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+# Cost and family decision for the source-bound producer/collector/consumer join
+
+This note addresses PR3382's complete-cost question for the new, actual source
+path. It provides a complete **direct logical operation inventory for the stated
+open program**, a ledger of the additional obligations required by a physical
+caller, and an inherited conditional stopping test. It does not price an
+all-size implementation, declare a new recursive primitive, or admit the whole
+P104 word.
+
+## 1. The comparison that would answer the question
+
+A meaningful comparison must implement the same external numerical map on the
+same admitted input set, with the same declared frames, reads, dirty-state
+restoration and endpoint ownership. If the reference is a physical-coordinate
+map `A`, the coefficient-coordinate map `E^-1 A E` is a different numerical
+contract until its caller and boundary conversions are specified. Its shorter
+internal formulas cannot be compared to `A` after silently discarding those
+conversions.
+
+The scientific source is canonical main
+`6f100d4bb5083f8c35d96fd95a539811c62f245c`, retaining ywz65's
+[PR2586](https://github.com/CrocSwap/integer-mult-bounds/pull/2586), head
+`7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1`. Its chart is
+`Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)`. The new numerical admission uses
+PR3382's `B9`, on one common grid `2^-f`; multiplying the entire discussion by
+that common scale does not change the stated integer divisibility conditions.
+
+The actual producer dependency cone before event 2025 has 257 events and 58
+initial dependencies: five dirty `D27` through `D31`, dirty `Q7`, and 52 distinct
+`Y` banks. The producer result requires the six dirty banks in `B9` and all 52
+initial `Y` banks in `4B9`. Adding the five dirty `G27` through `G31` banks in
+`B9` gives the bounded 63-bank internal state through event 4516. These are
+mutable numerical banks: the word transports the `Y` arrays too. A physical
+borrowed-bank or aliasing manifest has not been supplied.
+
+The open program retains **all actual outgoing reads**, not just the visibly
+paired `G` readouts. The destinations are external states whose omitted
+histories are not executed by this projection. Each port is the actual
+`target += coefficient * current_source` at the recorded event and source
+frame. Its increment is Gaussian integral on the admitted internal domain. It
+can be added exactly to any current Gaussian target; preserving `B9` at that
+target additionally requires the current target to be in `B9`. Neither the
+initial `X` producer nor a later external transport is admitted by that local
+observation.
+
+## 2. Exact source inventory; no double counting
+
+`cost_audit.py` independently walks destination-first writes backwards from the
+six collector entrances. It then selects every write/transport on the 63 named
+roles through 4516, the private collector at 2025–2039, and every outgoing ADD
+read from those roles. It checks all retained source frames and all internal
+target frames, binds every transport to its exact native recipe, and separately
+counts both literal wrappers of each recipe. It imports no predecessor Python
+implementation.
+
+| Source scope | Events | Native transports | Native rank sum | ADDs |
+| --- | ---: | ---: | ---: | ---: |
+| Backward producer dependency cone, a subset of the next row | 257 | 200 | 354 | 57 |
+| All retained internal work before event 2025 | 412 | 355 | 509 | 57 |
+| Collector events 2025–2039 | 15 | 2 | 14 | 11 |
+| Retained internal work after collector through 4516 | 149 | 35 | 58 | 114 |
+| **Internal total** | **576** | **392** | **581** | **182** |
+| **All outgoing ports** | **675** | **0** | **0** | **675** |
+| **Open-program total** | **1251** | **392** | **581** | **857** |
+
+The collector's zero and erase account for the two non-ADD/non-transport events.
+The 257-event producer is not added again to the 576-event total. In particular,
+`257 + 15 + 149` misses 155 retained precollector transports needed by the
+complete internal paths and their ports.
+
+| Port source and destination | Calls | Coefficients |
+| --- | ---: | --- |
+| `Y` to external `D` | 348 | signed quarters |
+| `Y` to external `Q` | 171 | signed quarters |
+| `G` to external `X` | 104 | 52 coefficients `-2`, 52 coefficients `+2` |
+| Initial `Q7` to external `X`, events 492–543 | 52 | 39 coefficients `-2`, 13 coefficients `+2` |
+| **All ports** | **675** | **220 coefficients `+1/4`, 299 coefficients `-1/4`, 91 coefficients `-2`, 65 coefficients `+2`** |
+
+There are 83 distinct external target names: 24 `D`, seven `Q`, and 52 `X`.
+These names are an interface inventory, not evidence that 83 fresh owned banks
+exist or that their storage/routing is free. Their exact chronological records
+and hashes are retained in the cost receipt.
+
+## 3. Direct logical schedule and counts
+
+The schedule uses 512 Gaussian coordinates per bank. A rank-`r` native call
+executes `256*r` credited signed-floor pairs, with the actual archived right
+wrapper followed by the native stages and the actual archived left wrapper.
+Each pair has eight real add/subtract operations, four real floor halvings,
+one Gaussian quarter turn and four real-component reads and writes. Each
+wrapper uses Tekalign's separately specified one-zero-scratch cycle schedule:
+`512 + number_of_cycles` Gaussian swaps and 512 unit-phase applications.
+These are direct logical counts, not the Turing-machine price of indexed
+array access or of a recursive child.
+
+Every field ADD reads both source and destination and writes the destination.
+A signed-quarter ADD forms each quotient with two exact real halvings per
+component, without mutating its source. A doubled-source ADD additionally
+performs one real doubling per component. Phase operations and doublings are
+listed separately so a later physical implementation can assign their tariff
+without double counting them as ordinary additions.
+
+| Direct logical work for all 1251 retained events/ports | Count | Status |
+| --- | ---: | --- |
+| Signed-floor Gaussian pair applications | 148,736 | Exact source count |
+| Real additions/subtractions in native pairs | 1,189,888 | Exact for the stated schedule |
+| Real floor halvings in native pairs | 594,944 | Exact for the stated schedule |
+| Gaussian quarter turns in native pairs | 148,736 | Exact for the stated schedule |
+| Actual wrapper executions | 784 | Exact source count |
+| Wrapper cycles | 23,822 | Exhaustively counted from pinned affine maps |
+| Wrapper Gaussian scratch swaps | 425,230 | Constructive cycle schedule |
+| Wrapper unit-phase applications, including identity cases | 401,408 | Constructive cycle schedule |
+| Field ADDs, including every outgoing port | 857 | Exact source count |
+| Real additions/subtractions in these ADDs | 877,568 | Exact for the stated schedule |
+| Extra real doublings for 156 doubled-source ADDs | 159,744 | Exact for the stated schedule |
+| Exact real halvings for 675 signed-quarter ADDs | 1,382,400 | Exact for the stated schedule |
+| **Total real additions/subtractions, before doublings** | **2,067,456** | Exact for the stated schedule |
+| **Total when each doubling is one real addition** | **2,227,200** | Same schedule, alternative tariff convention |
+
+The direct component traffic is also retained: native pairs use 594,944 reads
+and as many writes; wrapper swaps use 1,700,920 reads and as many writes; field
+ADDs use 1,755,136 reads and 877,568 writes. Source reads are a subtotal of field
+ADD reads, not an additional charge. Phase transformations act on the loaded
+scratch value. Private `C` has 1,024 component initializations and 1,024 final
+zero inspections. Semantic restoration of its value is a separate proof; a
+frame-consistent erase instruction alone does not prove zero.
+
+The core reference schedule holds `63*512 = 32,256` Gaussian state words,
+512 private `C` words, one Gaussian wrapper scratch and four real pair-work
+words. Its external target access is a port obligation. No physical owner
+identity, dirty helper reuse or independently restored alias is inferred from
+these array slots. A 512-entry wrapper plan may be compiled one wrapper at a
+time, giving `O(784*512*9^2)` Boolean/control setup operations and `O(512)`
+temporary plan entries in this direct indexing model. Setup, plan storage,
+bit widths and address access are not zero-cost physical operations.
+
+### A conservative width bound for the complete internal program
+
+Let `H >= 0` be an integer bounding the absolute value of every initial real
+component of the 63 admitted physical arrays, measured in common-grid integer
+numerators. Each initial Gaussian array has Euclidean norm at most
+`sqrt(2*512)*H = 32H`. Every native wrapper is a permutation followed by unit
+Gaussian phases, and every coordinate `C` is unitary. Thus every partial
+native prefix preserves that norm. The separately proved domain admission
+identifies the literal floor word with these ideal prefixes.
+
+Assign every initial bank a rational envelope `w=1`, in units of `32H`, and
+assign the owned zero `C` envelope zero. A transport preserves `w`; an internal
+ADD uses `w_target <- w_target + abs(coefficient)*w_source`. This triangle
+bound deliberately ignores every cancellation. The exact source scan gives
+maximum internal weight **49**, first attained at `G27` event 4165, and maximum
+outgoing increment weight **50**, first attained at the `X28` port at 3250.
+Therefore every internal payload component is bounded by **1568H**, and every
+individual port increment component by **1600H**.
+
+For the literal signed-floor pair, put `B=1568H`. If both input components
+have absolute value at most the integer `B`, the difference has bound `2B`,
+each signed floor of half that difference has bound `B`, the midpoint has
+bound `2B`, the second output formula has bound `3B`, and the first output
+formula has bound `5B`. Quarter rotation only swaps and negates components.
+This proves the sufficient internal pair-work bound **7840H** without treating
+negative division as truncation toward zero. A common signed core width `h`
+with `2^(h-1)>7840H` is sufficient for these numerical values and arithmetic
+temporaries. These are conservative bounds, not measured or minimal widths.
+
+An outgoing target is different: if its current component bound is
+`H_target`, the ADD requires capacity for `H_target+1600H`. That current bound,
+its external intervening updates and its physical storage remain caller
+obligations. The increment bound is not a bound on the complete target. Actual
+numerical values on grid `2^-f` scale all these numerator bounds by `2^-f`.
+
+## 4. Complete obligation ledger for a physical join
+
+| Term | Current evidence | Remaining condition or charge |
+| --- | --- | --- |
+| Actual producer dependence and source reads | Source-bound 257-event cone; 58 initial dependencies | This is a sufficient input contract, not an arbitrary-input admission theorem |
+| All 52 strengthened `Y` sources | Initial `4B9` is sufficient; native maps preserve the scaled module | An ordinary-input producer must prove it supplies `4B9`, or supply and pay for a map that changes the inputs and its consumer intertwiner |
+| Six dirty producer entrances and five dirty `G` entrances | Declared initial `B9`, with actual empty initial frames | Caller-derived admission and ownership remain to be supplied |
+| Internal arithmetic, private collector, downstream restoration | Exact admitted-domain theorem and finite source-bound checks in the producer/consumer work | The frame-path and literal-value certificates must be retained; no claim follows merely from equal final frame labels |
+| Native pair, wrapper, quarter and ADD execution | Counts above for a specified direct logical schedule | All-size physical lowering at the actual layout/grid/widths is not established by these counts |
+| 675 outgoing read ports | Every exact source, coefficient, frame and event is retained and charged | Recipient availability, current value/width, later consumer admission and external history remain caller obligations |
+| Common grid and finite signed width | Constructive bounds `1568H` for internal payload, `7840H` for pair work and `1600H` for each outgoing increment | Actual entrance `H`, current external target widths, grid/field layout and physical guard/storage instantiation remain caller obligations |
+| State storage and protected scratch | Constructive numerical array inventory | Physical tapes/records, owner map, alias exclusions, source borrowing, returned work and resident backing storage remain unproved |
+| Codec or adapter work | Explicit encoder/decoder per-bank counts are known | Actual conversions at exposed boundaries, required copies and cleanup depend on the chosen external contract |
+| Input-independent setup and control | Direct finite wrapper-plan construction has the bound above | Compiling/retaining/routing the actual physical descriptors and handling all caller rows is additional work |
+| Recursive children and remaining coverage | Existing fixed-consumer profile/coverage test is inherited below | A changed profile needs its own complete bill; the 581 local rank sum is not a replacement for the full nine-call histogram |
+| Outer multiplication transfer | None supplied by this local result | Complete corrections, chronological hosting, physical supplier admission and the transfer theorem remain separate obligations |
+
+In symbols, a completed same-map bill must retain
+
+`C_join = C_admission + C_adapter_in + C_setup + C_internal + C_ports`
+`       + C_adapter_out + C_width/routing + C_owned_storage/cleanup`
+`       + C_recursive + C_external_completion`.
