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+# A nonlinear terminal-information barrier at every rank-seven endpoint
+
+For each of the two pinned PR2894 providers, a fresh eligible-input
+quantity cannot be extracted at any endpoint of rank at most seven by
+the monotone suffix interface defined below. The local suffix operations
+may be nonlinear, and arbitrary recoding confined to the eligible entrance
+coordinates is allowed. The obstruction follows from a finite complete
+endpoint census and a written indistinguishability argument.
+
+This is a result about the frozen provider word and its declared entrance,
+observation, and frame contracts. It is not a word-independent rank-eight
+lower bound, a new supplier, or a multiplication-bound improvement.
+
+## Main theorem and exact interface
+
+Let `D=Z[1/2]`, and let `W` be any `D`-module. Every formal warp in the
+pinned provider is represented by an invertible `D`-linear endomorphism of
+`W`. Every live non-target entrance value ranges independently over `W`.
+The zero module is allowed, in which case statements about nonconstant
+functions are vacuous.
+
+The frozen middle operator `M` and the post-`restore` last frames are those
+of the two providers authenticated by PR2918 at
+`9360ba7312cf8961e672e9eb26c612719028d39d`. Its source pins are PR2908 at
+`51309592971e3b5be935599eed2a95404dc7781e`, carrying the PR2894 providers at
+`18d03c447886895ef9abf888398178e0428533ca`.
+
+The entrance coordinates are taken immediately after the provider's 84-event
+prelude, which `M` omits. Its only non-target operations are 24 invertible warps
+on protected registers outside `H`. Hence these coordinates still range
+independently over the full module, and the eligible coordinates are unchanged.
+The allowed entrance recoding below is applied at this declared cut.
+
+As in that package, the live non-target coordinate set is
+
+```
+L = {0,...,703} \ (removed union {112,...,223}),     |L|=520.
+```
+
+Let `P` contain all `helper_final` and `start_extra` registers and every
+source of an initial operator correction. The eligible entrance set is
+
+```
+H = {r in L : r>=224 and r not in P},               |H|=226.
+```
+
+Write the eligible entrance state as `h in W^H`. An entrance recoding is
+any map `S:W^H->W^H`, extended by the identity on all other coordinates.
+In particular it cannot inspect, modify, or correlate the protected
+entrance values. Allowing nonlinear or noninvertible `S` only enlarges the
+class covered by the negative result. The rank-eight comparison below uses
+an actual invertible scalar `S`.
+
+The suffix starts after the fixed `restore` word and before the prescribed
+final climbs. It has a fixed finite data-dependency network satisfying:
+
+1. Each local operation acts at a common frame containing the current
+   frames of all its data inputs. Its outputs have that frame or a larger
+   frame. The local map may be arbitrarily nonlinear.
+2. Frames only increase by subspace inclusion. There are no new warp
+   resets or other operations carrying a dependency to a smaller or
+   incomparable frame.
+3. Inputs consist of the live non-target state at this cut, together with
+   any constants or ancillas whose joint tuple is independent of the complete
+   entrance tuple and can be fixed identically in compared executions. There
+   are no target reads, additional source reads, earlier snapshots, or
+   retained data-dependent side values.
+4. The network, output identities and the frame assigned to every node are
+   fixed independently of input values. Data-dependent local branching is
+   allowed only inside a node's local function; every potential branch input
+   and every data/control dependency is an explicit incoming edge obeying
+   rule 1. Branch choice, output selection/presence, timing and frame choice
+   provide no additional observation.
+
+**Theorem.** Under these assumptions, no output at a final frame `E` with
+`dim_GF(2) E<=7` can equal a nonconstant function of `h` for all entrance
+values. The same conclusion holds for any tuple of outputs whose frames
+are all contained in one common such `E`.
+
+For a fresh eligible-input extraction using an allowed entrance recoding
+and this suffix interface, endpoint rank eight is therefore necessary.
+For every nonzero `W`, PR2908's calibrated rank-eight entrance/output pair
+attains that threshold algebraically. For `W=0` no nonconstant quantity exists
+at any rank, so there is no sharp recovery threshold. This comparison allows
+the `H`-only entrance recoding; it
+does not assert that a suffix alone, with identity entrance map, attains
+the threshold.
+
+## Finite certificate: every rank-seven readout is saturated by nuisances
+
+Let `F_r` be the exact frame of register `r` after the frozen `restore`
+word. The available terminal support at an endpoint `E` is
+
+```
+R(E) = {r in L : F_r is a subspace of E}.
+```
+
+The frame replay includes all recorded scalar incidents in `A`, `B` and
+`restore`, including their target writes' source incidents, as well as prelude
+warps and inserted `B` warps. The separate 176 target-only `cut` operations
+have unspecified (`None`) frames in the provider. They are interpreted using
+the inherited center-cut convention: every source is a recorded center whose
+current frame already equals its `center_frames` entry at the end of `A`.
+Both verification paths check this equality; neither reconstructs additional
+physical frame moves for that separate cut. Warps
+replace their incoming frame by the recorded outgoing frame. Taking the
+union of all historical frames would give a different and incorrect
+support. The middle operator omits target writes but retains all 4,583
+non-target gates; omitting those target writes does not omit their source
+frame incidents.
+
+Every rank-seven subspace of `GF(2)^9` is the orthogonal complement of a
+unique two-dimensional subspace for the standard nondegenerate dot
+product. Such a plane has three nonzero elements `{a,b,a+b}`. Counting its
+ordered bases gives
+
+```
+# {rank-seven endpoints} = (2^9-1)(2^9-2) / ((2^2-1)(2^2-2))
+                         = 511*510/6
+                         = 43,435.
+```
+
+Equivalently, choose the two least integer representatives of the three
+nonzero plane elements. They satisfy `0<a<b<a xor b<512`, and every plane
+occurs exactly once. A register belongs to the associated support exactly
+when every vector in its last-frame basis has even dot product with both
+`a` and `b`.
+
+For **each provider separately**, these 43,435 endpoints produce exactly
+239 distinct support sets. `certificates.json` records the complete
+support-class partition, its multiplicities, a representative annihilator
+plane, and a forbidden-input column set for every support. For every class
+with support `R`, it supplies `J_R subset L\H` such that
+
+```
+|J_R|=|R|,
+B_R = M[R,J_R] is a scalar matrix over D,
+det B_R is one of 1,-1,1/2,-1/2,1/4,-1/4.
+```
+
+Being scalar here means that each complete free-operator polynomial entry
+has only its empty-word coefficient; every nonempty-word coefficient
+vanishes. The selected minor has size at most 16. The empty support has
+the empty minor, whose determinant is one. Each provider has the following
+unweighted class counts:
+
+| Determinant | 1 | -1 | 1/2 | -1/2 | 1/4 | -1/4 |
+| --- | ---: | ---: | ---: | ---: | ---: | ---: |
+| Support classes | 157 | 34 | 11 | 17 | 8 | 12 |
+
+These are finite source-bound matrix claims. `verify.py` reconstructs the
+provider operator and last frames with the authenticated PR2918 engine,
+regenerates the entire endpoint partition, and checks the minors and their
+dyadic inverses. `verify_independent.py` is the separate verification entry
+point; its execution status must be established by its own run. The
+written proof below does not substitute for executing either verifier.
+
+Since each determinant is a unit of `D`, the adjugate identity makes
+`B_R` invertible over `D`. Hence it acts as an automorphism of `W^R` for
+**every** dyadic module `W`. Since each minor is already scalar as a
+formal-operator identity, this conclusion survives every specialization of
+the warps. It does not rely on distinct free words staying linearly
+independent after specialization, on `W` being free, or on finite dimension.
+
+For comparison, PR2918's original endpoint
+
+```
+E7 = span_GF(2)(256,128,66,36,22,8,1)
+```
+
+has
+
+```
+R = (105,307,309,314,369,371,373,378,408,572,573),
+J = (14,307,309,314,369,371,373,378,41,572,573),
+M[R,J] = diag(-1/2,1,1,1,1,1,1,1,1/2,1,1).
+```
+
+The new finite obligation is complete endpoint coverage with the same
+unit-minor property, rather than just this eleven-coordinate certificate.
+
+## Indistinguishability, including nonlinear recoding and decoding
+
+Fix any support `R` and its certified `J_R`. Split the entrance state
+into `h` on `H`, `z` on `J_R`, and `k` on all remaining coordinates. After
+the allowed entrance recoding, the complete observation on `R` has form
+
+```
+y = A S(h) + B_R z + C k,
+```
+
+where `A` and `C` may contain arbitrary specialized operator entries.
+Fix `k` and any two eligible states `h,h'`. Starting with any `z`, put
+
+```
+z' = z + B_R^-1 A(S(h)-S(h')).
+```
+
+Then
+
+```
+A S(h)+B_R z+C k = A S(h')+B_R z'+C k.
+```
+
+The two states are both allowed: protected entrances range independently
+over their entire module. Thus every eligible state can produce every
+observation `y` by a suitable choice of these protected inputs. If any
+decoder `g`, with no linearity assumption, recovered `f(h)` from `y` for
+all inputs, this collision would give `f(h)=f(h')` for every pair. Hence
+`f` would be constant.
+
+This is a deterministic exact-recoverability statement for all allowed
+inputs; it makes no probabilistic mutual-information claim.
+
+This proves the information obstruction for each rank-seven endpoint.
+Every endpoint of rank below seven extends to a rank-seven endpoint `E'`.
