diff --git a/research/qq16-complete-cost/ADMISSION.json b/research/qq16-complete-cost/ADMISSION.json
new file mode 100644
index 0000000000..e61a0645c3
--- /dev/null
+++ b/research/qq16-complete-cost/ADMISSION.json
@@ -0,0 +1,66 @@
+{
+  "source_main": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "candidate": "frozen4166D",
+  "baseline": "4167Bstar",
+  "scope": "complete original-root prepared fast-core through public return, source R/W/M",
+  "items": [
+    {
+      "obligation": "actual root, postremainder and child cutoff",
+      "status": "new exact symbolic domain certificate lambda5..44 at p2^8500; no production payload",
+      "evidence": "checker.root_leaf_domain_witness;FAIRNESS.md"
+    },
+    {
+      "obligation": "retained complete C histories and changed payloads",
+      "status": "inherited4172 unchanged",
+      "evidence": "authenticated nested archive; PROOF.md section2"
+    },
+    {
+      "obligation": "all removed wrapper bases/gates/scalars",
+      "status": "new literal source operation injection plus quantified uniform-cover gate supply",
+      "evidence": "NONCHILD.md;GATE-COVER.md;nonchild.census;gate_cover.source_checks"
+    },
+    {
+      "obligation": "complete terminal C including paid height guard and zero descendants",
+      "status": "new source upper with actual full-call/countdown/cutoff calibrations",
+      "evidence": "CBODY.md;cbody.check"
+    },
+    {
+      "obligation": "remaining negative copies/shells",
+      "status": "new conservative source upper, external B protocol",
+      "evidence": "NONCHILD.md;nonchild.removed_small_upper"
+    },
+    {
+      "obligation": "actual extra scans, compiler/service/publication/disposal",
+      "status": "disjoint positive gather/scatter lower; all other extra work retained nonnegative",
+      "evidence": "NONCHILD.md;nonchild.extra_group_lower"
+    },
+    {
+      "obligation": "Bstar return adoption, startup, backend epoch",
+      "status": "inherited exact prices retained once; B66496 total upper pessimistically debited percoordinate",
+      "evidence": "cost.py;FAIRNESS.md;RESOURCES.md"
+    },
+    {
+      "obligation": "native numerical/hosting/ordinary/Compact/stock/longrecords",
+      "status": "inherited hypotheses remain; compatible native configurations explicit",
+      "evidence": "PROOF.md;REUSE.json"
+    },
+    {
+      "obligation": "compiled finite control",
+      "status": "separate explicit signed threshold, no unconditional total-step conclusion",
+      "evidence": "PROOF.md section5;RESOURCES.md"
+    },
+    {
+      "obligation": "historical backing and engine inventories",
+      "status": "unchanged D inventories and per-role highwater obligations; no equal-space claim",
+      "evidence": "RESOURCES.md"
+    }
+  ],
+  "excluded_claims": [
+    "all QQ16 mechanisms",
+    "nonterminal C8 domain",
+    "production payload/fullRootLayer execution",
+    "all-node supplier/bootstrap",
+    "newkappa",
+    "human/formal-kernel acceptance"
+  ]
+}
diff --git a/research/qq16-complete-cost/BILL.json b/research/qq16-complete-cost/BILL.json
new file mode 100644
index 0000000000..55ca267e36
--- /dev/null
+++ b/research/qq16-complete-cost/BILL.json
@@ -0,0 +1 @@
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diff --git a/research/qq16-complete-cost/CBODY.md b/research/qq16-complete-cost/CBODY.md
new file mode 100644
index 0000000000..879e7d7504
--- /dev/null
+++ b/research/qq16-complete-cost/CBODY.md
@@ -0,0 +1,236 @@
+# Complete selected-C leaf action bound
+
+Chris R / Clear1nsight, with OpenAI Codex assistance. Apache-2.0. The source
+operations are Jose Manuel's retained complex controller (#3385), physical
+Gaussian leaf, encoded Count arithmetic and native source closure. #4172's
+successful coefficient opacity and phased history relation are inherited.
+No controller, arithmetic implementation or physical reset is added here.
+
+## Boundary and nonempty source domain
+
+The boundary is original `Machine.run(payload, descriptors)` entry through its
+successful root return, with output still resident and borrowed payload and
+Count heads restored. Subsequent caller consumption belongs to the shell bill.
+The named marker class is steady; a fresh nonempty original backend epoch adds
+703 writes once, as proved in #4172. This is not multiplied by calls.
+
+This lemma applies to complete admitted descriptor packets satisfying the actual
+terminal predicate `w < 73 OR w^1000 < d`. The original selected `node` first
+tests width against its dimension and, if needed, evaluates its capped-power
+cutoff. Both branches reach `apply_leaf` before stock allocation or the
+recursive group loop. **There are no descendants, monomial
+calls, Binary calls or Ordinary calls in this branch.** A fitted/fallback
+fixture does not price it and is not invoked as evidence.
+
+This is not a claim that every small width can arise from RootLayer. In
+particular the independently checked actual fast-entry condition excludes
+parent columns 1 through 4. The integrated checker supplies an exact nonempty
+fast RootPlan family with parent columns 5 through 44 and child widths lambda
+and 8 lambda. Source
+row stock, root grid, physical reserve and successful numerical inputs remain
+admission requirements. Reduced physical calibrations below are not that huge
+root's payload execution.
+
+Let `R=prefixes*rows`,
+
+    b = front + 3 compact_bits + before + w spacing + after + back,
+    Gs = R coefficients 2^b,
+    v = 2 H_b Gs,
+    L = 16 + b + sum(max(1, bit_length(descriptor)))
+
+where the sum includes all fourteen input descriptors, including root width,
+physical `H_b`, coefficient count and unused row stock. The letter `Gs` here
+counts Gaussian coefficients and is unrelated to the address guard `G`.
+The active rank changes `w` and `after` together; it does not reduce `b` or `v`.
+No logical coarse width substitutes for H_b. All quantities are positive where
+required by the actual source. Residue is less than spacing.
+
+## Exact amortized countdown, including ripple and terminal transition
+
+For a positive canonical countdown starting at n, put
+`z=n-popcount(n)` and `j=bit_length(n)-1`. All n calls to the actual
+`stream.Counter.decrement` cost exactly
+
+    reads  = 2z + 5n + 1,
+    writes =  z +  n + 2j + 3,
+    moves  = 2z + 4n + 2j + 4.
+
+The sum of trailing-zero lengths over k=1..n is z. A non-power of two has
+`(2 nu2(k)+5, nu2(k)+1, 2 nu2(k)+4)` actions. Powers of two greater than one
+add `(0,2,2)` for shrinking the high delimiter; the final k=1 transition adds
+`(1,3,4)`. The final rewind is included, so no head motion is hidden in the
+amortization. Initialization copies the canonical source, normalizes the new
+counter and restores the borrowed source; final close erases the canonical
+zero plus its delimiter. Both together are at most `64(bit_length(n)+2)` in
+each component. Zero initialization/close obey the same bound with bit length
+one and no decrement. Thus a full n-step countdown is bounded by
+`12n + 64(bit_length(n)+2)` separately in reads, writes and moves.
+
+`check_countdowns` compares the exact formula against actual source execution
+at zero, powers of two, their neighbors and multi-bit integers. This is a
+calibration and rejection control; the trailing-zero sum supplies the
+quantified proof. Charging log(n) at every decrement would lose the important
+amortization and give a misleading production comparison.
+
+## Hierarchical source upper bound
+
+The following deliberately generous, componentwise bound is sufficient for
+the comparison; it is not an exact fitted or whole-recursive-C tariff:
+
+    E_w(g) <= 2^32 (w+1) [v + (Gs+1)L^4].                  (1)
+
+Every coefficient-payload bit loop in the leaf is covered. The audit below
+bounds the retained source's syntactic loops, not elapsed Python time. It does
+not price a host algorithm substituted for those loops.
+
+1. **Encoded setup.** All live Count values in this leaf are input values,
+   sums of fixed-schema address widths, powers of two of those widths, products
+   for record/row/packet extents, axis suffix/pair counts, or loop positions.
+   Their canonical binary bodies have fewer than `4L` digits, including
+   intermediate products. The width<73 branch bypasses `fixed_power`; the second terminal branch pays
+   the fifteen capped products explained below, whose transient values are
+   at most d². A linear Count operation (literal/copy/normalize,
+   increment, small multiply, zero, compare, subtract or close) has at most
+   256L actions per component by counting at most a fixed number of full
+   scans over those bodies. General product scans at most 4L digits and makes
+   at most two such operations per digit. `power_two` makes at most b
+   `multiply_small(2)` iterations, with the exact countdown just proved.
+   The conservative common envelope is 4096L² per product/power operation.
+   There is no variable-exponent bisection or general native division here.
+
+2. **Coefficient pairs.** `signed_linear.c_pair` makes four width-H_b opaque
+   copies, four width-H_b `linear_word` calls, and buffer clear/rewinds. Each
+   linear word reads and moves four component ports and appends exactly H_b
+   result bits (first-bit suppression is offset by the sign-extension append).
+   Carries change bits but not the action schedule on successful inputs.
+   Complete width countdowns are amortized as above. Component copy, append,
+   clear and rewind traffic is linear in H_b. Per pair there are fewer than
+   1024 payload actions per component per H_b plus fewer than 1024 linear
+   Count/Counter setup operations; `1024 H_b + 2^20 L²` is an upper envelope.
+   This includes loop tests, append-blank checks, right-end reads and rewinds.
+
+3. **One axis.** `c_axis` processes exactly Gs/2 coefficient pairs. It performs
+   two suffix input copies and two suffix output copies per prefix, totaling
+   2v bits of opaque copying; input/output/intermediate erasure and rewind
+   lengths total at most a fixed multiple of v. The outer row loop has R
+   iterations and the nested prefix loop has `R*2^position` iterations, each
+   at most Gs (coefficients>=1 and position<b). All prefix/row/pair countdowns
+   are full countdowns, so their total variable decrement traffic is linear
+   in Gs and v, not Gs log Gs. Their constructor/close work is bounded by L
+   per activation. Fixed descriptor construction and cleanup makes fewer
+   than 4096 elementary/setup operations for this axis. Summing the preceding
+   bounds gives the simpler envelope `2^28[v+(Gs+1)L^4]` for a whole axis.
+   This loosens both the lower polynomial degree and coefficients deliberately.
+
+4. **Leaf and complete controller.** `run_leaf` makes w axis calls; its
+   pre/post copies add O(v) payload actions. Layout has eight fixed fields;
+   constructing all radices, records and row bits and closing them uses fewer
+   than 4096 of the elementary/setup operations above. It rearms/closes the
+   fixed 256-role leaf pool. `Machine.run/node/apply_leaf/return_node` includes
+   payload copy, all fourteen descriptor copies, positivity/width checks,
+   shape, complete-extent skip, leaf argument creation, returned payload
+   transfer, all parked-role clearing and borrowed rewinds. There are fewer
+   than 4096 fixed role/setup operations, besides linear complete-packet
+   traffic and the one leaf call. This includes the original selected
+   controller's 712 packet/private roles, its descriptors, capsule and
+   markers; closed native inventories are tested but never executed. Applying
+   the envelopes above and rounding upward gives (1), including w=0.
+
+The large margin in 2^32 is intentional. The proof needs the structural bounds
+in the table; passing a few calibrations does not establish that coefficient.
+No cancelled descendant or unpaid native tariff is hidden in (1), because the
+source branch has no descendants/native invocation. This lemma rejects failure of both terminal tests; width>=73 alone is insufficient
+to classify a call as nonterminal.
+
+For integer arithmetic the implementation rounds `L^4/(2H_b)` upward to give
+an affine bound in v:
+
+    A = 2^32 (w+1) [1 + ceil(L^4/(2H_b))],
+    D = 2^32 (w+1)L^4,
+    E_w <= A v + D.
+
+It can return this exact compact representation without constructing 2^b.
+For the particularly useful domain `H_b >= L^4`, `Gs>=1` implies
+`(Gs+1)L^4 <= v`, so a still simpler bound is
+
+    E_w <= 2^33 (w+1)v                  in each R/W/M component,
+    sum E_w <= 3*2^33 (w+1)v.                              (2)
+
+This is an upper bound on removed work and can therefore be subtracted safely
+in a lower bound for candidate-minus-baseline cost. Subtracting a leaf lower
+bound would have the wrong direction. Fresh-marker potential is explicit and
+is globally matched once in B/D by #4172; it is not a per-call refund.
+
+## Finite evidence and limitations
+
+The executable interface accepts every descriptor, the original selected
+binding and external root flag, and a named marker class. Its cache key keeps
+all of them, not just width/rank. Geometry mutations that move active axes into
+spectators preserve packet volume but change the axis schedule; they cannot
+reuse an arbitrary rank-only exact price. The returned object is an upper
+certificate, so a coarse bound may intentionally be equal for different keys.
+
+Seven complete reduced C calibrations use actual original selected-controller
+leaf execution, nonconstant exact-grid data, encoded descriptors, borrowed
+bytes/heads and repeated completed returns. An additional complete dimension-two
+fixture uses the same actual controller and an authenticated reduced binding to
+reach the capped-power terminal branch. It is identified separately. They independently compute the
+Gaussian endpoint. They exercise the zero/leaf and reduced cutoff branches and cold/warm markers;
+they do not exercise nonleaf C or Ordinary. The countdown calibration is
+exact; the complete-C calibration checks the stated upper bound and records
+actual measured R/W/M. Source authentication occurs before imports/execution.
+
+## Open next question
+
+For the actual terminal-child band this closes the removed rank-eight C-body upper term,
+with no recursive supplier underneath it. It does not close removed f>1
+monomial wrapper/native prices; those require matched source operation
+cancellation or a complete native upper bound. Failure of both terminal tests requires a genuine completed C recurrence and
+is explicitly outside this evaluator. This leaf
+lemma alone does not meet the publication significance gate or prove QQ16's
+complete sign.
+
+## The second terminal branch and the installed terminal-child band
+
+The dimension cutoff is sufficient but not necessary. The actual
+source next computes `fixed_power(width,1000,root_width)` and returns a leaf
+whenever `width^1000 < root_width`. Consequently a width of 80 or 144 is not
+a certificate of a recursive C call. At the actual p=2^8500 root witness these
+widths are still terminal. The admitted root's global d must remain in the
+cost key.
+
+Equations (1) and (2) use the exact terminal predicate
+
+    w < 73 OR w^1000 < d.
+
+The additional source work is paid as follows. Binary exponentiation for the
+fixed integer 1000 has six multiply-result sites and nine squaring sites.
+`encoded.product(...,cap)` tests its operands and either returns a copied cap
+or computes a product then caps it. Operands remain at most d and the transient
+uncapped product is at most d². Their Count bodies therefore remain below 4L.
+Fifteen general products plus the associated comparisons, copies and cleanup
+remain below the 4096 fixed setup-operation allowance in step 4 above. The
+4096L² primitive envelope and the conservative 2^32 whole-leaf coefficient
+therefore continue to hold. This supplies the additional paid branch; the cutoff test is not free.
+
+For parent columns lambda, the source-compatible terminal-child band includes
+
+    ((8 lambda)<73 OR (8 lambda)^1000<d) AND d<=(73 lambda)^1000,
+
+along with the separate actual RootPlan fast-entry, row stock, grid and width
+conditions. Both rank-one and rank-eight children are terminal throughout this
+band. In particular the independently checked p=2^8500 family admits lambda
+5 through 44. The first possible transition there is not lambda10: it occurs
+when the global-power cutoff fails. A proposed one-level columns-one recursive
+price without this admission check is rejected. The general upper certificate
+now tests the exact predicate; the reserve-dominated corollary can receive d
+explicitly for the same purpose.
+
+The full width-73 cutoff kernel at d=73^1000+1 was executed once: it
+returned the terminal decision with (230491720, 51790603, 174593792) source
+actions. The four-case calibration took 209.934 seconds including the smaller
+cases. It executed encoded Count arithmetic only, not a 2^73 payload. Fresh
+registered checks use both sides of the width-two power boundary and a small
+width-73 saturating cap; `check(include_large_cutoff=True)` explicitly repeats
+the larger calibration. The retained large-kernel receipt is once-executed
+evidence, not a claim that every normal/optimised/export replay reran it.
diff --git a/research/qq16-complete-cost/DECISION.md b/research/qq16-complete-cost/DECISION.md
new file mode 100644
index 0000000000..7885930fbb
--- /dev/null
+++ b/research/qq16-complete-cost/DECISION.md
@@ -0,0 +1,82 @@
+# Complete-cost decision after #4172
+
+Chris R / Clear1nsight with substantial coordinated OpenAI Codex assistance.
+Apache-2.0. This is one integrated Class-B decision-changing comparison on the explicit terminal-child domain.
+
+Canonical main is 12fa8c5c844be21bfefb38a19503fbd867a11244, priority 7.
+The frozen #4172 source is 59b46625a8b2f0dfff3e38ba0949b4247423938a;
+#4167 is 6749e458800f461535d64cc91c017552d9f55e5f; #4166 is
+0b082d22a0e9a442d264ab0633e35ef26c790630. Original source #3385 is
+7e5a187214126d31afc241a8f89f4a652352b58c. Publication/review heads are
+separate live observations. Frozen inputs and all source notices are retained.
+
+## Boundary and currency
+
+Compare original RootLayer prepared fast-core entry through the same complete
+public root return. B* is original arithmetic with the #4167 external shared
+pipeline and its proved internal child-return adoption. D is frozen #4166,
+including its already credited whole-bank publication. No D* is presumed.
+Reads, writes and unit moves are separate exact nonnegative currencies. Their
+sum is an explicitly named action tariff. Compiled control and physical-role
+historical backing remain separate. No supplier or kappa conclusion follows.
+
+The inherited retained-call theorem removes all 510646 Gamma complete C bodies,
+including 6972 changed-core and 493097 later occurrences. The exact comparison
+still retains Delta_N, Delta_shell, 14298088 Gamma header actions, added
+368 Gamma complete rank-one C calls and removed 16 Gamma complete rank-eight
+B calls. D versus B* additionally owes B*'s proved return saving and signed
+binding control. The once-only 703-write backend epoch potential cancels globally.
+
+## First discriminating experiment
+
+Derive valid lower and upper prices directly from the literal source and its
+complete geometry. First try a rigorous signed exclusion by retaining only
+positive candidate work and subtracting upper bounds on *removed* source work.
+Source-matched cancellation and operation injections are permitted; subtraction
+of unrelated upper bounds is not. A sign verdict must include all other terms
+by exact cancellation or a stated signed bound.
+
+The first orientation already rejects a tempting shortcut: legal small Machine
+packets need not be reachable at RootLayer.fast_core. Establish the actual
+RootPlan reservation, cutoff and stock domain before declaring a parameter
+admitted. Reduced physical calibrations are labelled separately from a
+symbolically constructed production-descriptor witness.
+
+The primary route prices the exact unmatched source word and complete C bodies.
+A genuinely different fallback is a proved source-operation dominance coupling
+that cancels expensive matching primitives directly. It may avoid deriving an
+unneeded whole-engine upper bound, but must match full packet geometry, marker
+phase, ownership and invocation scope. Neither route changes the frozen caller.
+
+## Outcome and stopping decision
+
+Success is a full signed verdict on an explicitly nonempty installed domain,
+or a substantial integrated source-cost theorem closing the dominant pricing
+gap. Preserve any real losing case. No PR is justified by an unreachable
+low-width example, another identity with unexplained input prices, or one local
+calibration. Stop fixed recovery expansion if its full necessary inequality
+fails or remains unpriced; retain the integrated evidence and exact next test.
+
+No production payload or unrelated heavy replay is part of orientation.
+Source authentication precedes inherited execution. Registered and committed
+read-only normal/optimised export replays are required before publication.
+
+
+The signed bound is now closed on the stated source domain: frozen D exceeds
+B* in each R/W/M component. Forty actual RootPlan descriptor choices lambda5
+through44 at p=2^8500 certify a nonempty installed domain, retaining inherited
+numerical/hosting hypotheses. The cost proof uses a literal source-operation
+injection plus a new quantified O73 gate-supply theorem, complete terminal-C
+and external-shell upper debits, and actual extra group scan/write lower prices.
+No unexplained E1/E8/Delta_N price remains in this exclusion. All other new
+candidate work is retained nonnegative in the correct lower-bound direction.
+
+Stop expanding this fixed recovery in that band. Nonterminal C8 calls require
+a separate complete comparison after authenticating the actual height cutoff;
+width73 alone does not imply recursion. The unreviewed Ordinary tariff sketch
+is retained only as a local artifact and is not a publication input or an
+admitted price. There is no new machine mechanism, reset, generic saving or kappa.
+
+The frozen16-file adversarial review passed with no unresolved blocker in the
+stated scope. Fresh primary/optimised checks and boundary controls passed;
+final registered/committed/export/hosted statuses are recorded separately.
diff --git a/research/qq16-complete-cost/EXECUTION.json b/research/qq16-complete-cost/EXECUTION.json
new file mode 100644
index 0000000000..f99cc8a33e
--- /dev/null
+++ b/research/qq16-complete-cost/EXECUTION.json
@@ -0,0 +1 @@
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invoked","payload_bits":10240,"production_root_admission":false,"result_sha256":"ac6d1161194dcd3fe2f5baa01a210e9f004767b38b163b9495251a6b21c71d0b","rwm":[5658538,1617390,5370406],"selected_binding":true,"upper":[67208043079856553984,67208043079856553984,67208043079856553984]},{"actual_binding_dimension":2,"actual_controller_branch":"capped-power cutoff","borrowed_preserved":true,"calibration_of_selected_geometry_bound":false,"complete_return":true,"generation":7,"geometry":{"after":0,"back":0,"before":0,"coefficients":1,"compact_bits":0,"component_bits":20,"front":0,"guard":1,"prefixes":1,"residue":0,"root_width":10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069377,"rows":1,"spacing":1,"width":2},"ordinary_branch":"not invoked","payload_bits":160,"production_root_admission":false,"result_sha256":"3943fac65bdc7105d479874186df3f3b644a628d88bafa6f011d657a03a022e1","rwm":[2047472,660529,1393550],"selected_binding":false,"upper":null}],"countdown_calibrations":[{"cycle":[20,8,26],"cycle_upper":[192,192,192],"decrements":[0,0,0],"n":0},{"cycle":[24,8,28],"cycle_upper":[198,196,200],"decrements":[6,4,8],"n":1},{"cycle":[36,13,40],"cycle_upper":[269,264,272],"decrements":[13,8,16],"n":2},{"cycle":[41,14,44],"cycle_upper":[274,265,276],"decrements":[18,9,20],"n":3},{"cycle":[55,20,58],"cycle_upper":[347,334,350],"decrements":[27,14,30],"n":4},{"cycle":[72,24,72],"cycle_upper":[364,338,364],"decrements":[44,18,44],"n":7},{"cycle":[88,31,88],"cycle_upper":[439,408,440],"decrements":[55,24,56],"n":8},{"cycle":[131,42,124],"cycle_upper":[482,419,476],"decrements":[98,35,92],"n":15},{"cycle":[149,50,142],"cycle_upper":[559,490,554],"decrements":[111,42,106],"n":16},{"cycle":[154,51,146],"cycle_upper":[564,491,558],"decrements":[116,43,110],"n":17},{"cycle":[246,76,224],"cycle_upper":[656,516,636],"decrements":[208,68,188],"n":31},{"cycle":[266,85,244],"cycle_upper":[735,588,716],"decrements":[223,76,204],"n":32},{"cycle":[271,86,248],"cycle_upper":[740,589,720],"decrements":[228,77,208],"n":33},{"cycle":[924,272,808],"cycle_upper":[1452,838,1340],"decrements":[876,262,764],"n":127},{"cycle":[948,283,832],"cycle_upper":[1535,912,1424],"decrements":[895,272,784],"n":128},{"cycle":[953,284,836],"cycle_upper":[1540,913,1428],"decrements":[900,273,788],"n":129},{"cycle":[7205,2070,6196],"cycle_upper":[7910,2825,6908],"decrements":[7142,2057,6140],"n":1023}],"cutoff_kernel_calibrations":[{"cap_bits":1001,"cap_relation":"power+1","complete_C_payload_executed":false,"exponent":1000,"leaf":true,"rwm":[2002103,648114,1350896],"width":2},{"cap_bits":1001,"cap_relation":"power","complete_C_payload_executed":false,"exponent":1000,"leaf":false,"rwm":[2002103,648114,1350896],"width":2},{"cap_bits":13,"cap_relation":"smaller","complete_C_payload_executed":false,"exponent":1000,"leaf":false,"rwm":[4399,624,3692],"width":73}],"negative_controls":["nonleaf recursion omitted","logical width substituted for stored width","bool descriptor alias","unnamed marker class","global cutoff equality treated as leaf"],"scope":"selected C terminal upper only; no nonterminal/Ordinary price or complete QQ16 sign","source_guards":{"literal_source_guards":8,"status":"PASS"}},"bank":{"cases":[{"bank_bits":6,"lower":[12,0,12],"prefixes":1,"row_bits":1,"rwm":[442,118,472],"scatter_rwm":[483,131,516],"scatter_write_lower":6,"unused":1},{"bank_bits":48,"lower":[96,0,96],"prefixes":2,"row_bits":4,"rwm":[1121,335,1148],"scatter_rwm":[1333,415,1364],"scatter_write_lower":48,"unused":1},{"bank_bits":90,"lower":[180,0,180],"prefixes":1,"row_bits":5,"rwm":[1425,368,1370],"scatter_rwm":[1741,485,1678],"scatter_write_lower":90,"unused":3}],"scope":"complete actual BankPackets.gather on reduced geometry; no selected O73 payload execution"},"phase":{"all_phases_same_actions":true,"cases":[{"H_b":4,"input":[3,-2],"phase":0,"rwm":[296,104,312]},{"H_b":4,"input":[3,-2],"phase":1,"rwm":[296,104,312]},{"H_b":4,"input":[3,-2],"phase":2,"rwm":[296,104,312]},{"H_b":4,"input":[3,-2],"phase":3,"rwm":[296,104,312]},{"H_b":8,"input":[3,-2],"phase":0,"rwm":[492,172,496]},{"H_b":8,"input":[3,-2],"phase":1,"rwm":[492,172,496]},{"H_b":8,"input":[3,-2],"phase":2,"rwm":[492,172,496]},{"H_b":8,"input":[3,-2],"phase":3,"rwm":[492,172,496]},{"H_b":17,"input":[3,-2],"phase":0,"rwm":[900,306,872]},{"H_b":17,"input":[3,-2],"phase":1,"rwm":[900,306,872]},{"H_b":17,"input":[3,-2],"phase":2,"rwm":[900,306,872]},{"H_b":17,"input":[3,-2],"phase":3,"rwm":[900,306,872]}],"scope":"actual reduced pair primitive; general phase equality follows source loop proof"}}
diff --git a/research/qq16-complete-cost/FAIRNESS.md b/research/qq16-complete-cost/FAIRNESS.md
new file mode 100644
index 0000000000..324cc29b68
--- /dev/null
+++ b/research/qq16-complete-cost/FAIRNESS.md
@@ -0,0 +1,249 @@
+# Fair boundary and independent signed comparison
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+The actual controller and root planner are Jose Manuel's retained #3385 source.
