main arguments.",
+  "budget_minutes": null,
+  "stop_rule": "This package ends at the exact forward observer ABI, complete local invoice and independently replayable proof. The parent research campaign continues on a full main/helper caller.",
+  "outcome": "partial",
+  "evidence": "verify.py regenerates all 632 endpoint rows and 358 first-departure rows; checks both 358-dimensional basis programs, 112 exact-phase response identities, 32 completion identities and four base mutations. The entrance-prologue replay checks 632 original plus 225 arbitrary owned input columns, 112 physical cut replacements, unchanged paid inventory and two rescheduling mutations. BANK.json and HOIST.json are compared read-only.",
+  "author": "Dillon / dillona",
+  "ai_assistance": "Substantial OpenAI Codex assistance, including separate discovery, package and caller-research agents.",
+  "open_questions": [
+    {
+      "question": "Can required main-caller arguments occupy these helper coordinates while returning all displaced independent helper inputs?",
+      "why_it_matters": "The current query arguments are independent helper inputs; making them main-derived without restoring the original helpers forfeits the productive-job contract.",
+      "first_step": "Use the early responses in one explicit main-entrance recoding, then emit a full chronological caller and prove every original main/helper output row and every owned clear obligation.",
+      "blocked_by": "No complete helper-restoring caller has been proved."
+    },
+    {
+      "question": "Can the same physical interface be supplied for the actual raw-dual backward word?",
+      "why_it_matters": "A multi-stage caller may need both orientations; forward observations alone do not establish backward snapshots or their phases.",
+      "first_step": "Regenerate backward first departures using conjugated physical frames and the X-only Q-squared convention in the credited physical interface; charge any changed children.",
+      "blocked_by": "The present certificate is forward only."
+    },
+    {
+      "question": "Does a complete caller using this bank beat the selected bound after ordinary work, storage and finite precision are charged?",
+      "why_it_matters": "A local response ABI and its paid profile are not a multiplication theorem or an exponent improvement.",
+      "first_step": "After exact caller closure, price all scalar and monomial passes, observation lifetimes and rational rounding in the compiler ABI, then compute the full moment.",
+      "blocked_by": "Complete caller closure and its invocation schedule remain open."
+    }
+  ],
+  "scientific_origin_commit": "a5df48c55ea806d7952b65acc9c76d878ff09b13",
+  "canonical_checkpoint": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19154057",
+  "checkpoint_utc": "2026-10-23T21:54:37Z",
+  "selected_kappa_at_checkpoint": "0.0030217758",
+  "checkpoint_decision": "Canonical main remains1ec111997; priority7 and scientific inputs unchanged. Reviewed newer owned-relation/transposition and observer-limit scopes; this forward helper-query hoist is distinct and does not consume their pending sources. Native caller research continues.",
+  "hoist_extension": "Copy selected D_K xi coordinates before T inverse, relocate their existing adapted children, then replace original child events by whole-field swaps with chart transport and owned clears. No Gaussian or scalar pass is added; ordinary storage/movement increases explicitly."
+}
diff --git a/research/native-helper-query-bank/VERIFY.json b/research/native-helper-query-bank/VERIFY.json
new file mode 100644
index 0000000000..e9fc7316c8
--- /dev/null
+++ b/research/native-helper-query-bank/VERIFY.json
@@ -0,0 +1,39 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/coded-native-caller/NORMALIZERS.json",
+    "research/coded-native-caller/PHYSICAL.md",
+    "research/coded-native-caller/clifford_exact.py",
+    "research/native-center-free-code/CODE.json",
+    "research/native-center-free-code/CODED-PROOF.md",
+    "research/native-center-free-code/CODED-WORDS.json.gz",
+    "research/native-center-free-code/SOURCE-WORD.json.gz",
+    "research/native-center-free-code/native_core.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Authenticated 632-row native endpoint, 358-owner scalar basis, 112 exact-phase responses, 32 charged completions and four base controls; entrance-prologue replay on 632 original plus 225 arbitrary owned inputs, 112 physical replacement cuts, unchanged paid inventory, explicit ordinary-work bill and two rescheduling controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "The same mathematical checks remain active when Python assertions are disabled."