+
+These symbols are categories of obligations, not terms all measured in the
+same unit. The direct logical vector above specifies part of `C_internal` and
+`C_ports`. A physical time or space theorem must give each term a compatible
+cost model and avoid overlapping charges. Unknown terms have not been assigned
+zero. An identical operation stream at identical widths and layouts can be
+cancelled from a comparison with the same reference caller; arithmetic identity
+alone does not justify that cancellation.
+
+## 5. When persistent coordinates remove conversions
+
+The current positive contract may keep its admitted physical `B9`/`4B9` values
+through producer, collector and consumer: no mathematical encode/decode occurs
+between those operations. This is valid because admission is an explicit
+entrance premise, not because arbitrary inputs can be renamed as lattice
+values for free.
+
+A coefficient-state implementation can likewise compose integral
+intertwiners. If maps `A` and `B` have the same intermediate codec `E`,
+
+`(E^-1 B E)(E^-1 A E) = E^-1 B A E`.
+
+The intermediate pair cancels only when both implementations agree on the
+actual representation, common grid, frame/address layout, ownership and
+intermediate observation contract. A source port, restored borrowed copy,
+different grid or externally visible intermediate physical value can require
+an adapter that this identity does not remove. The raw-coordinate map and
+the conjugated map must still be named separately.
+
+For reference, a nine-bit in-place encoder has 2,304 pairs: 9,216 real
+add/subtracts, 9,216 component reads and 4,608 writes. Its decoder has the same
+counts plus 4,608 exact real halves. Encoding and decoding 63 mutable banks
+once each would therefore add 1,161,216 real add/subtracts, 290,304 exact real
+halves, 1,161,216 reads and 580,608 writes. This conditional reference does
+not prepare `4B9` from arbitrary values, does not handle the 83 external target
+interfaces, and does not copy/restore borrowed inputs. PR3382's six-bank cold
+codec is not the price of this larger source contract.
+
+## 6. Conditional stop for the unchanged outer consumer
+
+This section restates an existing obstruction; it is not a new P104 barrier.
+Jose Manuel first posted the finding in
+[Discussion2619 comment18955566](https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18955566).
+Vasek (`flyingviper`) source-bound and audited it in
+[PR2744](https://github.com/CrocSwap/integer-mult-bounds/pull/2744), head
+`0166260409f55a56e7fefa48d859f7dd5b42b300`. The new local representation proof
+does not supply a change to the following frozen profile or coverage premises.
+
+Fix width `m=73`, `W=832` original live families, five calls of the PR2458
+forward profile and four calls of either the PR2712 or PR2725 dual profile.
+The rank-one through rank-eight profiles are
+
+| Profile | Counts H1 through H8 | Rank mass |
+| --- | --- | ---: |
+| PR2458 forward | `(1216,74,86,104,48,42,68,8)` | 3070 |
+| PR2712 dual | `(1498,60,74,92,58,56,92,8)` | 3542 |
+| PR2725 dual | `(1502,58,74,93,57,56,91,9)` | 3542 |
+
+Grant every call all `104*8 + 104*8 + 150*9 = 3014` persistent endpoint units.
+Each original family has exactly one unpaid coordinate; private lifetimes
+give no extra persistent credit. Remaining paid coverage, carried collectively
+by whatever correction/helper/residual/idle children realize it, is at least
+
+`I = 72*832 - 9*3014 = 32778`.
+
+Assume every positive child rank is at most 73, all other charges are
+nonnegative, and every finite number `B >= 0` of auxiliary banks is fully
+paid: each adds 73 units of required coverage and one family to the denominator.
+For `0 <= a < 1` and `0 < r <= 73`,
+
+`(r/73)^(1-a) >= r/73`.
+
+Consequently the normalized moment of this frozen consumer obeys
+
+`M_B(a) >= [5*3070 + 4*3542 + 32778 + 73B] / [73(832+B)]`
+`       = 1 + 1560 / [73(832+B)] > 1`.
+
+At `B=0` the bound is exactly `599/584`. No unknown nonnegative admission,
+codec, port, routing, cleanup or physical cost can turn this lower bound into
+a successful `<1` screen. Fully paid storage cannot repair it either; the
+positive margin gets smaller with larger finite `B`, but remains positive.
+The small rational checker includes the failure control `B=22`: adding only
+the denominator falsely gives `62296/62342 < 1`; paying the bank coverage gives
+`63902/62342 > 1`.
+
+This stop applies **only** while those exact profiles, call counts, width and
+coverage law are retained. It does not exclude an actual coarsened/resynthesized
+word, changed consumer, changed native-child interface, or replacement coverage
+theorem. It does not derive a full consumer from this local source projection.
+For the present unchanged-profile route, the family decision is to finish and
+retain the producer/consumer contract, then stop supplier/owner expansion aimed
+at a new selected saving. Reopen only for a concrete changed premise with a
+new same-map, fully charged candidate bill that first survives its favourable
+screen. Passing such a relaxation would justify the next bounded admission
+experiment, not certify a supplier.
+
+## 7. Physical context retained without importing its conclusion
+
+Jose Manuel's
+[PR3087](https://github.com/CrocSwap/integer-mult-bounds/pull/3087), head
+`e7e49fb8176772c71ad7006920a407109a89e440`, supplies a source-relative physical
+Gaussian-monomial refinement. Its common grid, signed-width guard, complete
+outer rows/spectators, record encoding, protected outputs, clean work, ordinary
+child assumptions and long-record regime must be instantiated before applying
+its asymptotic tariff. A 512-coordinate numerical fixture does not establish
+those hypotheses. The wrapper counts here give inputs to such an eventual
+bill, not its conclusion.
+
+Jose Manuel's
+[PR3131](https://github.com/CrocSwap/integer-mult-bounds/pull/3131), head
+`0c9e344d5a5295a218558fa4a51d867f39ff5311`, prices a dense **paired** floor
+collector under its specified batching, residue-history, physical layout and
+source assumptions. Its return uses the paired inverse. This task executes
+every independently archived return recipe; in particular, PR3382 already
+showed that its local actual `V` has 416 wrapper cycles/2,464 swaps across the
+four wrappers, while the paired-inverse substitution has 384/2,432. A tariff
+for the latter is not a byte-level implementation of the former on arbitrary
+states. Domain-specific equality needs its own preserved proof and invoice.
+
+The inspected pending
+[PR3385](https://github.com/CrocSwap/integer-mult-bounds/pull/3385), frozen head
+`7e5a187214126d31afc241a8f89f4a652352b58c`, joins the selected physical complex
+controller/root-return contracts under its own exact source identities,
+chronological hosting, word/profile, common grid, guard, field layout,
+ordinary `B1/C0` children and physical-refinement hypotheses. This is valuable
+context for what a complete bill contains. It does not authorize substituting
+this new P104 open program or restricted initial module into that selected
+controller for free. We did not replay or newly audit its all-size theorem or
+hosted CI, and do not treat it as established admission of our 63-bank caller.
+
+## 8. Sources, credit and reproducibility
+
+The principal authenticated scientific bytes are:
+
+| Input | SHA256 | Exact role |
+| --- | --- | --- |
+| `research/p104-rounded-collector/inputs/WORD.json` at main `6f100d4...` | `cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50` | Actual producer, internal path and outgoing reads |
+| `research/p104-rounded-collector/inputs/NATIVE.json.gz` at the same main | `ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d` | Every literal native recipe and wrapper |
+| `research/p104-consumer-budget-audit/README.md` at the same main | `13694215d0c1a245b392f7155e8395b9c4bad9c5db3558833c784d9449616417` | Inherited frozen-profile and coverage hypotheses |
+| PR3382 `PROOF.md` at `2834523b1cd4ea83ba7a043e2e2f5f3332cf9909` | `1ca8c0e7e78f0f39de6cff7accc68ccd3901bfb50759bf7a2e2896bcf63bf081` | Module, direct logical codec and actual-`V` boundary |
+
+[SOURCES.json](SOURCES.json) records the immutable runtime and retained
+predecessor inputs, including their exact commits and byte hashes. Its
+`context_sources` rows separately identify the inspected physical-context
+proofs and manifests by immutable commit and hash. These context sources are
+not imported by the verifier and need not be downloaded to replay this
+package. PR3385's inspected bytes were checked against their advertised Git
+blobs; that contextual check does not admit its theorem for this caller.
+
+Predecessor credit remains with ywz65's corrected dual word and native data;
+Arham Tahir's retained first-collector binding; Tekalign (`tekuuu`) for the
+literal pair, cycle algorithm and logical ledger in PR3025, head
+`a544ef068a46f4de3bc47d1d02149cbdc3ba547f`; Ross Richardson's PR3068 period
+contract, head `7d2c519a1fdcc6bf66f6f08757eed7c48762d3f2`; PR3382's proved
+phase-complete module and interface; Jose Manuel's original budget finding;
+Vasek's PR2744 audit; and the physical contributors preserved in the context
+manifests. The frozen profile heads are PR2458
+`3170afd2fc13a990bfe28f5ab6421bcda4ffd0f6`, PR2712
+`afa5d6649460dcdb93489babd74f0ee9d01a4911`, and PR2725
+`71d24b655c2fdddc063b9aaf285e8425ce197499`. Their alternative retimings are
+not combined. The new cost work is the complete actual open-path inventory and
+its interface audit, not a new origin claim for these algorithms or the
+`599/584` obstruction. Substantial AI assistance is disclosed.
+
+From the repository root, reproduce the source-bound producer, consumer,
+independent checks and complete cost audit with:
+
+```sh
+python3 -B research/p104-newton-interfaces/verify.py
+python3 -B -O research/p104-newton-interfaces/verify.py
+```
+
+The same commands apply at the root of the source-complete export, whose
+retained files preserve their repository-relative paths. The verifier binds
+the source and implementation bytes recorded in [SOURCES.json](SOURCES.json)
+and [RECEIPT.json](RECEIPT.json); its replay contract is in
+[VERIFY.json](VERIFY.json). It requires standard-library Python, with no Git,
+network or native compilation during replay.
+
+The separately callable `cost_audit.source_audit(source_root)` authenticates
+the three cost inputs listed in that module and reconstructs only the source,
+frame, operation and rational-bound evidence. The package verifier also runs
+the separate semantic producer/consumer and independent array/path checks;
+the cost-only function does not implicitly claim those proofs were executed.
diff --git a/research/p104-newton-interfaces/CONSUMER.md b/research/p104-newton-interfaces/CONSUMER.md
new file mode 100644
index 0000000000..6b06712c71
--- /dev/null
+++ b/research/p104-newton-interfaces/CONSUMER.md
@@ -0,0 +1,450 @@
+# Actual P104 downstream interface and frame-path closure
+
+Prepared by Clear1nsight, with substantial OpenAI assistance.
+
+## 1. Scope and frozen sources
+
+This proof follows the actual arithmetic surrounding the first P104 collector
+through **zero-based event 4516**. Its numerical state consists of the following
+63 persistent Gaussian arrays, each with 512 entries:
+
+- `Y22` through `Y32`, and `Y63` through `Y103`: 52 banks;
+- `D27` through `D31`: five banks;
+- `Q7`: one bank;
+- `G27` through `G31`: five banks.
+
+The owned private bank `C` exists only during events 2025–2039. Every write to a
+named persistent bank depends only on these banks or `C`. The selected state
+therefore has a closed chronological numerical evolution. All 675 ADDs which
+read these banks and write other banks remain explicit outgoing ports, with
+their event, target, coefficient, frame and initial-input row retained.