+The adopted-return method is inherited from #4167 (motivated by Tekalign's
+#3380); no earlier saving is claimed again.
+
+## Variants and signed direction
+
+The external boundary is the original RootLayer entry through its fixed public
+return. B preserves original arithmetic and uses #4167's shared closed primitive
+pipeline and external original child controller. B* additionally adopts each
+completed internal child output using that package's proved binding exchange.
+D is exactly the frozen #4166 adopted-bank recovery installation. No D* is
+implemented here and the checker rejects that label.
+
+For the complete successful-source domain inherited from #4172,
+
+```
+D - B = Delta_N + Delta_shell + 14298088 Gamma
+          + 368 Gamma E_1(g) - 16 Gamma E_8(g).
+D - B* = (D - B) + 510662 Gamma (11v+4)
+```
+
+These are source-action sums. The signed finite binding-control adjustment
+must be retained separately in a complete compiled-step comparison. The child
+body E includes its descendants and completed return once. Removed bodies and
+shells belong to B, never to the more expensive embedded A. The once-only703
+write original-controller marker potentials cancel over the two nonempty backend
+epochs; neither Gamma nor a callback count multiplies them. Other constructors,
+markers and terminal retirement remain charged.
+
+The header term includes every retained510646 occurrence and the493097 later
+occurrences. The candidate's368 added bodies split into32 producer and336 service
+calls;16 original centres are removed. The original total is510662, and D's root
+plus service total is511014. These literal occurrences give the B* saving above.
+A hypothetical implementation which additionally adopted all511014 D outputs
+would produce the both-adopt adjustment `-352 Gamma(11v+4)`, but this arithmetic
+is not permission to alter frozen D's bill.
+
+For a bound on `Delta=candidate-baseline`, positive candidate work contributes
+its lower endpoint to a lower bound, while removed baseline work contributes
+**minus its upper endpoint**. Exact matched cancellation is justified only by
+source/geometry/context correspondence. Dropping positive work is safe for a
+lower bound; omitting negative baseline work is not. Two unrelated upper bounds
+supply no sign. `checker.py` independently implements these interval directions
+without importing the evaluator. Its synthetic controls check arithmetic and
+receipt shape; they do not certify source-derived endpoints.
+
+## Actual-root reachability rejects the easiest apparent fixture
+
+The `lambda=1` proposal would eliminate Ordinary calls in removed monomials,
+but is not reachable at the installed fast RootLayer boundary. In fact the same
+obstruction excludes **all lambda<=4** under #4166's post-remainder contract.
+This is a reachability obstruction for that boundary, not a prohibition on
+standalone C entry descriptors or deeper source nodes.
+
+Write `e=73 lambda`. #4166 requires `d<=e^1000`; RootPlan computes
+`d=floor(p^(997/1000))`, `K=floor(d^(1/500))`,
+`G=4 ceil(log2 p)+6`, `H=dG`, and
+`Q0=q0+ceil(2H/K)+ceil(H/K)`. The fast branch requires
+`selected>Q0` with `selected<=d`.
+
+For lambda<=4, `d<=292^1000`. Also p>=d, so
+`G>=4 log2 d+6`. If d>=2 put x=log2 d. On
+`[1,1000 log2 292]` the convex function
+`h(x)=2^(x/500)-12x-18` is negative at both endpoints:
+`h(1)<2-30<0`, and
+`h(1000 log2 292)=292^2-12000 log2 292-18
+<85264-96018<0`, since292>256. Convexity makes it negative
+throughout the interval. Hence `K<3G`, so
+`Q0>=3dG/K>d>=selected`, contradicting fast entry. The d=1
+case has K=1 and G>=10 and gives the same conclusion.
+
+A nonempty leaf-child domain does exist at lambda=5. The independent exact
+integer checker follows RootPlan's formulas with
+
+- `p=2^8500`, `d=floor(sqrt(2^16949))`, `K=126519`, `G=34006`;
+- source depth13999 and `q0=depth*bit_length(14336 Gamma-1)`;
+- `selected=q0+ceil(2dG/K)+ceil(dG/K)+365`;
+- core width365, lambda5, and original outer rows/prefix/coefficient counts1,
+  residue0, left/right spectator fields0.
+
+It proves `selected<=d`, fast entry, and `d<=365^1000` using exact integers.
+The added rank-one child has width5 and the removed rank-eight child width40;
+both take the original C leaf branch. Root padding supplies rows
+`ceil(2^(q0 K)/stock)*stock`, with `stock=(14336 Gamma)^depth`.
+Here `q0*K=4679350508802` and the level divisor is
+`L0=14336 Gamma`. Since `log2(L0)<=bit_length(L0-1)` and K>=1,
+`stock=L0^13999<=2^(q0*K)`. Thus the padded row count R is a positive
+multiple of the full root stock and `R<2^(q0*K+1)`. The actual parent
+`prepare_child` uses `U=R/L0`, preserving all outer rows; U is positive and
+divisible by `L0^13998`. The child width5 has depth zero, so the compiler's
+direct child-stock test demands only divisibility by1, which is automatic.
+The removed width40 child is also a leaf. No absent rows are imported.
+
+The front and back residuals `qF*K-2dG` and `qB*K-dG` both lie in `[0,K)`.
+The complete packet address width is
+`b=3dG+front+365K+back=(selected-q0)K`, with bit length8492.
+Rank-one/ rank-eight reinterpretation replaces365K by5K/40K and moves the
+remaining axes to `after`; the complete b is identical. The physical H_b has
+bit length218476. Taking `bit_length(U)<=q0*K+1`, the independent integer
+certificate verifies `H_b>=Lbound^4` for the leaf descriptor bound of
+CBODY.md, without constructing R, U, 2^b or any payload. This is a bound on
+the real symbolic geometry, not use of logical width as a physical width.
+
+These enormous packet sizes are symbolic; no physical payload was allocated.
+The inherited numerical, exact-native, hosting, stock and long-record premises
+remain. This descriptor witness is not a production payload execution.
+
+This witness also explains why a crude `v*L^4` bound with L containing the
+complete address width can fail: the address width is enormous even though
+active rank is small. A useful bound must amortize encoded countdowns and price
+per-coefficient setup separately from per-bit traffic; the actual physical H_b
+is much larger than those descriptor polynomials in this witness. Logical
+coarse precision cannot be substituted for H_b.
+
+## Actual terminal-child extension
+
+Keeping p, d, K, G and root stock fixed, choose
+`selected=Q0+73 lambda` for every integer lambda in5,...,44.
+The independent witness verifies the actual fast branch and post-remainder
+admission throughout this family. For lambda5,...,9 the removed rank-eight
+child satisfies width<73. For lambda10,...,44 its width is at least73 but
+`(8 lambda)^1000<d`; the actual second branch in `Machine.node` therefore
+runs the Gaussian terminal body before group creation or descendants. Its
+paid capped `fixed_power` test belongs to the extended C-body upper bound.
+Actual terminal body depth zero must not be confused with coarse stock depth:
+at lambda44, `D0(3212)=8` and `D0(352)=3`, whereas the actual C8 body stops
+at entry. The root supplies stock exponent13999 and U retains13998, so both
+coarse stock requirements are satisfied despite that distinction.
+The first potential nonterminal removed child is lambda45; this family's
+certificate rejects it rather than extrapolating a terminal price.
+
+The general exclusion domain is the admitted terminal-child band
+`8 lambda<73 or (8 lambda)^1000<d`, together with
+`d<=(73 lambda)^1000`, the actual RootPlan/stock/numerical conditions,
+`H_b>=L^4` and the explicit positive-slope inequality below. A statement for
+this domain does not price nonterminal descendants.
+
+## Independent owner-cover counting check
+
+The two residual literal gate keys are `(add,6,8)` with multiplicity4Gamma
+and `(add,8,6)` with multiplicityGamma. The independent rational checker
+verifies the counting inequalities used to cover them from736 paid owner-basis
+monomial calls per owner. It does not assume the identity owner's gate word is
+representative.
+
+Fix an arbitrary9-by-9 head matrix A. Complete nine full orthonormal vectors
+by choosing their64-bit tails in order. At step i=0,...,8 the required tail
+parity and i pairings are i+1 independent linear constraints, provided the
+previous tails together with the64-bit all-ones vector are independent.
+There are exactly `2^(63-i)` solutions; at most `2^(i+1)` belong to the
+forbidden span. The number of good completions is therefore at least
+
+```
+2^531 product_(i=0..8)(1-2^(2i-62)) > 2^530.
+```
+
+The number of possible full orthonormal9-frames is at most2^612 by the
+analogous73-bit constraints. The uniform orthogonal group has constant fibres
+over its orbit. To justify that every counted completion belongs to this
+orbit, fix the characteristic all-ones vector omega73 and pass to its
+nondegenerate72-dimensional alternating orthogonal complement. The independent
+vectors `e_i+omega73` and `v_i+omega73` have identical alternating Gram
+matrices. The symplectic extension theorem extends this subspace isometry;
+extending it by identity on omega73 gives the required orthogonal matrix.
+This is an ordinary written linear-algebra proof, not formal-kernel evidence.
+Consequently each head has group probability greater than2^-82, at least half
+the uniform9-by-9 binary-head probability.
+
+For source `binary_word`, an invertible leading6-by-6 block together with
+Schur bits `(6,6)=(8,6)=1` forces `(add,8,6)`. An invertible leading8-by-8
+block, bit6 of its inverse times column8 equal to1, and the final Schur pivot
+bit1 force `(add,6,8)`. In each case the two constrained bits are independent
+uniform bits conditional on the invertible leading block. The probability of
+an invertible k-by-k binary matrix is `product_(j=1..k)(1-2^-j)>1/4` for
+k=6,8. Each forcing event therefore has uniform-head probability>1/16 and
+orthogonal-cover probability>1/32. Inversion preserves uniform owner coverage.
+Thus736 paid owner calls supply more than23Gamma occurrences of each key,
+which covers the respective4Gamma and Gamma deficits. NONCHILD.md must still
+bind those736 calls and literal geometry keys to the actual paid program; this
+count alone would not discharge that source obligation.
+
+## Independent normalized signed lower certificate
+
+On the source domain established by the integrated source proofs, take an
+admitted terminal rank-eight child, `f>=5`, `H_b>=L^4`, `v>=2685`, and
+`a=(281593/816)*14336*Gamma`. Let
+
+```
+X = 16*2^33*(8f+1) + 8*2^22 + 16*2^26.
+```
+
+The three terms in X bound removed C bodies, eight copies and sixteen B
+shells in each R/W/M component, per Gamma v. The complete leaf bound includes
+all descendants (zero on this literal branch), entry, return and cleanup.
+The copy/shell inequalities use `v+1+L^4+2685<=4v`; their constants are
+rounded upward. New child bodies and all other unneeded positive work may be
+dropped from a lower bound. No exact or upper price for E1 is being substituted
+with zero.
+
+After the proved literal monomial/base/scalar injection, candidate-only gathers
+and scatter output writes supply `(2a,a,2a) Gamma v`. Stronger B* contributes its already established
+return saving. The independent lower certificate is
+
+```
+Delta_R >= Gamma v (2a+5*510662-X) + Gamma(12*510646+2*510662) - 66496
+Delta_W >= Gamma v ( a+2*510662-X) + Gamma( 4*510646         ) - 66496
+Delta_M >= Gamma v (2a+4*510662-X) + Gamma(12*510646+2*510662) - 66496.
+```
+
+The known total startup/terminal upper66496 is pessimistically subtracted in
+each component; this loses precision but is safe. It requires the source
+matching of the common original engine and root-wrapper startup. Extra D
+constructors are nonnegative omitted work. The703-write original-backend
+potential has already cancelled once globally.
+
+`normalized_terminal_exclusion` derives these coefficients independently of the
+evaluator. It requires the explicit inequality `a+2*510662>X`, which also
+makes the read and move slopes positive. Equivalently, with exact integer a,
+
+```
+f <= floor((a+2*510662-16*2^33-8*2^22-16*2^26-1)/(128*2^33)).
+```
+
+This ceiling has2610 bits for selected Gamma. The checker tests the exact
+last integer and rejects the next one. This arithmetic ceiling does not assert
+that all those integers admit the additional terminal and physical-reserve
+conditions. It verifies strict positivity of each
+complete component at the smallest allowed v2685, including the once-only
+startup debit. This test passes for every concrete witness lambda5,...,44.
+The summed slope has2653 bits, and the conservative minimal total lower bound
+has5291 bits. All three action components are positive, so any fixed positive
+weighting of R/W/M also excludes improvement in that action currency. The
+separately signed finite-control difference must still satisfy the displayed
+control threshold; no elapsed-time or arbitrary machine-step claim follows.
+The source partition, root admission, coupling and upper bounds remain necessary
+premises. Exact counts and the comparison are independently checked; this is
+not formal-kernel verification.
+
+## Open next question
+
+The frozen recovery is excluded on the stated terminal-child domain. A larger
+nonterminal-child geometry needs a completed source recurrence or a different
+bound; lambda45 at the concrete fixed-p family is the first such boundary.
+A changed recovery demand or schedule is separate work and must identify paid
+bank scans or other work it can actually eliminate. The current certificate
+does not authorize speculative fixed-mechanism expansion.
diff --git a/research/qq16-complete-cost/GATE-COVER.md b/research/qq16-complete-cost/GATE-COVER.md
new file mode 100644
index 0000000000..55ac544dea
--- /dev/null
+++ b/research/qq16-complete-cost/GATE-COVER.md
@@ -0,0 +1,176 @@
+# Owner-cover supply of the two missing literal binary gates
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+The counting argument was developed jointly with the orchestrator. The source
+Gauss–Jordan compiler, orthogonal-cover indexing and physical monomial engine
+are inherited work; their implementation is not new here.
+
+## Claim and exact interface
+
+Let `g` run once through the authenticated `OrthogonalCover(73)`, of cardinality
+`Gamma`. Let `W(g)` be the literal `binary_word` on `matrix_rows=g, offset=0`.
+The coefficient, numerical width and packet data do not enter this fixed
+finite-control compiler. Then each of the following strict bounds holds:
+
+```
+sum_g multiplicity(("add", 6, 8), W(g)) > Gamma / 32,
+sum_g multiplicity(("add", 8, 6), W(g)) > Gamma / 32.
+```
+
+Consequently, 736 appearances of this owner word per owner supply more than
+`23 Gamma` gates of **each** named type. Even the 672 service appearances alone
+supply more than `21 Gamma` of each. This covers the separate histogram deficits
+`4 Gamma add(6,8)` and `Gamma add(8,6)` with room to spare. Inverse execution only
+reverses the literal word and preserves these multiplicities.
+
+The assertion is an aggregate statement across the complete cover. The identity
+owner has an empty word and is an explicit control against the false assertion
+that every owner supplies either gate. This lemma does not itself assert that
+arbitrary gate positions have equal physical cost. Its use in the signed action
+bound requires the surrounding source-derived matching theorem: same ordered
+`(kind,target,source)` and complete local packet geometry, including all
+spectators, widths, markers and operation boundary states. It supplies no
+axis-invariance shortcut and no finite-control or historical-space cancellation.
+
+## Source points and inherited finite-group fact
+
+The authenticated #4172 nested closure retains:
+
+* `research/physical-complex-controller/cover.py`, `group_orders`,
+  `OrthogonalCover._setup`, and its original `PROOF.md` section “Cover and
+  complete global dispatch”;
+* `research/physical-gaussian-leaf/inputs/pr3087.tar:phase_recipe.py`, whose
+  `Recipe` uses `reference.binary_word`;
+* that archive's retained physical-Compact/reference lineage,
+  `inputs/pr3055.tar -> inputs/pr2250.tar -> monomial.py:binary_word`;
+* `monomial_engine.py:run`, which visits `reversed(recipe.word)` for inverse
+  execution and the original word otherwise.
+
+The source reduction uses the first row `p >= j` with bit `j` set, emits a
+three-add row swap if needed, then adds pivot row `j` into **every** other row
+whose bit `j` is set. The returned word reverses the complete reduction. No gate
+multiplicity changes under that reversal.
+
+We retain the source cover invariant: any orthonormal prefix whose span does
+not contain the ambient characteristic vector has a nonalternating orthogonal
+complement and extends to an orthonormal basis. With `t` coordinates remaining,
+the number of completions is `|O(t,2)|`, with
+
+```
+|O(t,2)| = product_{k=1..t} (2^(k-1) - [k>1 and k odd]).
+```
+
+This is the original source's indexing/extension theorem, not an assumption that
+an arbitrary orthogonal prefix extends. Excluding the characteristic vector is
+essential. The new counting argument below enforces that exclusion explicitly.
+
+## Every nine-by-nine head has substantial mass
+
+Fix any binary `9 x 9` matrix `A` as the first nine coordinates of the first nine
+rows of a candidate 73-dimensional orthogonal matrix. Write those nine rows as
+`(a_i, t_i)`, with `t_i` of length 64, and write `omega` for the all-one vector of
+length 64. We count only choices for which
+
+```
+omega, t_0, ..., t_8
+```
+
+are linearly independent. At step `j`, the already chosen `j` tails and `omega`
+are independent. The constraints on `t_j` are
+
+```
+t_j · t_i = delta_ij + a_j · a_i        (0 <= i < j),
+t_j · omega = 1 + a_j · a_j.
+```
+
+There are `j+1` independent binary linear equations, so exactly
+`2^(63-j)` solutions. At most `2^(j+1)` of them lie in the span of the previous
+tails and `omega`. Discard those, leaving at least
+
+```
+L_j = 2^(63-j) - 2^(j+1),       j = 0,...,8.
+```
+
+Every resulting full nine-row frame is orthonormal. Its span does not contain
+the 73-dimensional all-one vector, because its 64-coordinate tail would then
+express `omega` in the span of the tails. It therefore has exactly `|O(64,2)|`
+completions by the inherited source cover theorem. Different tail choices and
+completions produce different matrices.
+
+Thus the exact probability for this fixed head under the uniform cover is at
+least
+
+```
+p_head >= (product L_j) |O(64,2)| / |O(73,2)|.
+```
+
+Also `|O(73,2)| / |O(64,2)| <= 2^612`, whereas
+
+```
+product L_j = 2^531 product_{j=0..8}(1 - 2^(2j-62)).
+```
+
+The product of the last nine factors exceeds one half (for example their
+omitted fractions sum to less than `9 * 2^-46 < 1/2`). Hence
+
+```
+p_head > 2^-82 = (1/2) * 2^-81.
+```
+
+This is a pointwise counting bound for **every** head, not a simulation,
+independence assertion about orthogonal entries, or probabilistic heuristic.
+For any set of nine-by-nine heads its uniform-cover mass is therefore at least
+half its ordinary independent-bit mass. `gate_cover.py` also evaluates the
+stronger exact rational bound, without enumerating Gamma.
+
+## Heads that force the named gates
+
+First consider `add(6,8)`. Require that the leading `8 x 8` block `A_8` is
+invertible. The first eight source pivot steps then find their pivots within
+rows 0 through 7: internal row swaps are allowed, but no row outside that block
+is chosen. After those steps, its column-eight entries in the top eight rows
+are `A_8^-1 b`. Its row-eight, column-eight entry is the Schur complement
+`s = d + c A_8^-1 b`. Require both coordinate six of `A_8^-1 b` and `s` to be
+one. Then source step eight has pivot row eight and emits `add(6,8)`.
+
+For a uniform independent-bit nine-by-nine head, invertibility of `A_8` has
+probability `product_{i=1..8}(1-2^-i) > 1/4`. Conditional on `A_8`, the first
+condition has probability one half because `b` is uniform. Conditional on
+`A_8,b,c`, the second has probability one half because `d` is an independent
+bit. This forcing event therefore has independent-bit mass greater than
+`1/16` and orthogonal-cover mass greater than `1/32`.
+
+For `add(8,6)`, instead require invertibility of the leading `6 x 6` block.
+After the first six pivots, require the transformed entries `(6,6)` and `(8,6)`
+both to be one. Each is a distinct original free diagonal/column entry plus a
+term fixed by the leading block and corresponding first-six row entries;
+they are independent uniform bits conditional on those data. Source step six
+has pivot six and emits `add(8,6)`. The same calculation, using
+`product_{i=1..6}(1-2^-i) > 1/4`, gives cover mass greater than `1/32`.
+
+Each forcing event guarantees at least one named gate; additional occurrences
+only increase the available supply. Applying the pointwise head bound and
+summing over the complete cover proves the two aggregate claims.
+
+## Executable evidence and boundaries
+
+`gate_cover.certificate()` uses exact integers and `Fraction`; it checks the
+source group orders, tail counts, head-density bound, event bound, and both
+736-occurrence and service-only inequalities. Its exact lower probabilities
+are approximately 0.07247977946 and 0.07333695889, but all acceptance decisions
+use rational comparisons. The coarse `1/32` bound is deliberately retained in
+the theorem for readability.
+
+`gate_cover.source_checks(cohort)` requires an already authenticated cold source
+cohort. It composes explicit even-weight orthogonal transvections to obtain
+actual 73-dimensional orthogonal witnesses, checks their head conditions,
+executes the retained `binary_word`, and confirms both literal gates and
+inverse-word multiplicity. The identity owner rejects a universal per-owner
+interpretation. These finite examples check the source interface; the tail
+count and leading-block arguments carry the quantified cover claim.
+
+This is an offline cost proof certificate. Its matrix arithmetic, rational
+counts and witness generation are not proposed machine operations, a runtime
+sampler, or free physical preparation. The surrounding package must charge the
+actual owner monomial executions and preserve the complete comparison's
+admission, finite-control and resource boundaries.
diff --git a/research/qq16-complete-cost/LARGE-CUTOFF.json b/research/qq16-complete-cost/LARGE-CUTOFF.json
new file mode 100644
index 0000000000..268b7c550b
--- /dev/null
+++ b/research/qq16-complete-cost/LARGE-CUTOFF.json
@@ -0,0 +1,63 @@
+{
+  "elapsed": 209.9338897599955,
+  "receipts": [
+    {
+      "width": 2,
+      "exponent": 1000,
+      "cap_bits": 1001,
+      "cap_relation": "power+1",
+      "leaf": true,
+      "rwm": [
+        2002103,
+        648114,
+        1350896
+      ],
+      "complete_C_payload_executed": false
+    },
+    {
+      "width": 2,
+      "exponent": 1000,
+      "cap_bits": 1001,
+      "cap_relation": "power",
+      "leaf": false,
+      "rwm": [
+        2002103,
+        648114,
+        1350896
+      ],
+      "complete_C_payload_executed": false
+    },
+    {
+      "width": 73,
+      "exponent": 1000,
+      "cap_bits": 13,
+      "cap_relation": "smaller",
+      "leaf": false,
+      "rwm": [
+        4399,
+        624,
+        3692
+      ],
+      "complete_C_payload_executed": false
+    },
+    {
+      "width": 73,
+      "exponent": 1000,
+      "cap_bits": 6190,
+      "cap_relation": "power+1",
+      "leaf": true,
+      "rwm": [
+        230491720,
+        51790603,
+        174593792
+      ],
+      "complete_C_payload_executed": false
+    }
+  ],
+  "status": "ONCE_EXECUTED_SOURCE_KERNEL_EVIDENCE",
+  "source_closure_archive_sha256": "ebfb717d60bf37b8edd894036827210a93c2594d637d4a6b8d617018567767a3",
+  "production_payload_executed": false,
+  "default_registered_replay": false,
+  "reproduce_optional": "After authenticated runtime.cold(), cbody.check_cutoff_kernel(include_large=True)",
+  "note": "Actual encoded Count arithmetic; retained once-run evidence, not an admitted runtime tariff or production width73 payload."
+}
diff --git a/research/qq16-complete-cost/NONCHILD.md b/research/qq16-complete-cost/NONCHILD.md
new file mode 100644
index 0000000000..0bade3dbc2
--- /dev/null
+++ b/research/qq16-complete-cost/NONCHILD.md
@@ -0,0 +1,215 @@
+# Signed nonchild partition and gatewise source coupling
+
+Chris R / Clear1nsight, substantial OpenAI Codex assistance. Apache-2.0.
+The physical controller, scalar and monomial sources are Jose Manuel's retained
+implementation. The producer/service compilation and caller installation are
+#4166; the shared external baseline and adoption are #4167; successful payload
+opacity and six-arena history coupling are #4172. None is new construction
+credit here.
+
+## Boundary and exact source partition
+
+Compare frozen D and original-arithmetic B over the same original root entry
+through public return. The stronger B* adjustment is applied separately. Work
+inside complete external original C calls is excluded from this nonchild bill.
+It must be counted by the C-body bound exactly once.
+
+`nonchild.census` builds an explicit occurrence injection between the literal
+forward/backward compiled original and clean-core instruction lists. The key
+removes only the raw source event number; it retains opcode, target/source,
+scalar literal, monomial recipe hash, inverse flag and child rank. Every old
+and new occurrence appears exactly once in the paired, removed or added sets.