+    }
+  ]
+}
diff --git a/research/native-helper-query-bank/verify.py b/research/native-helper-query-bank/verify.py
new file mode 100644
index 0000000000..b4b80e5378
--- /dev/null
+++ b/research/native-helper-query-bank/verify.py
@@ -0,0 +1,528 @@
+#!/usr/bin/env python3
+"""Source-bound forward helper-query interface; not a complete caller.
+Dillon / dillona, substantial OpenAI Codex assistance. Apache-2.0.
+Native producer and exact Clifford implementation retain their source credit.
+Read-only by default; --write emits the mathematical receipt.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+SOURCE_PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'
+N = 9
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def load_module(name, path):
+    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
+
+
+def authenticate():
+    manifest = json.loads((HERE / 'SOURCES.json').read_text())
+    for record in manifest['files']:
+        if record['usage'] == 'input':
+            data = (ROOT / record['path']).read_bytes()
+            need(sha256(data).hexdigest() == record['sha256'], 'Changed live source: ' + record['path'])
+    raw = gzip.decompress((ROOT / 'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes())
+    need(sha256(raw).hexdigest() == SOURCE_PAYLOAD, 'Changed scientific source payload')
+    source = json.loads(raw)
+    coded = json.loads(gzip.decompress((ROOT / 'research/native-center-free-code/CODED-WORDS.json.gz').read_bytes()))
+    core = load_module('helper_query_native_core', ROOT / 'research/native-center-free-code/native_core.py')
+    ce = load_module('helper_query_clifford', ROOT / 'research/coded-native-caller/clifford_exact.py')
+    return source, coded, core, ce
+
+
+def add(a, b, coefficient):
+    for key, value in b.items():
+        value = a.get(key, Q(0)) + coefficient * value
+        if value:
+            a[key] = value
+        else:
+            a.pop(key, None)
+
+
+def scalar_row(row, cold):
+    need(all(owner in cold and not word for owner, word in row),
+         'First departure must be scalar and read only cold helpers')
+    return {owner: value for (owner, word), value in row.items()}
+
+
+def replay(source, coded, core):
+    """Regenerate every final row and first departure, without a saved registry."""
+    c = coded['canonical']
+    need({k:v for k,v in c.items() if k != 'local_profile'} ==
+         {k:v for k,v in source['canonical'].items() if k != 'local_profile'}, 'Changed native charts')
+    program = coded['programs']['forward']
+    offset = len(program) - len(source['programs']['forward'])
+    need(offset == 6596, 'Source compensation length')
+    need(program[offset:] == core.clear_centers(source['programs']['forward']),
+         'Source event mapping after center deletion')
+    cold = {i for i in range(224, 632) if c['start'][i] == 0}
+    rows = [core.identity(i) for i in range(632)] + [{}]
+    charts = c['start'][:] + [None]
+    first, paid = {}, Counter()
+    for event, e in enumerate(program):
+        kind = e[0]
+        if kind == 'scalar':
+            gate, chart = e[1:]
+            dst = gate[1][1] + (632 if gate[1][0] == 'C' else 0)
+            if gate[0] == 'clear':
+                need(dst == 632, 'Persistent owner erasure')
+                rows[dst], charts[dst] = {}, chart
+                continue
+            need(charts[dst] == chart, 'Scalar destination chart')
+            if gate[0] in ('copy', 'add'):
+                src = gate[2][1] + (632 if gate[2][0] == 'C' else 0)
+                need(charts[src] == chart, 'Scalar source chart')
+                if gate[0] == 'copy':
+                    need(dst == 632, 'Persistent owner overwrite')
+                    rows[dst] = rows[src].copy()
+                else:
+                    need(dst != src, 'Self ADD')
+                    core.add(rows[dst], rows[src], Q(gate[3], gate[4]))
+            elif gate[0] == 'scale':
+                rows[dst] = {key: Q(gate[2], gate[3]) * value for key, value in rows[dst].items()}