+Since `R(E) subset R(E')`, the same conclusion holds on `R(E)`: any
+decoder of the smaller observation would also be a decoder of the larger
+one. The nuisance column set can depend on the endpoint; no common set of
+columns for all endpoints is required.
+
+## Causal proof for the complete suffix
+
+Consider a dependency path from an initial suffix register `r` to an
+output at frame `E`. By the common-frame rule, a frame on this path is
+contained in the frame of the next operation. All subsequent frame moves
+are inclusions. Therefore `F_r` is contained in `E`, so `r` belongs to
+`R(E)`.
+
+Induction through the finite network shows that the output is a function
+only of the initial `R(E)` values and the permitted input-independent
+constants or ancillas. Fix those ancillary values identically in the two
+colliding executions constructed above. The complete suffix produces the
+same output in both executions. It cannot recover a nonconstant eligible
+function. Multiple outputs with frames contained in one common `E` obey
+the identical argument. This proves the main theorem.
+
+Arbitrarily many nonlinear gates or intermediate buffers do not change
+this conclusion under the declared interface. A larger-frame computation
+cannot feed a smaller-frame output without violating monotonicity. Known
+local frame-conversion maps can be included in the arbitrary local
+functions; the proof uses their dependency and frame directions.
+
+The theorem concerns **fresh eligible-input** quantities. Existing cold
+outputs correspond to protected entrances outside `H` and are not ruled
+out. Nor is the joint information in freely pooled outputs at different,
+incomparable rank-seven frames covered: separately masked shares can reveal
+information jointly. A physical collector obeying the declared rules is
+covered if its own final frame has rank at most seven. An external free
+collector changes the observation contract.
+
+## Rank-eight attainment in the allowed pre/post interface
+
+The existing PR2908 construction has an invertible scalar entrance map
+`S` supported on `H` and an output map `T` supported at
+
+```
+E52 = span_GF(2)(256,128,64,36,20,8,2,1),    dim E52=8.
+```
+
+Its 24 entrance gates and three output gates yield the paired identities
+recorded and checked in PR2918. In particular, for the extracted helper,
+
+```
+v = S e408,
+y = Mv = 2 e42,
+alpha = e408^T+(1/2)e42^T+e105^T,
+alpha M = e408^T S^-1,
+alpha y = 1.
+```
+
+The terminal gates are
+
+```
+408 += (1/2)*42,
+408 += 105,
+42  -= 2*408.
+```
+
+Register42 is available at `E52`. These actual pre/post maps give the
+rank-eight algebraic witness in the same eligible-entrance class. For nonzero
+`W`, its recovered coordinate `h_408` is nonconstant. The
+lower bound and this witness establish a sharp endpoint-rank threshold
+for that interface; they do not re-prove the inherited native supplier,
+buffers, target compensation, owner allocation, or complete cost ledger.
+The construction and its costs remain credited to PR2908.
+
+## Secondary consequences: retained information and repairs
+
+The quantitative rank statements below assume that the entire observation
+map is linear in the same original coordinates used for the desired
+quantity `Lh` and the additional linear observations. They do not inherit the main
+theorem's allowance for arbitrary nonlinear entrance recoding: after such
+recoding, a linear side observation can reveal more original coordinates
+than these linear-map rank formulas permit.
+
+**General quotient.** For module observations `y=Ah+Bz`, let
+`pi:Y->Y/im B`. An arbitrary function of `h` is recoverable exactly when
+it is constant on each coset of `ker(pi A)`. Indeed, two eligible states
+admit a common observation exactly when their difference maps under `A`
+into `im B`; conversely `pi y=pi A h` supplies the quotient. In finite
+dimension over a field, the dimension of the recoverable linear quotient
+is `rank([A B])-rank(B)`. The unit-minor case has zero quotient.
+
+**Additional linear observations.** In a finite-dimensional vector-space
+specialization, let the original readout be `R0 x` and the desired linear
+answer be `D0 x`. The exact minimum number of unrestricted additional
+scalar linear observations is
+
+```
+rank(D0 restricted to ker R0) = rank([R0;D0])-rank(R0),
+```
+
+even if decoding is nonlinear. The extra observations must distinguish all
+pairs in `ker R0` that `D0` distinguishes, proving the lower bound. A basis
+of the desired row space modulo the original observation row space attains
+it. Under complete masking, projection of `ker R0` onto `H` is surjective;
+therefore recovering `D0 x=Lh` of rank `d` requires exactly `d` additional
+scalar linear observations. For `W=F^n`, recovering `t` independent full
+eligible arrays requires `tn` scalar linear coordinates, or `t` linear
+side arrays of the same capacity.
+
+This counts unrestricted linear information, not its acquisition,
+chronological retention, restoration, or recursive cost. Arbitrary
+nonlinear rational side encodings do not satisfy this dimension bound:
+one rational can encode a finite tuple of rationals because both sets are
+countable. Linearity or a separately specified capacity restriction is
+essential for the observation count; arbitrary nonlinear decoding is
+already covered.
+
+**Low-rank repair.** Over a field, suppose the original nuisance block
+`B` has full row rank `m` and a changed construction replaces it by
+`B'=B+Delta`, where `rank Delta<=q`. Allow its eligible block to change
+arbitrarily to `A'`. Then
+
+```
+rank([A' B'])-rank(B') <= m-rank(B') <= q.
+```
+
+At most `q` independent eligible linear directions become observable on
+the same output space. Extra independent nuisance columns can only reduce
+this capacity. Exposing `d` independent directions therefore requires a
+nuisance-block perturbation of rank at least `d`. This is necessary, not
+sufficient: `A'=0` exposes no eligible information even when `B'=0`.
+No vector-space rank assertion is made for a general dyadic module.
+
+## Prior work, evidence type, and unresolved implications
+
+The quotient and collision arguments are standard linear-algebraic
+identifiability principles. No novelty claim is made for those principles.
+PR2918 supplied the original endpoint obstruction and independent inverse
+certificate. PR2908 supplied the positive rank-eight paired construction.
+PR2979 already reports a complete 43,435-endpoint paired-extraction screen
+on a newer PR2942/stage1 word and a rank-seven positive example on PR2917
+V45. Those source words and contracts differ. In particular, the present
+claim is not the first rank-seven endpoint enumeration and does not rule
+out the changed-word positive example.
+
+The scoped extension is the unit-nuisance saturation certificate for every
+endpoint on the two pinned old providers, and its consequence for arbitrary
+nonlinear local processing throughout a monotone causal suffix. The source
+conventions and complete predecessor credits remain those in the package
+documentation and PR2918.
+
+The endpoint coverage and minors are a **finite exhaustive exact
+computation**. The implications for all input values, all allowed recodings,
+every dyadic-module representation, and every finite suffix satisfying the
+rules are **all-parameter written proofs**. Neither is a formal-kernel proof.
+An independent verifier run is separate evidence and must not be inferred
+merely from the presence of its source file.
+
+The result leaves open changed middle words, changed protected entrance
+access, correlated or restricted input domains, additional snapshots or
+source observations, untracked control dependencies, new warp resets,
+nonmonotone frames, and different observation contracts. It supplies no
+paid repair circuit, new native phase identity, full recursive moment,
+global supplier optimum, or improved multiplication bound.
diff --git a/research/rank7-terminal-information-barrier/README.md b/research/rank7-terminal-information-barrier/README.md
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+# A nonlinear recovery obstruction at every rank-seven endpoint
+
+For the two PR2894 providers pinned by PR2918, **no endpoint of rank at most
+seven permits exact recovery of any nonconstant function of the eligible
+entrance state**. This remains true with arbitrary nonlinear decoding,
+arbitrary recoding confined to eligible entrances, and arbitrary appended
+processing whose complete data dependencies obey monotone frame inclusion.
+All inputs retain the independent arbitrary-dirty contract. The word, entrance
+cut, protected inputs and observation interface are fixed.
+
+The entrance cut is immediately after the 84-event prelude. The separate
+target-only center cut uses the inherited, checked `center_frames` convention;
+this package does not reconstruct extra physical moves for its unspecified
+frames. Output registers and frames in the suffix are fixed independently of
+data, with all branch and control dependencies included.
+
+This strengthens PR2918's one-helper, one-endpoint, scalar paired-boundary
+obstruction. It concerns deterministic recovery for every input, not statistical
+mutual information. [PROOF.md](PROOF.md) gives the complete theorem and limits.
+
+## Exact evidence
+
+Each provider has 520 live non-target registers and 226 eligible entrances.
+We enumerate all **43,435** rank-seven subspaces of `GF(2)^9`, obtaining **239**
+distinct complete terminal supports, of size at most 16. Every support has a
+square purely scalar minor on protected input columns with determinant a unit
+of `Z[1/2]`. The census covers all 58 eligible helper slots whose current terminal
+frames have rank at most seven. Lower-rank endpoints follow by containment.
+
+| Determinant | Support classes, per provider |
+| --- | ---: |
+| 1 | 157 |
+| -1 | 34 |
+| 1/2 | 11 |
+| -1/2 | 17 |
+| 1/4 | 8 |
+| -1/4 | 12 |
+
+The empty support has determinant one by convention. Each nonempty certificate
+includes the entire terminal support, a representative annihilator, its endpoint
+multiplicity, and the forbidden input columns. All nonempty operator coefficients
+on the chosen blocks are zero. Thus these certificates remain valid under every
+invertible linear specialization of the formal warps on every dyadic module.