+
+The resulting object is an **open interface program**, not a claim to have
+numerically executed the entire 4,517-event prefix. Other writes and native
+transports of external banks remain outside this proof. In particular, no
+initial or terminal contract for the external `X` banks is inferred merely
+from their appearances as recipients.
+
+The source bytes are the PR2586 word and recipes retained by the rounded
+collector archive on canonical commit
+`6f100d4bb5083f8c35d96fd95a539811c62f245c`:
+
+| Input | SHA256 |
+|---|---|
+| `research/p104-rounded-collector/inputs/WORD.json` | `cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50` |
+| `research/p104-rounded-collector/inputs/NATIVE.json.gz` | `ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d` |
+
+The literal chart is
+`Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)`. Write
+
+\[
+ O=[256,136,64,40,16,4,2,1],\qquad Q=[364],\qquad
+ F=[256,128,64,32,16,8,4,2,1].
+\]
+
+The selected 576 state events consist of 392 native transports with total rank
+581, 182 ADDs, one private allocation and one erasure. They include the minimal
+257-event producer and the 15-event collector. These pieces must not be added
+to the 576-event bill a second time.
+
+## 2. Admitted initial states and real quarter sites
+
+Let \(\pi=1+i\) and retain PR3382's Newton module
+
+\[
+ \mathcal B_9=E\mathbb Z[i]^{512},\qquad
+ E=\begin{pmatrix}1&0\\1&\pi\end{pmatrix}^{\otimes9}.
+\]
+
+The strengthened initial contract is
+
+\[
+ Y_j^0\in4\mathcal B_9\quad(j\in\mathcal Y),\qquad
+ D_j^0,Q_7^0,G_j^0\in\mathcal B_9,
+\]
+
+where \(\mathcal Y=\{22,\ldots,32\}\cup\{63,\ldots,103\}\).
+Every one of these 63 initial physical frames is the empty frame. The D, Q and
+G arrays can be independently dirty within this contract.
+
+PR3382 proves that the actual Gaussian butterfly, its inverse and the source's
+affine address/quadratic phase wrapper alphabet are automorphisms of
+\(\mathcal B_9\). Consequently they also preserve \(4\mathcal B_9\).
+The executable here independently checks the actual wrapper schema and source
+convention, and executes the signed-floor arithmetic without importing
+PR3382's executable model.
+
+Every Y bank is transport-only throughout this word: it is never an ADD
+destination. Thus admission at a named later quarter site is tied to a real
+initial bank. For example, `Y103` is transported at events
+
+\[
+ 207,980,1088,1184,1315,1470,1645,1834
+\]
+
+before it reaches frame F. Its first relevant downstream quarter is
+
+```
+2162: D28 -= Y103 / 4    at F
+```
+
+and its first quarter into Q7 is
+
+```
+4174: Q7 -= Y103 / 4     at F.
+```
+
+For either site, the exact condition is
+
+\[
+ Y_{103}^{\rm current}\in4\mathcal B_9
+ \quad\Longleftrightarrow\quad Y_{103}^{0}\in4\mathcal B_9.
+\]
+
+This equivalence uses the actual path's bijective restriction to
+\(4\mathcal B_9\),
+not a mere forward sufficient bound. When the target is already in
+\(\mathcal B_9\), its quarter update remains in \(\mathcal B_9\) if and only
+if this source condition holds. Componentwise divisibility by four alone is
+weaker than this Newton-module condition.
+
+The same 52 initial Y banks supply all 52 producer quarter reads, all 52 D
+cleanup quarters and all 52 Q7 cleanup quarters. Every outgoing quarter port
+also has an admitted Y source. Thus this stronger *real initial contract*
+supports the later operations; no new preparation is silently inserted at
+event 2162 or 4174.
+
+## 3. Exact authentication of the actual frame paths
+
+Cancellation across different frame paths cannot be inferred from equal frame
+labels. The checker proves a finite operator certificate for all 392 native
+occurrences in the selected state program.
+
+Use Gaussian Pauli operators
+
+\[
+ P(u,v,k)|x\rangle=i^k(-1)^{v\cdot x}|x\mathbin\oplus u\rangle.
+\]
+
+For a source wrapper
+
+\[
+ W|x\rangle=i^{s(x)}|Ax+b\rangle,
+ \quad
+ s(x)=p+\sum_j\ell_jx_j+2\sum_{j<k}q_{jk}x_jx_k\pmod4,
+\]
+
+the address matrix is checked invertible over \(\mathbb F_2\). Only the strict
+upper triangle \(j<k\) of `quadratic_rows` is used. Diagonal and lower-triangle
+bits in the archive are not additional phase terms.
+
+The conjugated Pauli has
+
+\[
+ u'=Au,\qquad
+ \widetilde v=v+(\ell\bmod2)\odot u+Q_{\rm off}u,
+ \qquad v'=A^{-T}\widetilde v,
+\]
+
+\[
+ k'=k+s(u)-s(0)+2v'\cdot b\pmod4.
+\]
+
+For every Pauli encountered during the path proof, the implementation also
+checks this formula directly at all 512 basis addresses using the wrapper's
+captured permutation and phase values. This is a separate finite check of the
+formula used in the certificate.
+
+For the source butterfly C on bit j,
+
+\[
+ C X_j C^{-1}=X_j,\qquad C Z_j C^{-1}=-iX_jZ_j,
+\]
+
+so its action is \(u_j\leftarrow u_j+v_j\),
+\(k\leftarrow k+3v_j\pmod4\), with v unchanged. The right wrapper,
+coordinate butterflies and left wrapper are composed in the literal source
+order.
+
+The algorithm starts with the identity operator at the empty frame. When a
+new frame is first encountered, its exact operator is represented by a path
+of source native events. At every later occurrence of an already represented
+frame, it checks both:
+
+1. identical conjugation images of the 18 generators \(X_j,Z_j\);
+2. identical images of the nonzero anchor vector \(|0\rangle\), evaluated
+   with exact Gaussian numerators and powers-of-two denominators.
+
+These two conditions prove equality of the full 512-dimensional operators.
+Indeed, the ratio of two invertible operators with equal generator actions
+commutes with all Z generators, so it is diagonal, and commutes with all X
+generators, so all diagonal entries are equal. Equal nonzero anchor images
+then fix that scalar to one. A global phase cannot be discarded.
+
+The source certificate covers 163 distinct frames, 392 occurrences and 230
+redundant path equalities. In particular it covers the actual U at 2031 and
+the separately archived V at 2033, every producer path, and all later Y, D,
+Q7 and G paths. A legal-shaped mutation multiplying the actual return
+wrapper's global phase by i leaves all Pauli actions unchanged and is
+rejected by the anchor comparison.
+
+Let \(A_H\) be the resulting exact native path operator from the empty frame
+to a frame H. The finite certificate establishes
+
+\[
+ T_{H\to K}=A_KA_H^{-1}
+\]
+
+for every selected occurrence. This defines and authenticates the frame
+potentials used below. The source's broader geometric interpretation in terms
+of \(\Delta_H\) remains inherited from its compiler lineage; this finite
+certificate does not independently rebuild that compiler for arbitrary frames.
+
+## 4. What the actual producer, collector and later consumer restore
+
+The exact path certificate permits the induction
+\(\text{physical state}=A_{\text{current frame}}\,\text{logical row}\).
+A native event changes its frame potential and leaves the row unchanged; an
+ADD at a shared frame performs the same scalar row addition; zero and erase
+create and remove the literal zero row. Thus the following row calculations
+describe the actual physical state for every admitted input, independently
+of the dense numerical fixture.
+
+Put
+
+\[
+ s=\frac14\sum_{j\in\mathcal Y}Y_j^0.
+\]
+
+Each selected Y source is read once into exactly one of the five D banks in
+the producer. Write \(\mathcal Y_j\) for that source partition. Its sizes for
+D31, D30, D29, D28 and D27 are respectively 3, 7, 7, 11 and 24.
+
+The exact source frame paths and ADD rows give the collector entrance
+
+\[
+ D_j^{\rm entrance}=A_O\left(D_j^0+rac14\sum_{h\in\mathcal Y_j}Y_h^0\right),
+ \qquad
+ Q_7^{\rm entrance}=A_Q\left(Q_7^0-\sum_{j=27}^{31}D_j^0\right).
+\]
+
+Therefore the literal collector's endpoint is
+
+\[
+ Q_7^{\rm collected}=A_Q(Q_7^0+s),\qquad C=0,
+\]
+
+with its five sources unchanged during the collector. This statement uses the
+actual archived U/V composition authenticated above.
+
+The subsequent D cleanup quarters exactly reverse each D bank's producer
+source list. Their last events are:
+
+| Bank | Quarter count | Last cleanup event |
+|---|---:|---:|
+| D31 | 3 | 2213 |
+| D30 | 7 | 2279 |
+| D29 | 7 | 2308 |
+| D28 | 11 | 2390 |
+| D27 | 24 | 2480 |
+
+At these endpoints, the corresponding physical bank is \(A_FD_j^0\).
+
+The first subsequent reads of collected Q7 are the five real unit ADDs
+3052–3056, into G27–G31 at frame Q. Each G bank has been transported from its
+independently dirty initial empty-frame state at events 3020–3024. Just after
+the reads it contains
+
+\[
+ G_j=A_Q(G_j^0+Q_7^0+s).
+\]
+
+The G arrays are subsequently read by actual X-target ports and transported
+through their distinct source frame paths. Q7 is transported to F at 4164;
+the five unit subtractions at 4165, 4167, 4169, 4171 and 4173 give
+
+\[
+ G_j^{\rm final}=A_FG_j^0.
+\]
+
+Finally Q7 subtracts each of the same 52 Y banks once at F, from event 4174
+through 4516, so
+
+\[
+ Q_7^{\rm final}=A_FQ_7^0.
+\]
+
+All 63 actual final physical frames are explicitly checked to be F. Every
+persistent bank consequently ends with its initial value transported by
+\(A_F\). Gauge-coordinate rows return to their initial rows; physical arrays
+are not claimed unchanged across different frames. The private C bank is
+checked literally zero before erasure.
+
+Changing the actual event 2162 from `-1/4` to `+1/4` preserves the stated
+lattice admission but leaves D28 with residual
+\(A_F(Y_{103}^0/2)\). The endpoint check rejects this source-shaped control.
+
+## 5. Every outgoing side effect remains visible
+
+The 675 chronological outgoing ADD ports comprise:
+
+| Actual read | Port count |
+|---|---:|
+| Y to other D banks | 348 |
+| Y to other Q banks | 171 |
+| G27–G31 to X | 104 |
+| Q7 to X before its producer changes | 52 |
+
+The last row consists of events 492–543. Omitting it would discard the dirty
+Q7 compensation and misstate the useful external map. There are no outgoing
+D reads to external banks in the chosen range.
+
+The verifier derives integer input rows using \(Y_j^0/4\) as Y symbols and
+the initial D/Q/G arrays as other symbols. Since frame paths have already
+been authenticated, every port at frame H has its exact physical increment
+
+\[
+ \delta_{e}=A_H\sum_b r_{e,b}z_b,
+\]
+
+where \(z_Y=Y_Y^0/4\), the other \(z_b\) are initial arrays, and
+\(r_{e,b}\in\mathbb Z\) is retained in the receipt. Its literal source
+coefficient and source array are also recorded. No unobserved callback or
+recipient history is substituted for this interface.
+
+For the X ports, summing these increments after applying their respective
+\(A_H^{-1}\) yields, for each of 52 distinct targets,
+
+\[
+ \sum_{e\to X_t} A_{H_e}^{-1}\delta_e
+ =\frac{\epsilon_t}{2}\sum_{j\in\mathcal Y}Y_j^0,
+ \qquad\epsilon_t\in\{+1,-1\}.
+\]
+
+There are 39 positive and 13 negative target signs. All dirty D, Q and G
+coefficients cancel. The **52-by-52 scalar bank matrix** has rank one; after
+expanding every array into 512 Gaussian entries, the corresponding map has
+rank 512 over \(\mathbb Q(i)\). The complete sign map is retained in the
+receipt. An independently written Fraction-row interpreter agrees with all
+2,704 coefficients, the 63 restored input rows and all 675 port indices.