+The injection is a cost matching, not a proposed reordering of machine work.
+#4166's semantic refinement supplies the actual order and endpoint. #4172's
+successful opacity/history result supplies equality of the cost of matched
+closed primitive invocations at their common geometry.
+
+The complete removed list is:
+
+| Source interval | Forward | Backward | Total |
+|---|---:|---:|---:|
+| Centre wrapper monomial dispatch |16|16|32|
+| External rank-eight child |8|8|16|
+| Private copy dispatch |8|0|8|
+| Unit subtract scalar dispatch |0|6|6|
+| Control-only marker |1|1|2|
+
+The new clean cores add 404 and 402 scalar dispatches respectively. At least six
+of their literal keys are `('add', -1, 1)`, so six new unit subtract calls match
+the six removed ones. Targets are different where necessary; complete packet
+extent, signed component width, Gaussian count and actual scalar recipe agree.
+The physical engine's loops and restored borrowed ports depend on these values,
+not the fixed role selector. Both calls are on successful admitted inputs.
+They have no fitted or Ordinary dependency. Control-only markers perform no
+source tape action and retain their separately compiled control obligation.
+
+All other root source events, including both bridge legs and the complete
+later suffix, are inherited unchanged. The two source events replaced by the
+QQ16 expansion each retain their clean-core group with the original exact
+owner keys, 704 selected slots, eight private roles and full bank geometry.
+Their gather/scatter/commit, group entry/exit, private initialization and final
+zero checks match. Zero private values and structural extents at those checks
+are part of #4166's successful endpoint proof. Do not cancel a private-state
+check from a bare count of instructions.
+
+## Local monomial bases and exact gate atoms
+
+For each monomial, split the actual `MonomialEngine.run` at its source call
+sites into:
+
+1. descriptor/layout setup and complete input copy;
+2. one `signed_phase.scan`;
+3. one complete `single_column_rows` or `compact_gate` per compiled gate;
+4. complete output append/clear, closure and caller `transfer`/marker erasure.
+
+The sum of items 1, 2 and 4 is the **monomial base**. At equal complete geometry
+its R/W/M price does not depend on the recipe or inverse flag. In particular,
+`Recipe.phase` reads all 73 coordinate bits for every column even if its linear
+or quadratic coefficients vanish. Those coefficients affect only finite
+control arithmetic. The negative `emit_component` branch and positive
+`copy_bits` branch have the same source read/append/step/countdown schedule.
+Inverse mode moves the phase scan from before to after the gates; it does not
+alter its action count on successful inputs. All source numerical admission
+and borrowed-value obligations remain in force.
+
+A gate atom is keyed by its exact `(kind,target,source)` and full packet
+geometry, including the 73 vector widths, prefixes, unused rows, front/back
+and spectator fields, columns, K, G, residue, physical H_b and coefficient
+count. `compact_gate` passes precisely the corresponding source/target/late
+selector to the same closed Compact/Binary/Ordinary pipeline. It does not pass
+the surrounding recipe or inverse flag. Inverse traversal reverses the gate
+word and leaves each self-inverse gate selector unchanged.
+
+For this comparison, all added producer/service primitive backends must use
+the same admitted compiled q, profile, programs and capacities as B's pipeline.
+This is an explicit compatibility domain, not a consequence of the callable
+name `ordinary_factory`. Successful closed marker phases and six-arena state
+relations are the inherited #4172 boundary. Count scratch and packet roles
+begin at the same canonical head and structural lengths. Every gate atom
+includes its completed Binary/native descendants and output disposal; those
+costs are not added again after matching.
+
+The 32 removed centre wrappers contain exactly **736 gates**. The added
+producer line calls and service intrinsic right/left wrappers contribute
+**7,150 fixed gates** over 800 monomial bases, where the 64 producer owner-basis
+calls are represented by the identity owner for this fixed-gate count. That
+identity sample supplies no general-owner gate credit. The exact pointwise
+deficits are only:
+
+    add(target=6, source=8): 4 per owner,
+    add(target=8, source=6): 1 per owner.
+
+All other 731 removed gates have a literal same-selector injection into the
+added fixed words. The separate uniform-cover theorem supplies the remaining
+five using the actual 736 owner-basis calls per cover owner: 64 producer and
+672 service. Half are inverse traversals; this reverses order only. The literal
+`cover.unrank` rows, with zero offset/phase, are compiled as `literal(g)` in
+both entry and exit owner views. The same object `g` is used; even a proved
+transpose/inverse convention would require an explicit cover bijection.
+
+Match 32 removed bases against 32 of the 800 added bases. This does not count
+the 64 producer owner bases twice: their gate contribution is counted in the
+owner sum, while their base contribution appears only once in the 800. The
+additional 672 service owner bases are nonnegative and can be discarded.
+There is no assumption that a whole rank-eight wrapper costs the same as a
+rank-one wrapper. The matching occurs only at the source base and exact gate
+interfaces just defined.
+
+## A positive subset of the complete new bank work
+
+After matching the two old core groups, D has 41 additional non-map groups
+and 12286/51 map groups per Gamma on the complete parent bank. The service
+has 2022 groups per Gamma on a bank of B_bank/32. Each successful actual
+`BankPackets.gather` reads and steps across every bank bit and then rewinds
+the borrowed source. Consequently it contributes at least `(2B,0,2B)` in
+R/W/M, without counting Counter work or selected-packet appends.
+
+Additionally, the subsequent `scatter` appends exactly one output bit for
+every bit in the full bank, whether selected or unselected. Its B output
+writes are disjoint from the gather source reads/moves.
+
+The sum of these **candidate-only source intervals** is therefore at least
+
+    R >= (281593/408) Gamma B_bank,
+    W >= (281593/816) Gamma B_bank,
+    M >= (281593/408) Gamma B_bank,
+    R+W+M >= (1407965/816) Gamma B_bank.
+
+This is not the old diagnostic-volume subtraction relabelled as an action
+bound. The paired original two group cycles cancel by the source contract;
+each listed remaining gather is an actual nonnegative added interval. All other
+scatter actions, commit, selected field copies, Counter work, 448-family acquisition,
+encoded compiler, assembly, extraction, borrowed comparisons, publication,
+service disposal and fences are additional nonnegative intervals. No omitted
+candidate cost can make this lower bound smaller.
+
+The complete service census remains 1696 monomials, 3484 direct scalar calls,
+176 exchange-internal negations, 48 private zero calls and 336 children per
+Gamma. Internal negations are included in the exchange and never charged
+again. Whole family V=Gamma*v and B_bank=14336V already contain Gamma.
+
+## Conservative upper debit for the remaining removed small intervals
+
+Let v be the full per-owner packet extent and L the complete Count-length
+envelope used in CBODY.md, enlarged if required to dominate parent and child
+preparation descriptor lengths. The header width is the actual baseline
+h_B=2685. All Count bodies in these intervals have fewer than 4L binary digits.
+The inherited binary Count source gives a conservative 256L componentwise
+price for linear operations and 4096L² for product. The exact full-countdown
+amortization is proved and calibrated in CBODY.md; it must not be replaced by
+one logarithmic scan charge for every payload bit.
+
+`Machine.copy_step` consists of `packet_extent` (one product and multiplication
+by two), an exact `require_zero` scan and preserved `copy_symbols`, then Count
+retirement. The complete packet scans are linear in v after countdown
+amortization. Including all delimiters, rewinds and zero tests, the bound
+
+    U_copy = 2^20 (v+1+L^4)
+
+holds separately in each action coordinate. There are fewer than 64 Count/
+Counter setup operations in this source interval; each is bounded by 4096L²,
+and payload/read/write/move traffic is below 128v+128. Their sum is below the
+stated envelope for L>=16. This includes copying into the existing v-bit
+private zero packet, rather than an uncharged blank destination.
+
+One removed original external child **shell** consists of `prepare_child`,
+B's `enter_child` excluding `native_child.run`, and completed reconnection.
+It includes width/tail arithmetic, after-field product/addition, the current
+payload preserved copy, fourteen descriptor preserved copies, header write,
+primitive-boundary tests, header read, full returned output transfer into the
+old target, marker erasure, all fifteen capsule clears and final header clear.
+It has fewer than 128 Count/setup/descriptor operations and fewer than 128v
+payload actions per coordinate, plus fewer than 32h_B header actions. Thus
+
+    U_shell = 2^24 (v+1+L^4+h_B)
+
+is a conservative componentwise bound. Complete C.run, including all of its
+descendants, is explicitly excluded and debited separately. This is B's
+external shell, never A's expensive embedded/parking shell. These deliberately
+loose coefficients follow a source loop envelope; the sign proof uses upper
+bounds only on work that is removed.
+
+Accordingly the total remaining small negative debit is at most
+`8 U_copy + 16 U_shell` in each coordinate. Six scalar calls were already
+matched and must not be subtracted again. The fixed original engine
+construction is common. B's additional controller setup/terminal retirement
+may conservatively be debited by its entire inherited 66496-action bound;
+all additional D construction/inventory retirement is nonnegative. The matched
+original backend's 703-write cold/warm potential cancels once globally.
+Finite rebinding/control costs and historical backing remain separate.
+
+## Controls and limits
+
+The executable checks reject partial-cover denominators, wrong service-bank
+volume, Boolean cardinalities and negative removed upper prices. The source
+occurrence injection detects duplicated/dropped events independently of rank
+histograms. The integrated verifier must additionally bind the full gate
+cover certificate and geometry-specific C-body upper bound before claiming a
+sign. A failure of the owner-gate theorem leaves precisely the five named
+Compact atoms unresolved; this file does not replace their prices by zero.
+
+Actual reduced phase-pair calibrations execute all four unit phases at H_b=4,8,17
+with nonconstant signed input (3,-2); their R/W/M counts agree phase by phase.
+Actual BankPackets.gather calibrations use 6,48,90-bit banks with multiple
+prefix/unused-row cases and preserve complete borrowed banks and heads. These
+are primitive calibrations, not production O73 execution.
diff --git a/research/qq16-complete-cost/PROOF.md b/research/qq16-complete-cost/PROOF.md
new file mode 100644
index 0000000000..028b8359db
--- /dev/null
+++ b/research/qq16-complete-cost/PROOF.md
@@ -0,0 +1,204 @@
+# Complete incremental exclusion on the terminal-child band
+
+Chris R / Clear1nsight with substantial coordinated OpenAI Codex assistance.
+Apache-2.0. This is a source-relative written proof with executable certificates,
+not formal-kernel or independent human acceptance.
+
+## 1. Objects, external boundary and exact domain
+
+Use canonical scientific main 12fa8c5c844be21bfefb38a19503fbd867a11244 and
+the authenticated nested #4172 closure retained in inputs. B* is #4167 original
+arithmetic with its shared closed numerical pipeline, external root child
+controller and proved internal child-return adoption. D is frozen #4166 with
+adopted whole-bank publication and its original fixed-copy child returns.
+Both start at the original prepared RootLayer fast-core boundary and finish
+at the same public root output. All unchanged outer work remains common.
+No new D* or new protocol is implemented.
+
+Assume the original successful exact C, source-entry height/grid, Ordinary,
+Compact, chronological hosting, row-stock/depth and long-record hypotheses,
+and #4166's semantic installation refinement. Fix the same admitted compiled
+q, profile, native programs and capacities for corresponding primitive engines.
+Keep physical stored H_b, global p,d, K,G, address guard H_g, complete prefixes,
+unused rows, coefficients, residue and every spectator. H_b is not replaced by
+logical coarse width or an estimate.
+
+At the actual nonleaf installed parent after remainder processing let
+e=73 lambda and d<=e^1000. Require lambda>=5 and that the removed rank-eight
+child is terminal in the actual source:
+
+    8 lambda < 73 OR (8 lambda)^1000 < d.
+
+The strict second inequality matters. Its evaluation is paid. Rank-one added
+children are then terminal too, by the same inequalities. All complete
+descendant counts for these unmatched children are exactly zero, as a source
+branch theorem, not a missing recursive tariff.
+
+Write b for the complete within-row address width, c for coefficient count,
+P for prefixes and U for unused rows:
+
+    row_bits = 2 H_b c 2^b,    v = P U row_bits,
+    V = Gamma v,              B_bank = 14336 V.
+
+The service bank is 448V=B_bank/32. Rank reduction moves axes into spectators;
+it preserves b and v. Gamma=|O(73,2)| has 2628 bits and is never applied twice
+to a whole-family or bank volume.
+
+Choose L>=16 dominating the Count-body envelope of CBODY.md for parent,
+both child geometries and their preparation/return shells. The concrete
+witness enlarges it by 2^20 for the latter. Require actual H_b>=L^4 and
+v>=2685. The normalized column threshold in section 5 is an additional
+explicit inequality, not a claim that all geometries below it are admitted.
+
+## 2. Source-bound cancellation and a finite owner-cover theorem
+
+Reuse #4172's successful-payload and phased native-history result only at
+matching complete descriptors and successful closed/exclusive engine states.
+All 510646 Gamma retained complete C bodies cancel, including 6972 Gamma
+changed-core calls and the entire 493097 Gamma later suffix. Count all
+descendants once inside their complete calls. Retained header increments do
+not cancel.
+
+NONCHILD.md constructs a literal source occurrence partition. Besides the
+16 removed C calls, its only removed opcodes are 32 monomials, eight copies,
+six unit subtracts and two control-only markers. Six new subtracts have the
+same literal and complete geometry. Match them on successful payloads.
+The two original core bank cycles retain identical owner selections, private
+obligations and geometry; match their complete cycles and entry/exit checks.
+
+Split each monomial at actual source call sites into a recipe-independent
+setup/phase/return base and its completed gate atoms. The written source
+argument and actual phase calibrations show equal base R/W/M schedules,
+including both sign-emission paths. Match 32 old bases to 32 of 800 new bases.
+The remaining bases are nonnegative.
+
+Gate prices retain exact source/target/late selectors and complete packet
+geometry. Inverse execution reverses the gate word; it does not change the
+completed kernel. A gate includes Binary/Ordinary/native descendants and
+disposal. Shared q/profile/program/capacity and the inherited closed-state
+relation are explicit. No finite-control or storage equality is inferred.
+
+The 736 removed gates inject into 7150 fixed new gates except for 4 Gamma
+add(6,8) and Gamma add(8,6). GATE-COVER.md proves a new quantified supply
+result for the literal Gauss-Jordan compiler: each named gate appears more
+than Gamma/32 times in one complete owner cover. It counts every fixed 9x9
+head using 64-coordinate tails, explicitly excluding the characteristic
+vector from the span, then forces leading-block elimination events.
+The 736 actual new owner-basis words therefore supply more than 23 Gamma of
+each required gate. Inverse words preserve multiplicity. This is aggregate
+cover counting, not an identity-owner fixture or an axis-invariance claim.
+Thus every removed monomial base and gate is paid for by a disjoint added
+source subinterval of equal R/W/M cost. No unexplained native price remains.
+
+## 3. Bounds on the complete unmatched source intervals
+
+After matching the two old core cycles, actual additional groups comprise
+41 Gamma non-map and (12286/51) Gamma map groups on B_bank, plus 2022 Gamma
+service groups on B_bank/32. Their disjoint positive source subtraces give
+
+    (R,W,M) >= (2,1,2) (281593/816) Gamma B_bank.
+
+Reads/moves are actual complete gather scans and rewinds; writes are the
+subsequent complete scatter output appends. This is an operation lower bound,
+not the earlier diagnostic-volume subtraction. Other gather/scatter/commit,
+acquisition/compiler, service arithmetic, extraction, publication, disposal,
+fences and extra inventories are nonnegative and may be omitted from a
+LOWER bound on D minus baseline.
+
+CBODY.md proves, by source loop accounting and exact countdown amortization,
+the complete external terminal C bound in each coordinate:
+
+    E_w <= 2^32(w+1)[v + (G_s+1)L^4],  G_s=v/(2H_b).
+
+It includes descriptor copies, shape/extent checks, the paid height cutoff,
+all coefficient axes, return, cleanup and borrowed heads. The strict cutoff
+uses six capped result products and nine squarings. No nonterminal price is
+invented. H_b>=L^4 implies E_w<=2^33(w+1)v.
+
+The remaining eight copies and sixteen B external shells have componentwise
+upper debit
+
+    8 * 2^20(v+1+L^4) + 16 * 2^24(v+1+L^4+2685).
+
+NONCHILD.md gives their source loop envelopes. The shell excludes complete
+C.run and uses B's external protocol, never A's avoided embedded parking.
+Since v>=2H_b and v>=2685, this is at most
+
+    [8*2^22 + 16*2^26] v.
+
+Subtract these UPPER bounds on removed work. Discarding new positive work is
+safe; subtracting a lower bound or unrelated upper-bound differences is not.
+
+## 4. Fair B* and setup
+
+Retained header difference is (12,4,12) per call, totaling 14298088 Gamma
+actions. B* additionally saves (5v+2,2v,4v+2) on every 510662 Gamma original
+root call. Frozen D does not receive that exchange. No earlier generic
+parking, bank-publication or ownership saving is credited again.
+
+Common original backend construction and its once-only 703-write epoch
+potential cancel globally. D's additional inventories are nonnegative.
+Conservatively debit B's entire 66496-action controller setup/retirement
+upper bound in EACH coordinate once. This is looser than its total invoice
+and cannot overstate an exclusion. Finite binding/control steps remain separate.
+
+## 5. Complete normalized bound and exact threshold
+
+Put
+
+    a = (281593/816) * 14336 Gamma,
+    C(lambda) = 16*2^33(8lambda+1) + 8*2^22 + 16*2^26,
+    s = (2a+5*510662-C, a+2*510662-C, 2a+4*510662-C),
+    h = (12*510646+2*510662, 4*510646, 12*510646+2*510662).
+
+The COMPLETE same-boundary difference satisfies, componentwise,
+
+    (T_D - T_B*)_i >= Gamma v s_i + Gamma h_i - 66496.       (1)
+
+Every term outside (1) was either matched at a source interface, debited by a
+valid upper bound, or discarded as additional nonnegative candidate work.
+It includes complete acquisition/compiler/service/output/terminal effects in
+the correct signed direction. Native children are not double-counted.
+
+The write slope is the smallest. Define the explicit last positive integer
+
+    M = floor((a+2*510662-16*2^33-8*2^22-16*2^26-1)
+              / (128*2^33)).
+
+For 5<=lambda<=M, all slopes are strictly positive, and v>=2685 makes every
+right-hand side in (1) strictly positive even after startup. M has 2610 bits.
+The independent checker accepts M and rejects M+1. This is the arithmetic
+domain of this sufficient bound, not an optimal crossover or admission theorem.
+
+Therefore frozen D costs strictly more than B* in reads, writes and unit moves
+on the stated nonempty terminal-child domain. It loses under every fixed
+positive weighting of these three source actions. If compiled control is
+included, an additional signed control difference Delta_control preserves
+exclusion when it is at least minus the weighted lower bound in (1).
+No unrestricted elapsed-time or total compiler-step verdict is claimed.
+
+## 6. Genuine installed domain, evidence and stopping decision
+
+FAIRNESS.md independently proves lambda<=4 cannot satisfy actual fast-root
+entry under the admitted height cutoff. It constructs all forty descriptor
+choices lambda=5..44 at p=2^8500, d=floor(sqrt(2^16949)), K=126519,
+G=34006, selected=Q0+73lambda. Exact root reservation, post-remainder cutoff,
+complete physical H_b>=L^4 and original padded stock are checked. Coarse
+row-stock depth and actual terminal body depth are distinguished. Those
+gigantic payloads are not executed.
+
+Finite evidence executes the actual selected C leaf, reduced cutoff controller,
+Count cutoff kernels, phase branches, literal O73 gate compiler, and complete
+bank gather/scatter/commit with nonconstant values and borrowed preservation.
+The unchanged #4166/#4172 semantic, dirty-helper, both-bridge and lifecycle
+evidence remains inherited, with exact pins and scope. Source authentication,
+finite runs, source proof, assisted review and hosted CI are distinct evidence.
+
+This is a decision-changing exclusion of the frozen installation in this
+explicit domain. Stop improving that fixed recovery there. The result does
+not exclude QQ16 with a changed source-compatible demand or schedule, nor
+decide nonterminal rank-eight C calls. That next domain must pay actual
+embedded descendant parking and all local/native costs; width>=73 alone is
+not evidence of recursion. No all-node supplier, bootstrap or kappa improvement
+follows. Production payload/full RootLayer.run and formal-kernel acceptance
+are not claimed.
diff --git a/research/qq16-complete-cost/README.md b/research/qq16-complete-cost/README.md
new file mode 100644
index 0000000000..7497f4bb8a
--- /dev/null
+++ b/research/qq16-complete-cost/README.md
@@ -0,0 +1,68 @@
+# QQ16 complete source-action exclusion in the terminal-child band
+
+Chris R / Clear1nsight with substantial coordinated OpenAI Codex assistance.
+Apache-2.0; all predecessor notices and frozen scientific sources are retained.
+
+Frozen #4166 D is strictly more expensive than the strongest compatible #4167
+original-arithmetic B* in EACH source read/write/unit-move component on the
+explicit admitted terminal-child domain in PROOF.md. This is a complete signed
+same-boundary bound, not a homogeneous native screen, timing ratio or another
+identity with unexplained E1/E8 prices.
+
+The domain retains actual physical geometry, H_b>=L^4, v>=2685, common admitted
+primitive configurations, 5<=lambda<=the certified positive-slope threshold,
+and the actual C8 terminal predicate:
+
+    8lambda<73 OR (8lambda)^1000<d.
+
+Forty genuine production-descriptor choices lambda=5..44 at p=2^8500 establish
+nonemptiness under inherited source/numerical/hosting premises. Production
+payloads/full RootLayer.run are not executed. The broad arithmetic threshold
+does not assert admission of every geometry below it.
+
+The new mechanism is a COST COUPLING, not a changed machine: split monomials at
+literal source interfaces; match old bases and gates to paid new work; prove
+the two residual gate supplies over the complete O73 owner cover. This avoids
+unexplained fitted/native prices. Complete terminal C and removed-shell upper
+bounds, actual positive bank scans/writes, startup/retirement and B* adoption
+then yield a strict full comparison. See PROOF.md, NONCHILD.md, GATE-COVER.md,
+CBODY.md, FAIRNESS.md and RESOURCES.md.
+
+The action verdict is separate from arbitrary compiled-control cost and
+historical backing. D's extra inventories remain. There is no new reset,
+engine/tape reduction, D* implementation, supplier or kappa claim.
+
+Reproduce with standard-library CPython 3.12:
+
+    python3.12 -B scripts/research_package.py --package research/qq16-complete-cost
+
+Ordinary and optimised scientific replays regenerate all default finite
+calibrations. The optional large 6190-bit cutoff kernel was executed once and
+is retained separately in LARGE-CUTOFF.json; it is not rerun by default or
+represented as a production width-73 payload. Check-only export modes validate
+saved execution transport and recompute source/counting/cost certificates;
+they are distinct from fresh physical calibration replay.
+
+Sources: scientific main12fa8c5c844be21bfefb38a19503fbd867a11244, #4172
+59b46625a8b2f0dfff3e38ba0949b4247423938a, #4167
+6749e458800f461535d64cc91c017552d9f55e5f and #4166
+0b082d22a0e9a442d264ab0633e35ef26c790630. SOURCES.json and the retained
+manifest authenticate the entire nested closure before inherited execution.
+REUSE.json separates unchanged inputs, new adaptations and method-only sources.
+
+Credit Jose Manuel's physical controller/Ordinary/Compact lineage; ywz65's
+parking and monomial sources; Sagar Thakrar's restoration proof; Tekalign's
+already credited ownership method; Ali Romman/Arham Tahir and the retained
+QQ16/recovery lineage. Ross Richardson, Nick Petalas, commdata2338 and Wentao
+Li retain their scoped cost/backing/lifecycle credit. No local BIT/ADD/wrapper
+coefficients are transplanted. Coordinated agent review shares sources and
+checkers; it is not human or formal-kernel acceptance.
+
+## Open next questions
+
+The terminal-band fixed recovery loses and should not be expanded there.
+For a genuine nonterminal C8 domain, first prove the actual root-height cutoff
+admits recursion, then price the complete original embedded child tree,
+including its parent parking, against all candidate local work. The separate
+local first-nonleaf intuition is not a price certificate. A changed demand or
+schedule must identify removed scans and supply a new complete bill.
diff --git a/research/qq16-complete-cost/RESOURCES.md b/research/qq16-complete-cost/RESOURCES.md
new file mode 100644
index 0000000000..571b9e8510
--- /dev/null
+++ b/research/qq16-complete-cost/RESOURCES.md
@@ -0,0 +1,76 @@
+# Resource and control boundary of the complete-cost comparison
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+Source credit: Jose Manuel's #3385/#2899 controller and Ordinary implementation;
+#4167's shared controller and compatible return adoption; #4172's six-arena
+history and payload-action theorem. Ross Richardson #2831, Nick Petalas
+#2923/#2982/#2951 and Wentao Li #3993 retain their scoped backing, wrapper and
+lease-method attribution. No source tariff is transplanted between codecs.
+
+The cost evaluator and independent checker are research certificates, not
+additional machine-time operations. They install no reset, queue sorting,
+new physical engine, scratch tape or numerical-width change in B*, B or frozen D.
+All implementation inventories therefore retain their earlier contracts.
+With `M(q)=2q^2+100696145`, the inherited fixed-tape figures are:
+
+| Variant | Fixed tape inventory |
+| --- | ---: |
+| A | `678+M` |
+| B and B* | `678+M+1023` |
+| frozen C/D | conservative `678+3M+2^20` bound |
+
+B's1023 extra controller tapes share one closed scalar/leaf/monomial/Ordinary
+pipeline sequentially with its original backend. D retains the separate producer,
+service and original-child pipeline inventories specified by #4166. The original
+child endpoint is reused sequentially by producer and service. A paired action
+price does not establish that D has B's space use. The conservative D upper
+bound is not an exact live-role count and cannot be subtracted from B's count to
+prove a precise space difference.