+
+The mathematical reason is simple. In `y=A h+B z`, protected inputs `z` can
+produce every observation because `B` is invertible. Any eligible-input change
+can be canceled by `z -> z+B^-1 A(h-h')`. No decoder can distinguish those
+states. Monotone frame dependencies confine any output at endpoint `E` to the
+already masked terminal support `R(E)`.
+
+The known PR2908 rank-eight paired extraction passes both verification paths.
+For every nonzero dyadic module, eight is the sharp endpoint threshold in this
+frozen interface
+when the permitted eligible-input preprocessing is included. This does not
+assert that an output-only suffix can attain the threshold.
+
+## Reproduction and verification scope
+
+```sh
+python3.12 scripts/research_package.py --package research/rank7-terminal-information-barrier
+```
+
+The two direct commands are:
+
+```sh
+python3.12 -I -O -B research/rank7-terminal-information-barrier/verify.py
+python3.12 -I -O -B research/rank7-terminal-information-barrier/verify_independent.py
+```
+
+`verify.py` authenticates and directly executes PR2918's existing forward
+operator/frame engine, then regenerates the census and checks the fixed
+`certificates.json`. It checks both inverse products for every minor, eight
+rejecting controls per provider, a row/column reordering control, and the
+rank-eight construction. This path deliberately reuses the predecessor engine.
+
+`verify_independent.py` imports no predecessor code. It parses the two source
+providers, propagates 164 terminal covectors backward, enumerates endpoints by
+two-row reduced echelon normal matrices, and verifies complete scalar minors
+using fraction-free Bareiss determinants. It checks seven rejecting controls per
+provider and separately reconstructs the rank-eight positive pairing by a row
+pullback and inverse column. Its adjoint approach follows the credited PR2918
+checker; the implementation and all-endpoint coverage are separate.
+
+Both paths use exact rational arithmetic and explicit checks that remain active
+under Python `-O`. This is finite exhaustive computational evidence plus a
+written all-parameter argument. It is not a formal-kernel proof or independent
+human review. Four authenticated predecessor files are live inputs, declared in
+`VERIFY.json` and pinned by `SOURCES.json`; they are not duplicated here.
+
+## Prior work and importance
+
+PR2918 is pinned at `9360ba7312cf8961e672e9eb26c612719028d39d`; its sources bind
+PR2908 at `51309592971e3b5be935599eed2a95404dc7781e` and PR2894 at
+`18d03c447886895ef9abf888398178e0428533ca`.
+[PR2979](https://github.com/CrocSwap/integer-mult-bounds/pull/2979), head
+`be191346391661f4d35fc0d1508d0a6029572576`, already uses the all-43,435-endpoint
+pairing screen on later words and reports a rank-seven positive example for
+PR2917's changed word. We do not claim the enumeration technique or an
+all-endpoint linear screen is new. The scoped strengthening here is the complete
+unit-minor census on the old parent and its **nonlinear causal recovery
+obstruction**, together with explicit side-information and repair requirements.
+The underlying quotient and indistinguishability principles are standard.
+No comprehensive literature novelty claim is made.
+
+This excludes an entire family of endpoint/postprocessing repairs of the frozen
+construction. It gives a necessary boundary for further design; it supplies no
+new multiplication algorithm, improved kappa, paid recovery, owner allocation,
+or native/outer theorem admission. A different middle word, additional retained
+information, different entrance dependencies, a new warp reset, or a changed
+observation contract can escape the theorem. Pooling observations from
+incomparable low-rank endpoints is outside the single-common-endpoint result.
+
+## Open next questions
+
+The structured questions are in `TASK.json`. The useful next step is to identify
+one paid change that destroys a certified nuisance block and then price the
+entire resulting construction. A matrix-rank repair bound alone neither realizes
+such a change nor proves it improves the complete recursive cost. Existing
+changed-word rank-seven examples should be used as positive controls before
+starting any further synthesis.
+
+## Credit
+
+Prepared for Ross Richardson with substantial OpenAI Codex assistance, including
+separately assigned helper-boundaries, observation-kernels and exact-verification
+specialists. PR2918 is Ross Richardson's scoped obstruction; Jeremy Diviney's
+PR2908 supplies the rank-eight extraction, and Jeremy Kothe's PR2894 supplies the
+parent words. Marius-Paul Dumitrean's PR2979 supplies the prior all-endpoint
+screening comparison.
+Earlier contributions and license notices remain in
+`research/helper408-rank7-pairing/NOTICE.md` and its `sources/CREDITS.md`.
+This package is under the repository's Apache-2.0 license. No new copies of
+predecessor source files are vendored.
diff --git a/research/rank7-terminal-information-barrier/SOURCES.json b/research/rank7-terminal-information-barrier/SOURCES.json
new file mode 100644
index 0000000000..96f6684124
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/SOURCES.json
@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "files": [
+    {
+      "path": "research/helper408-rank7-pairing/verify_boundary.py",
+      "usage": "input",
+      "git_blob": "39756c56dd647c665e293506899db7e4b6ddb59c",
+      "sha256": "56ca12652c45f57c74341a06be2dbce4617415656e65dfe08223a4afcf8de541"
+    },
+    {
+      "path": "research/helper408-rank7-pairing/sources/data/PARENT-base.json.gz",
+      "usage": "input",
+      "git_blob": "0ca814951069c6f029eb375f3ed94053ba45bc63",
+      "sha256": "c20a470aec0f3e61833cb41fe190639eb358f58017143d2336c55c80fba265eb"
+    },
+    {
+      "path": "research/helper408-rank7-pairing/sources/data/PARENT-extra.json.gz",
+      "usage": "input",
+      "git_blob": "5c9e40118c599163571c10003db42eefa6f042a9",
+      "sha256": "db34e39876241087b581ed9374c53e9cd393e3e86ef6103bfb54f3077c3d2761"
+    },
+    {
+      "path": "research/helper408-rank7-pairing/sources/data/TRANSFORM.json",
+      "usage": "input",
+      "git_blob": "0e81cdc3e328fa8eedbdadda8f5065a3e3dc3dd6",
+      "sha256": "1d38f0369fce0b892d202ce2e5fd7ea95d9a95d3f80734b672cddd5cb93ce8ca"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "research/helper408-rank7-pairing/BOUNDARY.md",
+      "usage": "provenance",
+      "git_blob": "fd7de6b25bf3c642b37d060716dd44f7be100bda",
+      "sha256": "a59846249563d7229d471eab3b127f7333ff43fa5abe74b2555fc718c3a412f6"
+    },
+    {
+      "path": "research/helper408-rank7-pairing/INDEPENDENT.md",
+      "usage": "provenance",
+      "git_blob": "ecf922c35a00234b4bd8353bd8870691bea12c0e",
+      "sha256": "23981dd600ada4f9716800c51e8c0e397c86c557ace16cc6dcce5ab3e51fd228"
+    },
+    {
+      "path": "research/helper408-rank7-pairing/NOTICE.md",
+      "usage": "provenance",
+      "git_blob": "ec74fb826b1d5e33690d40848e23ecc5ec505146",
+      "sha256": "f37dd53e7ebb6af7a27084fff7f7b9e4112d020d207177e442a6182fcbdd197a"
+    },
+    {
+      "path": "research/rank7-joint-endframes/README.md",
+      "usage": "provenance",
+      "git_blob": "ad4fde698389d02543df632d46b54dcd93e53a97",
+      "sha256": "d00d123fc6cb7da627a8db1b8ae95b732ef7c55f802a784059de982159548634"
+    }
+  ]
+}
diff --git a/research/rank7-terminal-information-barrier/TASK.json b/research/rank7-terminal-information-barrier/TASK.json
new file mode 100644
index 0000000000..c87693b03d
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/TASK.json
@@ -0,0 +1,78 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 6,
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. 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": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "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": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "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": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Generalize PR2918 to all endpoints of rank at most seven on its two pinned providers, including arbitrary nonlinear decoding and monotone causal suffixes, with independent exact unit-minor certificates.",
+  "scope_change_reason": "Explicit user-assigned generalisation and publication review of PR2918. This keeps the old word and varies terminal readout/postprocessing, which is a scope-change trigger in the original card. The submission establishes a scoped obstruction; it does not satisfy the card's positive changed-interface construction or stronger-budget acceptance gate.",
+  "bottleneck_link": "The fixed provider cannot yield any new eligible-input function through any rank-seven terminal readout, so endpoint-only repairs cannot change its helper inventory. Any candidate must alter a certified premise and pay for that change.",
+  "budget_minutes": 240,
+  "stop_rule": "Finish the exact pinned census, independent verification and written causal proof; do not expand into changed-word synthesis or claim a new multiplication bound.",
+  "outcome": "negative-result",
+  "evidence": "PROOF.md, certificates.json, primary forward replay and independently written reverse-adjoint/RREF/Bareiss verification with rejecting controls and a rank-eight positive calibration.",
+  "author": "Ross Richardson",
+  "ai_assistance": "Substantial OpenAI Codex assistance, including separately assigned mathematical specialists. No independent human or formal-kernel review claimed.",
+  "open_questions": [
+    {
+      "question": "Which paid change to the fixed word or retained-source interface can destroy the certified nuisance saturation at a rank-seven endpoint?",
+      "why_it_matters": "Every endpoint-only monotone postprocessing repair is excluded, including nonlinear decoding; an escape must change a premise.",
+      "first_step": "Select one known changed-word rank-seven positive example, compute the induced change to the relevant nuisance block, and bind every changed entrance, source, restoration and recursive cost before proposing a new construction.",
+      "blocked_by": "This package proves a necessary obstruction, not a paid construction or a complete cost improvement."