+            else:
+                raise ValueError('Unknown scalar opcode')
+        elif kind == 'warp':
+            _, role, op, before, after = e
+            role = role[1] + (632 if role[0] == 'C' else 0)
+            need(charts[role] == before, 'Warp chart')
+            rows[role] = core.warp(rows[role], op, False)
+            charts[role] = after
+        elif kind == 'climb':
+            _, _, role, before, after, rank = e
+            need(charts[role] == before, 'Climb chart')
+            need(rank == len(c['frames'][after]) - len(c['frames'][before]) and rank > 0,
+                 'Climb Gaussian rank')
+            if role in cold and role not in first:
+                need(before == 0, 'Cold first-departure chart')
+                first[role] = dict(role=role, event=event, source_event=event-offset,
+                                   chart=after, rank=rank, row=scalar_row(rows[role], cold))
+            charts[role] = after
+            paid[rank] += 1
+        else:
+            need(kind in ('phase', 'adapter', 'residual_adapter'), 'Unexpected instruction')
+    need(set(first) == cold and len(cold) == 358, 'All cold first departures')
+    need(charts[:632] == c['final'] and not rows[632], 'Final charts and owned center')
+    A = json.loads((ROOT / 'research/native-center-free-code/CODE.json').read_text())['A']
+    for i in range(632):
+        expected = core.identity(i)
+        if 112 <= i < 224:
+            for j in range(112):
+                core.add(expected, core.identity(j), Q(A[i-112][j]))
+        need(rows[i] == expected, 'Arbitrary-input endpoint row ' + str(i))
+    need(dict(paid) == {1:2201, 2:412, 3:510, 4:127, 5:40}, 'Source paid profile')
+    return c, first, paid
+
+
+def inverse(matrix):
+    n = len(matrix)
+    a, b = [dict(row) for row in matrix], [{i: Q(1)} for i in range(n)]
+    ops = []
+    for j in range(n):
+        pivot = next((i for i in range(j, n) if a[i].get(j)), None)
+        need(pivot is not None, 'Singular cold-helper basis')
+        if pivot != j:
+            a[j], a[pivot] = a[pivot], a[j]
+            b[j], b[pivot] = b[pivot], b[j]
+            ops.append(['swap', j, pivot])
+        value = a[j][j]
+        if value != 1:
+            a[j] = {k: v / value for k, v in a[j].items()}
+            b[j] = {k: v / value for k, v in b[j].items()}
+            ops.append(['scale', j, str(1/value)])
+        for i in range(n):
+            if i != j and a[i].get(j):
+                value = -a[i][j]
+                add(a[i], a[j], value)
+                add(b[i], b[j], value)
+                ops.append(['add', i, j, str(value)])
+    need(a == [{i: Q(1)} for i in range(n)], 'Elimination identity')
+    return b, ops
+
+
+def compile_scalar(ops):
+    result = []
+    for op in ops:
+        if op[0] == 'swap':
+            a, b = op[1:]
+            result.extend([['add', a, b, '1'], ['add', b, a, '-1'],
+                           ['add', a, b, '1'], ['scale', b, '-1']])
+        else:
+            result.append(op)
+    return result
+
+
+def reverse_scalar(ops):
+    return [[op[0], *op[1:-1], str(-Q(op[-1]) if op[0] == 'add' else 1/Q(op[-1]))]
+            for op in reversed(ops)]
+
+
+def apply_scalar(ops, rows):
+    rows = [dict(row) for row in rows]
+    for op in ops:
+        if op[0] == 'add':
+            need(op[1] != op[2], 'Self scalar ADD')
+            add(rows[op[1]], rows[op[2]], Q(op[3]))
+        else:
+            need(op[0] == 'scale' and Q(op[2]) != 0, 'Reversible SCALE')
+            rows[op[1]] = {j: Q(op[2])*v for j, v in rows[op[1]].items()}
+    return rows
+
+
+def encode(rows):
+    return [[[j, str(v)] for j, v in sorted(row.items())] for row in rows]
+
+
+def reject(test, label):
+    try:
+        test()
+    except ValueError:
+        return label
+    raise ValueError('Mutation was not rejected: ' + label)
+
+
+def verify_hoist(coded, core, owners, inv, entrance, queries):
+    """Move the selected children before the scalar entrance program.