+
+The phase-dependent history relation covers all six native arenas, templates,
+codec, parked state and heads on the inherited successful closed domain. It
+removes no physical role and destroys no borrowed resident. Absence of escaped
+handles and legal successful closure remain ownership premises. Erasure preserves
+historical backing: for each physical tape t retain the maximum coordinate ever
+visited, and sum those maxima over all tapes and simultaneously allocated
+engines. A role exchange may distribute maxima across different physical roles.
+Blank current bodies and equal source-action counts are not equal-space proofs.
+
+The complete packet geometry is
+
+```
+row_bits = 2 H_b c 2^b
+v = P U row_bits
+V = Gamma v
+B_bank = 14336 V
+S_service = 448 V = B_bank/32.
+```
+
+Rank reduction moves active axes to spectators; it does not remove those bits.
+The source root plan fixes physical `H_b=p+2*2^210000*d+3`; the logical coarse
+width, working numerical reserve, `H_g=dG`, and physical H_b have different
+roles. The evaluator's complete geometry key retains widths, spacing, prefix
+and row counts, spectators, stock, compiled recipe/source binding and Ordinary
+selection/marker class. A changed field requires a separate price unless a
+source theorem explicitly proves insensitivity.
+
+New scans, assembly, retained protected output, compiler scratch, descriptor
+arithmetic, constructors and retirement must appear in disjoint source
+intervals. B's earlier66496 startup/retirement action bound is not free credit
+against D: a signed difference needs matched work or valid subtraction of a
+baseline upper bound. The original-controller703-write first-use potential is
+once per nonempty backend epoch and cancels for B and D; additional startup
+work does not disappear with it.
+
+Source reads, writes and unit moves remain separate from finite control, host
+elapsed time and historical backing. If a complete action lower bound is L>=0,
+then a compiled-step exclusion requires `Delta_control >= -L` under unit
+weights, or the corresponding weighted action bound. An action upper bound
+U<0 establishes total-step improvement only if `Delta_control < -U`.
+These inequalities retain the signed B* binding adjustment. No host-language
+operation is silently given a precision-independent zero tariff.
+
+The present package supplies no recursive-supplier or public-multiplication
+integration and changes no selected kappa. A result for the root comparison
+must state its reachability and parameter domain separately from reduced
+calibrations and symbolic full-geometry certificates.
diff --git a/research/qq16-complete-cost/RESULT.json b/research/qq16-complete-cost/RESULT.json
new file mode 100644
index 0000000000..e124ff7b18
--- /dev/null
+++ b/research/qq16-complete-cost/RESULT.json
@@ -0,0 +1 @@
+{"actual_production_descriptor_family":"p=2^8500, lambda=5..44; inherited numerical/hosting/source premises; no production payload execution","cost_currency":"source reads/writes/unit moves; compiled control and historical backing separate","execution_sha256":"e64286ca8aa58b7568f69d95e90c5786b31e54243487f0553edee29dc0179132","frozen_predecessor":"59b46625a8b2f0dfff3e38ba0949b4247423938a","no_kappa_change":true,"not_a_universal_QQ16_obstruction":true,"priority_revision":7,"scientific_main":"12fa8c5c844be21bfefb38a19503fbd867a11244","sources_authenticated_before_execution":108,"status":"PASS_QQ16_COMPLETE_TERMINAL_COST","verdict":"frozen D strictly costs more than Bstar in each source R/W/M component on the proved terminal-child domain"}
diff --git a/research/qq16-complete-cost/REUSE.json b/research/qq16-complete-cost/REUSE.json
new file mode 100644
index 0000000000..e6de5090dc
--- /dev/null
+++ b/research/qq16-complete-cost/REUSE.json
@@ -0,0 +1,89 @@
+{
+  "source_main": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "source_predecessor": 4172,
+  "items": [
+    {
+      "pr": 4172,
+      "head": "59b46625a8b2f0dfff3e38ba0949b4247423938a",
+      "classification": "reuse unchanged",
+      "use": "retained C history/payload action theorem, successful closed boundaries, full root census and physical backing discipline",
+      "limit": "paired admitted complete geometry; no runtime/control/backing equality"
+    },
+    {
+      "pr": 4167,
+      "head": "6749e458800f461535d64cc91c017552d9f55e5f",
+      "classification": "reuse unchanged",
+      "use": "fair B/B* pipeline and exact return/header/startup prices",
+      "limit": "generic savings not new QQ16 credit; no all-node substitution"
+    },
+    {
+      "pr": 4166,
+      "head": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+      "classification": "reuse unchanged",
+      "use": "actual frozen producer/service/continuation and exact output/owner/dirty-state semantics",
+      "limit": "inherited native/numerical/stock/hosting/long-record hypotheses"
+    },
+    {
+      "pr": 3385,
+      "head": "7e5a187214126d31afc241a8f89f4a652352b58c",
+      "author": "Jose Manuel",
+      "classification": "adapt with new proof/cost",
+      "use": "actual complex controller, root admission, bank source and complete terminal C action bounds",
+      "limit": "no source change or claim full nonterminal recurrence"
+    },
+    {
+      "pr": 2899,
+      "head": "2f0911ad735643a069b9790302fbf179e49f74f8",
+      "author": "Jose Manuel",
+      "classification": "reuse unchanged",
+      "use": "actual Ordinary/native pipeline inside matched gate atoms",
+      "limit": "no transplanted free allocator or new fitted tariff"
+    },
+    {
+      "pr": 2982,
+      "head": "b9ac0d07eb9cdc31c4dca8dcc218943998edd3e8",
+      "author": "Nick Petalas",
+      "classification": "method/regression only",
+      "use": "complete wrapper/descendant/disposal boundary discipline",
+      "limit": "265V/277V only for its route wrapper; no imported coefficients"
+    },
+    {
+      "pr": 2951,
+      "head": "d7a9287d6564bae5c7b19e2e3e655c2b578f8b72",
+      "author": "Nick Petalas",
+      "classification": "method/regression only",
+      "use": "exact countdown/popcount and explicit factory separation",
+      "limit": "1024V/local scaling not whole C; Arham PR2877/ywz65 PR2473 retain countdown predecessor credit"
+    },
+    {
+      "pr": 3233,
+      "head": "803f3593e8f00ed8591d5ff6fc69ce2a036a3293",
+      "author": "commdata2338",
+      "classification": "method/regression only",
+      "use": "signed bound and complete local source envelope discipline",
+      "limit": "4096V/4102V scoped upper prices not imported into whole C"
+    },
+    {
+      "pr": 3983,
+      "head": "a76ebcab36fdc78f2824fc59dceaabbeda8189ba",
+      "classification": "deferred",
+      "use": "no matching R437 codec coefficient imported",
+      "limit": "separate stream"
+    },
+    {
+      "pr": 4160,
+      "head": "4571a446e3a57d95667bade4d57788102865be06",
+      "classification": "method/regression only",
+      "use": "constructor/copy accounting distinction only",
+      "limit": "separate R437 codec, no numerical tariff"
+    }
+  ],
+  "inherited_credit": [
+    "ywz65 numerical parking/monomial/countdown lineage",
+    "Sagar Thakrar #3464 restoration",
+    "Tekalign #3380 already credited ownership adaptation",
+    "Ali Romman/Arham Tahir and #3985/#4015/#4106/#4109/#4129 lineage",
+    "Ross Richardson #2831, Nick Petalas #2923, Wentao Li #3993 backing/lifecycle methods retained via #4172"
+  ],
+  "live_heads_reviews": "Named heads unchanged;4160/3983 now merged; returned review/comment arrays empty. Bounded coverage; no novelty guarantee."
+}
diff --git a/research/qq16-complete-cost/REVIEW.json b/research/qq16-complete-cost/REVIEW.json
new file mode 100644
index 0000000000..553a91f2d6
--- /dev/null
+++ b/research/qq16-complete-cost/REVIEW.json
@@ -0,0 +1,39 @@
+{
+  "status": "PASS_ASSISTED_ADVERSARIAL_REVIEW",
+  "blocking_defects": [],
+  "freeze_files": {
+    "runtime.py": "d4070217df193d2ad5ff5f19ebcde98b5e928d7a4fbf47ad4e51c145ab5f7814",
+    "cost.py": "97ea778cf497212a3548e86b00793bc993d500e329c76422f7714e736930dd19",
+    "cbody.py": "923a5ee9aadb285106bdb78aeac2cb2d079d243cd417407e028ca7ddaadc9343",
+    "checker.py": "18df3667a6ec950ab425024b26d4f13f049736a8c82d543add4aca305d0a3c50",
+    "gate_cover.py": "260065dd23598a4fba21229388a619d6e11b840d643838059d6c93a7a6d221db",
+    "nonchild.py": "c717e5dbd61e09c76569ecb9aa55d632576963704a8c1f94d96b0bd57e4aee11",
+    "verify.py": "5c16dd906f28dd5f6e426b12b6980ff142b56454f523f66513dcac38e32e64a9",
+    "test_verify.py": "ab71aeff2c8fd97f1b46b0540efdae56fe539499109690eb115a7f65335b70c0",
+    "PROOF.md": "72d32d1ac285cd81873441850512b28daf41929005aa901462184024465de545",
+    "README.md": "38963e28c4e6ae39acf98f866ad108ffc42f04a70b441a9718dab88c789b1068",
+    "CBODY.md": "3670383249505575a9a5a159afb4376a207b6545f7fbefe6640f1dac19d25f72",
+    "NONCHILD.md": "61a9a5fbd9863ccdd80749a87f3e0157742c0fc33539ced9c3dcd03b425d06be",
+    "GATE-COVER.md": "cd692669893d1fffeaafacbcc82fc08b0f3cf7ffa2e005b0e586538ee449e73f",
+    "FAIRNESS.md": "9baa5b3fcc626928d3200c1418cb8907576c46924424c0d4b0dcfa12a5767afc",
+    "RESOURCES.md": "e12e28e8611e6a1e775f681aad224d3f2ff1e58e064d9ac52221eee6c0b30d39",
+    "SOURCES.json": "6602b0a0c3eb2292391c05ea993d6dda6b80ddaf78441e1a207504ef5a70a48a"
+  },
+  "freeze_aggregate_sha256": "771c972fbcd26fd4aa6ed11cfbe044bf5e416521ff70d11d2ed199d993944d61",
+  "scope": "complete terminal-child source-action exclusion frozen D vs Bstar; common successful native configurations and physical/stock admission remain",
+  "performed": [
+    "all16hashesbeforeandafter",
+    "actual MonomialEngine/signed_phase/Recipe.phase/controller source inspection",
+    "independent exact rational9x9tail/head/forcingevent reconstruction",
+    "independent sign reconstructions lambda5,9,10,44",
+    "full fresh verifier PASS",
+    "read-onlycheck-onlyPASS"
+  ],
+  "limits": [
+    "shared authenticated sources and package checker",
+    "not independent human or formal-kernel acceptance",
+    "source upper envelopes are written loop proofs supported by calibrations",
+    "no verdict for nonterminal C8/control/backing/all QQ16",
+    "no new fitted/fallback campaign; kernels matched under inherited4172 theorem"
+  ]
+}
diff --git a/research/qq16-complete-cost/SEALS.json b/research/qq16-complete-cost/SEALS.json
new file mode 100644
index 0000000000..507198207e
--- /dev/null
+++ b/research/qq16-complete-cost/SEALS.json
@@ -0,0 +1,9 @@
+{
+  "cbody.py": "923a5ee9aadb285106bdb78aeac2cb2d079d243cd417407e028ca7ddaadc9343",
+  "checker.py": "18df3667a6ec950ab425024b26d4f13f049736a8c82d543add4aca305d0a3c50",
+  "cost.py": "97ea778cf497212a3548e86b00793bc993d500e329c76422f7714e736930dd19",
+  "gate_cover.py": "260065dd23598a4fba21229388a619d6e11b840d643838059d6c93a7a6d221db",
+  "nonchild.py": "c717e5dbd61e09c76569ecb9aa55d632576963704a8c1f94d96b0bd57e4aee11",
+  "runtime.py": "d4070217df193d2ad5ff5f19ebcde98b5e928d7a4fbf47ad4e51c145ab5f7814",
+  "test_verify.py": "ab71aeff2c8fd97f1b46b0540efdae56fe539499109690eb115a7f65335b70c0"
+}
diff --git a/research/qq16-complete-cost/SOURCES.json b/research/qq16-complete-cost/SOURCES.json
new file mode 100644
index 0000000000..0f42085048
--- /dev/null
+++ b/research/qq16-complete-cost/SOURCES.json
@@ -0,0 +1,487 @@
+{
+  "schema_version": 1,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81"
+    },
+    {
+      "path": "notes/batched-complex-rows.tex",
+      "usage": "input",
+      "sha256": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c",
+      "git_blob": "e13bd96eb29bdc6526f10dc32e0a146bc17848a4"
+    },
+    {
+      "path": "notes/compact-control-layout.tex",
+      "usage": "input",
+      "sha256": "2bc28e50f3eb092195294cafa81213e520f6d42e7935e9905ad8a6199e2a7c87",
+      "git_blob": "16f4d233471a7d189163ae7e7902becadecbba64"
+    },
+    {
+      "path": "notes/compact-control-movement.tex",
+      "usage": "input",
+      "sha256": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+      "git_blob": "06b6a9ef24245ac7b724c53a204635415b402357"
+    },
+    {
+      "path": "research/bit2234-stock-threshold/README.md",
+      "usage": "input",
+      "sha256": "1e050c9f963421d751d9208092f9a15321ed77810e03912df8eb5eb56bbb06e7",
+      "git_blob": "ede0d322c477af91d4c2cc33db0fd10958f45eab"
+    },
+    {
+      "path": "research/community-frontier1042-audit/selected-replay.tar.gz",
+      "usage": "input",
+      "git_blob": "6f4dc6fe7631d8aacf8081fcaecf32197181685b",
+      "sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754"
+    },
+    {
+      "path": "research/community-frontier1094-audit/selected-replay.tar.gz",
+      "usage": "input",
+      "git_blob": "c24daf067f9c543421d89ca2eeaa4eb78a57fb6f",
+      "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6"
+    },
+    {
+      "path": "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL-TEMPLATE.json.gz",
+      "usage": "input",
+      "sha256": "0357b7cfbd7c29b4983982baf153c8a9f1e1e412690cd7fa9fc3d23d7963b20f",
+      "git_blob": "9eafb8776cbf78c72124f833534469ddfa5e98ec"
+    },
+    {
+      "path": "research/community-hyperplane599-audit/pr589/bit589/v9/nine/GEOMETRY.json",
+      "usage": "input",
+      "sha256": "0058c491d839142aa99ef86a5ec697ce99857632228531512ea3fa74fb24d734",
+      "git_blob": "44006542202ca6037533a754f0bcd00549d7e088"
+    },
+    {
+      "path": "research/complex-grid-prefix-audit/PROOF.md",
+      "usage": "input",
+      "sha256": "9c2473e080a64de5139abf66680534043143ec9f4488ceabf62403702047a3ad",
+      "git_blob": "30f019e14866200660cbd2ad82f3bff707003210"
+    },
+    {
+      "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+      "usage": "input",
+      "sha256": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+      "git_blob": "e293ddc557742637f9f679f083a1a282d87b1b13"
+    },
+    {
+      "path": "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz",
+      "usage": "input",
+      "sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+      "git_blob": "85a4499bf9e4911a705d50567a2c2ef6cf23739a"
+    },
+    {
+      "path": "research/gaussian-normalization-stream/SOURCES.json",
+      "usage": "input",
+      "sha256": "c434302f4489366c1763f918ba59e2f57efc0a41d72310fd3c6bbe1553370275",
+      "git_blob": "58fce750dc2814f36ac096b407dd28293539bf8f"
+    },
+    {
+      "path": "research/gaussian-normalization-stream/normalizer.py",
+      "usage": "input",
+      "sha256": "2b0acaa831219faf3e7776969bdcffc3f0f9c608b15d6b4c343ff20cf6a50107",
+      "git_blob": "5d1a0961ace6b7edccb26c05780623c5509a7597"
+    },
+    {
+      "path": "research/gaussian-parity-synthesis/REVIEW.md",
+      "usage": "input",
+      "sha256": "7d7b9ac63ccd2927f592e9edac1b4c11d58a6c74c5813d488e112f729090f60c",
+      "git_blob": "0a6a4c7c1e8bef9c9aa9c7fb636e5ad6c0c411ae"
+    },
+    {
+      "path": "research/gaussian-parity/gaussian-parity-certificates.tex",
+      "usage": "input",
+      "sha256": "e21e1063141cbc798e73052e22d01eec57f1c173a580041e55aa196b1b0479f8",
+      "git_blob": "e364cff719a12a5dfd52f2975cd07cc0318da511"
+    },
+    {
+      "path": "research/joint-query/certificate.json.gz",
+      "usage": "input",
+      "git_blob": "c6e876d8b48d768214deee265ade428f8983b566",
+      "sha256": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7"
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new file mode 100644
index 0000000000..8327fd3209
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+  "scope_key": "73442cf25caf1ed45f11",
+  "priority_revision": 7,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/qq16-caller-install/README.md"
+    ],
+    "methods": [
+      "Derive the matched whole-caller physical bill for installed and baseline protocols.",
+      "Change the actual demanded observations and prove a cheaper legal producer/consumer contract."
+    ],
+    "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. 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",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.",
+    "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+    "allowed_variations": [
+      "One paid query, one changed first pair, or one precisely specified affine helper state.",
+      "A counterexample or lower bound for that exact proposed repair.",
+      "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+    ],
+    "scope_change_triggers": [
+      "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+      "Treating cover-map counts as zero-cost physical address operations.",
+      "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+      "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.",
+      "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.",
+      "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving."
+    ],
+    "overlap_terms": [
+      "QQ16",
+      "joint-query",
+      "changing-chart controller",
+      "selected observation",
+      "1969",
+      "2540",
+      "early record",
+      "output-bank retention",
+      "complete native decoder",
+      "2965",
+      "producer defect",
+      "dirty-helper range",
+      "F17 consumer",
+      "4166",
+      "qq16-caller-install"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+        "evidence": "research/qq16-caller-install/README.md",
+        "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+        "status": "author-checked",
+        "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Derive complete geometry-sensitive signed source-action comparison of frozen QQ16 D against strongest compatible B*, including genuine outer-root admission, complete native bodies and disjoint nonchild/protocol costs.",
+  "scope_change_reason": "Assigned continuation after #4172; prior history/context theorem inherited. No generic savings or decoder expansion repeated.",
+  "bottleneck_link": "The dominant remaining gap is geometry-dependent E1/E8 and actual new/removed nonchild/protocol prices, with a reachable installed caller domain.",
+  "budget_minutes": 60,
+  "outcome": "completed",
+  "author": "Chris R / Clear1nsight with substantial coordinated OpenAI Codex assistance",
+  "selection_seed": "566fc860a35b9e6a839ca9fb89443452",
+  "checkpoint": {
+    "entry_main": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+    "priority_revision": 7,
+    "entry_utc": "2026-10-20T09:30:00Z",
+    "predecessor_head": "59b46625a8b2f0dfff3e38ba0949b4247423938a",
+    "overlap_coverage": "All-state QQ16/whole-C/geometry-sensitive connector search top30 capped; exact4172/4167/4166 heads and4172reviews; helper75localrecords32matches remote unavailable gh; bounded1163/1166/canonicalhandoff pages. No novelty guarantee."
+  },
+  "open_questions": [
+    {
+      "question": "What is the full incremental price on a genuinely nonterminal C8 domain?",
+      "why_it_matters": "Terminal-child exclusion is scoped and cannot decide an actual descendant tree.",
+      "first_step": "Prove the root-height test permits C8 recursion, then price embedded descendants and all new local work; retain Binary expansion, selection setup and marker/constructor bills.",
+      "blocked_by": "Unpriced complete recursive C plus candidate local/native tariffs outside the proved terminal band."
+    }
+  ],
+  "stop_rule": "Publish at most one substantial context result after integrated verification; otherwise preserve checkpoint. Stop fixed-mechanism recovery expansion if the complete necessary inequality fails or remains unpriced.",
+  "evidence": "Source-bound complete incremental exclusion of frozen D versus B* in each R/W/M component on explicit nonempty terminal-child domain. Source admission, actual primitive/C calibrations, independent signed/counting checker; final review/publication statuses separate.",
+  "ai_assistance": "Substantial coordinated OpenAI Codex assistance for source analysis, legal fixtures, context proof, cost/resource ledger, verification and read-only adversarial review. Shared source/checker dependencies are disclosed; no independent human or formal-kernel acceptance."
+}
diff --git a/research/qq16-complete-cost/VERIFICATION.md b/research/qq16-complete-cost/VERIFICATION.md
new file mode 100644
index 0000000000..8acc8a603a
--- /dev/null
+++ b/research/qq16-complete-cost/VERIFICATION.md
@@ -0,0 +1,53 @@
+# Verification boundary and publication record
+
+CPython 3.12.3, standard library, Linux. All scientific source inputs were
+SHA256/Git-blob authenticated before inherited execution. The retained #4172
+archive holds30 committed predecessor files and its unchanged nested archives;
+78 canonical inputs complete the108-file loader boundary. No foreign unmerged
+Git object is needed to execute the retained predecessor.
+
+Fresh primary generation and optimised replay passed. Six source/export/receipt
+boundary groups passed in72.350 seconds. They cover normal/optimised read-only
+Git-free check-only transport, canonical/local poison rejection before execution,
+outer manifest/archive seals, inner content/duplicate/link/missing-member controls,
+typed complete receipt mutations and duplicate JSON keys, and overwrite refusal.
+These fast transport runs recompute source/counting/cost certificates while
+reading saved finite execution; they are not fresh physical calibration runs.
+The separate primary and optimised primary regenerate all default calibrations.
+
+The default scientific replay includes17 exact countdown cases, seven complete
+selected-controller leaf executions, one explicitly reduced-binding complete
+height-cutoff execution, three encoded cutoff kernels,12 phase-pair cases,
+three complete bank gather/scatter/commit cases, literal O73 gate witnesses,
+the full source occurrence/service/later-root census,40 genuine symbolic
+RootPlan descriptor certificates, exact positive-bound endpoint/next-integer
+controls, and independent signed/counting/schema checks.
+
+LARGE-CUTOFF.json retains a once-executed optional6190-bit encoded cutoff
+kernel run,209.934seconds foritsfourcases. The width73 case cost
+(230491720,51790603,174593792) R/W/M and selected the strict terminal branch.
+It did not execute a width73 payload. The optional kernel is not repeatedly
+charged to the default registered or export checks.
+
+Preparation exposed two module-composition issues: monomial modules must join
+the authenticated cold cohort before standalone recipe imports, and local
+cost modules need unique names to avoid the predecessor cost module. Both
+were resolved before the final frozen scientific revision; failed preparation
+runs did not produce accepted receipts. No source arithmetic was changed.
+
+The final16-file frozen assisted adversarial review passed, with independently
+reconstructed cover counts and representative signs. REVIEW.json records
+hashes, exact scope and shared-source/checker limitations. It is not human
+acceptance or formal-kernel verification.
+
+The full registered launcher, committed-byte/source-history check, official
+committed export/check, and actual ordinary/optimised committed read-only
+Git-free scientific export replays are separate final gates. Their exact
+publication commit, timings, archive hash and hosted CI status are recorded
+in publication artifacts and the PR; do not infer them from metadata success.