+    }
+  ],
+  "scope_key": "pr2918-all-rank7-unit-nuisance-nonlinear-monotone-barrier",
+  "no_new_kappa": true,
+  "predecessors": [
+    {
+      "pr": 2918,
+      "head": "9360ba7312cf8961e672e9eb26c612719028d39d"
+    },
+    {
+      "pr": 2979,
+      "head": "be191346391661f4d35fc0d1508d0a6029572576"
+    }
+  ]
+}
diff --git a/research/rank7-terminal-information-barrier/VALIDATION.md b/research/rank7-terminal-information-barrier/VALIDATION.md
new file mode 100644
index 0000000000..23d05263c1
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/VALIDATION.md
@@ -0,0 +1,52 @@
+# Local validation receipt
+
+Validated on 2026-10-17 UTC using Python 3.12, on base
+`997e6a9ca7b4f95d50e366f61412fd640d72a88a`:
+
+```sh
+python3.12 scripts/research_package.py --package research/rank7-terminal-information-barrier
+```
+
+Result: `PASS_REGISTERED_RESEARCH_PACKAGE`, outcome `negative-result`.
+Both registered commands ran with `-I -O -B` and returned success:
+
+- `PASS_ALL_RANK_LE7_ENDPOINTS_DYADIC_NUISANCE_SURJECTIVITY`
+- `PASS_INDEPENDENT_TERMINAL_INFORMATION_BARRIER`
+
+Both authenticated providers produced 43,435 endpoints, 239 support classes,
+maximum support size 16, 58 eligible low-rank slots, and the determinant counts
+in the README. The primary path checked both inverse products for each minor,
+eight rejecting controls per provider and the actual rank-eight pre/post maps.
+The independent path checked seven rejecting controls with exact expected
+diagnostics, complete scalar blocks over the dyadic ring, and a separate
+rank-eight inverse-column/adjoint-row pairing. The fixed certificate SHA256 is
+`aa720fe2591cc511b58a0faea7752aba3c72ef90164b606eb9c0e437b9fa8863`.
+
+A separate specialist review compared the two implementations on all 4,583
+operations, 520 frame spans, 165 complete output rows (164 of rank at most seven
+plus register42), 239 support multiplicities, and the rank-eight inverse vector.
+It found exact agreement. Mathematical review confirmed the causal and
+indistinguishability arguments and led to the explicit linear-encoding
+restriction on the secondary dimension bounds.
+
+A fresh pre-submission review additionally compared all 520 complete operator
+rows and 11,912 coefficients on each provider, all 520 frames, the endpoint
+partition and the rank-eight inverse vector. Fourteen disposable variants with
+named validation checks removed were detected by the existing controls; a valid
+alternative gzip encoding separately tested source-byte authentication, and a
+noncommuting two-generator fixture checked word direction and cancellation.
+This was additional author-review work, not a third registered independent
+verifier; its scripts and receipts are retained by the author outside the package.
+
+The pre-submission mathematical fixes make the post-prelude entrance cut and
+inherited center-cut frame convention explicit, fix the dependency graph and
+output identities against control side channels, require joint ancillary
+independence, and qualify sharpness by a nonzero module. The task card now
+declares changed scope: this negative result does not satisfy the original
+positive-construction acceptance gate. Fresh mathematical and packaging reviews
+found no remaining issue within those stated limits.
+
+This receipt records local computation and AI-assisted mathematical review.
+It is not hosted CI, human peer review, formal-kernel verification, a full native
+supplier replay, or admission of a new multiplication bound. The original selected
+certificate and all predecessor sources are unchanged.
diff --git a/research/rank7-terminal-information-barrier/VERIFY.json b/research/rank7-terminal-information-barrier/VERIFY.json
new file mode 100644
index 0000000000..ea7582744b
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/VERIFY.json
@@ -0,0 +1,36 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/helper408-rank7-pairing/verify_boundary.py",
+    "research/helper408-rank7-pairing/sources/data/PARENT-base.json.gz",
+    "research/helper408-rank7-pairing/sources/data/PARENT-extra.json.gz",
+    "research/helper408-rank7-pairing/sources/data/TRANSFORM.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Pinned forward replay; complete endpoint census; dyadic-unit scalar minors and inverse products; eight rejecting controls per provider; rank-eight calibration."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify_independent.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Separate source parser and reverse adjoint; RREF endpoint coverage; Bareiss determinants; seven rejecting controls per provider; independent rank-eight pairing."
+    }
+  ]
+}
diff --git a/research/rank7-terminal-information-barrier/certificates.json b/research/rank7-terminal-information-barrier/certificates.json
new file mode 100644
index 0000000000..45e515da12
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/certificates.json
@@ -0,0 +1,11727 @@
+{
+  "providers": {
+    "base": {
+      "H": [
+        224,
+        225,
+        226,
+        227,
+        228,
+        229,
+        230,
+        231,
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+        382,
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+        386,
+        388,
+        390,
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+        399,
+        400,
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+        403,
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+        406,
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+        409,
+        410,
+        411,
+        412,
+        413,
+        414,
+        415,
+        416,
+        417,
+        418,
+        419,
+        420,
+        421,
+        422,
+        423,
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+        425,
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+        427,
+        428,
+        429,
+        430,
+        431,
+        432,
+        433,
+        434,
+        435,
+        436,
+        437,
+        438,
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+        456,
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+        461,
+        463,
+        464,
+        465,
+        466,
+        467,
+        468,
+        469,
+        470,
+        471,
+        479,
+        481,
+        490,
+        491,
+        492,
+        493,
+        499,
+        502,
+        503,
+        504,
+        505,
+        511,
+        514,
+        515,
+        516,
+        517,
+        546,
+        547,
+        548,
+        549,
+        558,
+        560,
+        568,
+        570
+      ],
+      "H_rank_distribution": {
+        "6": 24,
+        "7": 34,
+        "8": 167,
+        "9": 1
+      },
+      "all_rank_distribution": {
+        "4": 26,
+        "6": 56,
+        "7": 82,
+        "8": 355,
+        "9": 1
+      },
+      "classes": [
+        {
+          "H_eligible": [],
+          "R": [],
+          "annihilator": [
+            1,
+            2
+          ],
+          "forbidden_minor_columns": [],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 42061,
+          "pure_scalar_forbidden_rank": 0,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            32
+          ],
+          "annihilator": [
+            30,
+            70
+          ],
+          "forbidden_minor_columns": [
+            24
+          ],
+          "forbidden_minor_determinant": "1/2",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            50
+          ],
+          "annihilator": [
+            30,
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+          ],
+          "forbidden_minor_columns": [
+            22
+          ],
+          "forbidden_minor_determinant": "-1/2",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
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+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
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+        {
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+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
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+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
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+          ],
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+          "multiplicity": 1,
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+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
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+          ],
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+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
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+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
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+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
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+          ],
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+          ],
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+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
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+          ],
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+          ],
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+          ],
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+          ],
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+          "multiplicity": 4,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
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+          ],
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+          ],
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+          ],
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+          "multiplicity": 4,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
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+          ],
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+          ],
+          "annihilator": [
+            35,
+            75
+          ],
+          "forbidden_minor_columns": [
+            4
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 4,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [
+            391
+          ],
+          "R": [
+            391
+          ],
+          "annihilator": [
+            120,
+            133
+          ],
+          "forbidden_minor_columns": [
+            4
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 4,
+          "pure_scalar_forbidden_rank": 1,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [
+            402
+          ],
+          "R": [
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+            120,
+            426
+          ],