+
+    Cold input labels here denote w = D_K xi.  Observation copies are tracked
+    before their separately phase-checked monomial readouts; the native word
+    never reads those copies, so their readouts can run immediately.
+    """
+    c = coded['canonical']
+    raw_start, observation_start, count = 633, 745, 112
+    rows = [core.identity(i) for i in range(observation_start + count)]
+    charts = c['start'][:] + [None] * (1 + 2 * count)
+    paid, ordinary = Counter(), Counter()
+    program, cuts = [], []
+
+    def clear(slot, chart):
+        need(slot >= 632, 'Hoist cannot clear a persistent owner')
+        rows[slot], charts[slot] = {}, chart
+        ordinary['owned_clear'] += 1
+        program.append(['owned_clear', slot, chart])
+
+    def copy(dst, src, chart):
+        need(dst >= 633 and charts[src] == chart, 'Owned copy chart')
+        rows[dst], charts[dst] = rows[src].copy(), chart
+        ordinary['owned_copy'] += 1
+        program.append(['owned_copy', dst, src, chart])
+
+    def replacement(owner, raw, target_chart, transport_charts=True):
+        need(charts[owner] == 0 and charts[raw] == target_chart,
+             'Hoist replacement chart')
+        need(rows[owner] == rows[raw], 'Hoist replacement input row')
+        rows[owner], rows[raw] = rows[raw], rows[owner]
+        if transport_charts:
+            charts[owner], charts[raw] = charts[raw], charts[owner]
+        need(charts[owner] == target_chart and charts[raw] == 0,
+             'Whole-field swap must transport physical chart tags')
+
+    for query in queries:
+        q, owner, chart = (query[k] for k in ('query_index', 'native_role', 'first_chart'))
+        event = coded['programs']['forward'][query['coded_event']]
+        need(event[0] == 'climb' and event[2:] == [owner, 0, chart, 1],
+             'Hoisted event is the exact funded first H1 child')
+        raw, observation = raw_start + q, observation_start + q
+        clear(raw, 0)
+        copy(raw, owner, 0)
+        charts[raw] = chart
+        paid[1] += 1
+        program.append(['relocated_child', raw, query['coded_event']])
+        clear(observation, chart)
+        copy(observation, raw, chart)
+        # Its O_s readout is checked in the base bank.  Leave this isolated
+        # copy in its raw representation for the all-input symbolic replay.
+        program.append(['readout_on_observation', observation, q])
+
+    for op in entrance:
+        dst = owners[op[1]]
+        need(charts[dst] == 0, 'Hoist entrance target chart')
+        if op[0] == 'add':
+            src = owners[op[2]]
+            need(charts[src] == 0, 'Hoist entrance source chart')
+            core.add(rows[dst], rows[src], Q(op[3]))
+        else:
+            need(op[0] == 'scale' and Q(op[2]), 'Hoist entrance SCALE')
+            rows[dst] = {key: Q(op[2]) * value for key, value in rows[dst].items()}
+    for i, owner in enumerate(owners):
+        need(rows[owner] == {(owners[j], ()): a for j, a in inv[i].items()},
+             'Hoist entrance on every cold input')
+
+    by_event = {q['coded_event']: q for q in queries}
+    need(len(by_event) == count, 'Distinct hoisted child events')
+    controls = []
+    for event_index, e in enumerate(coded['programs']['forward']):
+        if event_index in by_event:
+            query = by_event[event_index]
+            owner, raw = query['native_role'], raw_start + query['query_index']
+            need(rows[owner] == core.identity(owner), 'First departure after T inverse')
+            if not controls:
+                original_row = rows[raw]
+                rows[raw] = core.identity(0)
+                controls.append(reject(lambda: replacement(owner, raw, query['first_chart']),
+                                       'wrong held query argument'))
+                rows[raw] = original_row
+                controls.append(reject(lambda: replacement(owner, raw, query['first_chart'], False),
+                                       'swap without physical chart transport'))
+                # The rejected no-tag swap exchanged equal rows only.