+
+Production O73 payloads/full RootLayer.run were not executed. The cost proof
+is quantified under the stated inherited numerical/hosting/stock/ordinary/
+Compact/long-record premises. Fitted/fallback kernel equality is inherited
+only on the proved matching complete geometry and successful closed-state
+domain; this contribution does not supply a new fitted numerical tariff.
diff --git a/research/qq16-complete-cost/VERIFY.json b/research/qq16-complete-cost/VERIFY.json
new file mode 100644
index 0000000000..5e68d0e526
--- /dev/null
+++ b/research/qq16-complete-cost/VERIFY.json
@@ -0,0 +1,122 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "notes/batched-complex-rows.tex",
+    "notes/compact-control-layout.tex",
+    "notes/compact-control-movement.tex",
+    "research/bit2234-stock-threshold/README.md",
+    "research/community-frontier1042-audit/selected-replay.tar.gz",
+    "research/community-frontier1094-audit/selected-replay.tar.gz",
+    "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL-TEMPLATE.json.gz",
+    "research/community-hyperplane599-audit/pr589/bit589/v9/nine/GEOMETRY.json",
+    "research/complex-grid-prefix-audit/PROOF.md",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz",
+    "research/gaussian-normalization-stream/SOURCES.json",
+    "research/gaussian-normalization-stream/normalizer.py",
+    "research/gaussian-parity-synthesis/REVIEW.md",
+    "research/gaussian-parity/gaussian-parity-certificates.tex",
+    "research/joint-query/certificate.json.gz",
+    "research/joint-query/evidence/BRIDGE-REVIEW.md",
+    "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md",
+    "research/joint-query/source_data.py",
+    "research/joint-query/verify_native.py",
+    "research/joint-query/verify_scalar.py",
+    "research/p104-whole-word-internal-grid/README.md",
+    "research/physical-complex-controller/PROOF.md",
+    "research/physical-complex-controller/SOURCES.json",
+    "research/physical-complex-controller/bank_packets.py",
+    "research/physical-complex-controller/cohort.py",
+    "research/physical-complex-controller/cover.py",
+    "research/physical-complex-controller/fixture_binding.py",
+    "research/physical-complex-controller/grid_boundary.py",
+    "research/physical-complex-controller/machine.py",
+    "research/physical-complex-controller/monomial_packets.py",
+    "research/physical-complex-controller/native_program.py",
+    "research/physical-complex-controller/parking.py",
+    "research/physical-complex-controller/root_layer.py",
+    "research/physical-complex-controller/root_plan.py",
+    "research/physical-complex-controller/root_streams.py",
+    "research/physical-complex-controller/scalar_packets.py",
+    "research/physical-complex-controller/scalar_program.py",
+    "research/physical-complex-controller/selected_binding.py",
+    "research/physical-complex-controller/selected_source.py",
+    "research/physical-gaussian-leaf/PROOF.md",
+    "research/physical-gaussian-leaf/SOURCES.json",
+    "research/physical-gaussian-leaf/axis_stream.py",
+    "research/physical-gaussian-leaf/coefficient_engine.py",
+    "research/physical-gaussian-leaf/inputs/pr3087.tar",
+    "research/physical-gaussian-leaf/leaf_sources.py",
+    "research/physical-gaussian-leaf/signed_linear.py",
+    "research/physical-scalar-stream/scalar_engine.py",
+    "research/physical-scalar-stream/scalar_words.py",
+    "research/pr589-five-helper-hosting/PROOF.md",
+    "research/pr589-five-helper-hosting/verify.py",
+    "research/qq16-all-depth-producer-grid/PROOF.md",
+    "research/qq16-line-normalized-decoder/PREDECESSORS.json",
+    "research/qq16-line-normalized-decoder/PROOF.md",
+    "research/qq16-line-normalized-decoder/RESULT.json",
+    "research/qq16-line-normalized-decoder/SOURCES.json",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/PROOF.md",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/README.md",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/RESULT.json",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/SOURCES.json",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/WORD.json",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/references/PR2540-PROOF.md",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/references/PR2540-README.md",
+    "research/qq16-line-normalized-decoder/vendor/pr2681/verify.py",
+    "research/qq16-line-normalized-decoder/verify.py",
+    "research/qq16-tagged-cover-routing/PROOF.md",
+    "research/qq16-tagged-cover-routing/oracle.py",
+    "research/qq16-tagged-cover-routing/router.py",
+    "research/qq16-tagged-cover-routing/verify.py",
+    "research/recursive-parking-boundary/README.md",
+    "research/selected-bit-local-ring-sweeps/PROOF.md",
+    "research/selected-bit-recursive-closure/PROOF.md",
+    "research/selected-complex-layer-closure/PROOF.md",
+    "research/selected-complex-layer-closure/arithmetic.py",
+    "upstream/build/sections/02-streams.tex",
+    "research/physical-complex-controller/production_native.py",
+    "research/physical-complex-controller/check_bounds.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-Werror",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 150,
+      "checks": "complete-terminal-cost"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-Werror",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 150,
+      "checks": "complete-terminal-cost-optimized"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-Werror",
+        "-B",
+        "{package}/test_verify.py"
+      ],
+      "timeout_seconds": 240,
+      "checks": "source-export-and-receipt-boundaries"
+    }
+  ]
+}
diff --git a/research/qq16-complete-cost/cbody.py b/research/qq16-complete-cost/cbody.py
new file mode 100644
index 0000000000..41bbafd5c1
--- /dev/null
+++ b/research/qq16-complete-cost/cbody.py
@@ -0,0 +1,379 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Source-derived successful external C leaf bounds and finite calibrations.
+
+This is a cost checker, not an implementation of a compressed tape machine.
+The exact countdown tariff is for the retained stream.Counter implementation.
+Complete nonterminal C tariffs are deliberately rejected, rather than fabricated.
+"""
+from dataclasses import dataclass, asdict
+
+INPUTS = ('prefixes','rows','front','compact_bits','before','width','after','back',
+          'spacing','guard','residue','component_bits','coefficients','root_width')
+
+
+def need(ok, reason):
+    if not ok:
+        raise ValueError(reason)
+
+
+def nat(x, positive=False):
+    need(type(x) is int and x >= int(positive), 'exact nonnegative integer geometry')
+    return x
+
+
+def countdown_decrements(n):
+    """Exact R/W/M for n successive decrement calls, including the final one.
+
+    Initialization and close are excluded here and bounded separately below.
+    Binary digit lengths are canonical, no spare high zero digit is assumed.
+    """
+    nat(n, True)
+    z = n-n.bit_count()
+    powers = n.bit_length()-1
+    return (2*z+5*n+1, z+n+2*powers+3, 2*z+4*n+2*powers+4)
+
+
+def countdown_cycle_upper(n):
+    """Componentwise bound for construction, all decrements and final close.
+
+    Source word is canonical, starts at head one, and is restored. Actual
+    initialization normalizes the newly copied countdown; source ownership is
+    unchanged. The zero case is included and has no decrement.
+    """
+    nat(n)
+    d = max(1,n.bit_length())
+    return tuple((countdown_decrements(n)[i] if n else 0)+64*(d+2)
+                 for i in range(3))
+
+
+@dataclass(frozen=True)
+class Geometry:
+    prefixes:int
+    rows:int
+    front:int
+    compact_bits:int
+    before:int
+    width:int
+    after:int
+    back:int
+    spacing:int
+    guard:int
+    residue:int
+    component_bits:int
+    coefficients:int
+    root_width:int
+
+    def validate(self):
+        for name,value in asdict(self).items():
+            nat(value,name in ('prefixes','rows','spacing','guard','component_bits',
+                              'coefficients','root_width'))
+        need(self.component_bits>=2,'signed component width')
+        need(self.residue<self.spacing,'selected residue')
+        need(self.width<=self.root_width,'global root width')
+        return self
+
+    @property
+    def b(self):
+        return self.front+3*self.compact_bits+self.before+self.width*self.spacing+self.after+self.back
+
+    @property
+    def v(self):
+        return self.prefixes*self.rows*2*self.component_bits*self.coefficients*(1<<self.b)
+
+    @property
+    def gaussians(self):
+        return self.prefixes*self.rows*self.coefficients*(1<<self.b)
+
+    @property
+    def L(self):
+        # Counts in source setup include powers 2**b, not just encoding of b.
+        return 16+self.b+sum(max(1,x.bit_length()) for x in asdict(self).values())
+
+    def key(self, marker_class='steady'):
+        need(marker_class in ('steady','fresh'),'explicit original-controller marker class')
+        return (*tuple(asdict(self).items()),('marker_class',marker_class),
+                ('binding','original-selected-73'),('root',True))
+
+
+def terminal_branch(width, root_width, dimension=73):
+    nat(width);nat(root_width,True);nat(dimension,True)
+    need(width<=root_width,'node within global width')
+    if width<dimension:return 'below dimension'
+    return 'capped-power cutoff' if width**1000<root_width else None
+
+
+def leaf_upper_geometry(g, marker_class='steady', materialize=True):
+    """Complete external C.run leaf upper, separately in R/W/M.
+
+    Applicable to either actual terminal branch of original selected C.
+    It includes entry copies, shape/extent validation, all coefficient axes,
+    exit transfer, private/controller cleanup and borrowed-head restoration.
+    A fresh controller adds its explicit once-only 703-write potential.
+    Successful arithmetic and source endpoint admission are premises.
+
+    For enormous b, materialize=False returns a compact exact polynomial in
+    v instead of allocating an integer with b binary digits.
+    """
+    need(isinstance(g,Geometry),'complete typed descriptor packet')
+    g.validate();g.key(marker_class)
+    branch=terminal_branch(g.width,g.root_width)
+    need(branch is not None,'nonterminal C requires an evaluated completed recursion')
+    L=g.L; C=1<<32
+    # Each action component is <= C(w+1)[v+(G+1)L^4]. G=v/(2Hb).
+    # Keep integer coefficients (A*v + D) by moving denominator upward:
+    # G*L^4 <= v*ceil(L^4/(2Hb)). This rounding is in an upper direction.
+    per_gaussian=(L**4+2*g.component_bits-1)//(2*g.component_bits)
+    coefficient=C*(g.width+1)*(1+per_gaussian)
+    constant=C*(g.width+1)*L**4
+    marker=(0,703 if marker_class=='fresh' else 0,0)
+    result={'kind':'componentwise source upper bound','branch':'selected C terminal: '+branch,
+            'descendant_calls':0,'ordinary_calls':0,'L':L,'b':g.b,
+            'component_upper_affine_in_v':{'coefficient':coefficient,'constant':constant,
+                                         'marker':list(marker)},
+            'leaf_axes':g.width,'geometry':asdict(g),
+            'complete_external_boundary':True,'marker_class':marker_class,
+            'not_a_production_root_admission_certificate':True}
+    if materialize:
+        v=g.v
+        result['v']=v
+        result['rwm_upper']=[coefficient*v+constant+x for x in marker]
+        result['sum_upper']=sum(result['rwm_upper'])
+    return result
+
+
+def reserve_dominated_leaf_upper(width, L_upper, component_bits, *, descriptor_bound_certified, root_width=None):
+    """Compact corollary for a separately certified full-descriptor L upper.
+
+    A compressed RootPlan certificate may bound the bit length of a huge row
+    count without materializing that Count. This function verifies the scalar
+    reserve inequality; it does not certify the supplied descriptor bound.
+    Returned integers multiply the same complete physical packet volume v.
+    """
+    nat(width);nat(L_upper,True);nat(component_bits,True)
+    need(width<73 if root_width is None else terminal_branch(width,root_width) is not None,'selected terminal branch')
+    need(descriptor_bound_certified is True,'external complete-descriptor bound certificate required')
+    need(component_bits>=L_upper**4,'physical reserve dominates per-Gaussian setup')
+    coefficient=(1<<33)*(width+1)
+    return {'rwm_coefficients_of_v':[coefficient]*3,
+            'sum_coefficient_of_v':3*coefficient,
+            'width':width,'L_upper':L_upper,'component_bits':component_bits,
+            'descendants':0,'source_bound':'CBODY equation (2)',
+            'depends_on_external_descriptor_bound_certificate':True}
+
+
+def shape(g):
+    g.validate()
+    return {'b':g.b,'row_bits':2*g.component_bits*g.coefficients*(1<<g.b),
+            'v':g.v,'gaussians':g.gaussians,'descriptors':asdict(g)}
+
+
+def source_guards():
+    """Authenticated-source structure regression, not the proof of the bound."""
+    import inspect, machine, axis_stream, coefficient_engine, stream, signed_linear
+    checks=[(machine.Machine.node,'compare(self.c("width"), dimension) < 0'),
+            (machine.Machine.apply_leaf,'self.leaf.run_leaf('),
+            (machine.Machine.node,'test = fixed_power(self.c("width"), 1000, self.c("root_width"))'),
+            (axis_stream.c_axis,'pairs = Counter(pair_count)'),
+            (axis_stream.c_axis,'prefixes = Counter(before)'),
+            (coefficient_engine.CoefficientEngine.run_leaf,'remaining = Counter(f)'),
+            (signed_linear.linear_word,'remaining = Counter(width)'),
+            (stream.Counter.decrement,'while tape.read() == ZERO:')]
+    for function,text in checks:
+        need(text in inspect.getsource(function),'literal leaf cost-source guard')
+    return {'literal_source_guards':len(checks),'status':'PASS'}
+
+
+def check_countdowns():
+    from cardinal_counts import Count
+    from stream import Counter
+    cases=[]
+    for n in (0,1,2,3,4,7,8,15,16,17,31,32,33,127,128,129,1023):
+        source=Count.literal(n)
+        initial=tuple(getattr(source.tape.meter,k) for k in ('reads','writes','moves'))
+        counter=Counter(source)
+        start=tuple(getattr(counter.tape.meter,k) for k in ('reads','writes','moves'))
+        while not counter.finished:counter.decrement()
+        end=tuple(getattr(counter.tape.meter,k) for k in ('reads','writes','moves'))
+        delta=tuple(y-x for x,y in zip(start,end))
+        expected=countdown_decrements(n) if n else (0,0,0)
+        need(delta==expected,'exact source countdown decrement formula')
+        counter.close()
+        total=tuple(getattr(counter.tape.meter,k)+getattr(source.tape.meter,k)-initial[i]
+                    for i,k in enumerate(('reads','writes','moves')))
+        upper=countdown_cycle_upper(n)
+        need(all(x<=y for x,y in zip(total,upper)),'complete countdown cycle bound')
+        cases.append({'n':n,'decrements':list(delta),'cycle':list(total),'cycle_upper':list(upper)})
+        source.close()
+    return cases
+
+
+def check_leaf_calls():
+    """Complete reduced actual selected-controller leaves; no endpoint doubles.
+
+    All source classes are loaded only after the caller authenticates runtime.
+    Unused Ordinary exists because the real Machine constructor requires its
+    closed inventory. No Ordinary branch executes in these leaf calls.
+    """
+    from fractions import Fraction
+    from hashlib import sha256
+    from types import SimpleNamespace
+    import sys
+    from cardinal_counts import Count
+    from macro_code import Code
+    from ordinary import Ordinary
+    from records import Tape
+    from words import BLANK
+    from machine import Machine
+    from selected_binding import SelectedBinding
+    from selected_source import load
+    from session import erase_marker
+    import runtime
+    history_state=runtime.module('qq16_cbody_state_model',runtime.predecessor()/'state_model.py')
+    native=Ordinary(2,SimpleNamespace(codes=SimpleNamespace(q=2)),
+                    SimpleNamespace(families=0),(Code((('unreachable',),),0),),capacity=64)
+    binding=SelectedBinding(load())
+    # Catalogue has no influence on a leaf but use the actual selected compiler.
+    from scalar_program import ScalarProgram
+    catalogue={}
+    for code in binding.codes.values():
+        for op in code:
+            if op[0]=='scalar':catalogue[op[-1]]=ScalarProgram(*op[-1])
+    catalogue[('scale',-1,1)]=ScalarProgram('scale',-1,1)
+    machine=Machine(binding,native,catalogue)
+    cases=[]
+    def body(t):return bytes(t.cells[1:]).rstrip(bytes([BLANK]))
+    def enc(values,H):return bytes((int(x)>>j)&1 for pair in values for x in pair for j in range(H))
+    def oracle(values,g):
+        out=[tuple(Fraction(x) for x in pair) for pair in values]
+        # Active field address bits are from the left; actual coefficient
+        # packing traverses the low selected active bit first.
+        right=g.after+g.compact_bits+g.back
+        records=1<<g.b
+        for axis in range(g.width):
+            bit=1<<(right+axis*g.spacing+g.residue)
+            for row in range(g.prefixes*g.rows):
+                for address in range(records):
+                    if address&bit:continue
+                    for c in range(g.coefficients):
+                        i=(row*records+address)*g.coefficients+c
+                        j=(row*records+address+bit)*g.coefficients+c
+                        a,b=out[i];d,e=out[j]
+                        out[i]=((a-b+d+e)/2,(a+b-d+e)/2)
+                        out[j]=((a+b+d-e)/2,(-a+b+d+e)/2)
+        need(all(x.denominator==1 for p in out for x in p),'independent exact leaf grid')
+        return out
+    # Include correlated nonconstant payload, an untouched spectator, repeated
+    # successful generations, and coefficient/prefix domains. Keep tiny.
+    specs=[(0,2,1,1),(1,2,1,1),(2,2,1,1),(1,3,2,2),(2,3,2,2),(5,5,1,1),(8,8,1,1),(2,2,1,1)]
+    for generation,(width,b,prefixes,coefficients) in enumerate(specs):
+        cutoff_fixture=generation==len(specs)-1
+        if cutoff_fixture:
+            machine.discard()
+            from fixture_binding import FixtureBinding
+            binding=FixtureBinding()
+            native=Ordinary(2,SimpleNamespace(codes=SimpleNamespace(q=2)),
+                            SimpleNamespace(families=0),(Code((('unreachable',),),0),),capacity=64)
+            machine=Machine(binding,native,binding.catalogue)
+        g=Geometry(prefixes,1,0,0,0,width,b-width,0,1,1,0,20,coefficients,
+                   width**1000+1 if cutoff_fixture else 73)
+        source=Tape(); counts={k:Count.literal(v) for k,v in asdict(g).items()}
+        values=[(512*((i*7+generation)%11-5),512*((i*3+generation)%7-3))
+                for i in range(g.gaussians)]
+        raw=enc(values,g.component_bits)
+        for bit in raw:source.append(bit)
+        source.rewind()
+        snap={k:(v.tape.head,body(v.tape)) for k,v in counts.items()}
+        roles=history_state.tapes(machine,source,counts)
+        initial=tuple(sum(getattr(t.meter,k) for _,t in roles) for k in ('reads','writes','moves'))
+        native_calls=[]
+        oldrun=native.run
+        def reject_native(*args,**kwargs):
+            native_calls.append(True)
+            raise ValueError('leaf unexpectedly entered Ordinary')
+        native.run=reject_native
+        try:output=machine.run(source,counts)
+        finally:native.run=oldrun
+        observed=tuple(sum(getattr(t.meter,k) for _,t in roles)-initial[j]
+                       for j,k in enumerate(('reads','writes','moves')))
+        expected=enc(oracle(values,g),g.component_bits)
+        need(body(output)==expected,'independent completed Gaussian endpoint')
+        need(body(source)==raw and source.head==1,'borrowed payload bytes and head')
+        need(all((v.tape.head,body(v.tape))==snap[k] for k,v in counts.items()),'borrowed descriptors')
+        need(machine.closed and not native_calls,'successful leaf return without descendants/native')
+        upper=leaf_upper_geometry(g,'fresh' if generation==0 or cutoff_fixture else 'steady')
+        need(all(a<=b for a,b in zip(observed,upper['rwm_upper'])),'source-derived complete C upper')
+        cases.append({'generation':generation,'geometry':asdict(g),'payload_bits':len(raw),
+                      'rwm':list(observed),'upper':upper['rwm_upper'] if not cutoff_fixture else None,
+                      'calibration_of_selected_geometry_bound':not cutoff_fixture,
+                      'result_sha256':sha256(expected).hexdigest(),
+                      'actual_binding_dimension':binding.dimension,
+                      'actual_controller_branch':'capped-power cutoff' if cutoff_fixture else 'below dimension leaf',
+                      'selected_binding':not cutoff_fixture,
+                      'ordinary_branch':'not invoked','borrowed_preserved':True,
+                      'complete_return':True,'production_root_admission':False})
+        output.clear();source.clear()
+        for x in counts.values():x.close()
+    machine.discard()
+    need(all(t.read()==BLANK for t in machine.parked),'terminal controller packet cleanup')
+    return cases
+
+
+def check(include_large_cutoff=False):
+    guards=source_guards()
+    counters=check_countdowns()
+    leaves=check_leaf_calls()
+    g=Geometry(1,1,0,0,0,8,65,0,1,1,0,16,1,73)
+    need(g.b==73 and g.v==2*16*(1<<73),'active/spectator packet preservation')
+    one=Geometry(1,1,0,0,0,1,72,0,1,1,0,16,1,73)
+    need(one.v==g.v and one.key()!=g.key(),'equal volume does not imply rank-only cache key')
+    rejected=[]
+    for label,call in (
+        ('nonleaf recursion omitted',lambda:leaf_upper_geometry(Geometry(1,1,0,0,0,73,0,0,1,1,0,16,1,73))),
+        ('logical width substituted for stored width',lambda:Geometry(1,1,0,0,0,1,0,0,1,1,0,1,1,73).validate()),
+        ('bool descriptor alias',lambda:Geometry(True,1,0,0,0,1,0,0,1,1,0,16,1,73).validate()),
+        ('unnamed marker class',lambda:leaf_upper_geometry(one,'unknown')),
+        ('global cutoff equality treated as leaf',lambda:need(terminal_branch(144,144**1000) is not None,'strict cutoff equality'))):
+        try:call()
+        except ValueError:rejected.append(label)
+        else:raise ValueError('accepted invalid cost claim: '+label)
+    return {'source_guards':guards,'countdown_calibrations':counters,
+            'complete_reduced_C_calibrations':leaves,'cutoff_kernel_calibrations':check_cutoff_kernel(include_large_cutoff),
+            'negative_controls':rejected,
+            'scope':'selected C terminal upper only; no nonterminal/Ordinary price or complete QQ16 sign'}
+
+
+def check_cutoff_kernel(include_large=False):
+    """Actual encoded capped-power branch tests, without loading 2**w payload.
+
+    All temporary Count work uses the real fixed scratch pool. This is a
+    source control-kernel calibration, not a completed width-73 C payload.
+    """
+    from cardinal_counts import Count
+    from encoded import fixed_power, compare
+    from scratch_pool import ScratchPool
+    from session import OuterScope
+    from words import BLANK
+    tests=[(2,1000,2**1000+1),(2,1000,2**1000),(73,1000,73**2)]
+    if include_large:tests.append((73,1000,73**1000+1))
+    receipts=[]
+    for value,exponent,cap in tests:
+        pool=ScratchPool(256);scope=OuterScope(pool)
+        x=Count.literal(value);limit=Count.literal(cap)
+        roles=(*pool.tapes,x.tape,limit.tape)
+        before=tuple(sum(getattr(t.meter,k) for t in roles) for k in ('reads','writes','moves'))
+        with scope.installed():
+            out=fixed_power(x,exponent,limit)
+            # The following comparison is a real source instruction, included
+            # in the calibration just as Machine.node evaluates its cutoff.
+            is_leaf=compare(out,limit)<0
+            out.close()
+        observed=tuple(sum(getattr(t.meter,k) for t in roles)-before[i]
+                       for i,k in enumerate(('reads','writes','moves')))
+        need(is_leaf==(value**exponent<cap),'actual capped-power cutoff agrees')
+        need(not pool.live and all(t.read()==BLANK for t in pool.tapes),'cutoff scratch closes')
+        receipts.append({'width':value,'exponent':exponent,'cap_bits':cap.bit_length(),
+                         'cap_relation': 'power+1' if cap==value**exponent+1 else 'power' if cap==value**exponent else 'smaller',
+                         'leaf':is_leaf,'rwm':list(observed),
+                         'complete_C_payload_executed':False})
+        x.close();limit.close()
+    return receipts
diff --git a/research/qq16-complete-cost/checker.py b/research/qq16-complete-cost/checker.py
new file mode 100644
index 0000000000..af1ef51b90
--- /dev/null
+++ b/research/qq16-complete-cost/checker.py
@@ -0,0 +1,495 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent signed-interval arithmetic and physical-boundary checker.
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance.
+This module does not import the evaluator. Its arithmetic checks do not prove
+that a supplied endpoint bounds an actual source interval: those endpoints must
+be certified by the package's authenticated source derivation/calibration.
+"""
+from dataclasses import dataclass
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def integer(x, lower=None):
+    require(type(x) is int, 'exact integer, excluding bool')
+    require(lower is None or x >= lower, 'integer outside admitted range')
+    return x
+
+
+@dataclass(frozen=True)
+class Bound:
+    lo: int
+    hi: int
+
+    def __post_init__(self):
+        integer(self.lo); integer(self.hi)
+        require(self.lo <= self.hi, 'reversed interval')
+
+    def plus(self, other):
+        return Bound(self.lo + other.lo, self.hi + other.hi)
+
+    def minus(self, other):
+        # In particular, subtract the REMOVED upper endpoint for a lower bound.
+        return Bound(self.lo - other.hi, self.hi - other.lo)
+
+    def times(self, coefficient):
+        integer(coefficient)
+        a, b = coefficient * self.lo, coefficient * self.hi
+        return Bound(min(a, b), max(a, b))
+
+    def json(self):
+        return {'lower': self.lo, 'upper': self.hi}
+
+
+def exact(x):
+    return Bound(x, x)
+
+
+def triple(values):
+    require(type(values) in (list, tuple) and len(values) == 3,
+            'separate read/write/unit-move components')
+    return tuple(Bound(*value) if type(value) in (list, tuple) else exact(value)
+                 for value in values)
+
+
+def add(a, b):
+    return tuple(x.plus(y) for x, y in zip(a, b, strict=True))
+
+
+def subtract(a, b):
+    return tuple(x.minus(y) for x, y in zip(a, b, strict=True))
+
+
+def scale(a, k):
+    return tuple(x.times(k) for x in a)
+
+
+def summed(a):
+    result = exact(0)
+    for x in a:
+        result = result.plus(x)
+    return result
+
+
+CENSUS = {'original': 510662, 'same_payload': 503674, 'changed_core': 6972,
+          'later': 493097, 'producer_added': 32, 'service_added': 336,
+          'removed': 16}
+
+
+def census_check(record):
+    require(type(record) is dict and record == CENSUS and
+            all(type(x) is int for x in record.values()), 'complete literal occurrence census')
+    retained = record['same_payload'] + record['changed_core']
+    require(retained + record['removed'] == record['original'], 'original partition')
+    return {'retained': retained, 'candidate_external': retained +
+            record['producer_added'] + record['service_added'],
+            'retained_header_actions': 28 * retained,
+            'later_header_actions': 28 * record['later']}
+
+
+def volumes(*, gamma, prefixes, unused_rows, physical_component_bits,
+            coefficients, address_bits, recorded=None):
+    for value in (gamma, prefixes, unused_rows, physical_component_bits, coefficients):
+        integer(value, 1)
+    integer(address_bits, 0)
+    # This is complete packet extent, not active rank or logical precision.
+    row = 2 * physical_component_bits * coefficients * (1 << address_bits)
+    owner = prefixes * unused_rows * row
+    family = gamma * owner
+    result = {'row_bits': row, 'owner_packet_bits': owner,
+              'family_bits': family, 'bank_bits': 14336 * family,
+              'service_bank_bits': 448 * family}
+    require(result['bank_bits'] == 32 * result['service_bank_bits'], 'service bank extent')
+    if recorded is not None:
+        require(recorded == result and all(type(v) is int for v in recorded.values()),
+                'complete compiler physical geometry, Gamma exactly once')
+    return result
+
+
+# A cost grouping must retain complete descriptors, original source binding,
+# compiled program/recipe and marker class. History is removed only by #4172's
+# paired successful-domain theorem; production-selector policy is not omitted.