+          "forbidden_minor_columns": [
+            277,
+            282,
+            307,
+            309,
+            314,
+            353,
+            355,
+            357,
+            362,
+            385,
+            387,
+            389,
+            394
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            277,
+            282,
+            323,
+            325,
+            330,
+            337,
+            339,
+            341,
+            346,
+            385,
+            387,
+            389,
+            394
+          ],
+          "annihilator": [
+            75,
+            409
+          ],
+          "forbidden_minor_columns": [
+            277,
+            282,
+            323,
+            325,
+            330,
+            337,
+            339,
+            341,
+            346,
+            385,
+            387,
+            389,
+            394
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            277,
+            282,
+            323,
+            325,
+            330,
+            353,
+            355,
+            357,
+            362,
+            369,
+            371,
+            373,
+            378
+          ],
+          "annihilator": [
+            97,
+            435
+          ],
+          "forbidden_minor_columns": [
+            277,
+            282,
+            323,
+            325,
+            330,
+            353,
+            355,
+            357,
+            362,
+            369,
+            371,
+            373,
+            378
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            293,
+            298,
+            307,
+            309,
+            314,
+            337,
+            339,
+            341,
+            346,
+            385,
+            387,
+            389,
+            394
+          ],
+          "annihilator": [
+            76,
+            414
+          ],
+          "forbidden_minor_columns": [
+            293,
+            298,
+            307,
+            309,
+            314,
+            337,
+            339,
+            341,
+            346,
+            385,
+            387,
+            389,
+            394
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            293,
+            298,
+            307,
+            309,
+            314,
+            353,
+            355,
+            357,
+            362,
+            369,
+            371,
+            373,
+            378
+          ],
+          "annihilator": [
+            102,
+            436
+          ],
+          "forbidden_minor_columns": [
+            293,
+            298,
+            307,
+            309,
+            314,
+            353,
+            355,
+            357,
+            362,
+            369,
+            371,
+            373,
+            378
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            293,
+            298,
+            323,
+            325,
+            330,
+            337,
+            339,
+            341,
+            346,
+            369,
+            371,
+            373,
+            378
+          ],
+          "annihilator": [
+            85,
+            391
+          ],
+          "forbidden_minor_columns": [
+            293,
+            298,
+            323,
+            325,
+            330,
+            337,
+            339,
+            341,
+            346,
+            369,
+            371,
+            373,
+            378
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            293,
+            298,
+            323,
+            325,
+            330,
+            353,
+            355,
+            357,
+            362,
+            385,
+            387,
+            389,
+            394
+          ],
+          "annihilator": [
+            127,
+            429
+          ],
+          "forbidden_minor_columns": [
+            293,
+            298,
+            323,
+            325,
+            330,
+            353,
+            355,
+            357,
+            362,
+            385,
+            387,
+            389,
+            394
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 13,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            307,
+            309,
+            314,
+            323,
+            325,
+            330,
+            337,
+            339,
+            341,
+            346,
+            353,
+            355,
+            357,
+            362
+          ],
+          "annihilator": [
+            30,
+            460
+          ],
+          "forbidden_minor_columns": [
+            307,
+            309,
+            314,
+            323,
+            325,
+            330,
+            337,
+            339,
+            341,
+            346,
+            353,
+            355,
+            357,
+            362
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 14,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            307,
+            309,
+            314,
+            323,
+            325,
+            330,
+            369,
+            371,
+            373,
+            378,
+            385,
+            387,
+            389,
+            394
+          ],
+          "annihilator": [
+            52,
+            466
+          ],
+          "forbidden_minor_columns": [
+            307,
+            309,
+            314,
+            323,
+            325,
+            330,
+            369,
+            371,
+            373,
+            378,
+            385,
+            387,
+            389,
+            394
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 14,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        },
+        {
+          "H_eligible": [],
+          "R": [
+            337,
+            339,
+            341,
+            346,
+            353,
+            355,
+            357,
+            362,
+            369,
+            371,
+            373,
+            378,
+            385,
+            387,
+            389,
+            394
+          ],
+          "annihilator": [
+            7,
+            466
+          ],
+          "forbidden_minor_columns": [
+            337,
+            339,
+            341,
+            346,
+            353,
+            355,
+            357,
+            362,
+            369,
+            371,
+            373,
+            378,
+            385,
+            387,
+            389,
+            394
+          ],
+          "forbidden_minor_determinant": "1",
+          "multiplicity": 1,
+          "pure_scalar_forbidden_rank": 16,
+          "status": "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION"
+        }
+      ],
+      "engine_sha256": "56ca12652c45f57c74341a06be2dbce4617415656e65dfe08223a4afcf8de541",
+      "frame_replay_counts": {
+        "middle_warps": 72,
+        "prelude_warps": 24,
+        "scalar_incidents": 10456
+      },
+      "label": "extra",
+      "operator_sha256": "d1c29a23fbe07da932c44d9e9b1467ab866894faac115d456eae8e42069aec68",
+      "pin": "9360ba7312cf8961e672e9eb26c612719028d39d",
+      "rank7_endpoint_count": 43435,
+      "reuse": "PR2918 forward operator and frame engine; new endpoint census",
+      "source_sha256": "db34e39876241087b581ed9374c53e9cd393e3e86ef6103bfb54f3077c3d2761",
+      "status_distribution": {
+        "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION": 239
+      },
+      "support_class_count": 239,
+      "weighted_status_distribution": {
+        "UNIVERSAL_SCALAR_MINOR_OBSTRUCTION": 43435
+      }
+    }
+  },
+  "schema_version": 1
+}
diff --git a/research/rank7-terminal-information-barrier/verify.py b/research/rank7-terminal-information-barrier/verify.py
new file mode 100644
index 0000000000..758d12522b
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/verify.py
@@ -0,0 +1,342 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Exact source-bound census of all rank-seven terminal supports.
+
+The existing PR2918 forward operator/frame engine is reused, not independent.
+It is executed directly from the authenticated source bytes (no pyc importer).
+The complete endpoint enumeration and certificate extraction are new here.
+"""
+import argparse
+from collections import Counter, defaultdict
+import copy
+from fractions import Fraction as Q
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import types
+
+HERE = Path(__file__).resolve().parent
+PACKAGE = HERE.parent / 'helper408-rank7-pairing'
+PIN = '9360ba7312cf8961e672e9eb26c612719028d39d'
+ENGINE_SHA = '56ca12652c45f57c74341a06be2dbce4617415656e65dfe08223a4afcf8de541'
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def authenticate(raw, expected, message):
+    need(hashlib.sha256(raw).hexdigest() == expected, message)
+
+
+def dyadic_unit(value):
+    numerator = abs(value.numerator)
+    denominator = value.denominator
+    return bool(numerator) and numerator & (numerator - 1) == 0 and denominator & (denominator - 1) == 0
+
+
+def engine():
+    source = (PACKAGE / 'verify_boundary.py').read_bytes()
+    authenticate(source, ENGINE_SHA, 'engine source pin mismatch')
+    module = types.ModuleType('pinned_pr2918_boundary')
+    module.__file__ = str(PACKAGE / 'verify_boundary.py')
+    exec(compile(source, module.__file__, 'exec'), module.__dict__)
+    return module
+
+
+def endpoint_classes(frames):
+    """Every codim-two endpoint is annihilator of unique triple {a,b,a^b}.
+
+    Choose its two least nonzero members a<b<a^b. Distinct annihilator
+    planes have distinct orthogonal complements. Lower-dimensional endpoints
+    embed into rank-seven endpoints, and R(E) grows monotonically with E.
+    """
+    registers = sorted(frames)
+    masks = [sum((1 << i) for i, r in enumerate(registers)
+                 if all((a & f).bit_count() % 2 == 0 for f in frames[r]))
+             for a in range(512)]
+    classes = {}
+    total = 0
+    for a in range(1, 512):
+        for b in range(a + 1, 512):
+            if b >= (a ^ b):
+                continue
+            total += 1
+            mask = masks[a] & masks[b]
+            if mask not in classes:
+                classes[mask] = {'R': [r for i, r in enumerate(registers) if (mask >> i) & 1],
+                                 'annihilator': [a, b], 'multiplicity': 0}
+            classes[mask]['multiplicity'] += 1
+    need(total == 43435, 'rank-seven endpoint coverage mismatch')
+    need(sum(c['multiplicity'] for c in classes.values()) == total, 'endpoint partition mismatch')
+    return sorted(classes.values(), key=lambda c: (len(c['R']), c['R']))
+
+
+def row_pivots(rows):
+    """Exact row elimination returns rank and original pivot columns."""