+            replacement(owner, raw, query['first_chart'])
+            ordinary['physical_field_swap'] += 1
+            program.append(['replace_child_by_swap', event_index, owner, raw])
+            clear(raw, 0)
+            cuts.append([event_index, owner, query['first_chart'], raw])
+            continue
+        kind = e[0]
+        if kind == 'scalar':
+            gate, chart = e[1:]
+            dst = gate[1][1] + (632 if gate[1][0] == 'C' else 0)
+            if gate[0] == 'clear':
+                need(dst == 632, 'Native persistent owner erasure')
+                rows[dst], charts[dst] = {}, chart
+                continue
+            need(charts[dst] == chart, 'Native scalar destination chart after hoist')
+            if gate[0] in ('copy', 'add'):
+                src = gate[2][1] + (632 if gate[2][0] == 'C' else 0)
+                need(charts[src] == chart, 'Native scalar source chart after hoist')
+                if gate[0] == 'copy':
+                    need(dst == 632, 'Native persistent owner overwrite')
+                    rows[dst] = rows[src].copy()
+                else:
+                    core.add(rows[dst], rows[src], Q(gate[3], gate[4]))
+            elif gate[0] == 'scale':
+                rows[dst] = {key: Q(gate[2], gate[3])*a for key, a in rows[dst].items()}
+            else:
+                raise ValueError('Unknown native scalar instruction')
+        elif kind == 'warp':
+            _, ref, op, before, after = e
+            owner = ref[1] + (632 if ref[0] == 'C' else 0)
+            need(charts[owner] == before, 'Native warp chart after hoist')
+            rows[owner], charts[owner] = core.warp(rows[owner], op, False), after
+        elif kind == 'climb':
+            _, _, owner, before, after, rank = e
+            need(charts[owner] == before, 'Native child chart after hoist')
+            need(rank == len(c['frames'][after]) - len(c['frames'][before]) and rank > 0,
+                 'Native child rank after hoist')
+            charts[owner] = after
+            paid[rank] += 1
+        else:
+            need(kind in ('phase', 'adapter', 'residual_adapter'), 'Unknown native marker')
+
+    A = json.loads((ROOT / 'research/native-center-free-code/CODE.json').read_text())['A']
+    oi = {owner: i for i, owner in enumerate(owners)}
+    for owner in range(632):
+        expected = core.identity(owner)
+        if owner in oi:
+            expected = {(owners[j], ()): a for j, a in inv[oi[owner]].items()}
+        elif 112 <= owner < 224:
+            for j in range(112):
+                core.add(expected, core.identity(j), Q(A[owner-112][j]))
+        need(rows[owner] == expected, 'Hoisted arbitrary-input endpoint ' + str(owner))
+    need(charts[:632] == c['final'], 'Hoisted final physical charts')
+    need(all(not row for row in rows[632:observation_start]), 'Hoisted raw workspace and native center zero')
+    for query in queries:
+        observation = observation_start + query['query_index']
+        need(rows[observation] == core.identity(query['native_role']) and
+             charts[observation] == query['first_chart'], 'Early observation retained intact')
+        clear(observation, query['first_chart'])
+    need(all(not row for row in rows[632:]), 'All arbitrary owned inputs removed and outputs cleared')
+    need(paid == Counter({1:2201, 2:412, 3:510, 4:127, 5:40}), 'Hoist paid inventory unchanged')
+    need(ordinary == {'owned_clear':448, 'owned_copy':224, 'physical_field_swap':112},
+         'Hoist ordinary-work invoice')
+    return dict(schema='native-helper-query-hoist/1', status='PASS_EARLY_112_FUNDED_HELPER_QUERIES',
+                original_inputs_checked=632, arbitrary_owned_inputs_checked=225,
+                raw_observation_rows_checked=112, replacement_cuts_checked=112,