+GEOMETRY_FIELDS = ('prefixes', 'unused_rows', 'active_width', 'spectator_before',
+                   'spectator_after', 'coefficients', 'physical_component_bits',
+                   'spacing', 'root_width', 'address_guard', 'row_stock',
+                   'compiled_recipe', 'source_binding', 'marker_class',
+                   'ordinary_selection')
+
+
+def geometry_key(record):
+    require(type(record) is dict and set(record) == set(GEOMETRY_FIELDS),
+            'complete cost-sensitive descriptor key')
+    require(all(type(record[k]) in (int, str, tuple) for k in GEOMETRY_FIELDS),
+            'canonical descriptor representation')
+    return tuple(record[k] for k in GEOMETRY_FIELDS)
+
+
+def certify_same_geometry(a, b):
+    require(geometry_key(a) == geometry_key(b), 'unsafe geometry grouping')
+
+
+def complete_body(receipt):
+    require(type(receipt) is dict and set(receipt) ==
+            {'geometry', 'own_actions', 'descendant_actions', 'total_actions',
+             'includes_descendants_once', 'successful_return'}, 'complete body receipt fields')
+    geometry_key(receipt['geometry'])
+    require(receipt['includes_descendants_once'] is True and
+            receipt['successful_return'] is True, 'completed recursion and return required')
+    own, descendants, total = (triple(receipt[k]) for k in
+                              ('own_actions', 'descendant_actions', 'total_actions'))
+    require(add(own, descendants) == total, 'omitted or double-counted descendants')
+    require(all(x.lo >= 0 for part in (own, descendants) for x in part),
+            'physical costs cannot be negative')
+    return total
+
+
+# Mandatory disjoint root intervals. 'body' is excluded here. The evaluator
+# must derive both endpoints and the partition; the checker never supplies zero
+# for a missing invoice. Exact common cancellation may legitimately have zero.
+NONCHILD = ('producer_nonchild', 'acquisition_compiler', 'service_nonchild',
+            'bank_scans_fences', 'extraction_publication_disposal',
+            'constructor_startup_terminal')
+SHELLS = ('producer_added_shells', 'service_added_shells', 'removed_B_shells')
+
+
+def ledger_check(ledger):
+    require(type(ledger) is dict and set(ledger) == set(NONCHILD + SHELLS),
+            'complete disjoint nonchild and unmatched-shell ledger')
+    return {key: triple(ledger[key]) for key in NONCHILD + SHELLS}
+
+
+def compare(*, gamma, owner_packet_bits, rank_one, rank_eight, ledger,
+            header_actions, census=None, variant='D_minus_Bstar'):
+    """Bound the entire R/W/M difference from certified disjoint intervals.
+
+    Nonchild entries are already signed WHOLE-ROOT differences, including Gamma.
+    Added shell entries are whole-root positive bills; removed_B_shells is the
+    positive baseline bill subtracted exactly once. Each native body is per call.
+    Frozen D is the only implemented candidate admitted by this checker.
+    Finite binding control is deliberately absent from the R/W/M currency.
+    """
+    integer(gamma, 1); integer(owner_packet_bits, 1)
+    require(variant in ('D_minus_B', 'D_minus_Bstar'), 'unimplemented candidate adoption')
+    counts = census_check(CENSUS if census is None else census)
+    require(type(header_actions) is int and header_actions ==
+            counts['retained_header_actions'] * gamma, 'retained headers including later calls')
+    costs = ledger_check(ledger)
+    a, b = complete_body(rank_one), complete_body(rank_eight)
+    result = triple((0, 0, 0))
+    for name in NONCHILD:
+        result = add(result, costs[name])
+    result = add(result, costs['producer_added_shells'])
+    result = add(result, costs['service_added_shells'])
+    result = subtract(result, costs['removed_B_shells'])
+    result = add(result, scale(a, (32 + 336) * gamma))
+    result = subtract(result, scale(b, 16 * gamma))
+    # Source header_write+header_read+clear has slope (6,2,6) per bit;
+    # D headers are two bits longer. This preserves the R/W/M distinction.
+    header = scale(triple((12, 4, 12)), counts['retained'] * gamma)
+    require(summed(header) == exact(header_actions), 'literal header R/W/M sum')
+    result = add(result, header)
+    # #4167 protocol.adoption_credit with both origin checks charged.
+    adoption = scale(triple((5*owner_packet_bits+2, 2*owner_packet_bits,
+                             4*owner_packet_bits+2)), 510662*gamma) if variant.endswith('Bstar') else triple((0,0,0))
+    result = add(result, adoption)
+    action_sum = summed(result)
+    verdict = ('strict_action_improvement' if action_sum.hi < 0 else
+               'no_strict_action_improvement' if action_sum.lo >= 0 else 'undecided')
+    return {'variant': variant, 'RWM_difference': [v.json() for v in result],
+            'retained_header_actions': header_actions,
+            'credited_Bstar_adoption_actions': summed(adoption).lo,
+            'action_difference': action_sum.json(),
+            'verdict_from_certified_endpoints_only': verdict,
+            'finite_control_difference': 'separate signed charge; not set to zero',
+            'negative_control_threshold_for_full_step_exclusion': -action_sum.lo,
+            'notes': 'No new evaluator prices are manufactured by this arithmetic checker.'}
+
+
+def controls():
+    """Arithmetic/schema rejection controls, not physical execution evidence."""
+    rejected = []
+    def fails(label, thunk):
+        try:
+            thunk()
+        except (ValueError, TypeError):
+            rejected.append(label)
+        else:
+            raise ValueError('accepted negative control: ' + label)
+    require(Bound(3, 5).minus(Bound(7, 11)) == Bound(-8, -2), 'signed subtraction endpoints')
+    require(Bound(3, 5).times(-2) == Bound(-10, -6), 'negative coefficient direction')
+    fails('reversed signed bound', lambda: Bound(2, 1))
+    fails('upper-minus-upper used as lower', lambda: require(
+        Bound(3, 5).minus(Bound(7, 11)).lo == 5 - 11, 'invalid lower'))
+    fails('omitted later-root census', lambda: census_check(dict(CENSUS, later=0)))
+    fails('boolean multiplicity', lambda: integer(True, 1))
+    g = dict(zip(GEOMETRY_FIELDS, (1, 2, 8, 0, 65, 1, 80, 3, 73, 4, 2,
+                                  'original-C', '3385', 'warm-erased', 'production-select')))
+    for key in GEOMETRY_FIELDS:
+        bad = dict(g); bad[key] = str(g[key]) + '_changed'
+        fails('false grouping: ' + key, lambda bad=bad: certify_same_geometry(g, bad))
+    v = volumes(gamma=51, prefixes=1, unused_rows=2, physical_component_bits=80,
+                coefficients=1, address_bits=3)
+    bad = dict(v, bank_bits=v['bank_bits'] * 51)
+    fails('double Gamma bank volume', lambda: volumes(gamma=51, prefixes=1, unused_rows=2,
+          physical_component_bits=80, coefficients=1, address_bits=3, recorded=bad))
+    fails('logical width replaces physical width', lambda: volumes(gamma=51, prefixes=1,
+          unused_rows=2, physical_component_bits=79, coefficients=1, address_bits=3, recorded=v))
+    body = dict(geometry=g, own_actions=[1, 2, 3], descendant_actions=[4, 5, 6],
+                total_actions=[5, 7, 9], includes_descendants_once=True, successful_return=True)
+    require(summed(complete_body(body)) == exact(21), 'complete synthetic body')
+    fails('omitted descendants', lambda: complete_body(dict(body, total_actions=[1, 2, 3])))
+    fails('doubled descendants', lambda: complete_body(dict(body, total_actions=[9, 12, 15])))
+    fails('uncompleted child', lambda: complete_body(dict(body, successful_return=False)))
+    zeros = {k: [0, 0, 0] for k in NONCHILD + SHELLS}
+    fails('omitted shell', lambda: ledger_check({k:v for k,v in zeros.items() if k != SHELLS[0]}))
+    fails('internal exchange negation charged twice', lambda: ledger_check(dict(zeros, internal_negations=[0,0,0])))
+    kwargs = dict(gamma=51, owner_packet_bits=v['owner_packet_bits'], rank_one=body,
+                  rank_eight=body, ledger=zeros, header_actions=14298088 * 51)
+    fails('unimplemented Dstar adoption', lambda: compare(**kwargs, variant='Dstar_minus_Bstar'))
+    base = compare(**kwargs, variant='D_minus_B')
+    fair = compare(**kwargs)
+    require(fair['action_difference']['lower'] - base['action_difference']['lower'] ==
+            510662 * 51 * (11 * v['owner_packet_bits'] + 4), 'adoption credited once')
+    return {'scope': 'independent arithmetic/schema controls; synthetic prices are not an admitted geometry',
+            'rejections': rejected, 'passed': True}
+
+
+def root_leaf_domain_witness(columns=5):
+    """Exact host certificate for a real RootPlan descriptor domain.
+
+    No giant physical packet is allocated. This follows the named RootPlan
+    formulas and certifies a nonempty fast-root, lambda=5 descriptor domain;
+    actual source numerical/hosting/stock implementation remains inherited.
+    """
+    from math import isqrt, prod
+    integer(columns, 5)
+    require(columns <= 44, 'certified concrete terminal-root family')
+    core_width = 73 * columns
+    precision = 1 << 8500
+    # precision**(997/1000)=2**8474.5 exactly.
+    d = isqrt(1 << 16949)
+    require(d*d <= (1 << 16949) < (d+1)*(d+1), 'exact root width')
+    low, high = 1, 1 << 17
+    while low + 1 < high:
+        mid = (low + high) // 2
+        if pow(mid, 500) <= d:
+            low = mid
+        else:
+            high = mid
+    spacing = low
+    require(pow(spacing, 500) <= d < pow(spacing+1, 500), 'actual spacing floor')
+    guard = 4 * 8500 + 6
+    address_guard = d * guard
+    gamma = (1 << 1296) * prod((1 << (2*j)) - 1 for j in range(1, 37))
+    divisor = 14336 * gamma
+    depth, width = 0, d
+    while width >= 73:
+        width = 48 * (width // 73)
+        depth += 1
+    q0 = depth * (divisor - 1).bit_length()
+    qF = (2 * address_guard + spacing - 1) // spacing
+    qB = (address_guard + spacing - 1) // spacing
+    threshold = q0 + qF + qB
+    selected = threshold + core_width
+    require(selected <= d and selected > threshold, 'actual fast-root branch')
+    require(d <= core_width**1000, 'post-remainder source nonleaf admission')
+    require(8*columns < 73 or pow(8*columns, 1000) < d, 'both unmatched bodies take the actual terminal C branch')
+    physical_bits = precision + 2 * ((1 << 210000) * d) + 3
+    row_axes = q0 * spacing
+    # stock<=2^(q0*K), so padded rows<2^(q0*K+1).
+    require(depth * divisor.bit_length() <= row_axes, 'original rows dominate stock')
+    front, back = qF * spacing - 2 * address_guard, qB * spacing - address_guard
+    require(0 <= front < spacing and 0 <= back < spacing, 'root guards fit')
+    address_bits = 3 * address_guard + front + core_width * spacing + back
+    require(address_bits == (selected - q0) * spacing, 'complete root rectangle')
+    lengths = []
+    for rank in (1, 8):
+        known = (1, front, address_guard, 0, rank*columns, (73-rank)*columns*spacing,
+                 back, spacing, guard, 0, physical_bits, 1, d)
+        # The sole huge unmaterialized field is rows=U; its bit length is at
+        # most row_axes+1 because U<=padded_rows<2^(row_axes+1).
+        lengths.append(16 + address_bits + row_axes + 1 +
+                       sum(max(1, x.bit_length()) for x in known))
+    descriptor_bound = max(lengths) + (1 << 20)  # parent/shell/header envelope slack
+    require(pow(descriptor_bound, 4) <= physical_bits, 'physical width absorbs descriptor fourth power')
+    require(columns < 73, 'rank-one child row stock exponent zero')
+    def coarse_depth(w):
+        answer = 0
+        while w >= 73:
+            w = 48*(w//73)
+            answer += 1
+        return answer
+    parent_coarse = coarse_depth(core_width)
+    rank_eight_coarse = coarse_depth(8*columns)
+    require(depth >= parent_coarse and depth-1 >= rank_eight_coarse,
+            'inherited root stock supplies both actual child geometries')
+    return {'precision': '2^8500', 'root_width': 'floor(sqrt(2^16949))',
+            'root_width_bit_length': d.bit_length(), 'spacing': spacing,
+            'guard': guard, 'lambda': columns, 'core_width': core_width,
+            'selected': 'q0+qF+qB+73*lambda', 'source_depth': depth,
+            'row_axis_count': row_axes, 'front_back_less_than_spacing': True,
+            'address_bits_bit_length': address_bits.bit_length(),
+            'leaf_descriptor_bound_bit_length': descriptor_bound.bit_length(),
+            'H_b_ge_leaf_descriptor_bound_fourth_power': True,
+            'root_stock_depth': depth, 'rank_one_coarse_stock_depth': 0,
+            'parent_coarse_stock_depth': parent_coarse,
+            'rank_eight_coarse_stock_depth': rank_eight_coarse,
+            'actual_rank_eight_terminal_body_depth': 0,
+            'row_stock': '(14336*Gamma)^source_depth',
+            'padded_rows': 'ceil(2^(q0*K)/row_stock)*row_stock',
+            'component_bits_bit_length': physical_bits.bit_length(),
+            'gamma_bit_length': gamma.bit_length(), 'fast_root_and_post_remainder_tests': True,
+            'rank_eight_terminal_branch': 'width<73' if 8*columns<73 else 'width^1000<d',
+            'packet_executed': False,
+            'remaining': 'inherited exact arithmetic, native, chronological hosting and long-record premises'}
+
+
+def owner_gate_cover_certificate(owner_calls=736, deficits=None):
+    """Exact independent arithmetic for the written O(73,2) completion proof.
+
+    This checks the counting inequalities, not a formal-kernel Witt extension.
+    The source census must independently justify owner_calls and the deficit
+    geometry keys. Uniform inversion of owner matrices is permitted.
+    """
+    from fractions import Fraction
+    integer(owner_calls, 1)
+    require(owner_calls == 736, 'literal paid owner basis call census')
+    expected = {('add', 6, 8): 4, ('add', 8, 6): 1}
+    if deficits is not None:
+        require(deficits == expected and all(type(v) is int for v in deficits.values()),
+                'literal uncovered gate geometries')
+    tail_fraction = Fraction(1)
+    for i in range(9):
+        choices = 1 << (63-i)
+        forbidden = 1 << (i+1)
+        require(choices > forbidden, 'tail extension room')
+        tail_fraction *= Fraction(choices-forbidden, choices)
+    require(tail_fraction > Fraction(1, 2), 'head fibre density')
+    require(sum(63-i for i in range(9)) == 531 and
+            sum(72-i for i in range(9)) == 612, 'head/tail constraint exponents')
+    events = {}
+    for size, key in ((6, ('add', 8, 6)), (8, ('add', 6, 8))):
+        gl = Fraction(1)
+        for j in range(1, size+1):
+            gl *= 1-Fraction(1, 1 << j)
+        require(gl > Fraction(1, 4), 'invertible leading-block probability')
+        event = gl / 4  # two independent prescribed Schur/column bits
+        require(event > Fraction(1, 16), 'literal elimination event probability')
+        cover = tail_fraction * event
+        require(cover > Fraction(1, 32), 'uniform orthogonal cover gate frequency')
+        require(Fraction(owner_calls, 32) >= expected[key], 'paid owner gates cover deficit')
+        events[str(key)] = {'leading_block_size': size,
+                           'cover_frequency_strictly_above': '1/32',
+                           'paid_available_per_Gamma_strictly_above': str(Fraction(owner_calls, 32)),
+                           'required_per_Gamma': expected[key]}
+    return {'all_9_by_9_heads_supported': True,
+            'minimum_head_mass_strictly_above': '2^-82',
+            'tail_solution_exponent': 531, 'full_frame_upper_exponent': 612,
+            'events': events, 'owner_calls_per_Gamma': owner_calls,
+            'premises': 'written characteristic-vector/symplectic extension proof; literal paid source census; complete uniform O73 cover',
+            'formal_kernel_verification': False}
+
+
+def normalized_terminal_exclusion(columns=5):
+    """Independent signed lower-bound arithmetic on the stated source domain.
+
+    Source premises: actual installed fast-root admission; columns>=5; actual terminal C8 branch;
+    physical Hb>=complete leaf/count envelope L^4; v>=2685; the literal
+    monomial/base/scalar injection and extra-only gather partition proved in
+    NONCHILD.md; original common startup matched, with B extra retirement
+    bounded by66496. No E1 upper price is needed in this exclusion: all added
+    native bodies are nonnegative and may be dropped from a LOWER bound.
+    """
+    from math import prod
+    from fractions import Fraction
+    integer(columns, 5)
+    gamma = (1 << 1296) * prod((1 << (2*j)) - 1 for j in range(1, 37))
+    require(gamma % 51 == 0, 'complete cover denominator')
+    volume_per_gamma_v = Fraction(281593, 816) * 14336 * gamma
+    require(volume_per_gamma_v.denominator == 1, 'integer added gather volume')
+    volume = int(volume_per_gamma_v)
+    scan = 2 * volume
+    # Source C upper, removed with the correct sign. It is per R/W/M.
+    body_upper_per_v = (1 << 33) * (8*columns+1)
+    # Since Hb>=L^4 and v>=2Hb and v>=header_bits, each entire local
+    # expression v+1+L^4(+header_bits) is <=4v.
+    copies_upper_per_v = 8 * (1 << 22)
+    shells_upper_per_v = 16 * (1 << 26)
+    removed_per_gamma_v = 16*body_upper_per_v + copies_upper_per_v + shells_upper_per_v
+    maximum_columns = (volume + 2*510662 - 16*(1 << 33) -
+                       copies_upper_per_v - shells_upper_per_v - 1) // (128*(1 << 33))
+    require(columns <= maximum_columns, 'exact positive-slope column threshold')
+    # Frozen D receives no additional child-return adoption. B* does.
+    slope = (scan + 5*510662 - removed_per_gamma_v,
+             volume + 2*510662 - removed_per_gamma_v,
+             scan + 4*510662 - removed_per_gamma_v)
+    constant_per_gamma = (12*510646 + 2*510662,
+                          4*510646,
+                          12*510646 + 2*510662)
+    # A known total upper66496 also bounds each nonnegative R/W/M component.
+    # Subtracting it in every component is safe and deliberately loose.
+    startup_per_component = 66496
+    require(min(slope) > 0, 'strict normalized R/W/M slopes; no unlimited column extrapolation')
+    # v>=2685, Gamma>=1 gives a finite strict sign, including all displayed
+    # constants and the conservative triple startup subtraction.
+    minimal_total = gamma * (2685 * sum(slope) + sum(constant_per_gamma)) - 3*startup_per_component
+    require(minimal_total > 0 and all(gamma*(2685*x+y)-startup_per_component>0
+            for x,y in zip(slope,constant_per_gamma)), 'complete componentwise lower bounds including once-only startup')
+    return {'variant': 'frozen D minus Bstar', 'columns': columns,
+            'maximum_columns_from_action_inequality': maximum_columns,
+            'maximum_columns_bit_length': maximum_columns.bit_length(),
+            'domain': 'actual fast-root; C8 width<73 or width^1000<d; Hb>=L^4; v>=2685; stated positive slope test; proved gate/base/scalar injection and disjoint interval partition',
+            'lower_bound_RWM': {'Gamma_times_v_coefficients': list(slope),
+                                'Gamma_constant_coefficients': list(constant_per_gamma),
+                                'subtract_once_per_component': startup_per_component},
+            'strict_total_action_exclusion': True,
+            'minimal_total_lower_bound_bit_length': minimal_total.bit_length(),
+            'sum_slope_bit_length': sum(slope).bit_length(),
+            'gamma_bit_length': gamma.bit_length(),
+            'all_RWM_components_strictly_positive': min(slope) > 0,
+            'finite_control': 'signed total control difference must be at least minus the action lower bound for total-step exclusion',
+            'source_proof_required': True, 'production_payload_executed': False}
+
+
+# Compatibility name for integration code written before the height-stop branch
+# was included. The result always reports its exact terminal-branch domain.
+def normalized_leaf_exclusion(columns=5):
+    return normalized_terminal_exclusion(columns)
+
+
+def check():
+    basic = controls()
+    witnesses = [root_leaf_domain_witness(i) for i in (5, 9, 10, 44)]
+    for i in range(5,45):
+        root_leaf_domain_witness(i)
+        normalized_terminal_exclusion(i)
+    first = normalized_terminal_exclusion(5)
+    limit = first['maximum_columns_from_action_inequality']
+    normalized_terminal_exclusion(limit)
+    rejected = []
+    for label, call in (
+        ('empty actual fast-root lambda4', lambda: root_leaf_domain_witness(4)),
+        ('first uncovered concrete nonterminal lambda45', lambda: root_leaf_domain_witness(45)),
+        ('next integer beyond signed column threshold', lambda: normalized_terminal_exclusion(limit+1)),
+        ('omitted paid owner bases', lambda: owner_gate_cover_certificate(735)),
+        ('wrong uncovered gate geometry', lambda: owner_gate_cover_certificate(deficits={('add',6,7):4,('add',8,6):1})),
+    ):
+        try: call()
+        except ValueError: rejected.append(label)
+        else: raise ValueError('accepted domain control: '+label)
+    return {'arithmetic_controls': basic, 'root_domain_witnesses': witnesses,
+            'all_40_concrete_terminal_geometries_checked': True,
+            'owner_cover': owner_gate_cover_certificate(),
+            'first_geometry_exclusion': first,
+            'exact_action_column_threshold_and_next_integer_checked': True,
+            'domain_rejections': rejected,
+            'scope': 'independent integer/rational arithmetic and source-bound parameter certificates; no new physical payload replay'}
+
+
+if __name__ == '__main__':
+    import json
+    print(json.dumps(check(), sort_keys=True))
diff --git a/research/qq16-complete-cost/cost.py b/research/qq16-complete-cost/cost.py
new file mode 100644
index 0000000000..a26f55fb82
--- /dev/null
+++ b/research/qq16-complete-cost/cost.py
@@ -0,0 +1,69 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Source-derived normalized complete signed lower certificate.
+
+The three published prices are derived bounds, not unexplained oracle inputs.
+This evaluator deliberately does not manufacture a price for recursive C.
+"""
+from fractions import Fraction
+from math import prod
+
+def need(ok,why):
+    if not ok:raise ValueError(why)
+
+def gamma():
+    # Authenticated OrthogonalCover.group_orders recurrence, independently
+    # checked against the source by gate_cover and the separate checker.
+    return prod((1 << (k-1))-int(k>1 and k%2==1) for k in range(1,74))
+
+def exclusion(columns=5):
+    need(type(columns) is int and columns>=5,'exact installed column count')
+    g=gamma()
+    volume=Fraction(281593,816)*14336*g
+    need(volume.denominator==1,'whole cover source group volume')
+    a=int(volume)
+    # Complete terminal C bound E_w <= 2^33(w+1)v in each component,
+    # derived from the actual source with Hb>=L^4; all 16 removed calls.
+    body=16*(1<<33)*(8*columns+1)
+    copies=8*(1<<22)
+    shells=16*(1<<26)
+    debit=body+copies+shells
+    ordinary_original_calls=510662
+    retained=510646
+    slope=[2*a+5*ordinary_original_calls-debit,
+           a+2*ordinary_original_calls-debit,
+           2*a+4*ordinary_original_calls-debit]
+    constant=[12*retained+2*ordinary_original_calls,
+              4*retained,
+              12*retained+2*ordinary_original_calls]
+    maximum=(a+2*ordinary_original_calls-16*(1<<33)-copies-shells-1)//(128*(1<<33))
+    need(columns<=maximum and min(slope)>0,'complete positive signed bound domain')
+    at_minimum=[g*(2685*x+y)-66496 for x,y in zip(slope,constant)]
+    need(min(at_minimum)>0,'once-only startup and retirement debit')
+    return {
+        'variant':'frozen D minus Bstar','columns':columns,'gamma':g,
+        'terminal_predicate':'8 lambda < 73 OR (8 lambda)^1000 < d',
+        'parent_predicate':'actual RootPlan fast entry; e=73 lambda; d <= e^1000',
+        'geometry_domain':'complete P,U,c,stored Hb,address b; Hb>=L^4; v>=2685; common admitted q/profile/programs/capacities',
+        'body_removed_per_Gamma_v_upper_each':body,
+        'copies_removed_per_Gamma_v_upper_each':copies,
+        'shells_removed_per_Gamma_v_upper_each':shells,
+        'added_groups_volume_per_Gamma_v':a,
+        'lower_bound_RWM':{'Gamma_times_v_coefficients':slope,
+                          'Gamma_constant_coefficients':constant,
+                          'subtract_once_per_component':66496},
+        'maximum_positive_columns':maximum,
+        'strict_all_RWM_exclusion':True,
+        'minimal_component_lower_bit_lengths':[x.bit_length() for x in at_minimum],
+        'compiled_control':'separate signed difference; all-step exclusion requires control difference >= minus weighted action lower bound',
+        'unknown_prices_used':False,
+        'new_engine_tapes_or_reset':False,
+        'production_payload_executed':False}
+
+def controls():
+    last=exclusion()['maximum_positive_columns'];bad=[]
+    for label,value in [('bool columns',True),('unreachable small columns',4),
+                        ('negative columns',-1),('first nonpositive bound',last+1)]:
+        try:exclusion(value)
+        except ValueError:bad.append(label)
+        else:raise ValueError('accepted bound control:'+label)
+    return {'last_positive_columns':last,'endpoint':exclusion(last),'rejections':bad}
diff --git a/research/qq16-complete-cost/gate_cover.py b/research/qq16-complete-cost/gate_cover.py
new file mode 100644
index 0000000000..3ff6571b5d
--- /dev/null
+++ b/research/qq16-complete-cost/gate_cover.py
@@ -0,0 +1,143 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Finite-control owner-cover gate supply, with exact counting certificates.
+
+Chris R / Clear1nsight with substantial OpenAI Codex assistance.
+This is an offline source-cost proof checker, not a physical matrix sampler.