+    pivots = {}
+    for original in rows:
+        row = dict(original)
+        while row:
+            lead = min(row)
+            if lead not in pivots:
+                d = row[lead]
+                pivots[lead] = {k: c / d for k, c in row.items()}
+                break
+            d = -row[lead]
+            for k, c in pivots[lead].items():
+                value = row.get(k, Q(0)) + d * c
+                if value:
+                    row[k] = value
+                else:
+                    row.pop(k, None)
+    return sorted(pivots)
+
+
+def exact_determinant(matrix):
+    n = len(matrix)
+    need(all(len(row) == n for row in matrix), 'nonsquare determinant')
+    a = [list(row) for row in matrix]
+    determinant = Q(1)
+    for i in range(n):
+        pivot = next((j for j in range(i, n) if a[j][i]), None)
+        if pivot is None:
+            return Q(0)
+        if pivot != i:
+            a[i], a[pivot] = a[pivot], a[i]
+            determinant = -determinant
+        d = a[i][i]
+        determinant *= d
+        for j in range(i + 1, n):
+            c = a[j][i] / d
+            for k in range(i + 1, n):
+                a[j][k] -= c * a[i][k]
+            a[j][i] = Q(0)
+    return determinant
+
+
+def screen(module, M, H, item):
+    R = item['R']
+    allowed = set(H)
+    forbidden = set(M) - allowed
+    nonscalar_columns = {c for r in R for c, word in M[r] if word}
+    safe = forbidden - nonscalar_columns
+    scalar_rows = [{c: a for (c, word), a in M[r].items() if c in safe and not word} for r in R]
+    pivots = row_pivots(scalar_rows)
+    result = dict(item)
+    result['H_eligible'] = sorted(allowed.intersection(R))
+    result['pure_scalar_forbidden_rank'] = len(pivots)
+    if len(pivots) == len(R):
+        determinant = exact_determinant([[M[r].get((c, ()), Q(0)) for c in pivots] for r in R])
+        need(determinant != 0, 'chosen scalar minor singular')
+        need(dyadic_unit(determinant), 'chosen scalar minor not dyadic unit')
+        result['forbidden_minor_columns'] = pivots
+        result['forbidden_minor_determinant'] = str(determinant)
+        result['status'] = 'UNIVERSAL_SCALAR_MINOR_OBSTRUCTION'
+        return result
+    constraints = defaultdict(dict)
+    for r in R:
+        for (c, word), a in M[r].items():
+            if c not in allowed or word:
+                constraints[c, word][r] = a
+    A, info = module.kernel(constraints.values(), R)
+    result['A_dimension'] = len(A)
+    result['A_info'] = info
+    if not A:
+        result['status'] = 'FREE_WORD_COEFFICIENT_OBSTRUCTION'
+    else:
+        exact = module.analyze(M, H, R)
+        result['V_dimension'] = len(exact['V'])
+        result['pairing_rank'] = len(row_pivots([{j: a for j, a in enumerate(row) if a} for row in exact['pairing']]))
+        result['status'] = 'POSITIVE_PAIRING' if result['pairing_rank'] else 'ZERO_PAIRING_OBSTRUCTION'
+        for field in ['V', 'Y', 'Alpha', 'U']:
+            result[field] = [module.encode_vector(v) for v in exact[field]]
+        result['pairing'] = [[str(a) for a in row] for row in exact['pairing']]
+    return result
+
+
+def run(label):
+    v = engine()
+    raw = (PACKAGE / 'sources/data' / ('PARENT-' + label + '.json.gz')).read_bytes()
+    authenticate(raw, v.EXPECTED_SHA256[label], 'provider pin mismatch')
+    p = json.loads(gzip.decompress(raw))
+    frames, counts = v.terminal_frames(p)
+    need(all(isinstance(x, int) and 0 <= x < 512 for frame in frames.values() for x in frame),
+         'terminal frame outside F2^9')
+    protected = set(map(int, p['helper_final'])) | set(map(int, p['start_extra'])) | {r['source'] for r in p['initial_corrections']}
+    H = sorted(r for r in frames if r >= 224 and r not in protected)
+    prelude_lenders = {g[1] for g in p['A'][:p['prelude_events']] if g[0] == 'warp'}
+    need(not prelude_lenders.intersection(H), 'eligible input helper affected by prelude warp')
+    classes = endpoint_classes(frames)
+    M = v.replay(p)
+    need(set(M) == set(frames), 'operator and frame coordinate sets differ')
+    screens = [screen(v, M, H, c) for c in classes]
+    need(all(c['status'] == 'UNIVERSAL_SCALAR_MINOR_OBSTRUCTION' for c in screens),
+         'an endpoint lacks a dyadic scalar minor')
+    report = {'label': label, 'pin': PIN, 'engine_sha256': ENGINE_SHA, 'source_sha256': hashlib.sha256(raw).hexdigest(),
+            'operator_sha256': v.operator_digest(M), 'reuse': 'PR2918 forward operator and frame engine; new endpoint census',
+            'H': H, 'H_rank_distribution': dict(sorted(Counter(len(frames[r]) for r in H).items())),
+            'all_rank_distribution': dict(sorted(Counter(map(len, frames.values())).items())),
+            'frame_replay_counts': counts, 'rank7_endpoint_count': 43435,
+            'support_class_count': len(classes), 'status_distribution': dict(Counter(c['status'] for c in screens)),
+            'weighted_status_distribution': dict(sum((Counter({c['status']: c['multiplicity']}) for c in screens), Counter())),
+            'classes': screens}
+    return report, {'module': v, 'provider_raw': raw, 'M': M, 'H': H, 'frames': frames}
+
+
+def dyadic_inverse(matrix):
+    """Construct a rational inverse, then verify both complete products."""
+    n = len(matrix)
+    a = [[Q(c) for c in row] + [Q(i == j) for j in range(n)] for i, row in enumerate(matrix)]
+    for i in range(n):
+        pivot = next((j for j in range(i, n) if a[j][i]), None)
+        need(pivot is not None, 'minor singular')
+        a[i], a[pivot] = a[pivot], a[i]
+        d = a[i][i]
+        a[i] = [c / d for c in a[i]]
+        for j in range(n):
+            if j != i:
+                d = a[j][i]
+                a[j] = [c - d * b for c, b in zip(a[j], a[i])]
+    inverse = [row[n:] for row in a]
+    need(all(c.denominator & (c.denominator - 1) == 0 for row in inverse for c in row), 'minor inverse not dyadic')
+    for left, right in [(matrix, inverse), (inverse, matrix)]:
+        need(all(sum(left[i][k] * right[k][j] for k in range(n)) == Q(i == j)
+                 for i in range(n) for j in range(n)), 'inverse product identity failed')
+    return inverse
+
+
+def validate_class(item, M, H, frames):
+    a, b = item['annihilator']
+    need(0 < a < 512 and 0 < b < 512 and a != b, 'annihilator dimension mismatch')
+    expected = {r for r, f in frames.items()
+                if all((a & x).bit_count() % 2 == 0 and (b & x).bit_count() % 2 == 0 for x in f)}
+    R = item['R']
+    need(len(R) == len(set(R)) and set(R) == expected, 'terminal support incomplete')
+    J = item['forbidden_minor_columns']
+    need(len(J) == len(R) and len(set(J)) == len(J), 'minor dimensions mismatch')
+    need(set(J) <= set(frames) - set(H), 'minor input is not forbidden')
+    matrix = []
+    for r in R:
+        row = []
+        for c in J:
+            poly = {w: coefficient for (j, w), coefficient in M[r].items() if j == c}
+            need(set(poly) <= {()}, 'minor contains nonempty word')
+            row.append(poly.get((), Q(0)))
+        matrix.append(row)
+    determinant = exact_determinant(matrix)
+    need(determinant and str(determinant) == item['forbidden_minor_determinant'], 'minor determinant mismatch')
+    need(dyadic_unit(determinant), 'minor determinant not dyadic unit')
+    inverse = dyadic_inverse(matrix)
+    return max((c.denominator.bit_length() - 1 for row in inverse for c in row), default=0)
+
+
+def validate_partition(items, partition):
+    received = Counter()
+    for item in items:
+        key = tuple(sorted(item['R']))
+        need(key not in received, 'duplicate support class')
+        need(isinstance(item['multiplicity'], int) and item['multiplicity'] > 0, 'invalid support multiplicity')
+        received[key] = item['multiplicity']
+    need(received == partition, 'support partition incomplete')
+
+
+def verify_provider(fixed, regenerated, context):
+    """Check complete certificate semantics before canonical regeneration equality."""
+    M, H, frames = (context[k] for k in ['M', 'H', 'frames'])
+    partition = Counter({tuple(item['R']): item['multiplicity'] for item in regenerated['classes']})
+    validate_partition(fixed['classes'], partition)
+    inverse_bits = [validate_class(item, M, H, frames) for item in fixed['classes']]
+    need(fixed == regenerated, 'fixed certificate differs from exact regeneration')
+    controls = {}
+
+    def rejects(name, action, expected):
+        try:
+            action()
+        except ValueError as error:
+            need(str(error) == expected, 'wrong control rejection: ' + str(error))
+            controls[name] = {'rejected': True, 'reason': expected}
+            return
+        raise ValueError('invalid certificate accepted: ' + name)
+
+    selected = next(item for item in fixed['classes'] if len(item['R']) > 1)
+    rejects('source_drift', lambda: authenticate(context['provider_raw'] + b'!', fixed['source_sha256'],
+                                                'provider pin mismatch'), 'provider pin mismatch')
+    mutant = copy.deepcopy(selected)
+    mutant['forbidden_minor_determinant'] = str(Q(mutant['forbidden_minor_determinant']) * 2)
+    rejects('determinant_coefficient_mutation', lambda: validate_class(mutant, M, H, frames), 'minor determinant mismatch')
+    mutant = copy.deepcopy(selected)
+    mutant['forbidden_minor_columns'][0] = H[0]
+    rejects('allow_eligible_input_as_nuisance', lambda: validate_class(mutant, M, H, frames), 'minor input is not forbidden')
+    mutant = copy.deepcopy(selected)
+    mutant['R'].pop()
+    rejects('omit_terminal_register', lambda: validate_class(mutant, M, H, frames), 'terminal support incomplete')
+    rejects('omit_support_class', lambda: validate_partition(fixed['classes'][1:], partition), 'support partition incomplete')
+    mutant_matrix = copy.deepcopy(M)
+    first_r, first_c = selected['R'][0], selected['forbidden_minor_columns'][0]
+    mutant_matrix[first_r][first_c, (99,)] = Q(1)
+    rejects('hidden_nonempty_operator_word', lambda: validate_class(selected, mutant_matrix, H, frames), 'minor contains nonempty word')
+    mutant_matrix = copy.deepcopy(M)
+    columns = set(selected['forbidden_minor_columns'])
+    mutant_matrix[first_r] = {key: a for key, a in mutant_matrix[first_r].items() if key[0] not in columns}
+    rejects('singular_nuisance_block', lambda: validate_class(selected, mutant_matrix, H, frames), 'minor determinant mismatch')
+    mutant_matrix = copy.deepcopy(M)
+    mutant_matrix[first_r] = {key: 3 * a for key, a in mutant_matrix[first_r].items()}
+    mutant = copy.deepcopy(selected)
+    mutant['forbidden_minor_determinant'] = str(3 * Q(mutant['forbidden_minor_determinant']))
+    rejects('rational_but_not_dyadic_unit', lambda: validate_class(mutant, mutant_matrix, H, frames), 'minor determinant not dyadic unit')
+    positive = copy.deepcopy(selected)
+    positive['R'] = list(reversed(positive['R']))
+    positive['forbidden_minor_columns'] = list(reversed(positive['forbidden_minor_columns']))
+    validate_class(positive, M, H, frames)
+    controls['simultaneous_row_column_reversal'] = {'accepted': True}
+    v = context['module']
+    transform_raw = (PACKAGE / 'sources/data/TRANSFORM.json').read_bytes()
+    authenticate(transform_raw, v.TRANSFORM_SHA256, 'calibration transform pin mismatch')
+    calibration = v.calibrate(M, H, frames, json.loads(transform_raw))
+    return {'rank7_endpoints': fixed['rank7_endpoint_count'], 'support_classes': len(fixed['classes']),
+            'nonempty_support_classes': sum(bool(c['R']) for c in fixed['classes']),
+            'classes_with_eligible_H_slot': sum(bool(c['H_eligible']) for c in fixed['classes']),
+            'endpoints_with_eligible_H_slot': sum(c['multiplicity'] for c in fixed['classes'] if c['H_eligible']),
+            'eligible_H_slots': len({r for c in fixed['classes'] for r in c['H_eligible']}),
+            'scalar_minor_determinants': dict(sorted(Counter(c['forbidden_minor_determinant'] for c in fixed['classes']).items())),
+            'max_support_size': max(len(c['R']) for c in fixed['classes']),
+            'max_minor_inverse_denominator_bits': max(inverse_bits),
+            'all_minor_entries_scalar': True, 'all_minor_inverses_dyadic': True,
+            'source_sha256': fixed['source_sha256'], 'operator_sha256': fixed['operator_sha256'],
+            'H_rank_distribution': fixed['H_rank_distribution'],
+            'controls': controls, 'rank8_calibration': calibration}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--write', action='store_true', help='explicitly regenerate the fixed certificate before verifying')
+    args = parser.parse_args()
+    path = HERE / 'certificates.json'
+    # Missing evidence is a failure unless generation was explicitly requested.