+
+This is the frame-normalised outgoing port operator. A terminal X-bank claim
+would additionally require its actual omitted updates and transports to be
+composed with these ports. The other 519 Y ports remain separately retained;
+they are not removed from the interface or its bill.
+
+Each admitted port increment belongs to \(\mathcal B_9\), and is a Gaussian
+integer array. The ADD is therefore exact for an arbitrary Gaussian recipient.
+It preserves the recipient's membership in \(\mathcal B_9\) when that
+recipient is in \(\mathcal B_9\) at the read. Future native arithmetic on an
+external recipient needs its own domain proof. No claim about a recipient's
+initial state follows from this local conditional statement.
+
+## 6. The actual coefficient-coordinate maps
+
+If values are stored as encoded arrays \(Ec\), the actual logical map of a
+native frame operator A is
+
+\[
+ \widehat A=E^{-1}AE.
+\]
+
+Every admitted state or port row above then has coefficient map
+\(\widehat A_H\) applied to the corresponding initial coefficient row. Unit
+ADDs between two fields already in the same representation are unchanged.
+Quarter coefficients apply only after the required fourfold Newton
+divisibility is supplied.
+
+This map is explicit for an arbitrary captured wrapper. For a Boolean subset
+S and \(x_T=A^{-1}(1_T\oplus b)\), its Newton-coordinate action is
+
+\[
+ (\widehat Wc)_S=
+ \pi^{-|S|}\sum_{T\subseteq S}(-1)^{|S|-|T|}
+ i^{s(x_T)}\sum_{R\subseteq\operatorname{supp}(x_T)}\pi^{|R|}c_R.
+\]
+
+The native coordinate butterfly becomes the integer coefficient map
+\((a,b)\mapsto(a+b,ib)\). Composing these formulas in the captured right,
+butterfly and left order gives every real readout/transport intertwiner.
+
+For the actual empty-to-Q operator, the canonical path is event 972. Its
+complete 512-column integer matrix has 12,288 nonzero entries and maximum
+absolute real/imaginary component four. Its ordered JSON-column hash is
+`f6a4c95e33941a42fe2460195b9daee2d071f5396c9a441556e2f28e0e2076b3`.
+
+For the actual empty-to-F operator, path `[203,984,1233,1818]`, the independent
+Pauli-plus-anchor test proves the more explicit identity
+
+\[
+ A_F=(C^{-1})^{\otimes9},\qquad
+ E^{-1}A_FE=
+ \begin{pmatrix}1&i\\0&-i\end{pmatrix}^{\otimes9}.
+\]
+
+Its 512-column matrix has \(3^9=19683\) nonzero Gaussian-unit entries, with
+ordered JSON-column hash
+`727b837e10103ebda8ce33f8284f5204c317b2518a27f39e5e77d7413dfc2cfd`.
+
+The distinction between A and its conjugate is visible in the actual source
+map. On coefficient input \(e_0\), \((E^{-1}A_QE e_0)_0=1\), whereas
+\((A_Qe_0)_0=(1-i)/2\); 17 coordinates differ. Thus the representation is
+retained with its proved intertwiner. A caller requesting the unconjugated
+map on arbitrary coefficient inputs cannot identify the two.
+
+No encode/decode pair is needed at the producer/collector/consumer cuts when
+the fields already have this persistent representation. Supplying arbitrary
+external data through a new codec still requires a priced implementation and
+acceptance of the conjugated logical map. The narrower initial Y domain is
+not free preparation.
+
+## 7. Independent execution and remaining boundaries
+
+The checker imports no producer, PR3382 model or predecessor arithmetic
+module. Its executable derivations consist of:
+
+- exact source authentication and full-prefix frame/lifetime syntax;
+- the all-occurrence operator path certificate and phase-only rejection;
+- complete 512-column conjugated maps for the actual Q and F operators;
+- integer symbolic rows for every selected state event and outgoing port;
+- one chronological dense signed fixture on all 63 initial banks, including
+  every retained Y transport from its initial value;
+- 148,736 literal signed-floor versus independent exact-pair comparisons,
+  784 complete-wrapper domain checks, 581 complete-coordinate domain checks,
+  182 internal ADDs, 675 exact outgoing increment arrays and literal C erasure.
+
+The complete-coordinate checks occur after each coordinate's disjoint
+butterflies; complete-wrapper checks occur after each wrapper. Individual
+permutation-cycle intermediates need only be Gaussian integers, since no
+division occurs inside the wrapper. They are not separately claimed to be
+members of the global Newton module.
+
+The dense fixture's largest observed internal real/imaginary component is
+1122. This is an observation about that fixture, not a universal bit-width or
+physical precision admission. The operator identities and symbolic row proof
+quantify over all admitted initial arrays independently of this fixture.
+
+This establishes a real downstream representation contract and exact restored
+internal endpoint. It does not establish the complete P104 word, an external
+recipient's future domain, a physical allocation/routing implementation, a
+recursive caller or a favourable supplier moment. All 675 ports, storage,
+precision, control and cleanup obligations remain available to the separate
+whole-bill analysis.
+
+The final package verifier authenticates the sources and combines this
+consumer evidence with the producer, independent witness and bill checks:
+
+```sh
+python3 -I -B research/p104-newton-interfaces/verify.py
+python3 -I -O -B research/p104-newton-interfaces/verify.py
+```
+
+For a focused consumer replay, `consumer.py` accepts `--repo` and otherwise
+resolves the source root from its package location. Its optional `--output`
+path is created exclusively, so an existing receipt is never overwritten.
+
+Credit the ywz65/PR2586 native P104 word, Arham Tahir's retained rounded
+collector archive, Tekalign/PR3025's signed-floor and wrapper conventions, and
+the PR3382 Newton-module theorem and independent reconstruction. Classical
+Clifford/coding provenance and repository license/notice obligations remain
+as recorded in the frozen predecessor packages.
diff --git a/research/p104-newton-interfaces/PRODUCER.md b/research/p104-newton-interfaces/PRODUCER.md
new file mode 100644
index 0000000000..01c1369500
--- /dev/null
+++ b/research/p104-newton-interfaces/PRODUCER.md
@@ -0,0 +1,310 @@
+# Actual producer admission for the first P104 collector
+
+This note answers the producer question left by PR #3382. The actual source
+path can supply its numerical entrance under an explicit stronger initial
+contract. Admission from arbitrary initial lattice states is false: a single
+initial coordinate gives a source-bound counterexample, even though all
+arithmetic on that execution remains exact before the collector.
+
+The result is a conditional producer theorem and one reachable counterexample.
+It does not admit a complete P104 supplier, classify all possible final-cut
+cancellations, or supply physical access to the numerical banks.
+
+## 1. Exact source and dependency boundary
+
+The word and native recipes are ywz65's PR #2586, head
+`7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1`, retained in
+`research/p104-rounded-collector/inputs/WORD.json` and `NATIVE.json.gz`.
+Their SHA256 digests are respectively
+`cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50` and
+`ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d`.
+The referenced Gaussian model is the byte-identical PR #3382 `model.py`,
+SHA256 `74c83367887dd885137b222155c86389fe0be9f1293a6f0e5fdb51d71f435fdd`.
+This package retains it as [`inputs/pr3382_model.py`](inputs/pr3382_model.py),
+alongside its credited [`inputs/PR3382_PROOF.md`](inputs/PR3382_PROOF.md).
+The consolidated source manifest is `SOURCES.json`; source bytes are
+authenticated before the model is executed. The word and native inputs
+remain at their original repository paths in both the checkout and the
+portable source export.
+
+The collector starts at zero-based event 2025. An ADD record is
+`["add", destination, source, coefficient, frame]`. This direction matters:
+the appearances of Q7 at events 492–543 are reads into X targets, not writes
+to Q7. Backward dataflow from D31, D30, D29, D28, D27 and Q7 produces exactly
+257 events and 58 initial dependencies:
+
+- The five initial D banks and initial Q7.
+- Y22 through Y32 and Y63 through Y103: 52 initial Y banks.
+
+All 58 start at frame `[]`. The slice contains 200 actual native transports,
+of total native rank 354, and 57 ADDs: 52 positive quarter-source ADDs and
+five unit subtractions into Q7. There is no X, G or N dependency in these
+six numerical outputs.
+
+| Produced bank | Quarter source count | First quarter event | Last write before the cut |
+|---|---:|---:|---:|
+| D31 | 3 | 1090 | 1233 |
+| D30 | 7 | 1093 | 1395 |
+| D29 | 7 | 1177 | 1461 |
+| D28 | 11 | 1087 | 1643 |
+| D27 | 24 | 1157 | 1831 |
+| Q7 | 0 | — | 972 |
+
+Every one of the 52 Y banks is used exactly once by these five D targets.
+Each Y bank changes only by native transports before its required read.
+The complete event lists and source names are derived from the frozen word
+and retained in the receipt.
+
+Q7 subtracts the five *initial* D values at 908, 910, 912, 914 and 916.
+Each D bank's own initial transport follows its subtraction. Hence, writing
+`q` and `d_j` for initial values, its cut value is exactly the event-972 map
+applied to `q-sum(d_j)` whenever the stated admission condition holds.
+
+The five D outputs reach frame `[256,136,64,40,16,4,2,1]`, and Q7 reaches
+`[364]`. Frame checks establish the specified program boundary. They do not
+construct physical ownership or read permissions. The initial D and Q banks
+are mutable dirty inputs. The Y banks are also numerically transported; they
+cannot be charged as immutable borrowed raw arrays without a separate copy
+or representation contract.
+
+Only the six target outputs of a minimal backward slice are actual cut
+states. A sliced auxiliary Y bank stops at its last required read, even if
+the original word transports it later. A downstream execution must use the
+actual initial-to-cut Y transport, not that historical read state.
+
+## 2. The exact conditional theorem
+
+Put `pi=1+i` and use PR #3382's Gaussian Newton lattice
+
+\[
+ \mathcal B_9=\left\{f(x)=\sum_S a_Sx^S:
+                      \pi^{|S|}\mid a_S\right\}.
+\]
+
+The earlier proof establishes that every actual affine/quadratic Gaussian
+wrapper and every coordinate butterfly is a linear automorphism of this
+lattice. The literal signed-floor butterfly equals the ideal one on it,
+including negative integers. Thus each full literal native transport
+restricts to an automorphism of `B9`, and of `4B9`.
+
+**Producer theorem.** Assume the 58 initial numerical banks belong to
+`2^-f B9`, and the 52 listed Y banks belong to the stronger module
+`2^-f 4B9`. Keep their distinct program roles and declared frames. Then every
+relevant native stage and ADD is exact on the retained grid, every tracked
+bank remains in `2^-f B9`, and all six produced collector inputs meet
+PR #3382's numerical entrance contract.
+
+The initial D and Q values are arbitrary within the stated module; they
+need not be zero, small, independent, or uncorrelated. To prove the theorem,
+observe that each Y path preserves `4B9`, so its quarter is in `B9` at its
+actual read. An ADD of two lattice elements stays in the lattice. All
+native transports preserve it, and Q7's five initial subtractions preserve
+it. Induction through the extracted source order proves the claim.
+
+There is a sharp converse for this *prefix* invariant. Under the weaker
+assumption that all 58 initial banks are in `B9`, every tracked complete
+native stage and event remains in `B9` if and only if all 52 initial Y banks
+are in `4B9`. A complete native stage here means a complete wrapper or all
+disjoint butterflies on one coordinate. A physical permutation cycle's
+intermediate partially rearranged array is not asserted to lie in `B9`;
+its operations use Gaussian integers and contain no division.
+For necessity, take any quarter event. Its destination before and after the
+event is in `B9`, so their difference, the quarter source, must be in `B9`.
+Its source is therefore in `4B9` at that read. The source's preceding native
+path is an automorphism of both modules, so its initial value was in `4B9`.
+Every listed Y is read, proving the necessity of all 52 conditions.