+                all_owned_outputs_zero_after_consumer_clear=True,
+                source_paid=dict(sorted(paid.items())), added_gaussian_children=0,
+                ordinary_work=dict(ordinary), extra_scalar_passes=0,
+                owned_fields_additional_to_native=224,
+                added_owned_fields_over_chronological_observer=112,
+                prologue_after='All diagonal K maps, before the existing T-inverse program.',
+                source_readout_boundary='Observation copies are tracked raw; the same 112 exact-phase O_s identities normalize them independently.',
+                recipe_semantics='Ordered patch recipe, not a standalone instruction stream.',
+                splice=dict(source='research/native-center-free-code/CODED-WORDS.json.gz:programs.forward',
+                            prologue_items=6 * count,
+                            after_prologue='Execute BANK.json entrance_scalar_program on the cold owners.',
+                            source_events='Replay every original source event in order; replace only the listed child events by their tagged SWAP and owned CLEAR.',
+                            after_source='Apply unchanged BANK.json cold_completions, exit_scalar_program and inverse K maps.',
+                            observation_clears='The final 112 recipe items are consumer obligations after each observation last use.'),
+                program=program, replacement_cuts=cuts, rejected_controls=controls)
+
+
+def run():
+    source, coded, core, ce = authenticate()
+    c, first, paid = replay(source, coded, core)
+    owners = sorted(first)
+    oi = {owner: i for i, owner in enumerate(owners)}
+    T = [{oi[j]: v for j, v in first[owner]['row'].items()} for owner in owners]
+    inv, elimination = inverse(T)
+    entrance = compile_scalar(elimination)
+    exit_program = reverse_scalar(entrance)
+    identity = [{i: Q(1)} for i in range(358)]
+    need(apply_scalar(entrance, identity) == inv, 'Literal entrance on all 358 inputs')
+    need(apply_scalar(exit_program, identity) == T, 'Literal exit on all 358 inputs')
+    need(apply_scalar(exit_program, inv) == identity, 'T times inverse')
+    need(apply_scalar(entrance, T) == identity, 'Inverse times T')
+
+    def equal(a, b):
+        return a.tab == b.tab and a.zero_state() == b.zero_state()
+
+    def rank(op):
+        return ce.rank([x for x, z, phase in op.tab[N:]])
+
+    def literal(word):
+        op = ce.ident(N)
+        for e in word:
+            if e[0] == 'P': term = ce.perm(N, tuple(e[1]))
+            elif e[0] == 'D': term = ce.diag(N, tuple(e[1]), tuple(e[2]))
+            elif e[0] == 'X': term = ce.xgate(N, e[1])
+            elif e[0] == 'phase': term = ce.Op(N, ce.identity(N), [tuple(e)])
+            elif e[0] == 'C': term = ce.cgate(N, e[1], e[2])
+            else: raise ValueError('Unknown literal Clifford instruction')
+            op = op.then(term)
+        return op
+
+    def receipt(op):
+        vector, denominator = op.zero_state()
+        anchor = next(i for i, value in enumerate(vector) if value != (0, 0))
+        return dict(word=op.circuit, signed_tableau=op.tab, fourier_rank=rank(op),
+                    zero_column_anchor=[anchor, vector[anchor], denominator])
+
+    normal = json.loads((ROOT / 'research/coded-native-caller/NORMALIZERS.json').read_text())
+    ks = {record['q']: literal(record['K_word']) for record in normal['ports']}
+    R, common_Q = ce.canonical_frame(N, c['frames'][1]), ce.cgate(N, 1)
+    eligible = [record for record in first.values()
+                if record['rank'] == 1 and len(c['frames'][c['final'][record['role']]]) == 9
+                and c['frames'][record['chart']][0].bit_count() % 2
+                and c['frames'][record['chart']][0] != 511]
+    need(len(eligible) == 198, 'Native H1 query census')