+"""
+from fractions import Fraction
+from math import prod
+from collections import Counter
+import sys
+
+
+def need(ok, reason):
+    if not ok:
+        raise ValueError(reason)
+
+
+def order(n):
+    return prod((1 << (k-1)) - int(k > 1 and k % 2) for k in range(1, n+1))
+
+
+def certificate():
+    n, head, tail = 73, 9, 64
+    choices = [(1 << (tail-j-1)) - (1 << (j+1)) for j in range(head)]
+    frame_lower = prod(choices)
+    gamma, completions = order(n), order(tail)
+    head_probability = Fraction(frame_lower * completions, gamma)
+    relative_density = head_probability * (1 << (head*head))
+    gl_prob = lambda k: prod(Fraction((1 << i)-1, 1 << i) for i in range(1,k+1))
+    event_lower = {"add_6_8": relative_density*gl_prob(8)/4,
+                   "add_8_6": relative_density*gl_prob(6)/4}
+    need(relative_density > Fraction(1,2), 'every head has at least half uniform mass')
+    need(all(x > Fraction(1,32) for x in event_lower.values()), 'uniform gate supply')
+    need(736*event_lower['add_6_8'] > 4, 'four missing target6 source8 gates')
+    need(736*event_lower['add_8_6'] > 1, 'one missing target8 source6 gate')
+    need(672*event_lower['add_6_8'] > 4, 'service-only target6 source8 supply')
+    need(672*event_lower['add_8_6'] > 1, 'service-only target8 source6 supply')
+    return {
+        'dimension':n,'head_dimension':head,'tail_dimension':tail,
+        'tail_choice_lower':choices,'tail_frame_lower':frame_lower,
+        'gamma':gamma,'suffix_completions':completions,
+        'head_probability_lower':head_probability,
+        'relative_uniform_density_lower':relative_density,
+        'gate_probability_lower':event_lower,
+        'coarse_gate_probability_lower':Fraction(1,32),
+        'owner_word_occurrences':736,'service_owner_word_occurrences':672,
+        'coarse_owner_supply_per_gamma':Fraction(736,32),
+        'coarse_service_supply_per_gamma':Fraction(672,32),
+        'deficits_per_gamma':{'add_6_8':4,'add_8_6':1},
+        'strict_inequalities':True,
+    }
+
+
+def _reduce_prefix(rows, k):
+    """Check the exact source leading-block event; reject an outside pivot."""
+    rows=list(rows)
+    for j in range(k):
+        pivot=next((i for i in range(j,k) if (rows[i] >> j)&1),None)
+        if pivot is None:
+            return None
+        if pivot != j:
+            for target,source in ((j,pivot),(pivot,j),(j,pivot)):
+                rows[target] ^= rows[source]
+        for i in range(len(rows)):
+            if i != j and (rows[i] >> j)&1:
+                rows[i] ^= rows[j]
+    return rows
+
+
+def event(rows, target, source):
+    need((target,source) in ((6,8),(8,6)), 'named gate class')
+    work=_reduce_prefix(rows, source)
+    return work is not None and bool((work[source] >> source)&1) and bool((work[target] >> source)&1)
+
+
+def _orthogonal(rows):
+    return all(((a&b).bit_count()&1)==(i==j)
+               for i,a in enumerate(rows) for j,b in enumerate(rows))
+
+
+def _transvection(rows, support):
+    need(support.bit_count()%2 == 0, 'isotropic transvection direction')
+    # Left multiplication by I + u u^T. Its square is I for even-weight u.
+    total=0
+    for i,row in enumerate(rows):
+        if (support >> i)&1:
+            total ^= row
+    return tuple(row ^ (total if (support >> i)&1 else 0)
+                 for i,row in enumerate(rows))
+
+
+def source_checks(cohort):
+    """Call only after the containing runtime authenticated its source closure."""
+    cohort.monomial_api()
+    reference=sys.modules['phase_recipe'].reference
+    word=reference.binary_word
+    witnesses={}
+    rows=tuple(1<<i for i in range(73))
+    # Deterministic orthogonal witnesses, not evidence for the counting theorem.
+    seed=7
+    for step in range(160):
+        positions=[]
+        while len(positions)<4:
+            seed=(1103515245*seed+12345)&0x7fffffff
+            p=(seed>>9)%13
+            if p not in positions:
+                positions.append(p)
+        rows=_transvection(rows,sum(1<<i for i in positions))
+        need(_orthogonal(rows),'actual orthogonal witness')
+        for target,source in ((6,8),(8,6)):
+            key=f'add_{target}_{source}'
+            if key not in witnesses and event(rows,target,source):
+                gates=Counter(word({'matrix_rows':rows,'offset':0}))
+                need(gates[('add',target,source)]>=1,'literal source emits guaranteed gate')
+                need(Counter(reversed(word({'matrix_rows':rows,'offset':0})))==gates,
+                     'inverse execution preserves gate histogram')
+                witnesses[key]={'step':step,'matrix_rows':rows,'gate_multiplicity':gates[('add',target,source)]}
+        if len(witnesses)==2:
+            break
+    need(len(witnesses)==2,'both real orthogonal source witnesses')
+    identity=tuple(1<<i for i in range(73))
+    need(not event(identity,6,8) and not event(identity,8,6),'identity rejects false universal per-owner claim')
+    need(not word({'matrix_rows':identity,'offset':0}),'identity has no gates')
+    c=certificate()
+    # The named source cover counts prefixes with precisely these orders.
+    import importlib.util
+    cover_path=cohort.ROOT/'research/physical-complex-controller/cover.py'
+    spec=importlib.util.spec_from_file_location('qq16_gate_cover_source',cover_path)
+    cover=importlib.util.module_from_spec(spec);spec.loader.exec_module(cover)
+    need(tuple(order(n) for n in range(74))==cover.group_orders(73),'authenticated cover order match')
+    need(all(cover.is_orthogonal(w['matrix_rows']) for w in witnesses.values()),'source orthogonal admission')
+    return {'witnesses':witnesses,'identity_negative_control':True,
+            'source_group_orders_match':True,'count_certificate':c}
+
+
+def jsonable(value):
+    if isinstance(value,Fraction):
+        return {'numerator':value.numerator,'denominator':value.denominator}
+    if isinstance(value,dict):
+        return {k:jsonable(v) for k,v in value.items()}
+    if isinstance(value,(list,tuple)):
+        return [jsonable(v) for v in value]
+    return value
diff --git a/research/qq16-complete-cost/inputs/PR4172-MANIFEST.json b/research/qq16-complete-cost/inputs/PR4172-MANIFEST.json
new file mode 100644
index 0000000000..d993d16eb5
--- /dev/null
+++ b/research/qq16-complete-cost/inputs/PR4172-MANIFEST.json
@@ -0,0 +1,156 @@
+{
+  "head": "59b46625a8b2f0dfff3e38ba0949b4247423938a",
+  "archive_sha256": "ebfb717d60bf37b8edd894036827210a93c2594d637d4a6b8d617018567767a3",
+  "files": [
+    {
+      "path": "research/qq16-native-history/ADMISSION.json",
+      "sha256": "b4dd23faf3c88d604c5e8085893692b38ae1911b9550947d94ac1cdfa36f7ef8",
+      "git_blob": "43ebceccc50947657d73523bea62c8b617544ff5"
+    },
+    {
+      "path": "research/qq16-native-history/BILL.json",
+      "sha256": "1ba489384490f8733f14ddfde1a153edf48885f2e2c29fdfc84615b64ad4b6ed",
+      "git_blob": "d1f924e5206928c331a351c57799a78e004c4366"
+    },
+    {
+      "path": "research/qq16-native-history/COMPARISON.md",
+      "sha256": "a903d65869025d94f5302c27a20608edba0309c70be9b442965018bbcb5aa259",
+      "git_blob": "22ba49c92c7bf6ce738045c04cbf6ca0766642a4"
+    },
+    {
+      "path": "research/qq16-native-history/DECISION.md",
+      "sha256": "e2b56d376b3974e3cfa85d07bcfac58cb073c992a82045e905e2acce84dca199",
+      "git_blob": "5124526653b55ae8864ccc7416631affb0e11ea4"
+    },
+    {
+      "path": "research/qq16-native-history/EXECUTION.json",
+      "sha256": "58f741149036f3e8f71309db4574ce5aea4ee6aa4cf329e65562ac1399ab267c",
+      "git_blob": "688097030b3506a6648cb50f985f7a0429a9d894"
+    },
+    {
+      "path": "research/qq16-native-history/HISTORY.md",
+      "sha256": "abedc7bc1b1e1693feb4534439090f90737c76c61a543d4e27798d2c6de75115",
+      "git_blob": "3a47716922d0d9dfdc8a6dbc52ceeaa81dcf5d47"
+    },
+    {
+      "path": "research/qq16-native-history/LIFECYCLE.md",
+      "sha256": "0b7d0536f15bb5db0b21c45ea8d0def6bd1590687b9368cf7f58a0aa330201e4",
+      "git_blob": "b8626ea86f13261d47e093ffb74f37b5c8ff2325"
+    },
+    {
+      "path": "research/qq16-native-history/MECHANISM.md",
+      "sha256": "31dc3638cba407c453bb1c529394c885ff5d87bdd8cec0d876ab4c13b733ca3e",
+      "git_blob": "86245d2d30f8ee8a51bdfb46bee4b6db3cb76f72"
+    },
+    {
+      "path": "research/qq16-native-history/PROOF.md",
+      "sha256": "79bd0240bb716c0e098405a0a66e0e18e69009a40616ac0c03b87daaecd90d37",
+      "git_blob": "4d6ba8ce8c6abb176cc239ad67ff5b63148d7612"
+    },
+    {
+      "path": "research/qq16-native-history/README.md",
+      "sha256": "1583383506a21ad519f3c19eb267d74d2a0c518c671271b375b176007a94c22e",
+      "git_blob": "feb2db1671757e5fc7d1f4c0cb2e826296a5ec52"
+    },
+    {
+      "path": "research/qq16-native-history/RESOURCE.md",
+      "sha256": "7a61180f77fee633b1f3d5b4b26cc35e6bbfec79143b46c3c7db7639632a9489",
+      "git_blob": "deccb70cdfb4ab98496749b49e0a5f5f0d930c1a"
+    },
+    {
+      "path": "research/qq16-native-history/RESULT.json",
+      "sha256": "4062058ce14eb27ded3b89e6c80864f07404b8258097e91f630c920ca683c7c1",
+      "git_blob": "ec602569bab75b52fdf81b1f21c8224274247a56"
+    },
+    {
+      "path": "research/qq16-native-history/REUSE.json",
+      "sha256": "be912512ab69cb9f5d4d35297f4a7cd2f8e89aedcd81be9539c9e0df128268cf",
+      "git_blob": "b75eb7357d6f64fd1dc719956cd121576ec69be7"
+    },
+    {
+      "path": "research/qq16-native-history/REVIEW.json",
+      "sha256": "57d57ea8cdcc12ee03ed75ed34b07c8515b502e037e56aae5b53332c32caa964",
+      "git_blob": "f48c57bbbc5b2b06acd5dbf28cb543666369743e"
+    },
+    {
+      "path": "research/qq16-native-history/SEALS.json",
+      "sha256": "8289fe78ae5d3e65c4219569cf23f16537c374309ee1a67dc5d253c57e4b5b9a",
+      "git_blob": "ea3c763d1ed46184028478201164cea8293b8424"
+    },
+    {
+      "path": "research/qq16-native-history/SOURCES.json",
+      "sha256": "cd9d64160ea578afa4cd7f4fefd6b7e04e7011136ed2b2ace2462060ffb3fad2",
+      "git_blob": "fa5dd6878f01bdcd70700134439545e70d38c15b"
+    },
+    {
+      "path": "research/qq16-native-history/TASK.json",
+      "sha256": "39b7b6ee046cc50e892da6f1bcb18230b993fed6b483cc1e09da020483eef2a0",
+      "git_blob": "ce4d1ef50a58e9664c765dc02106a42673c6ecd7"
+    },
+    {
+      "path": "research/qq16-native-history/VERIFICATION.md",
+      "sha256": "a9ea34ea5ab9ea4b6c8977c988257e2b19f447dc646d22e79b053661b3bd97ea",
+      "git_blob": "bd2db43e77ab129454b33b76b6ecf6bd86374c29"
+    },
+    {
+      "path": "research/qq16-native-history/VERIFY.json",
+      "sha256": "8cabb7fca903a00dee82196c6c8aae9ec1775e9acf16d0ccdfe1fafb7f257b8f",
+      "git_blob": "e3f84c396a409bc8d4b20cf406f6fd509c967a11"
+    },
+    {
+      "path": "research/qq16-native-history/comparison.py",
+      "sha256": "9d3d002ab1b2b29fa2260f71c8f108a2b84de22785998a2d167102888932bc4f",
+      "git_blob": "cbadc4d4c9426355f746f9d2bc739ae213c114ef"
+    },
+    {
+      "path": "research/qq16-native-history/fitted_fixture.py",
+      "sha256": "6ab76ec516b5e7da08fe178698935f9b92948396afddb4d2df5153da10d83a57",
+      "git_blob": "0fb59dee126cd9da2931285a73ca2ba0d70eac95"
+    },
+    {
+      "path": "research/qq16-native-history/inputs/PR4167-MANIFEST.json",
+      "sha256": "abea80414d41fce44a738dae8d1b10c9e1d901765552a56e69b60add286f43fb",
+      "git_blob": "3731fc43115988e522caf1902d00c0791ae3fbd8"
+    },
+    {
+      "path": "research/qq16-native-history/inputs/PR4167.tar",
+      "sha256": "68ff3b4b541434cb9df15884d027838cbc80300e9d78015eb82c395c5168d166",
+      "git_blob": "32ccbf658e697bacc8949462f9adca4392aabe8b"
+    },
+    {
+      "path": "research/qq16-native-history/lifecycle.py",
+      "sha256": "43a418849f013d80e400f78b3db8f9273f66844239b0dc4217b5a82b84e2ded2",
+      "git_blob": "a54d3c2d0723d042f123be0767c05b8157900ad9"
+    },
+    {
+      "path": "research/qq16-native-history/mechanism.py",
+      "sha256": "e5ad8ce4e8654f1e79e168154cb988f23d278f9a4e3a7bba6e946cedc4051772",
+      "git_blob": "a8c05b025e696ce72aa2417d048630d59fb81936"
+    },
+    {
+      "path": "research/qq16-native-history/native_nested.py",
+      "sha256": "0e7999e6b99be1434556025d719ea1733cb0aed6b46522025b4910468c2d51e9",
+      "git_blob": "62cbb1801d43526ff692559f557db43086a06b6c"
+    },
+    {
+      "path": "research/qq16-native-history/runtime.py",
+      "sha256": "c5b1b3959dc7922b05a3ad67c3a2d8a6f5e7a9a04001dde4f805438d7705c5e4",
+      "git_blob": "46d8f38a677597bf1091cdc0d2ca776e1dd8e563"
+    },
+    {
+      "path": "research/qq16-native-history/state_model.py",
+      "sha256": "25c3ae85a6a31ce93ad2e4cc8fbe2d1e1fa52aceabe343440b6ffbcb2809df74",
+      "git_blob": "250583b2b58118ac4e965449ec67814d812dfad0"
+    },
+    {
+      "path": "research/qq16-native-history/test_verify.py",
+      "sha256": "6edbd2d9853e19886c4959dac63e5d14971478f365c5c781b7c9d119c29bd2da",
+      "git_blob": "e83e83284f8bd72e2cbe0861a180157a74bf550b"
+    },
+    {
+      "path": "research/qq16-native-history/verify.py",
+      "sha256": "09faa2fab35591124e19048ed5ce188b025cb3f813e609a7af72e81dcf6441f4",
+      "git_blob": "764b75ad38438c53c019df0839c9a69df9a22386"
+    }
+  ]
+}
diff --git a/research/qq16-complete-cost/inputs/PR4172.tar b/research/qq16-complete-cost/inputs/PR4172.tar
new file mode 100644
index 0000000000..9c28c6447f
Binary files /dev/null and b/research/qq16-complete-cost/inputs/PR4172.tar differ
diff --git a/research/qq16-complete-cost/nonchild.py b/research/qq16-complete-cost/nonchild.py
new file mode 100644
index 0000000000..aa613038c4
--- /dev/null
+++ b/research/qq16-complete-cost/nonchild.py
@@ -0,0 +1,286 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Literal nonchild partition and conservative signed-cost building blocks.
+
+Chris R / Clear1nsight, substantial OpenAI Codex assistance. Jose Manuel's
+physical controller and monomial implementation supply the source operations.
+All inherited imports must occur after the package's authenticated cold load.
+This module computes certificates; it is not an encoded runtime compiler.
+"""
+from collections import Counter, defaultdict, deque
+from copy import copy
+from fractions import Fraction
+from functools import lru_cache
+
+
+def need(ok, why):
+    if not ok: raise ValueError(why)
+
+
+def nat(n, positive=False):
+    need(type(n) is int and n >= int(positive), 'exact nonnegative integer')
+    return n
+
+
+def operation_key(op):
+    """Ignore only raw source-event index; retain roles, literal and direction."""
+    return (op[0], *op[2:])
+
+
+def occurrence_partition(old, new):
+    """Explicit stable occurrence injection, never a rank-only histogram."""
+    available=defaultdict(deque)
+    for j,op in enumerate(new): available[operation_key(op)].append(j)
+    paired=[]; removed=[]; used=set()
+    for i,op in enumerate(old):
+        key=operation_key(op)
+        if available[key]:
+            j=available[key].popleft();used.add(j);paired.append((i,j))
+        else: removed.append(i)
+    added=[j for j in range(len(new)) if j not in used]
+    need(len(paired)+len(removed)==len(old) and len(paired)+len(added)==len(new),
+         'disjoint complete occurrence partition')
+    need(all(operation_key(old[i])==operation_key(new[j]) for i,j in paired),
+         'literal matched operation')
+    return paired,removed,added
+
+
+def census(parent, service):
+    """Audit authenticated compiled source and derive fixed recipe gate debit.
+
+    Owner-basis words are NOT replaced by identity-owner fixtures. They are
+    inventoried separately for the uniform-cover theorem.
+    """
+    from phase_recipe import Recipe
+    vectors=tuple('v'+str(i) for i in range(parent.dimension))
+    need(parent.dimension==73 and parent.families==14336,'selected source binding')
+    need(parent.core.owner_specs is parent.source.owner_specs and
+         parent.core.events is parent.source.events and
+         parent.core.cover is parent.source.cover, 'unchanged exact core owner/group geometry')
+    removed_gates=Counter();added_gates=Counter();rows={};removed_kinds=Counter()
+    added_kinds=Counter();removed_scalar=Counter();added_scalar=Counter()
+    removed_monomials=[]
+    for direction in ('forward','backward'):
+        old=parent.source.codes[direction];new=parent.core.codes[direction]
+        paired,removed,added=occurrence_partition(old,new)
+        need(all(old[i][0]!='monomial' or parent.source.recipes[old[i][3]]==parent.core.recipes[new[j][3]]
+                 for i,j in paired), 'matched monomial literal bytes')
+        for i in removed:
+            op=old[i];removed_kinds[op[0]]+=1
+            if op[0]=='scalar':removed_scalar[op[4]]+=1
+            if op[0]=='monomial':
+                literal=parent.source.recipes[op[3]]
+                word=tuple(Recipe(literal,vectors).word)
+                removed_gates.update(word)
+                removed_monomials.append({'direction':direction,'pc':i,'role':op[2],
+                    'recipe':op[3],'inverse':op[4],'gate_count':len(word)})
+        for j in added:
+            op=new[j];added_kinds[op[0]]+=1
+            if op[0]=='scalar':added_scalar[op[4]]+=1
+        rows[direction]={'old_operations':len(old),'new_operations':len(new),
+            'paired_occurrences':paired,'removed_pcs':removed,'added_pcs':added}
+    need(removed_kinds==Counter(monomial=32,copy=8,child=16,scalar=6,marker=2),
+         'complete removed nonchild and child alphabet')
+    need(removed_scalar==Counter({('add',-1,1):6}), 'six removed unit subtract dispatches')
+    need(not (removed_scalar-added_scalar),'same-literal added scalar witnesses')
+    # Cache only checker copies of finite cover arithmetic. Production is unchanged.
+    p=copy(parent);p.cover=copy(parent.cover)
+    p.cover.unrank=lru_cache(None)(parent.cover.unrank)
+    p.cover.rank=lru_cache(None)(parent.cover.rank)
+    s=copy(service);s.cover=p.cover
+    need(tuple(p.cover.unrank(0))==tuple(1<<i for i in range(73)), 'identity-owner fixed-gate separator')
+    new_monomials=0;owner_basis=0;extra_nonmap_groups=0
+    for i,event in enumerate(p.events):
+        if event[0]!='qq16' or event[4][0] in ('retained_core','cover_map'):continue
+        group=p.group(i,0,0)
+        need(bool(group.code),'emitted extra producer group')
+        extra_nonmap_groups+=1
+        for op in group.code:
+            if op[0]!='monomial':continue
+            # Each line emits owner inverse,right,left,owner forward. Identity
+            # owner contributes zero gates but remains a paid monomial call.
+            new_monomials+=1
+            added_gates.update(Recipe(group.recipes[op[3]],vectors).word)
+        owner_basis+=2*sum(op[0]=='child' for op in group.code)
+    for i,event in enumerate(s.events):
+        if len(event[2])==1 and event[2][0][1][0]=='map':continue
+        group=s.group(i,0,0)
+        for op in group.code:
+            if op[0]=='monomial' and op[3] in ('right','left'):
+                new_monomials+=1
+                added_gates.update(Recipe(group.recipes[op[3]],vectors).word)
+        owner_basis+=sum(op[0]=='monomial' and op[3]=='owner' for op in group.code)
+    need(new_monomials==800 and owner_basis==736,'complete fixed and owner basis monomial census')
+    from qq16_producer import order
+    map_orders=Counter(order(tuple(parent.packet['map_registry'][event[4][2]]['owner_right_matrix_columns']))
+                       for event in parent.events if event[0]=='qq16' and event[4][0]=='cover_map')
+    map_groups=sum((Fraction(count,k) for k,count in map_orders.items()),Fraction(0))
+    service_inventory=service.audit()['physical_per_cover']
+    need(extra_nonmap_groups==41 and map_groups==Fraction(12286,51), 'literal candidate-only producer groups')
+    expected_service={'all_gather_scatter_commit_groups':2022,
+        'all_monomial_calls_including_map_translations':1696,
+        'scalar_engine_calls_including_map_sign_corrections':3484,
+        'map_exchanges':176,'private_zero_calls':48,'rank_one_children':336}
+    need(all(service_inventory[k]==v for k,v in expected_service.items()), 'complete service invoice without doubled exchange negation')
+    # 64 of the 800 measured call bases above are identity-owner placeholders;
+    # their general-owner gate contribution is in the separate owner sum.
+    deficits=removed_gates-added_gates
+    need(sum(removed_gates.values())==736 and sum(added_gates.values())==7150,
+         'literal fixed gate inventories')
+    need(deficits==Counter({('add',6,8):4,('add',8,6):1}), 'exact uncovered gate geometries')
+    def entries(counter):return [[list(k),v] for k,v in sorted(counter.items())]
+    return {'units':'per complete cover divided by Gamma',
+        'occurrence_partition':rows,'removed_kinds':dict(removed_kinds),
+        'added_core_kinds':dict(added_kinds),'removed_scalars':entries(removed_scalar),
+        'added_matching_scalars':entries(added_scalar),
+        'removed_monomials':removed_monomials,
+        'removed_gates':entries(removed_gates),'added_fixed_gates':entries(added_gates),
+        'fixed_gate_deficits':entries(deficits),'owner_basis_monomials':owner_basis,
+        'fixed_recipe_call_bases':800,'added_calls_after_32_base_matches':768,
+        'producer_extra_nonmap_groups':extra_nonmap_groups,'producer_map_groups':str(map_groups),
+        'service_source_inventory':service_inventory,
+        'service_groups':2022,'service_bank_fraction':'1/32',
+        'source_call_base_geometry':'same P,U,H_b,c,73 vector fields; family-bank size excluded from local monomial packet',
+        'requires_owner_cover_gate_theorem':True}
+
+
+def extra_gather_lower(gamma, bank_bits):
+    """Candidate-only scans after exact matching of the two original core groups.
+
+    Read and step every bank bit, then rewind. The nonnegative omitted work
+    includes every Counter, selected-packet append, scatter, commit and all
+    service/compiler activity. This is not diagnostic-volume subtraction.
+    """
+    nat(gamma,True);nat(bank_bits,True)
+    need(gamma%51==0 and bank_bits%32==0,'complete cover and service-bank divisibility')
+    volume=(41*gamma+12286*(gamma//51))*bank_bits+2022*gamma*(bank_bits//32)
+    need(volume==Fraction(281593,816)*gamma*bank_bits,'literal added-only scan volume')
+    return {'reads':2*volume,'writes':0,'moves':2*volume,
+        'total':4*volume,'discarded_positive_intervals':True,
+        'coefficient_total_Gamma_B':'281593/204'}
+
+
+def removed_small_upper(v,L,header_bits=2685):
+    """Componentwise conservative bounds for 8 copies and 16 external shells.
+
+    L is the complete inherited Count-length envelope, not log of active width.
+    The bound follows the source loop table in NONCHILD.md. Complete C bodies,
+    monomial atoms, constructor/retirement and finite control are excluded.