+
+The 52 stronger source conditions are therefore sufficient for the six
+final-cut inputs and necessary for the stated prefix invariant. They are
+not asserted necessary for admission at only the final cut. Outside-lattice
+contributions can cancel after earlier bad prefixes.
+Neither such a cancellation domain nor arbitrary rounded executions are
+classified here. The quarter operation in this theorem is the exact scalar
+ADD appearing in the word; a componentwise rounded quarter is a different
+operation and has not been substituted.
+
+The encoder makes the positive contract constructive as a numerical
+representation: initial D and Q may be `E9*c`, and initial Y may be
+`4*E9*c`, for arbitrary Gaussian coefficient arrays. All conversion,
+preservation and eventual inverse-conversion costs remain part of the
+caller's bill. In particular the old six-field local codec does not prepare
+these 52 stronger Y sources for free.
+
+## 3. One-coordinate actual-source counterexample
+
+Set the original persistent input `Y27[0]=64`, and set every other initial
+component of all 358 persistent banks to zero. This is one explicit input
+choice, not a zero assumption about general dirty state. Its initial Y27 is
+`64*delta_0`. Every Newton coefficient of that impulse is `+64` or `-64`.
+Since `v_pi(64)=12` and every degree is at most nine, all initial banks lie
+in `B9`. But Y27 is not in `4B9`: the degree-nine condition would require
+valuation at least thirteen.
+
+The actual Y27 producer transports are events 131 and 1056, of ranks one
+and two. Event 1090 adds one quarter of their output into D31. For this
+fixture the division is componentwise integral, and every literal native
+pair in the producer cone agrees exactly with its ideal pair. Nevertheless
+the first lattice failure **in the 257-event producer cone** occurs at 1090:
+
+\[
+ S=349\quad(|S|=6),\qquad a_S=-4-4i,\qquad
+ v_\pi(a_S)=5<6.
+\]
+
+D31 subsequently receives zero from Y26 and Y99 and executes the actual
+transports 1092, 1131 and 1233. At the collector entrance its output has
+256 nonzero entries, each a Gaussian unit. A two-address witness suffices:
+
+\[
+ D31[8]-D31[0]=-1.
+\]
+
+This is its degree-one Newton coefficient at address bit three. It is not
+divisible by `1+i`, so D31 fails the entrance condition. The other four D
+inputs and Q7 are zero and satisfy it.
+
+There are two useful conceptual checks on this failure. First, an exact
+native transport is an automorphism of `B9`; applying its inverse to an
+admitted output would give an admitted input. Second, the unrestricted
+literal signed-floor pair is a bijection, with the credited negative pair
+as its inverse, and both restrict to lattice automorphisms. Consequently
+even an outside-lattice *literal* native cannot move a state into `B9`.
+The latter argument does not assume that unrestricted floors are linear.
+For this particular fixture, the stronger direct literal/ideal comparison
+also passes at every producer pair.
+
+Multiplying the input amplitude by four, to `Y27[0]=256`, gives a positive
+control. It starts in `4B9`; the whole producer cone remains admitted, and
+its D31 cut output is four times the negative fixture's output. Amplitude
+64 is a simple constructive witness, not a claimed minimum over all inputs.
+
+## 4. Why this witness can reach the cut
+
+A counterexample at a chosen read would not by itself show that the earlier
+word can supply that read on the retained grid. Here a small Gaussian
+valuation certificate establishes reachability for the explicit initial
+point through events 0–2024.
+
+If every component is divisible by `pi^k`, a Gaussian monomial wrapper
+preserves this property. Each coordinate butterfly has coefficients equal
+to Gaussian units divided by `pi`, so it loses at most one power. If the
+available lower bound is at least the native rank, every ideal stage stays
+Gaussian integral, and the literal floor implementation agrees with it at
+each stage. A quarter coefficient loses four powers. Exact zero banks have
+an infinite bound until a nonzero source is added; for additions take the
+minimum of the two source bounds. This is a conservative valuation argument,
+so cancellation can only improve it.
+
+Starting from valuation twelve in Y27, exactly 20 native occurrences and
+six quarter-source events are active before the cut. The latter are:
+
+| Event | Destination | Y27 cumulative native rank | Valuation lower bound after quarter |
+|---|---|---:|---:|
+| 1090 | D31 | 3 | 5 |
+| 1190 | D10 | 4 | 4 |
+| 1303 | D20 | 5 | 3 |
+| 1499 | D24 | 6 | 2 |
+| 1763 | D1 | 7 | 1 |
+| 1937 | D16 | 8 | 0 |
+
+Each listed D branch spends at most that remaining valuation in its later
+native stages and ends with a nonnegative lower bound. Y27's final native
+stage leaves bound three. Every fractional source in the full prefix is
+therefore exactly representable on this one execution; all other source
+banks remain zero. The certificate binds all 20 active native occurrences
+to their archived frames, ranks and actual wrapper alphabet, and checks
+the coefficients and unit signs of the entire prefix.
+
+This valuation certificate proves exact arithmetic and existence of this
+one prefix execution. It does not by itself prove lattice membership at
+the outside-cone events or a universal full-prefix admission theorem.
+
+There is also a separate direct replay in [`independent.py`](independent.py).
+It imports neither the producer or consumer checker nor the PR #3382 model.
+Starting from all 358 original persistent banks, it executes every event
+from 0 through 2024, authenticates all 883 native occurrences in that prefix,
+and tracks the actual states and frames. Exact-zero native inputs remain
+zero; the 20 active native occurrences require 6,144 independent literal
+signed-floor versus ideal pair comparisons. All six active quarter ADDs
+are checked componentwise integral, and every initial bank is independently
+checked for Newton membership.
+
+This replay passes and agrees with the producer on all six collector-input
+frames and array hashes. In particular its D31 output is
+`adde9450101abb38b9f2c225459b1068526a1fc6dede4957615e2b0ef5ed8a21`,
+with the same degree-one failure at mask 8. Its earliest failure in the
+**full 2,025-event prefix** is also event 1090, D31, coefficient `-4-4i`
+at mask 349. Thus the stronger full-prefix location is established by this
+separate replay; it is not inferred from the smaller producer slice.
+
+The negative example is consequently reachable on the retained exact grid
+from explicit admitted initial lattice states. This remains a one-point
+result. It does not claim general membership throughout the full prefix,
+execute the later events of the 5,398-event word, or establish a physical
+implementation.
+
+## 5. Reproduction, controls and limits
+
+`producer.py` exposes
+`verify_producer(word_path, native_path, model_path) -> deterministic JSON`.
+It uses standard-library Python and the authenticated PR #3382 model; no
+native compiler, Git, network, large search or predecessor test suite is
+needed. From the repository root, or the same root in the portable source
+export, run the package's dedicated verifier:
+
+```sh
+python3 -B research/p104-newton-interfaces/verify.py
+```
+
+The same obligations can be checked with assertions disabled:
+
+```sh
+python3 -O -B research/p104-newton-interfaces/verify.py
+```
+
+`VERIFY.json` records the package replay contract and `RECEIPT.json` records
+the consolidated execution, source bindings, environment and controls.
+This is a dedicated package workflow; it does not require registration in
+the repository's shared verification suite. The caller supplies the exact
+vendored model path to the producer API. `independent.py` supplies its separate
+full-prefix and symbolic-port evidence to the same consolidated verifier.
+
+The verifier extracts and checks the exact source order, frames and native
+recipes. It compares 90,624 literal/ideal pair obligations per fixture:
+one dense signed fixture with arbitrary dirty initial D/Q banks, the
+one-coordinate counterexample, and the amplitude-256 positive control.
+On admitted fixtures it also checks every native stage and event's lattice
+membership. Written invariance and necessity arguments establish the
+universal conditional theorem; those finite cases do not replace it.
+
+Small controls reject corrupt source bytes, a changed quarter coefficient,
+an omitted Y27 source, and swapped chronological source reads. Signed
+exact quarters are accepted, while a negative nonintegral quarter is
+rejected explicitly. All checks use exceptions and remain active with
+Python optimization. The frozen all-rank model's original broad tests are
+not repeated by this follow-up.
+
+The producer's three-fixture replay passes in both ordinary and optimized
+CPython 3.12.14, producing byte-identical proof-relevant child receipts. Each
+mode checks 271,872 pair obligations in total. The independent full-prefix
+replay supplies a different source-wide reachability check for the one
+counterexample, while the universal conditional theorem relies on the
+written invariant and its inherited all-rank lattice proof.
+
+The substantive answer is that a real source path is now bound, but its
+admission is a stronger input contract rather than a property of arbitrary
+lattice inputs. A complete caller must supply the 52 `4B9` states with their
+actual source access and prices, and a downstream consumer must preserve
+the requested logical map. The actual downstream contract is developed in
+[`CONSUMER.md`](CONSUMER.md), and the complete retained interface bill and
+conditional outer stop test are in [`COMPARISON.md`](COMPARISON.md).
+Any full physical or recursive improvement must include those obligations
+and the literal restoration bill.
+
+Prepared by Clear1nsight with substantial OpenAI assistance. Credit remains
+with ywz65 and the P104 native lineage, Arham Tahir's retained rounded
+collector archive, Tekalign's PR #3025 signed-floor bijection,
+Ross Richardson's PR #3068 exactness-domain question, and
+PR #3382's Gaussian Newton/Clifford proof and model. The new claims are the
+actual producer binding, its quantified stronger entrance condition, and
+the reachable one-coordinate counterexample. Apache-2.0.
diff --git a/research/p104-newton-interfaces/README.md b/research/p104-newton-interfaces/README.md
new file mode 100644
index 0000000000..ffee347d28
--- /dev/null
+++ b/research/p104-newton-interfaces/README.md
@@ -0,0 +1,327 @@
+# Actual P104 Newton producer and downstream interfaces
+
+This package answers the three explicitly assigned open questions of
+[PR #3382](https://github.com/CrocSwap/integer-mult-bounds/pull/3382), frozen
+head `2834523b1cd4ea83ba7a043e2e2f5f3332cf9909`. It binds the Gaussian Newton
+representation to the actual producer and downstream operations of the first
+P104 collector, proves the restored internal endpoint, retains every outgoing
+read, and gives the complete direct logical bill and its physical obligations.
+The selected frontier is unchanged.
+
+The presubmission overlap check found Nick Petalas's complementary
+[PR #3406](https://github.com/CrocSwap/integer-mult-bounds/pull/3406), exact
+head `18a054fd585ab4b2010770ec83cba0c9f28184e3`. It classifies the whole-word
+independent-product entrance, with 104 Y inputs in `4B9` and 78 N inputs in
+`2B9`, while retaining the native change-of-chart identities as a premise.
+It explicitly links our active local-interface claim. The new evidence here
+is the independently certified finite frame paths, actual producer and
+consumer join with every outgoing port, reachable exact counterexample, and
+complete direct bill. PR #3406 is credited pending context; its broader suite
+is not rerun or claimed as this package's result.
+
+| Assigned question | Answer on this scope | Evidence |
+| --- | --- | --- |
+| Can the actual producer supply the collector's `B9` entrance? | Yes when all 52 named initial Y banks are in `4B9` and the six dirty D/Q entrances are in `B9`. This condition is necessary and sufficient for the specified prefix invariant. Initial `B9` alone fails on an explicit reachable input. | [PRODUCER.md](PRODUCER.md) |
+| Can the actual downstream consumer preserve the representation and requested map? | Yes for the 63-bank open program through event 4516, with five additional dirty G inputs in `B9`, exact native frame paths and explicit coefficient intertwiners. External recipient histories remain separate. | [CONSUMER.md](CONSUMER.md) |
+| Does this establish an improved complete physical bill? | The direct logical bill and conservative internal widths are now explicit. Physical caller admission and tariffs remain open. The inherited unchanged five-forward/four-dual consumer still fails its favourable screen at `599/584`. | [COMPARISON.md](COMPARISON.md) |
+
+## Source and exact boundary
+
+The scientific base is canonical main
+`6f100d4bb5083f8c35d96fd95a539811c62f245c`. The actual word and native recipes
+come from ywz65's [PR #2586](https://github.com/CrocSwap/integer-mult-bounds/pull/2586),
+head `7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1`, retained in
+`research/p104-rounded-collector/inputs/WORD.json` and `NATIVE.json.gz`.