+    selected = sorted(eligible, key=lambda record: record['event'])[:112]
+    queries = []
+    for i, record in enumerate(selected):
+        line = c['frames'][record['chart']][0]
+        K = ks[line]
+        E = ce.canonical_frame(N, c['frames'][record['chart']])
+        need(rank(E) == 1, 'Physical rank of the relocated first child')
+        response = common_Q.adjoint().then(K).then(E).adjoint()
+        need(rank(K) == rank(response) == 0, 'Monomial query wrappers')
+        need(equal(K.then(E).then(response), common_Q), 'Exact common-Q response')
+        need(equal(K.then(R).then(K.adjoint()), R), 'Exact R centralizer')
+        km, _ = ce.monomial(K)
+        rm, _ = ce.monomial(response)
+        need(equal(km, K) and equal(rm, response), 'Compiled query phase')
+        need(all(e[0] in ('P','D','X','phase') for e in km.circuit+rm.circuit), 'No hidden query Gaussian')
+        queries.append(dict(query_index=i, mode_coordinate=oi[record['role']], native_role=record['role'],
+                            coded_event=record['event'], source_event=record['source_event'],
+                            first_chart=record['chart'], line=line,
+                            input_K=receipt(km), response=receipt(rm)))
+
+    completions = []
+    cold_profile, hot_profile, added = Counter(), Counter(), Counter()
+    for role in range(224, 632):
+        birth, final = c['start'][role], c['final'][role]
+        target = len(c['frames'][final]) - len(c['frames'][birth])
+        (cold_profile if role in oi else hot_profile)[target] += 1
+        if role not in oi or target == 9:
+            continue
+        F = ce.canonical_frame(N, c['frames'][final])
+        complement = F.adjoint().then(R)
+        child_recipe, compiled = ce.lower_child(complement)
+        need(rank(complement) == child_recipe['rank'] == 9-target, 'Cold completion Gaussian rank')
+        need(equal(compiled, complement) and equal(F.then(compiled), R), 'Exact completed cold return')
+        gaussian = [e for e in compiled.circuit if e[0] == 'C']
+        need(len(gaussian) == 9-target and all(e[2] == 1 for e in gaussian), 'One literal complement child')
+        positions = [i for i,e in enumerate(compiled.circuit) if e[0] == 'C']
+        need(positions == list(range(positions[0], positions[0]+9-target)), 'Contiguous Gaussian block')
+        need([e[1] for e in gaussian] == [1 << i for i in range(9-target)], 'Complement child axes')
+        added[9-target] += 1
+        completions.append(dict(native_role=role, original_rank=target, final_chart=final,
+                                charged_child_rank=9-target, operator=receipt(compiled)))
+    need(dict(cold_profile) == {4:26, 8:6, 9:326}, 'Cold productive census')
+    need(dict(hot_profile) == {4:2, 7:7, 8:41}, 'Hot productive census')
+    need(dict(added) == {1:6, 5:26}, 'Cold completion bill')
+    controls = []
+    bad = {(0, ()): Q(1)}
+    controls.append(reject(lambda: scalar_row(bad, set(owners)), 'foreign-main first-departure contamination'))
+    singular = [dict(row) for row in T]
+    singular[0] = dict(singular[1])
+    controls.append(reject(lambda: inverse(singular), 'singular helper basis'))
+    first_query = queries[0]
+    K, response = literal(first_query['input_K']['word']), literal(first_query['response']['word'])
+    E = ce.canonical_frame(N, c['frames'][first_query['first_chart']])
+    wrong = ce.Op(N, response.tab, response.circuit+[('phase', 1)])
+    controls.append(reject(lambda: need(equal(K.then(E).then(wrong), common_Q), 'Absolute query phase'),
+                           'absolute phase invisible to tableau'))
+    omitted = next(record for record in completions if record['original_rank'] == 8)
+    F = ce.canonical_frame(N, c['frames'][omitted['final_chart']])