+    if not args.write:
+        need(path.is_file(), 'fixed certificates.json is missing')
+    generated, contexts = {}, {}
+    for label in ['base', 'extra']:
+        generated[label], contexts[label] = run(label)
+        generated[label] = json.loads(json.dumps(generated[label], sort_keys=True))
+    envelope = {'schema_version': 1, 'providers': generated}
+    if args.write:
+        path.write_text(json.dumps(envelope, indent=2, sort_keys=True) + '\n')
+    fixed = json.loads(path.read_text())
+    need(set(fixed) == {'schema_version', 'providers'} and fixed['schema_version'] == 1,
+         'certificate schema mismatch')
+    need(set(fixed['providers']) == {'base', 'extra'}, 'certificate provider coverage mismatch')
+    summaries = {label: verify_provider(fixed['providers'][label], generated[label], contexts[label])
+                 for label in ['base', 'extra']}
+    need(fixed == envelope, 'canonical certificate envelope mismatch')
+    print(json.dumps({'status': 'PASS_ALL_RANK_LE7_ENDPOINTS_DYADIC_NUISANCE_SURJECTIVITY',
+                      'schema_version': 1, 'scientific_pin': PIN, 'engine_sha256': ENGINE_SHA,
+                      'certificate_sha256': hashlib.sha256(path.read_bytes()).hexdigest(),
+                      'providers': summaries}, indent=2, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/rank7-terminal-information-barrier/verify_independent.py b/research/rank7-terminal-information-barrier/verify_independent.py
new file mode 100644
index 0000000000..b97c69be7c
--- /dev/null
+++ b/research/rank7-terminal-information-barrier/verify_independent.py
@@ -0,0 +1,323 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Independent source parser, reverse adjoint, RREF census and Bareiss checks.
+
+No predecessor Python module or primary verifier is imported. Shared scientific
+inputs are the two authenticated JSON providers and the proposed certificates.
+The reverse-adjoint method follows the credited PR2918 independent checker;
+its implementation here also checks every low-rank terminal row and endpoint.
+"""
+import copy
+from collections import Counter
+from fractions import Fraction as F
+import gzip
+import hashlib
+import json
+from math import lcm, prod
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+DATA = HERE.parent / 'helper408-rank7-pairing/sources/data'
+HASHES = {
+    'base': 'c20a470aec0f3e61833cb41fe190639eb358f58017143d2336c55c80fba265eb',
+    'extra': 'db34e39876241087b581ed9374c53e9cd393e3e86ef6103bfb54f3077c3d2761',
+}
+PIN = '9360ba7312cf8961e672e9eb26c612719028d39d'
+TARGET = set(range(112, 224))
+
+
+def check(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+
+def load_provider(raw, variant):
+    check(hashlib.sha256(raw).hexdigest() == HASHES[variant], 'provider bytes changed')
+    return json.loads(gzip.decompress(raw))
+
+
+def span(basis):
+    values = {0}
+    for v in basis:
+        check(isinstance(v, int) and 0 <= v < 512, 'frame outside GF(2)^9')
+        values |= {x ^ v for x in values}
+    return frozenset(values)
+
+
+def parse(p):
+    check(len(p['ports']) == 112 and len(p['warps']) == 72, 'provider shape')
+    live = set(range(704)) - set(p['removed'])
+    frames = [span([p['ports'][r]]) if r < 112 else span([]) for r in range(704)]
+    for r, f in p['start_extra'].items():
+        frames[int(r)] = span(f)
+    after = {}
+    for i, w in enumerate(p['warps']):
+        check(0 <= w[0] <= len(p['B']), 'warp position')
+        after.setdefault(w[0], []).append(['warp', w[1], i + 1, w[3], w[4]])
+    events = list(p['A'])
+    for i in range(len(p['B']) + 1):
+        events.extend(after.get(i, []))
+        if i < len(p['B']):
+            events.append(p['B'][i])
+    events.extend(p['restore'])
+    seen = set()
+    for i, g in enumerate(events):
+        kind, d = g[:2]
+        check(d in live, 'gate uses removed destination')
+        if kind == 'warp':
+            check(frames[d] == span(g[3]), 'warp before-frame')
+            check(1 <= abs(g[2]) <= 72 and p['warps'][abs(g[2]) - 1][1] == d,
+                  'warp register identity')
+            regs, nxt = [d], span(g[4])
+        else:
+            check(kind in ('add', 'scale'), 'unknown operation')
+            regs = [d, g[2]] if kind == 'add' else [d]
+            nxt = span(g[-1])
+            check(all(r in live and frames[r] <= nxt for r in regs), 'nonmonotone frame')
+            q = F(g[3], g[4]) if kind == 'add' else F(g[2], g[3])
+            check(q.denominator & (q.denominator - 1) == 0, 'non-dyadic gate coefficient')
+            if kind == 'scale':
+                check(unit(q), 'scale is not a dyadic unit')
+        for r in regs:
+            frames[r] = nxt
+            seen.add(r)
+        if i + 1 == len(p['A']):
+            check(all(frames[r] == span(f) for r, f in zip(p['centers'], p['center_frames'])),
+                  'center frame cut')
+            check(all(g[0] == 'add' and g[1] in TARGET and g[2] in p['centers']
+                      for g in p['cut']), 'center cut access')
+    check(live <= seen, 'unaccounted terminal incidence')
+    check(all(frames[int(r)] == span(f) for r, f in p['helper_final'].items()),
+          'protected helper frame')
+    eligible = (set(range(224, 704)) & live) - (
+        set(map(int, p['helper_final'])) | set(map(int, p['start_extra'])) |
+        {c['source'] for c in p['initial_corrections']})
+    prelude = events[:p['prelude_events']]
+    check(all(not ({g[1]} | ({g[2]} if g[0] == 'add' else set())) & eligible
+              for g in prelude if g[1] not in TARGET), 'prelude touches eligible input')
+    ops = []
+    for g in events[p['prelude_events']:]:
+        if g[1] in TARGET:
+            continue
+        check(g[0] != 'add' or g[2] not in TARGET, 'non-target depends on target')
+        ops.append(g)
+    check(len(ops) == 4583 and len(eligible) == 226, 'frozen interface size')
+    return ops, {r: frames[r] for r in live - TARGET}, eligible
+
+
+def add(dest, source, q):
+    for key, c in list(source.items()):
+        value = dest.get(key, F(0)) + q * c
+        if value:
+            dest[key] = value
+        else:
+            dest.pop(key, None)
+
+
+def rows_by_adjoint(ops, terminals):
+    state = [{} for _ in range(704)]
+    for r in terminals:
+        state[r][r, ()] = F(1)
+    for g in reversed(ops):
+        kind, d = g[:2]
+        if kind == 'add':
+            add(state[g[2]], state[d], F(g[3], g[4]))
+        elif kind == 'scale':
+            q = F(g[2], g[3])
+            state[d] = {key: q * c for key, c in state[d].items()}
+        else:
+            t = g[2]
+            state[d] = {(r, w[:-1] if w and w[-1] == -t else w + (t,)): c
+                        for (r, w), c in state[d].items()}
+    rows = {r: {} for r in terminals}
+    for j, polynomials in enumerate(state):
+        for (r, word), c in polynomials.items():
+            rows[r][j, word] = c
+    return rows
+
+
+def inverse_column(ops, output):
+    state = [{} for _ in range(704)]
+    for r, c in output.items():
+        state[r][()] = F(c)
+    for g in reversed(ops):
+        kind, d = g[:2]
+        if kind == 'add':
+            add(state[d], state[g[2]], -F(g[3], g[4]))
+        elif kind == 'scale':
+            q = F(g[3], g[2])
+            state[d] = {w: q * c for w, c in state[d].items()}
+        else:
+            t = -g[2]
+            state[d] = {w[1:] if w and w[0] == -t else (t,) + w: c
+                        for w, c in state[d].items()}
+    check(all(set(poly) <= {()} for poly in state), 'rank-eight inverse not scalar')
+    return {r: poly[()] for r, poly in enumerate(state) if poly}
+
+
+def endpoint_partition(frames):
+    """Enumerate unique two-row reduced echelon normal matrices, low pivots.