+[SOURCES.json](SOURCES.json) pins these bytes, the copied PR #3382 model/proof,
+the budget source and the contextual predecessors.
+
+Every bank has 512 Gaussian entries indexed by nine bits. The source chart is
+`Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)`. All event numbers below are
+zero-based. Put
+
+\[
+ \mathcal Y=\{22,\ldots,32\}\cup\{63,\ldots,103\},\qquad
+ \pi=1+i,
+ \qquad E=\begin{pmatrix}1&0\\1&\pi\end{pmatrix}^{\otimes9}.
+\]
+
+PR #3382's module is
+\(\mathcal B_9=E\mathbb Z[i]^{512}\), equivalently the arrays whose Newton
+coefficient at subset \(S\) is divisible by \(\pi^{|S|}\). The actual
+butterfly and affine/quadratic Gaussian wrapper alphabet preserve it. We use
+one common grid `2^-f`; the formulas below use its Gaussian integer numerators.
+
+The admitted persistent state is:
+
+| Initial banks, all at frame `[]` | Count | Numerical domain |
+| --- | ---: | --- |
+| `Y22`–`Y32`, `Y63`–`Y103` | 52 | `4B9` |
+| `D27`–`D31`, `Q7` | 6 | Arbitrary dirty `B9` |
+| `G27`–`G31` | 5 | Arbitrary dirty `B9` |
+
+Private `C` is owned zero at event 2025 and literally zero before erasure at
+2039. The 63 persistent banks undergo **576 actual internal events** through
+4516. Every outgoing read is retained as one of **675 ADD ports**, giving
+**1,251 retained events and ports**. The omitted external histories are not
+numerically executed by this open program. No physical ownership or aliasing
+permission follows merely from these distinct numerical bank names.
+
+## 1. The producer theorem and a reachable failure
+
+Backward dataflow from the five D entrances and Q7 at event 2025 gives a
+**257-event dependency cone**, with 58 initial dependencies, 200 native
+transports of total rank 354, 52 quarter ADDs and five initial-D subtractions
+from Q7. Each named Y bank is read once into exactly one of the five D banks;
+the D31/D30/D29/D28/D27 source group sizes are **3, 7, 7, 11 and 24**.
+
+The actual Y paths are invertible on both `B9` and `4B9`. Their quarter
+contributions therefore lie in `B9` exactly when the corresponding initial
+Y belongs to `4B9`. With initially admitted D/Q banks, all 52 stronger Y
+conditions are necessary and sufficient for membership after every tracked
+event and completed native layer. This is a prefix-invariant characterisation;
+it does not classify additional final-cut admissions obtained by cancellation.
+
+The weaker initial contract is false even when arithmetic remains exactly on
+the grid. Set **`Y27[0]=64`** and every other initial component of all 358
+persistent source banks to zero. Every initial bank lies in `B9`, while Y27
+fails `4B9`. The actual full prefix through event 2024 remains arithmetically
+exact. At the collector entrance,
+
+\[
+ D31[8]-D31[0]=-1,
+\]
+
+so its degree-one Newton coefficient is not divisible by `1+i`. This supplies
+an actual producer failure, rather than an arbitrary value invented at a later
+quarter site. The separately implemented full-prefix replay agrees with the
+producer's valuation certificate: **20 active native calls and six active
+quarter reads**. Amplitude 256 supplies the positive control.
+[PRODUCER.md](PRODUCER.md) gives the quantified theorem, precise source paths,
+counterexample and controls.
+
+## 2. The downstream endpoint, outgoing reads and actual intertwiners
+
+The consumer authenticates the operator paths for all **392 retained native
+occurrences**, covering **163 frames and 230 redundant path equalities**.
+It compares the exact action on all 18 Pauli generators and a nonzero dyadic
+anchor vector. The generator images fix an operator up to scalar; the anchor
+fixes its global phase. A changed return phase that preserves every Pauli image
+is explicitly rejected. Both literal archived U and V are covered.
+
+Let \(A_H\) denote the resulting source-bound operator from the empty frame
+to frame \(H\), and set
+
+\[
+ O=[256,136,64,40,16,4,2,1],\quad Q=[364],\quad
+ F=[256,128,64,32,16,8,4,2,1],\quad
+ s=\frac14\sum_{j\in\mathcal Y}Y_j^0.
+\]
+
+The literal collector produces \(Q_7=A_Q(Q_7^0+s)\) and restores `C` to
+zero. The real D cleanup quarters, G reads and later unit subtractions, and
+Q7 cleanup quarters give, at the last relevant event 4516,
+
+\[
+ b^{\rm final}=A_F b^0
+ \quad\text{for every one of the 63 persistent banks}.
+\]
+
+Thus the initial values are restored in the authenticated final-frame
+coordinates. Physical arrays at two different frames are not claimed equal.
+The finite path certificate also proves
+
+\[
+ A_F=(C^{-1})^{\otimes9},\qquad
+ E^{-1}A_FE=
+ \begin{pmatrix}1&i\\0&-i\end{pmatrix}^{\otimes9}.
+\]
+
+Every outgoing side effect remains in the interface and the bill:
+
+| Source read | Outgoing ports |
+| --- | ---: |
+| Y to other D banks | 348 |
+| Y to other Q banks | 171 |
+| G to X | 104 |
+| Initial Q7 to X, events 492–543 | 52 |
+| **Total** | **675** |
+
+For each port at frame \(H_e\), its literal increment \(\delta_e\) is
+retained. Normalising each X-port increment by its own authenticated frame
+map gives
+
+\[
+ \sum_{e\to X_t} A_{H_e}^{-1}\delta_e
+ =\frac{\epsilon_t}{2}\sum_{j\in\mathcal Y}Y_j^0,
+ \qquad\epsilon_t\in\{+1,-1\}.
+\]
+
+There are 39 positive and 13 negative target signs; all dirty D/Q/G
+coefficients cancel. The resulting **52-by-52 bank-coefficient matrix has
+rank one**; expanding the 512 entries of each array gives rank 512 over
+\(\mathbb Q(i)\). This is a frame-normalised outgoing-port operator.
+A final physical X-bank claim also needs its omitted updates and transports.
+The other 519 Y ports remain separately retained.
+
+Each port increment belongs to `B9`. Its ADD is exact for any current Gaussian
+recipient, and preserves `B9` when that recipient is currently in `B9`.
+An external recipient's initial admission and future native operations require
+their own proof.
+
+The coefficient-coordinate map is explicitly \(E^{-1}AE\). The checker
+derives all 512 columns for the actual empty-to-Q and empty-to-F maps, with
+12,288 and 19,683 nonzero entries respectively. Their distinction from the
+unconjugated numerical map is visible on one input: the first coordinate of
+\(E^{-1}A_QE e_0\) is 1, while that of \(A_Qe_0\) is \((1-i)/2\).
+Persistent coordinates remove intermediate codec pairs only under this
+compatible logical contract. Arbitrary-input preparation and exposed port
+adapters still need to be supplied and charged.
+[CONSUMER.md](CONSUMER.md) proves these statements and records the complete
+source/frame conventions.
+
+## 3. Complete known costs and the inherited stop
+
+[COMPARISON.md](COMPARISON.md) reconstructs every retained operation and port
+from the frozen word. The minimal 257-event producer is already included in
+the 576 internal events and is not counted again.
+
+| Work for the complete open program | Direct logical count |
+| --- | ---: |
+| Native signed-floor pair applications | 148,736 |
+| Actual wrapper executions | 784 |
+| Wrapper cycles / Gaussian scratch swaps | 23,822 / 425,230 |
+| Wrapper unit-phase applications | 401,408 |
+| Field ADDs, including all ports | 857 |
+| Real additions/subtractions, before doublings | 2,067,456 |
+| Additional real doublings | 159,744 |
+| Native real floor halvings | 594,944 |
+| Exact real halvings for the quarter ADDs | 1,382,400 |
+
+Component traffic, private initialization/zero inspections, wrapper setup and
+the numerical storage inventory are also retained. If every initial component
+is bounded by integer `H`, a conservative unitary-norm/triangle proof bounds
+internal payload by **1568H**, literal pair work by **7840H**, and each outgoing
+increment by **1600H**. A current target bound `H_target` still requires capacity
+for `H_target+1600H`; the increment bound does not price or bound the recipient's
+omitted history.
+
+These are direct logical counts and constructive width bounds. The complete
+physical caller still owes the 52 strengthened Y admissions; actual incoming
+heights, external targets and representation adapters; ownership, record layout,
+routing, control and scratch cleanup; and all recursive/outer-completion costs.
+The logical array inventory is not a physical allocation theorem. Unknown
+charges are not assigned zero, and PR #3382's six-bank codec is not the cost of
+this 63-bank interface.
+
+For the unchanged consumer, an existing favourable screen already stops
+expansion. Retain width 73, 832 original live families, the exact five PR #2458
+forward and four PR #2712 or PR #2725 dual profiles, the 3,014-unit persistent
+credit per call and remaining coverage mass 32,778. For `0 <= a < 1`, every
+finite number `B` of fully paid auxiliary banks obeys
+
+\[
+ M_B(a)\ge
+ \frac{5\cdot3070+4\cdot3542+32778+73B}{73(832+B)}
+ =1+\frac{1560}{73(832+B)}>1.
+\]
+
+At `B=0` this is **599/584**. This inherited result is credited to Jose
+Manuel's [original finding](https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18955566)
+and Vasek's [PR #2744 audit](https://github.com/CrocSwap/integer-mult-bounds/pull/2744).
+It is conditional on those exact profiles and coverage hypotheses. The local
+representation theorem does not change them or establish a universal P104
+obstruction.
+
+The family decision is to retain this source/consumer result and stop supplier
+expansion aimed at a new selected saving with that unchanged consumer. A
+concrete changed profile, coverage law or caller must first supply and pass its
+own compatible, fully charged favourable screen.
+
+## Evidence and reproduction
+
+The package combines written admission/restoration proofs, exhaustive finite
+operator certificates, separately written exact interpreters and bounded dense
+fixtures. [RECEIPT.json](RECEIPT.json) binds their implementation/source bytes
+and outcomes. In particular:
+
+- The producer verifies its actual dependency order, reachable counterexample
+  and strengthened-domain positive controls using the authenticated PR #3382
+  model.
+- The consumer imports no producer or predecessor numerical model. It proves
+  the actual frame-path equalities, reconstructs the two coefficient maps, and
+  checks 148,736 literal/ideal pairs and all 675 source increments on a dense
+  signed 63-bank fixture.
+- `independent.py` separately replays the full-prefix counterexample and the
+  Fraction-valued scalar port rows. The cost audit independently reconstructs
+  the complete event/port inventory, actual wrapper counts and rational bounds.
+- Controls reject source drift, swapped or omitted producer reads, a changed
+  quarter coefficient/sign, and a globally phased return invisible to Pauli
+  actions. Separate exact controls distinguish the conjugated and unconjugated
+  maps and expose the false favourable screen caused by unpaid auxiliary-bank
+  denominator credit.
+
+Independent here means separately written automated checks and cross-review;
+substantial AI assistance is disclosed. The source-bound finite operator proof
+and quantified module argument are distinguished from the dense fixture, which
+does not establish arbitrary-input or all-size physical execution.
+
+From the repository root, run:
+
+```sh
+python3 -B research/p104-newton-interfaces/verify.py
+python3 -B -O research/p104-newton-interfaces/verify.py
+```
+
+The same commands apply at the root of the source-complete export. Runtime
+requires standard-library Python and the files pinned in
+[SOURCES.json](SOURCES.json), preserving repository-relative paths; replay needs
+no Git, network or native compilation. [VERIFY.json](VERIFY.json) records the
+replay contract, and [TASK.json](TASK.json) preserves the explicit assignment,
+overlap coverage, checkpoint evidence and stopping decision. Context-only
+sources are identified separately in `SOURCES.json.context_sources` and are
+not runtime dependencies.