+    controls.append(reject(lambda: need(equal(F, R), 'Missing H1 completion'), 'omitted cold-H8 completion'))
+    final_paid = paid + added
+    targets = hot_profile + Counter({9:358})
+    counts = Counter(op[0] for op in entrance)
+    need(counts == {'add':3210, 'scale':204}, 'Expanded scalar invoice')
+    result = dict(schema='native-helper-query-bank/1', status='PASS_FORWARD_NATIVE_112_HELPER_QUERY_BANK',
+                  scientific_source_payload_sha256=SOURCE_PAYLOAD, direction='forward_only',
+                  original_owner_count=632, original_helper_count=408, cold_helper_owners=owners,
+                  hot_helper_owners=[i for i in range(224,632) if i not in oi],
+                  query_count=112, eligible_existing_H1_queries=198, queries=queries,
+                  T_rows=encode(T), inverse_rows=encode(inv),
+                  entrance_scalar_program=entrance, exit_scalar_program=exit_program,
+                  cold_completions=completions,
+                  invoice=dict(source_paid=dict(sorted(paid.items())), query_gaussian_delta={},
+                               completion_paid_delta=dict(sorted(added.items())),
+                               completed_paid=dict(sorted(final_paid.items())),
+                               old_cold_targets=dict(sorted(cold_profile.items())),
+                               unchanged_hot_targets=dict(sorted(hot_profile.items())),
+                               new_helper_targets=dict(sorted(targets.items())),
+                               added_paid_rank_mass=sum(k*v for k,v in added.items())),
+                  ordinary_work=dict(entrance_adds=3210, entrance_scales=204, exit_adds=3210, exit_scales=204,
+                                     basis_monomial_field_maps=224, response_monomial_field_maps=112,
+                                     observation_copies=112, observation_initial_clears=112,
+                                     observation_terminal_clears=112, owned_observation_fields=112,
+                                     basis_scratch_fields=0, completion_wrapper_field_maps_upper=64),
+                  checks=dict(all_arbitrary_endpoint_rows=632, all_scalar_basis_inputs=358,
+                              exact_phase_queries=112, exact_phase_completions=32,
+                              T_nonzeros=sum(map(len,T)), inverse_nonzeros=sum(map(len,inv)),
+                              inverse_elimination_operations=len(elimination), rejected_controls=controls),
+                  inherited_obligations=['Physical implementation of authenticated native operations and their cost model.',
+                                         'All-width evaluation lemma from CODED-PROOF.md and PHYSICAL.md.',
+                                         'No backward observer, complete caller, global rounding budget, TM tariff or new kappa.'])
+    hoist = verify_hoist(coded, core, owners, inv, entrance, queries)
+    return json.loads(json.dumps(result)), json.loads(json.dumps(hoist))
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--write', action='store_true')
+    args = parser.parse_args()
+    result, hoist = run()
+    for filename, receipt in [('BANK.json', result), ('HOIST.json', hoist)]:
+        path = HERE / filename
+        if args.write:
+            path.write_text(json.dumps(receipt, sort_keys=True, separators=(',', ':')) + '\n')
+        else:
+            need(json.loads(path.read_text()) == receipt, 'Changed mathematical ' + filename + ' receipt')
+    print(result['status'], json.dumps(result['checks'], sort_keys=True))
+    print(hoist['status'], json.dumps({key: hoist[key] for key in
+          ('original_inputs_checked', 'arbitrary_owned_inputs_checked',
+           'replacement_cuts_checked', 'ordinary_work', 'rejected_controls')}, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()