+    """
+    nat(v,True);nat(L,True);nat(header_bits,True)
+    need(L>=16 and header_bits==2685,'complete Count envelope and frozen B header')
+    copy_bound=(1<<20)*(v+1+L**4)
+    shell_bound=(1<<24)*(v+1+L**4+header_bits)
+    each=8*copy_bound+16*shell_bound
+    return {'copy_count':8,'shell_count':16,'copy_per_component_upper':copy_bound,
+        'shell_per_component_upper':shell_bound,'rwm_upper':[each]*3,
+        'total_upper':3*each,'six_unit_scalars_matched_to_identical_added_literals':True,
+        'body_and_descendants_excluded':True}
+
+
+def controls():
+    old=[('scalar',0,1,2,('add',-1,1)),('scalar',1,1,2,('add',-1,1)),('child',2,4,8)]
+    new=[('scalar',5,1,2,('add',-1,1)),('child',7,4,8)]
+    paired,removed,added=occurrence_partition(old,new)
+    need(paired==[(0,0),(2,1)] and removed==[1] and added==[], 'duplicate occurrence identity')
+    result=extra_gather_lower(51,32)
+    need(result['total']==281593*8,'exact one-cover denominator')
+    rejected=[]
+    for label,call in (
+        ('partial cover',lambda:extra_gather_lower(1,32)),
+        ('wrong service bank volume',lambda:extra_gather_lower(51,33)),
+        ('Boolean multiplicity',lambda:extra_gather_lower(True,32)),
+        ('negative removed upper',lambda:removed_small_upper(-1,8))):
+        try:call()
+        except ValueError:rejected.append(label)
+        else:raise ValueError('accepted nonchild mutation:'+label)
+    return {'duplicate_occurrence_control':True,'rejections':rejected}
+
+
+def phase_pair_calibrations():
+    """Actual four-phase source pair traffic, not a production admission test."""
+    import records, signed_phase
+    from cardinal_counts import Count
+    from words import BLANK
+    tracked=[];original=records.Tape.__init__
+    def recording(tape):
+        original(tape);tracked.append(tape)
+    records.Tape.__init__=recording
+    def meter():return tuple(sum(getattr(t.meter,k) for t in tracked) for k in ('reads','writes','moves'))
+    def body(t):return bytes(t.cells[1:]).rstrip(bytes([BLANK]))
+    cases=[]
+    try:
+        for h in (4,8,17):
+            values=(3,-2)
+            raw=bytes((x>>i)&1 for x in values for i in range(h))
+            for phase in range(4):
+                width=Count.literal(h);source=records.Tape();target=records.Tape()
+                real,imag=records.Tape(),records.Tape()
+                for bit in raw:source.append(bit)
+                source.rewind();before=meter()
+                signed_phase.pair(source,target,width,phase,real,imag)
+                actual=tuple(a-b for a,b in zip(meter(),before))
+                expected=(values,(-values[1],values[0]),(-values[0],-values[1]),(values[1],-values[0]))[phase]
+                encoded=bytes((x>>i)&1 for x in expected for i in range(h))
+                need(body(target)==encoded,'actual signed phase endpoint')
+                need(body(source)==raw and width.tape.head==1,'borrowed phase width and source bytes')
+                need(not body(real) and not body(imag) and real.head==imag.head==1,'phase scratch retired')
+                cases.append({'H_b':h,'phase':phase,'rwm':list(actual),'input':[3,-2]})
+                source.clear();target.clear();width.close()
+        for h in (4,8,17):
+            need(len({tuple(x['rwm']) for x in cases if x['H_b']==h})==1,'all four actual phase action schedules')
+        return {'cases':cases,'all_phases_same_actions':True,
+                'scope':'actual reduced pair primitive; general phase equality follows source loop proof'}
+    finally:records.Tape.__init__=original
+
+
+def gather_calibrations():
+    """Actual borrowed bank scan lower bounds, including all allocated Counters."""
+    import records
+    from bank_packets import BankPackets
+    from cardinal_counts import Count
+    from words import BLANK
+    tracked=[];original=records.Tape.__init__
+    def recording(tape):original(tape);tracked.append(tape)
+    records.Tape.__init__=recording
+    def meter():return tuple(sum(getattr(t.meter,k) for t in tracked) for k in ('reads','writes','moves'))
+    def body(t):return bytes(t.cells[1:]).rstrip(bytes([BLANK]))
+    cases=[]
+    try:
+        for prefixes,unused,row_bits in ((1,1,1),(2,1,4),(1,3,5)):
+            bank=BankPackets(3,2,1);counts=tuple(Count.literal(x) for x in (prefixes,unused,row_bits))
+            length=prefixes*3*2*unused*row_bits
+            raw=bytes((i*7+i//3)%2 for i in range(length));source=records.Tape()
+            for bit in raw:source.append(bit)
+            source.rewind();bank.select(((1,0),));before=meter()
+            returned=bank.gather(source,*counts)
+            actual=tuple(a-b for a,b in zip(meter(),before))
+            need(actual[0]>=2*length and actual[2]>=2*length,'literal gathered source scan lower')
+            need(body(source)==raw and source.head==1,'borrowed entire bank restored')
+            segment=unused*row_bits
+            expected=b''.join(raw[(p*6+2)*segment:(p*6+3)*segment] for p in range(prefixes))
+            need(body(returned[0])==expected,'selected owner payload extent')
+            scatter_before=meter();scattered=bank.scatter(source,*counts)
+            scatter_actions=tuple(a-b for a,b in zip(meter(),scatter_before))
+            need(scatter_actions[1]>=length and body(scattered)==raw, 'complete scatter output writes')
+            bank.commit(source)
+            need(body(source)==raw and source.head==1, 'unchanged complete group bank endpoint')
+            source.clear()
+            for value in counts:value.close()
+            need(bank.state=='closed' and all(not body(t) for t in bank.packets),'gather roles retired')
+            cases.append({'prefixes':prefixes,'unused':unused,'row_bits':row_bits,
+                          'bank_bits':length,'rwm':list(actual),'lower':[2*length,0,2*length],
+                          'scatter_rwm':list(scatter_actions),'scatter_write_lower':length})
+        return {'cases':cases,'scope':'complete actual BankPackets.gather on reduced geometry; no selected O73 payload execution'}
+    finally:records.Tape.__init__=original
+
+
+def extra_group_lower(gamma, bank_bits):
+    """Disjoint gather R/M and scatter-output W subset of extra group cycles."""
+    result=extra_gather_lower(gamma,bank_bits)
+    volume=result['reads']//2
+    need(result['reads']==2*volume and result['moves']==2*volume,'even gather scan bound')
+    return {'reads':2*volume,'writes':volume,'moves':2*volume,'total':5*volume,
+            'coefficient_total_Gamma_B':'1407965/816',
+            'intervals':['BankPackets.gather source reads and moves',
+                         'BankPackets.scatter output writes'],
+            'disjoint_nonnegative_source_subtraces':True}
diff --git a/research/qq16-complete-cost/runtime.py b/research/qq16-complete-cost/runtime.py
new file mode 100644
index 0000000000..dfe8f25e41
--- /dev/null
+++ b/research/qq16-complete-cost/runtime.py
@@ -0,0 +1,69 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Authenticate retained #4172 and canonical nested closure before execution.
+
+Chris R / Clear1nsight with substantial OpenAI Codex assistance.
+The original physical/numerical sources and all prior notices are unchanged.
+"""
+from pathlib import Path
+import hashlib, io, json, sys, tarfile, tempfile, types
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+MANIFEST_SHA='0efdb3b0a648bedf80b4f1e4f36b6bcfc76fd03f9626c700db4ce09476ee0025'
+_temporary=None
+_history=None
+def need(ok,why):
+    if not ok: raise ValueError(why)
+def sha(raw): return hashlib.sha256(raw).hexdigest()
+def unique(pairs):
+    result={}
+    for key,value in pairs:
+        need(key not in result,'duplicate JSON key');result[key]=value
+    return result
+def parse(raw):return json.loads(raw,object_pairs_hook=unique)
+def module(name,path):
+    result=types.ModuleType(name);result.__file__=str(path)
+    sys.modules[name]=result
+    exec(compile(path.read_bytes(),str(path),'exec'),result.__dict__)
+    return result
+def authenticated_inputs():
+    raw=(HERE/'inputs/PR4172-MANIFEST.json').read_bytes()
+    need(sha(raw)==MANIFEST_SHA,'retained manifest integrity')
+    manifest=parse(raw);archive=(HERE/'inputs/PR4172.tar').read_bytes()
+    need(sha(archive)==manifest['archive_sha256'],'retained archive integrity')
+    expected={row['path']:row['sha256'] for row in manifest['files']}
+    need(len(expected)==len(manifest['files']),'duplicate retained path')
+    files={}
+    with tarfile.open(fileobj=io.BytesIO(archive),mode='r:') as source:
+        for member in source:
+            if member.isdir():continue
+            need(member.isfile() and member.name in expected and member.name not in files,'retained member/path')
+            need(not Path(member.name).is_absolute() and '..' not in Path(member.name).parts,'safe retained path')
+            raw=source.extractfile(member).read()
+            need(sha(raw)==expected[member.name],'retained content integrity')
+            files[member.name]=raw
+    need(set(files)==set(expected),'complete retained archive')
+    sources=parse(files['research/qq16-native-history/SOURCES.json'])
+    for row in sources['files']:
+        if row['usage']!='input':continue
+        rel=row['path'];need(not Path(rel).is_absolute() and '..' not in Path(rel).parts,'canonical path')
+        raw=(ROOT/rel).read_bytes()
+        need(sha(raw)==row['sha256'] and hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()==row['git_blob'],'canonical input integrity:'+rel)
+        need(rel not in files,'canonical collision');files[rel]=raw
+    return files
+def cold():
+    global _temporary,_history
+    need(_temporary is None,'one cold source cohort per process')
+    files=authenticated_inputs()
+    _temporary=tempfile.TemporaryDirectory(prefix='qq16-cost-')
+    root=Path(_temporary.name)
+    for rel,raw in files.items():
+        path=root/rel;path.parent.mkdir(parents=True,exist_ok=True);path.write_bytes(raw)
+    _history=module('qq16_history_runtime',root/'research/qq16-native-history/runtime.py')
+    return _history.cold()
+def predecessor():
+    need(_temporary is not None,'cold cohort required')
+    return Path(_temporary.name)/'research/qq16-native-history'
+def cleanup():
+    global _temporary
+    if _history is not None:_history.cleanup()
+    if _temporary is not None:_temporary.cleanup();_temporary=None
diff --git a/research/qq16-complete-cost/test_verify.py b/research/qq16-complete-cost/test_verify.py
new file mode 100644
index 0000000000..85ebc7df55
--- /dev/null
+++ b/research/qq16-complete-cost/test_verify.py
@@ -0,0 +1,251 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Source and receipt boundary controls for the complete terminal-cost package.
+
+Chris R with substantial OpenAI Codex assistance. Adapted from #4167's export
+controls. These checks exercise transport and authentication failure modes;
+the ordinary/optimised scientific replays are separate registered evidence.
+"""
+import copy
+import hashlib
+import importlib.util
+import io
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tarfile
+import tempfile
+import unittest
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def digest(raw):
+    return hashlib.sha256(raw).hexdigest()
+
+
+def snapshot(root):
+    """Reading may alter atime; all other recorded filesystem state is fixed."""
+    result = {}
+    for path in sorted(root.rglob('*')):
+        stat = path.stat()
+        result[str(path.relative_to(root))] = (
+            stat.st_mode, stat.st_mtime_ns, stat.st_ino,
+            digest(path.read_bytes()) if path.is_file() else None,
+        )
+    return result
+
+
+def raw_module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def alias_mutation(value):
+    """Produce a Python-equal, JSON-type-distinct bool/integer replacement."""
+    if isinstance(value, bool):
+        return int(value), True
+    if isinstance(value, int) and value in (0, 1):
+        return bool(value), True
+    if isinstance(value, dict):
+        for key, child in value.items():
+            changed, found = alias_mutation(child)
+            if found:
+                result = copy.deepcopy(value)
+                result[key] = changed
+                return result, True
+    if isinstance(value, list):
+        for index, child in enumerate(value):
+            changed, found = alias_mutation(child)
+            if found:
+                result = copy.deepcopy(value)
+                result[index] = changed
+                return result, True
+    return value, False
+
+
+class Boundary(unittest.TestCase):
+    def setUp(self):
+        self.tmp = tempfile.TemporaryDirectory(prefix='qq16-complete-cost-export-')
+        self.root = Path(self.tmp.name) / 'checkout'
+        self.package = self.root / 'research' / HERE.name
+        self.addCleanup(self.remove_export)
+        shutil.copytree(HERE, self.package,
+                        ignore=shutil.ignore_patterns('__pycache__'))
+        registration = json.loads((HERE / 'VERIFY.json').read_bytes())
+        for rel in registration['inputs']:
+            path = Path(rel)
+            self.assertFalse(path.is_absolute())
+            self.assertNotIn('..', path.parts)
+            source, target = ROOT / path, self.root / path
+            self.assertTrue(source.is_file(), rel)
+            target.parent.mkdir(parents=True, exist_ok=True)
+            shutil.copyfile(source, target)
+
+    def remove_export(self):
+        if self.root.exists():
+            self.root.chmod(0o755)
+            for path in self.root.rglob('*'):
+                if path.is_dir():
+                    path.chmod(0o755)
+        self.tmp.cleanup()
+
+    def replay(self, *args, optimized=True, ok=True, needle=None):
+        result = subprocess.run(
+            [sys.executable, '-I', '-Werror', '-B',
+             *(['-O'] if optimized else []),
+             str(self.package / 'verify.py'), *args],
+            cwd=self.root,
+            env=dict(os.environ, PATH='/nonexistent-qq16-git-free'),
+            capture_output=True, text=True, timeout=60,
+        )
+        output = result.stdout + result.stderr
+        self.assertEqual(result.returncode == 0, ok, output)
+        if needle is not None:
+            self.assertIn(needle, output)
+        if ok:
+            self.assertFalse(result.stderr, output)
+        return output
+
+    def test_normal_and_optimized_readonly_check_only_export(self):
+        """Fast transport check, explicitly not the complete scientific replay."""
+        for path in self.root.rglob('*'):
+            path.chmod(0o555 if path.is_dir() else 0o444)
+        self.root.chmod(0o555)
+        before = snapshot(self.root)
+        for optimized in (False, True):
+            self.replay('--check-only', optimized=optimized,
+                        needle='PASS_QQ16_COMPLETE_TERMINAL_COST')
+            self.assertEqual(before, snapshot(self.root))
+        self.assertFalse((self.root / '.git').exists())
+
+    def test_authentication_precedes_inherited_and_local_execution(self):
+        source = self.root / 'research/physical-complex-controller/machine.py'
+        raw = source.read_bytes()
+        source.write_bytes(b"raise RuntimeError('INHERITED_POISON_EXECUTED')\n" + raw)
+        fixture = self.package / 'cbody.py'
+        fixture_raw = fixture.read_bytes()
+        fixture.write_bytes(b"raise RuntimeError('LOCAL_POISON_EXECUTED')\n" + fixture_raw)
+        # Default entry point, not check-only: rejected before C-cost execution.
+        output = self.replay(ok=False, needle='canonical input integrity')
+        self.assertNotIn('INHERITED_POISON_EXECUTED', output)
+        self.assertNotIn('LOCAL_POISON_EXECUTED', output)
+        source.write_bytes(raw)
+        output = self.replay(ok=False, needle='local source seal')
+        self.assertNotIn('LOCAL_POISON_EXECUTED', output)
+
+    def test_outer_archive_and_manifest_seals(self):
+        for name, message in (
+            ('inputs/PR4172-MANIFEST.json', 'retained manifest integrity'),
+            ('inputs/PR4172.tar', 'retained archive integrity'),
+        ):
+            with self.subTest(name=name):
+                path = self.package / name
+                raw = path.read_bytes()
+                path.write_bytes(raw + b' ')
+                self.replay('--check-only', ok=False, needle=message)
+                path.write_bytes(raw)
+
+    def test_retained_members_below_outer_seal(self):
+        """Test-only resealing reaches inner validation; no inherited execution."""
+        archive_path = self.package / 'inputs/PR4172.tar'
+        manifest_path = self.package / 'inputs/PR4172-MANIFEST.json'
+        original_archive = archive_path.read_bytes()
+        original_manifest = manifest_path.read_bytes()
+        members = []
+        with tarfile.open(fileobj=io.BytesIO(original_archive), mode='r:') as src:
+            for member in src:
+                if member.isfile():
+                    with src.extractfile(member) as stream:
+                        members.append((copy.copy(member), stream.read()))
+        self.assertTrue(members)
+        for mutation, message in (
+            ('content', 'retained content integrity'),
+            ('duplicate', 'retained member/path'),
+            ('link', 'retained member/path'),
+            ('missing', 'complete retained archive'),
+        ):
+            with self.subTest(mutation=mutation):
+                out = io.BytesIO()
+                with tarfile.open(fileobj=out, mode='w:') as dst:
+                    selected = members[:-1] if mutation == 'missing' else members
+                    for index, (member, raw) in enumerate(selected):
+                        member = copy.copy(member)
+                        if index == 0 and mutation == 'content':
+                            raw = b'X' + raw
+                            member.size = len(raw)
+                        if index == 0 and mutation == 'link':
+                            member.type = tarfile.SYMTYPE
+                            member.linkname = '/outside-export'
+                            member.size = 0
+                            dst.addfile(member)
+                        else:
+                            dst.addfile(member, io.BytesIO(raw))
+                    if mutation == 'duplicate':
+                        member, raw = members[0]
+                        dst.addfile(copy.copy(member), io.BytesIO(raw))
+                archive = out.getvalue()
+                manifest = json.loads(original_manifest)
+                manifest['archive_sha256'] = digest(archive)
+                manifest_bytes = json.dumps(manifest).encode()
+                archive_path.write_bytes(archive)
+                manifest_path.write_bytes(manifest_bytes)
+                loader = raw_module('qq16_history_member_loader', self.package / 'runtime.py')
+                loader.MANIFEST_SHA = digest(manifest_bytes)
+                with self.assertRaisesRegex(ValueError, message):
+                    loader.authenticated_inputs()
+        archive_path.write_bytes(original_archive)
+        manifest_path.write_bytes(original_manifest)
+
+    def test_generation_refuses_to_overwrite_receipts(self):
+        before = snapshot(self.root)
+        self.replay('--generate', str(self.package), ok=False, needle='refuse receipt overwrite')
+        self.assertEqual(before, snapshot(self.root))
+
+    def test_whole_typed_receipts_and_duplicate_keys(self):
+        # Test the production transport comparator against a saved expected
+        # result. Separate full replays independently regenerate that result.
+        saved_path = list(sys.path)
+        saved_runtime = sys.modules.pop('runtime', None)
+        self.addCleanup(lambda: setattr(sys, 'path', saved_path))
+        def restore_runtime():
+            sys.modules.pop('runtime', None)
+            if saved_runtime is not None:
+                sys.modules['runtime'] = saved_runtime
+        self.addCleanup(restore_runtime)
+        sys.path.insert(0, str(self.package))
+        verifier = raw_module('qq16_history_export_verifier', self.package / 'verify.py')
+        typed_mutations = 0
+        for name in verifier.NAMES:
+            path = self.package / name
+            raw = path.read_bytes()
+            expected = json.loads(raw)
+            verifier.check_receipt(name, expected, self.package)
+            mutations = [dict(expected, unexpected_receipt_field=True),
+                         {k: v for index, (k, v) in enumerate(expected.items()) if index != 0}]
+            changed, found = alias_mutation(expected)
+            if found:
+                self.assertEqual(changed, expected)
+                typed_mutations += 1
+                mutations.append(changed)
+            for changed in mutations:
+                path.write_text(json.dumps(changed))
+                with self.assertRaisesRegex(ValueError, 'whole typed receipt mismatch:'):
+                    verifier.check_receipt(name, expected, self.package)
+            path.write_bytes(raw)
+            key = next(iter(expected))
+            duplicate = b'{' + json.dumps(key).encode() + b':false,' + raw.lstrip()[1:]
+            path.write_bytes(duplicate)
+            with self.assertRaisesRegex(ValueError, 'duplicate'):
+                verifier.check_receipt(name, expected, self.package)
+            path.write_bytes(raw)
+        self.assertGreater(typed_mutations, 0, 'no concrete bool/integer alias exercised')
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/research/qq16-complete-cost/verify.py b/research/qq16-complete-cost/verify.py
new file mode 100644
index 0000000000..0247ae38ba
--- /dev/null
+++ b/research/qq16-complete-cost/verify.py
@@ -0,0 +1,113 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Authenticated integrated source-cost certificate and finite execution."""
+from pathlib import Path
+import argparse,hashlib,json,sys,types
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+sys.path.insert(0,str(HERE))
+STATUS='PASS_QQ16_COMPLETE_TERMINAL_COST'
+NAMES=('RESULT.json','BILL.json','EXECUTION.json')
+def need(ok,why):
+    if not ok:raise ValueError(why)
+def sha(raw):return hashlib.sha256(raw).hexdigest()
+def unique(pairs):
+    out={}
+    for k,v in pairs:
+        need(k not in out,'duplicate key');out[k]=v
+    return out
+def parse(raw):return json.loads(raw,object_pairs_hook=unique)
+def canonical(value):return json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode()
+def typed(value):
+    if isinstance(value,dict):return ('dict',tuple((k,typed(v)) for k,v in sorted(value.items())))
+    if isinstance(value,list):return ('list',tuple(map(typed,value)))
+    return (type(value).__name__,value)
+def normalized(value):return parse(json.dumps(value,sort_keys=True,allow_nan=False))
+def bootstrap():
+    seals=parse((HERE/'SEALS.json').read_bytes())
+    need(sha((HERE/'runtime.py').read_bytes())==seals['runtime.py'],'runtime seal')
+    loader=types.ModuleType('runtime');loader.__file__=str(HERE/'runtime.py')
+    sys.modules['runtime']=loader
+    exec(compile((HERE/'runtime.py').read_bytes(),str(HERE/'runtime.py'),'exec'),loader.__dict__)
+    pins=loader.authenticated_inputs()
+    for name,digest in seals.items():
+        need(sha((HERE/name).read_bytes())==digest,'local source seal:'+name)
+    return loader,pins
+def compute(loader,pins,execution=None):
+    cohort=loader.cold()
+    try:
+        # Join physical monomial modules before finite recipe imports. This
+        # preserves the inherited cold cohort's module-identity contract.
+        cohort.monomial_api()
+        connection=loader.module('cost_connection',loader._history._prior.predecessor()/'connection.py')
+        data,packet,word,parent,service=connection.bindings()
+        prior=loader._history.predecessor()
+        ledger=loader.module('cost_prior_ledger',prior/'ledger.py')
+        census=ledger.literal_census(data,parent)
+        nonchild=loader.module('complete_cost_nonchild',HERE/'nonchild.py')
+        cbody=loader.module('complete_cost_cbody',HERE/'cbody.py')
+        gate_cover=loader.module('complete_cost_gate_cover',HERE/'gate_cover.py')
+        cost=loader.module('complete_cost_evaluator',HERE/'cost.py')
+        checker=loader.module('complete_cost_checker',HERE/'checker.py')
+        parts=nonchild.census(parent,service)
+        proof=gate_cover.source_checks(cohort)
+        counted=proof['count_certificate']
+        need(counted['gamma']==cost.gamma(),'literal source orthogonal cover')
+        independent_gate=checker.owner_gate_cover_certificate(
+            parts['owner_basis_monomials'],
+            {tuple(k):v for k,v in parts['fixed_gate_deficits']})
+        cases=[]
+        for columns in (5,9,10,44):
+            derived=cost.exclusion(columns)
+            checked=checker.normalized_terminal_exclusion(columns)
+            need(derived['lower_bound_RWM']==checked['lower_bound_RWM'],'independent signed evaluator')
+            cases.append(derived)
+        edge=cost.controls()
+        checked=checker.normalized_terminal_exclusion(edge['last_positive_columns'])
+        need(edge['endpoint']['lower_bound_RWM']==checked['lower_bound_RWM'],'exact normalized endpoint')
+        independent=checker.check()
+        need(census['retained']['calls']==510646 and census['retained_suffix']['calls']==493097,
+             'complete later-root census')
+        if execution is None:
+            execution={'C':cbody.check(),
+                       'phase':nonchild.phase_pair_calibrations(),
+                       'bank':nonchild.gather_calibrations()}
+        else:
+            need(type(execution) is dict and set(execution)=={'C','phase','bank'},'saved execution scope')
+        controls={'cost':edge,'nonchild':nonchild.controls(),
+                  'independent':independent}
+    finally:loader.cleanup()
+    result={'status':STATUS,'scientific_main':'12fa8c5c844be21bfefb38a19503fbd867a11244',
+        'priority_revision':7,'frozen_predecessor':'59b46625a8b2f0dfff3e38ba0949b4247423938a',
+        'verdict':'frozen D strictly costs more than Bstar in each source R/W/M component on the proved terminal-child domain',
+        'not_a_universal_QQ16_obstruction':True,'no_kappa_change':True,
+        'actual_production_descriptor_family':'p=2^8500, lambda=5..44; inherited numerical/hosting/source premises; no production payload execution',
+        'sources_authenticated_before_execution':len(pins),
+        'cost_currency':'source reads/writes/unit moves; compiled control and historical backing separate',
+        'execution_sha256':sha(canonical(normalized(execution)))}
+    bill={'source_occurrence_partition':parts,'complete_root_census':census,
+          'gate_cover':gate_cover.jsonable(proof),'independent_gate_check':independent_gate,
+          'derived_cost_cases':cases,'controls':controls}
+    return tuple(normalized(x) for x in (result,bill,execution))
+def check_receipt(name,expected,folder=HERE):
+    need(typed(parse((folder/name).read_bytes()))==typed(normalized(expected)),
+         'whole typed receipt mismatch:'+name)
+def main():
+    p=argparse.ArgumentParser()
+    p.add_argument('--generate',type=Path)
+    p.add_argument('--check-only',action='store_true')
+    a=p.parse_args()
+    if a.generate:
+        need(all(not (a.generate/n).exists() for n in NAMES),'refuse receipt overwrite')
+    loader,pins=bootstrap()
+    execution=parse((HERE/'EXECUTION.json').read_bytes()) if a.check_only else None
+    result=compute(loader,pins,execution)
+    if a.generate:
+        a.generate.mkdir(parents=True,exist_ok=True)
+        need(all(not (a.generate/n).exists() for n in NAMES),'refuse receipt overwrite')
+        for name,value in zip(NAMES,result):
+            (a.generate/name).write_text(json.dumps(value,sort_keys=True,separators=(',',':'))+'\n')
+    else:
+        for name,value in zip(NAMES,result):check_receipt(name,value)
+    print(STATUS)
+if __name__=='__main__':main()