+
+The two package-local PR #3382 files are retained byte for byte and checked
+against fixed SHA256 values before execution. Their original commit and blob
+identities are recorded in `SOURCES.json.retained_sources`. They deliberately
+do not require an unmerged predecessor commit in the new branch's ancestry:
+the generic provenance gate checks the canonical-base source pins, and the
+direct verifier checks these retained bytes. The unchanged predecessor suite
+is not rerun, and byte identity does not establish external mathematical review.
+
+## Open next questions
+
+1. **Can the 675 ports be joined to an actual external consumer?** Bind the
+   external target updates, frames, reads and widths, then prove the composed
+   terminal map. The retained port operator gives exact inputs to that task;
+   its frame-normalised X sum does not replace those histories.
+2. **Can a changed caller or profile pass a complete cost screen?** Produce a
+   compatible input/adaptor contract paying the 52 `4B9` admissions, all exposed
+   conversions and physical/recursive charges, and name the exact old-profile
+   or coverage premise it changes. Stop if even its favourable relaxation fails;
+   a passing relaxation would justify the next admission test, not certify a
+   supplier.
+
+## Credit and license
+
+Prepared by **Clear1nsight**, with substantial OpenAI assistance in mathematics,
+implementation, verification, source review and prose, including concurrent
+analysis agents. Apache-2.0; copied inputs retain their source notices.
+
+Credit remains with **ywz65 / PR #2586** for the corrected dual word and native
+recipes; **Arham Tahir / PR #2665** for the retained collector binding;
+**Tekalign (`tekuuu`) / PR #3025** for the literal signed-floor pair, wrapper
+convention, cycle schedule and logical ledger; **Ross Richardson / PR #3068**
+for the period-domain contract and larger-exactness question; and **PR #3382**
+for the phase-complete Gaussian Newton theorem and model. Its classical
+Clifford/Barnes–Wall coding context is inherited, not claimed as a new lattice
+family here.
+
+The `599/584` finding and audit retain **Jose Manuel (`jmbarrancoml`)** and
+**Vasek (`flyingviper`) / PR #2744** credit, with the exact PR #2458, #2712 and
+#2725 profiles preserved. Jose Manuel's physical monomial, dense paired
+collector and selected-controller work in **PRs #3087, #3131 and #3385** is
+inspected context with its own retained assumptions; it is not imported as an
+admission of this changed caller. Exact predecessor heads and context-source
+hashes are recorded in [SOURCES.json](SOURCES.json) and
+[COMPARISON.md](COMPARISON.md).
diff --git a/research/p104-newton-interfaces/RECEIPT.json b/research/p104-newton-interfaces/RECEIPT.json
new file mode 100644
index 0000000000..45914989a5
--- /dev/null
+++ b/research/p104-newton-interfaces/RECEIPT.json
@@ -0,0 +1,35855 @@
+{
+  "authenticated_inputs": {
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd",
+    "package/inputs/PR3382_PROOF.md": "1ca8c0e7e78f0f39de6cff7accc68ccd3901bfb50759bf7a2e2896bcf63bf081",
+    "package/inputs/pr3382_model.py": "74c83367887dd885137b222155c86389fe0be9f1293a6f0e5fdb51d71f435fdd",
+    "research/p104-consumer-budget-audit/PREDECESSORS.json": "63b609650a4bcfb65241f3eccb8921cb10bde0212a8782212ad01242b13b96df",
+    "research/p104-consumer-budget-audit/README.md": "13694215d0c1a245b392f7155e8395b9c4bad9c5db3558833c784d9449616417",
+    "research/p104-invariant-lifting-lattice/PROOF.md": "7a34534dd75a2ae4b77d9779fee9ce43372d8a6d2038c6a763deff1f99ce7830",
+    "research/p104-invariant-lifting-lattice/README.md": "426721af0f8b391aa56ce2c6968b78bf4e9b386e794eb5b4854d88243762c19d",
+    "research/p104-retimed-internal-grid/README.md": "8ed5890fa0cb995ad90c0b2f8306735ef43c53a00681cc42797bb3a6d4b8a72b",
+    "research/p104-reversible-lifting/README.md": "051a886e9777b6ace444920df1fd46c285dc0251d7ef6fac570dc12cca7c4bc8",
+    "research/p104-rounded-collector/PREDECESSORS.json": "89f17ce76729101536cfc0be02ad153451c6606ebcfd3a1d6588226a83c88c64",
+    "research/p104-rounded-collector/README.md": "a77514952eda13fac047c5a4daba92d6c01d3e83bb1b41da4b87211bec6c37c9",
+    "research/p104-rounded-collector/inputs/NATIVE.json.gz": "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d",
+    "research/p104-rounded-collector/inputs/WORD.json": "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50",
+    "upstream/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+  },
+  "consumer": {
+    "authenticated_wrapper_count": 404,
+    "chart": "Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)",
+    "closed_event_indices": [
+      126,
+      127,
+      128,
+      129,
+      130,
+      131,
+      132,
+      133,
+      134,
+      135,
+      136,
+      167,
+      168,
+      169,
+      170,
+      171,
+      172,
+      173,
+      174,
+      175,
+      176,
+      177,
+      178,
+      179,
+      180,
+      181,
+      182,
+      183,
+      184,
+      185,
+      186,
+      187,
+      188,
+      189,
+      190,
+      191,
+      192,
+      193,
+      194,
+      195,
+      196,
+      197,
+      198,
+      199,
+      200,
+      201,
+      202,
+      203,
+      204,
+      205,
+      206,
+      207,
+      908,
+      909,
+      910,
+      911,
+      912,
+      913,
+      914,
+      915,
+      916,
+      917,
+      972,
+      980,
+      981,
+      982,
+      983,
+      984,
+      985,
+      986,
+      987,
+      988,
+      989,
+      990,
+      991,
+      992,
+      993,
+      994,
+      995,
+      996,
+      997,
+      998,
+      999,
+      1000,
+      1001,
+      1002,
+      1003,
+      1004,
+      1005,
+      1006,
+      1007,
+      1008,
+      1009,
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+        {
+          "coefficient": "-1/4",
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+          "initial_symbol_row": {
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+      ],
+      "external_port_records_sha256": "0a6387492e1d17651d005e3ba3b9203788543a358b8ce319399071fab0eae2dc",
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+        "dirty_D_Q_G_coefficients": "all zero",
+        "expanded_512_entry_array_map_rank_over_Q_i": 512,
+        "input_sources": [
+          "Y22",
+          "Y23",
+          "Y24",
+          "Y25",
+          "Y26",
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+          "Y63",
+          "Y64",
+          "Y65",
+          "Y66",
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+          "Y74",
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+          "Y77",
+          "Y78",
+          "Y79",
+          "Y80",
+          "Y81",
+          "Y82",
+          "Y83",
+          "Y84",
+          "Y85",
+          "Y86",
+          "Y87",
+          "Y88",
+          "Y89",
+          "Y90",
+          "Y91",
+          "Y92",
+          "Y93",
+          "Y94",
+          "Y95",
+          "Y96",
+          "Y97",
+          "Y98",
+          "Y99",
+          "Y100",
+          "Y101",
+          "Y102",
+          "Y103"
+        ],
+        "scalar_52_by_52_bank_matrix_rank_over_Q_i": 1,
+        "scope": "sum of frame-normalized outgoing ports; omitted external bank histories and terminal states are not executed",
+        "target_signs": {
+          "X1": 1,
+          "X100": 1,
+          "X103": 1,
+          "X13": -1,
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+          "X18": 1,
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+          "X2": 1,
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+          "X36": -1,
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+          "X75": -1,
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+          "X81": 1,
+          "X83": 1,
+          "X84": 1,
+          "X85": 1,
+          "X87": 1,
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+          "X92": 1,
+          "X94": 1,
+          "X95": 1,
+          "X98": 1,
+          "X99": 1
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+      },
+      "persistent_banks_restored_in_full_frame": [
+        "D27",
+        "D28",
+        "D29",
+        "D30",
+        "D31",
+        "G27",
+        "G28",
+        "G29",
+        "G30",
+        "G31",
+        "Q7",
+        "Y100",
+        "Y101",
+        "Y102",
+        "Y103",
+        "Y22",
+        "Y23",
+        "Y24",
+        "Y25",
+        "Y26",
+        "Y27",
+        "Y28",
+        "Y29",
+        "Y30",
+        "Y31",
+        "Y32",
+        "Y63",
+        "Y64",
+        "Y65",
+        "Y66",
+        "Y67",
+        "Y68",
+        "Y69",
+        "Y70",
+        "Y71",
+        "Y72",
+        "Y73",
+        "Y74",
+        "Y75",
+        "Y76",
+        "Y77",
+        "Y78",
+        "Y79",
+        "Y80",
+        "Y81",
+        "Y82",
+        "Y83",
+        "Y84",
+        "Y85",
+        "Y86",
+        "Y87",
+        "Y88",
+        "Y89",
+        "Y90",
+        "Y91",
+        "Y92",
+        "Y93",
+        "Y94",
+        "Y95",
+        "Y96",
+        "Y97",
+        "Y98",
+        "Y99"
+      ],
+      "status": "PASS_EXACT_OPEN_INTERFACE_ROWS",
+      "symbol_convention": "Y symbol = initial Y / 4; other symbol = initial bank, all in B_9",
+      "wrong_actual_quarter_sign_control": {
+        "event": 2162,
+        "lattice_admission_unchanged": true,
+        "mutation": "1/4",
+        "original": "-1/4",
+        "residual_on_initial_Y103": "1/2",
+        "result": "REJECT_D28_RESTORATION"
+      }
+    },
+    "through_event": 4516
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+  "cost": {
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+        "component_reads": 1161216,
+        "component_writes": 580608,
+        "decodes": 63,
+        "encodes": 63,
+        "exact_real_halves": 290304,
+        "real_add_subtracts": 1161216
+      },
+      "limitations": [
+        "These count separately specified in-place coordinate conversions.",
+        "A 63-bank roundtrip is not a complete adapter for the 83 external port targets.",
+        "52 Y banks still require 4B admission; encoding ordinary coefficients into B is insufficient.",
+        "Original A and E^-1 A E are distinct external numerical contracts.",
+        "Borrowed-input copying, setup, routing, widths and physical storage are not included."