+
+    Primary census instead chooses the two least elements of each normal
+    plane. This code forms each endpoint's full set of 128 bit vectors and
+    tests containment of each full terminal-frame span.
+    """
+    orthogonal = [sum(1 << x for x in range(512) if (a & x).bit_count() % 2 == 0)
+                  for a in range(512)]
+    by_frame = {}
+    for r, f in frames.items():
+        if len(f) <= 128:
+            by_frame.setdefault(sum(1 << x for x in f), []).append(r)
+    groups = Counter()
+    endpoints = set()
+    for i in range(9):
+        for j in range(i + 1, 9):
+            free = [(0, c) for c in range(i + 1, 9) if c != j]
+            free += [(1, c) for c in range(j + 1, 9)]
+            for bits in range(1 << len(free)):
+                normals = [1 << i, 1 << j]
+                for k, (row, col) in enumerate(free):
+                    if bits >> k & 1:
+                        normals[row] |= 1 << col
+                e = orthogonal[normals[0]] & orthogonal[normals[1]]
+                check(e.bit_count() == 128 and e not in endpoints, 'endpoint repeated or wrong rank')
+                endpoints.add(e)
+                support = tuple(sorted(r for f, regs in by_frame.items() if f & ~e == 0 for r in regs))
+                groups[support] += 1
+    check(len(endpoints) == 43435 and len(groups) == 239, 'independent endpoint count')
+    return groups
+
+
+def bareiss(matrix):
+    n = len(matrix)
+    check(all(len(row) == n for row in matrix), 'minor not square')
+    if not n:
+        return F(1)
+    scales = [lcm(*(c.denominator for c in row)) for row in matrix]
+    a = [[int(c * scale) for c in row] for row, scale in zip(matrix, scales)]
+    previous, sign = 1, 1
+    for k in range(n - 1):
+        p = next((i for i in range(k, n) if a[i][k]), None)
+        if p is None:
+            return F(0)
+        if p != k:
+            a[k], a[p] = a[p], a[k]
+            sign = -sign
+        pivot = a[k][k]
+        for i in range(k + 1, n):
+            for j in range(k + 1, n):
+                numerator = a[i][j] * pivot - a[i][k] * a[k][j]
+                check(numerator % previous == 0, 'Bareiss inexact division')
+                a[i][j] = numerator // previous
+            a[i][k] = 0
+        previous = pivot
+    return F(sign * a[-1][-1], prod(scales))
+
+
+def unit(q):
+    a, b = abs(q.numerator), q.denominator
+    return a != 0 and a & (a - 1) == 0 and b & (b - 1) == 0
+
+
+def validate_minor(item, rows, frames, eligible):
+    rr, jj = item['R'], item['forbidden_minor_columns']
+    a, b = item['annihilator']
+    check(0 < a < 512 and 0 < b < 512 and a != b, 'annihilator invalid')
+    actual = {r for r, f in frames.items()
+              if all((a & x).bit_count() % 2 == 0 and (b & x).bit_count() % 2 == 0 for x in f)}
+    check(set(rr) == actual and len(rr) == len(actual), 'complete terminal support mismatch')
+    check(len(jj) == len(rr) and len(set(jj)) == len(jj), 'minor size mismatch')
+    check(set(jj) <= set(frames) - eligible, 'illegal nuisance input')
+    matrix = []
+    for r in rr:
+        check(all(not word for (j, word) in rows[r] if j in jj), 'hidden operator in scalar minor')
+        matrix.append([rows[r].get((j, ()), F(0)) for j in jj])
+    check(all(c.denominator & (c.denominator - 1) == 0 for row in matrix for c in row),
+          'minor coefficient is not dyadic')
+    determinant = bareiss(matrix)
+    check(unit(determinant), 'minor determinant is not a dyadic unit')
+    check(determinant == F(item['forbidden_minor_determinant']), 'determinant certificate mismatch')
+    check(item['pure_scalar_forbidden_rank'] == len(rr), 'certified rank mismatch')
+    check(item['H_eligible'] == sorted(eligible & set(rr)), 'eligible terminal intersection')
+    check(item['status'] == 'UNIVERSAL_SCALAR_MINOR_OBSTRUCTION', 'class status mismatch')
+    return determinant
+
+
+def coverage(items, groups):
+    check(len(items) == len(groups), 'support class omitted')
+    received = {tuple(c['R']): c['multiplicity'] for c in items}
+    check(len(received) == len(items) and received == groups, 'endpoint partition differs')
+
+
+def rejects(action, name, expected):
+    try:
+        action()
+    except ValueError as error:
+        check(str(error) == expected, 'negative control failed for wrong reason: ' + name + ': ' + str(error))
+        return name
+    raise ValueError('negative control accepted: ' + name)
+
+
+def controls(raw, variant, report, rows, frames, eligible, groups):
+    items = report['classes']
+    item = next(c for c in items if c['R'])
+    out = [rejects(lambda: load_provider(raw + b' ', variant), 'source drift', 'provider bytes changed')]
+    bad = copy.deepcopy(item)
+    bad['forbidden_minor_determinant'] = str(F(bad['forbidden_minor_determinant']) * 2)
+    out.append(rejects(lambda: validate_minor(bad, rows, frames, eligible), 'wrong determinant', 'determinant certificate mismatch'))
+    bad = copy.deepcopy(item)
+    bad['forbidden_minor_columns'][0] = min(eligible)
+    out.append(rejects(lambda: validate_minor(bad, rows, frames, eligible), 'eligible nuisance', 'illegal nuisance input'))
+    out.append(rejects(lambda: coverage(items[:-1], groups), 'omitted class', 'support class omitted'))
+    badrows = dict(rows)
+    r, j = item['R'][0], item['forbidden_minor_columns'][0]
+    badrows[r] = dict(rows[r])
+    badrows[r][j, (72,)] = F(1)
+    out.append(rejects(lambda: validate_minor(item, badrows, frames, eligible), 'hidden word', 'hidden operator in scalar minor'))
+    badrows[r] = {key: c for key, c in rows[r].items() if key[0] not in item['forbidden_minor_columns']}
+    out.append(rejects(lambda: validate_minor(item, badrows, frames, eligible), 'singular block', 'minor determinant is not a dyadic unit'))
+    badrows[r] = dict(rows[r])
+    badrows[r][j, ()] = F(1, 3)
+    out.append(rejects(lambda: validate_minor(item, badrows, frames, eligible), 'non-dyadic entry', 'minor coefficient is not dyadic'))
+    check(bareiss([[F(0), F(1)], [F(2), F(3)]]) == -2, 'Bareiss pivot-swap calibration')
+    check(not unit(F(3)) and unit(F(-1, 4)) and not unit(F(0)), 'dyadic unit calibration')
+    return out
+
+
+def main():
+    envelope = json.loads((HERE / 'certificates.json').read_text())
+    check(envelope['schema_version'] == 1 and set(envelope['providers']) == set(HASHES), 'certificate envelope')
+    receipts = {}
+    for variant in HASHES:
+        raw = (DATA / ('PARENT-' + variant + '.json.gz')).read_bytes()
+        ops, frames, eligible = parse(load_provider(raw, variant))
+        low = {r for r, f in frames.items() if len(f) <= 128}
+        rows = rows_by_adjoint(ops, low | {42})
+        check(len(low) == 164 and len(frames) == 520, 'terminal row count')
+        groups = endpoint_partition(frames)
+        report = envelope['providers'][variant]
+        check(report['pin'] == PIN and report['source_sha256'] == HASHES[variant], 'report pin')
+        check(report['H'] == sorted(eligible), 'report eligible inputs')
+        coverage(report['classes'], groups)
+        histogram = Counter(str(validate_minor(c, rows, frames, eligible)) for c in report['classes'])
+        e8 = span([256, 128, 64, 36, 20, 8, 2, 1])
+        alpha = {408: F(1), 42: F(1, 2), 105: F(1)}
+        check(all(frames[r] <= e8 for r in alpha), 'rank-eight alpha support')
+        u = {}
+        for r, c in alpha.items():
+            add(u, rows[r], c)
+        check(all(j in eligible and not w for j, w in u), 'rank-eight alpha pullback support')
+        v = inverse_column(ops, {42: F(2)})
+        check(set(v) <= eligible, 'rank-eight inverse support')
+        check(sum(c * v.get(j, F(0)) for (j, w), c in u.items()) == 1, 'rank-eight pairing')
+        receipts[variant] = {'endpoints': sum(groups.values()), 'support_classes': len(groups),
+            'max_support': max(map(len, groups)), 'eligible_rank_at_most_7': len(low & eligible),
+            'determinants': dict(sorted(histogram.items())), 'rank_eight_calibration': 'PASS',
+            'negative_controls': controls(raw, variant, report, rows, frames, eligible, groups)}
+    check(receipts['base'] == receipts['extra'], 'provider conclusions differ')
+    print(json.dumps({'status': 'PASS_INDEPENDENT_TERMINAL_INFORMATION_BARRIER',
+                      'no_new_kappa': True, 'providers': receipts}, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()