+      ],
+      "one_bank_decode": {
+        "component_reads": 9216,
+        "component_writes": 4608,
+        "exact_real_halves": 4608,
+        "pairs": 2304,
+        "real_add_subtracts": 9216
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+      "one_bank_encode": {
+        "component_reads": 9216,
+        "component_writes": 4608,
+        "pairs": 2304,
+        "real_add_subtracts": 9216
+      }
+    },
+    "fixed_consumer": {
+      "all_additional_physical_costs": "unresolved nonnegative charges, not zero",
+      "all_finite_fully_paid_banks_formula": "1 + 1560/(73*(832+B))",
+      "bank_examples_not_the_universal_proof": {
+        "0": "599/584",
+        "1": "62369/60809",
+        "1000000": "9132787/9132592",
+        "22": "31951/31171",
+        "63": "13379/13067",
+        "83": "4557/4453",
+        "832": "1183/1168"
+      },
+      "capacity": 60736,
+      "credit": "Jose Manuel, Discussion2619 comment18955566; Vasek/flyingviper PR2744",
+      "dual_calls": 4,
+      "excess_mass": 1560,
+      "forward_calls": 5,
+      "negative_control": {
+        "correct_fully_paid_B22": "31951/31171",
+        "reason_rejected": "Every added bank owes 73 paid coverage units.",
+        "unauthorised_denominator_only_B22": "31148/31171"
+      },
+      "no_bank_lower_bound": "599/584",
+      "original_families": 832,
+      "predecessor_head": "0166260409f55a56e7fefa48d859f7dd5b42b300",
+      "profiles": {
+        "D2712": [
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+          60,
+          74,
+          92,
+          58,
+          56,
+          92,
+          8
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+        "D2725": [
+          1502,
+          58,
+          74,
+          93,
+          57,
+          56,
+          91,
+          9
+        ],
+        "F2458": [
+          1216,
+          74,
+          86,
+          104,
+          48,
+          42,
+          68,
+          8
+        ]
+      },
+      "progress_per_call": 3014,
+      "proof_step": "For 0 < r <= 73, (r/73)^(1-a) >= r/73.",
+      "rank_masses": {
+        "D2712": 3542,
+        "D2725": 3542,
+        "F2458": 3070
+      },
+      "remaining_coverage_mass": 32778,
+      "saving_domain": "0 <= a < 1",
+      "scope": "Fixed profiles and coverage only; no universal P104 obstruction.",
+      "unmodified_total": 62296,
+      "width": 73
+    },
+    "source_audit": {
+      "authenticated_inputs": [
+        {
+          "bytes": 288482,
+          "git_blob": "93acaabc0a523789ef2f1b06f6eeeefed5551397",
+          "path": "research/p104-rounded-collector/inputs/WORD.json",
+          "sha256": "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50"
+        },
+        {
+          "bytes": 49610,
+          "git_blob": "04f2877aa5444948b7ae37efd267745af82cb34d",
+          "path": "research/p104-rounded-collector/inputs/NATIVE.json.gz",
+          "sha256": "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d"
+        },
+        {
+          "bytes": 15737,
+          "git_blob": "7317fa775e5942e66237b9053aa5e0ed8dc6b1a3",
+          "path": "research/p104-consumer-budget-audit/README.md",
+          "sha256": "13694215d0c1a245b392f7155e8395b9c4bad9c5db3558833c784d9449616417"
+        }
+      ],
+      "chart": "Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)",
+      "conservative_norm_bounds": {
+        "assumption": "Every initial real component of all63 admitted internal arrays has absolute value <= integer H>=0, in common-grid numerator units.",
+        "first_max_internal_event": 4165,
+        "first_max_internal_field": "G27",
+        "first_max_port_event": 3250,
+        "first_max_port_target": "X28",
+        "initial_array_l2_norm": "<=32H since sqrt(2*512)=32",
+        "internal_payload_component_bound": "1568H",
+        "literal_pair_work_component_bound": "7840H",
+        "max_internal_l2_weight": 49,
+        "max_port_increment_l2_weight": 50,
+        "native_prefix_fact": "Every affine/unit-phase wrapper and partial C product is unitary; literal equality is supplied by the admitted-domain proof.",
+        "port_increment_component_bound": "1600H",
+        "port_target_condition": "A current target bound H_target needs capacity for H_target+1600H; H_target and its intervening external history remain caller obligations.",
+        "propagation": "w_target <- w_target + abs(coefficient)*w_source; w_initial=1; w_C_zero=0; native w unchanged.",
+        "signed_core_width_sufficient_condition": "2^(h-1)>7840H",
+        "signed_floor_lemma": "For integer |a|,|b|<=B, |d|<=2B, |floor(d/2)|<=B, |middle|<=2B, |second|<=3B, |first|<=5B, componentwise and after quarter rotation.",
+        "status": "Conservative constructive bounds, not minimum widths or physical time/space tariffs."
+      },
+      "direct_reference_schedule": {
+        "codecs_or_admission_included": false,
+        "core_persistent_gaussian_state_words": 32256,
+        "distinct_external_target_banks": 83,
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+            4,
+            2,
+            1
+          ],
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D30": {
+          "frame": [
+            256,
+            136,
+            64,
+            40,
+            16,
+            4,
+            2,
+            1
+          ],
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D31": {
+          "frame": [
+            256,
+            136,
+            64,
+            40,
+            16,
+            4,
+            2,
+            1
+          ],
+          "newton_failure": {
+            "coefficient": [
+              -1,
+              0
+            ],
+            "degree": 1,
+            "mask": 8,
+            "pi_valuation": 0
+          },
+          "nonzero_complex_entries": 256,
+          "sha256": "adde9450101abb38b9f2c225459b1068526a1fc6dede4957615e2b0ef5ed8a21"
+        },
+        "Q7": {
+          "frame": [
+            364
+          ],
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        }
+      },
+      "first_full_prefix_B9_failure": {
+        "coefficient": [
+          -4,
+          -4
+        ],
+        "degree": 6,
+        "event": 1090,
+        "field": "D31",
+        "mask": 349,
+        "pi_valuation": 5
+      },
+      "initial_Y27_not_in_4B9": {
+        "coefficient": [
+          -16,
+          0
+        ],
+        "degree": 9,
+        "mask": 511,
+        "pi_valuation": 8
+      },
+      "initial_banks": 358,
+      "point": {
+        "Y27[0]": [
+          64,
+          0
+        ],
+        "all_other_components": 0
+      },
+      "prefix_native_occurrences_bound": 883,
+      "scope": "one explicit point, full events0..2024",
+      "status": "PASS"
+    },
+    "scalar_ports": {
+      "X_map": "Sum of outgoing increments pulled back through the certified port-frame gauges is sign_j * sum_{s in Y22..32,Y63..103} y_s / 2; this is not a final external X-array endpoint.",
+      "X_target_signs": {
+        "X1": 1,
+        "X100": 1,
+        "X103": 1,
+        "X13": -1,
+        "X14": 1,
+        "X18": 1,
+        "X19": 1,
+        "X2": 1,
+        "X20": 1,
+        "X22": 1,
+        "X23": 1,
+        "X27": 1,
+        "X28": 1,
+        "X29": 1,
+        "X3": -1,
+        "X32": 1,
+        "X35": 1,
+        "X36": -1,
+        "X4": -1,
+        "X40": -1,
+        "X44": -1,
+        "X45": -1,
+        "X46": -1,
+        "X48": 1,
+        "X49": 1,
+        "X50": 1,
+        "X54": 1,
+        "X58": 1,
+        "X59": -1,
+        "X64": 1,
+        "X65": 1,
+        "X66": 1,
+        "X7": -1,
+        "X70": 1,
+        "X74": 1,
+        "X75": -1,
+        "X79": 1,
+        "X8": -1,
+        "X80": 1,
+        "X81": 1,
+        "X83": 1,
+        "X84": 1,
+        "X85": 1,
+        "X87": 1,
+        "X88": 1,
+        "X89": 1,
+        "X9": -1,
+        "X92": 1,
+        "X94": 1,
+        "X95": 1,
+        "X98": 1,
+        "X99": 1
+      },
+      "all_initial_D_Q_G_coefficients_cancel_in_X_ports": true,
+      "excluded": "External target updates/transports and all other word operations are not a full numerical execution.",
+      "external_port_count": 675,
+      "external_port_counts": {
+        "G->X": 104,
+        "Q->X": 52,
+        "Y->D": 348,
+        "Y->Q": 171
+      },
+      "external_port_indices_sha256": "04b3a0bc022c336c9b177eeed49036f1257ab81ea9d0459b8170075b002a24a4",
+      "frame_map_certificate_required": true,
+      "private_zero": true,
+      "restored_initial_rows": 63,
+      "scope": "scalar rows in separately certified frame gauges",
+      "status": "PASS"
+    },
+    "source_sha256": {
+      "native": "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d",
+      "word": "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50"
+    },
+    "status": "PASS"
+  },
+  "integrity_controls": {
+    "bool_as_integer_receipt": "REJECTED: typed scientific receipt mismatch",
+    "corrupt_actual_native_input": "REJECTED: source SHA256 mismatch: research/p104-rounded-collector/inputs/NATIVE.json.gz",
+    "corrupt_retained_model_before_execution": "REJECTED: source SHA256 mismatch: inputs/pr3382_model.py",
+    "duplicate_json_key": "REJECTED: duplicate JSON key",
+    "float_json": "REJECTED: non-integer JSON number",
+    "nonfinite_json": "REJECTED: non-integer JSON number",
+    "partial_component_result": "REJECTED: all component evidence must report complete PASS",
+    "undeclared_live_input": "REJECTED: complete declared input closure"
+  },
+  "producer": {
+    "amplitude256_admitted_control": {
+      "all_fractional_adds_exact": true,
+      "all_literal_native_pairs_exact": true,
+      "counts": {
+        "coordinate_stages": 354,
+        "native_calls": 200,
+        "pair_obligations": 90624,
+        "quarter_adds": 52,
+        "unit_adds": 5
+      },
+      "entrance": {
+        "D27": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D28": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D29": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D30": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D31": {
+          "in_B9": true,
+          "max_absolute_component": 4,
+          "newton_failure": null,
+          "nonzero_complex_entries": 256,
+          "sha256": "534026fdb20a36bde87b0a0221a0a366f15a9c58a77ab3dea673abe1af093602"
+        },
+        "Q7": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        }
+      },
+      "failing_event_outputs": [],
+      "first_lattice_failure": null,
+      "initial_admission": {
+        "Y_fields_outside_4B9": [],
+        "all_initial_fields_in_B9": true
+      }
+    },
+    "claim": "B9 prefix admission under exactly the stated strengthened initial contract",
+    "controls": {
+      "negative_nonintegral_quarter": {
+        "reason": "fractional ADD is not exact on the retained grid",
+        "rejected": true
+      },
+      "omitted_Y27_source": {
+        "reason": "exact 58 initial dependencies",
+        "rejected": true
+      },
+      "signed_exact_quarters": {
+        "inputs": [
+          [
+            -4,
+            4
+          ],
+          [
+            -8,
+            -12
+          ]
+        ],
+        "outputs": [
+          [
+            -1,
+            1
+          ],
+          [
+            -2,
+            -3
+          ]
+        ]
+      },
+      "source_byte_corruption": {
+        "reason": "source digest mismatch: word",
+        "rejected": true
+      },
+      "source_reads1090_1129_swapped": {
+        "reason": "ADD common frame",
+        "rejected": true
+      },
+      "wrong_quarter_at1090": {
+        "reason": "actual quarter source",
+        "rejected": true
+      }
+    },
+    "counterexample_full_prefix_valuation": {
+      "active_fractional_source_events": [
+        {
+          "coefficient": "1/4",
+          "event": 1090,
+          "source": "Y27",
+          "source_after_coefficient_lower_pi_valuation": 5,
+          "target": "D31"
+        },
+        {
+          "coefficient": "1/4",
+          "event": 1190,
+          "source": "Y27",
+          "source_after_coefficient_lower_pi_valuation": 4,
+          "target": "D10"
+        },
+        {
+          "coefficient": "-1/4",
+          "event": 1303,
+          "source": "Y27",
+          "source_after_coefficient_lower_pi_valuation": 3,
+          "target": "D20"
+        },
+        {
+          "coefficient": "-1/4",
+          "event": 1499,
+          "source": "Y27",
+          "source_after_coefficient_lower_pi_valuation": 2,
+          "target": "D24"
+        },
+        {
+          "coefficient": "-1/4",
+          "event": 1763,
+          "source": "Y27",
+          "source_after_coefficient_lower_pi_valuation": 1,
+          "target": "D1"
+        },
+        {
+          "coefficient": "1/4",
+          "event": 1937,
+          "source": "Y27",
+          "source_after_coefficient_lower_pi_valuation": 0,
+          "target": "D16"
+        }
+      ],
+      "active_native_events": [
+        {
+          "event": 131,
+          "field": "Y27",
+          "lower_pi_valuation": 11
+        },
+        {
+          "event": 1056,
+          "field": "Y27",
+          "lower_pi_valuation": 9
+        },
+        {
+          "event": 1091,
+          "field": "Y27",
+          "lower_pi_valuation": 8
+        },
+        {
+          "event": 1092,
+          "field": "D31",
+          "lower_pi_valuation": 4
+        },
+        {
+          "event": 1131,
+          "field": "D31",
+          "lower_pi_valuation": 3
+        },
+        {
+          "event": 1191,
+          "field": "Y27",
+          "lower_pi_valuation": 7
+        },
+        {
+          "event": 1192,
+          "field": "D10",
+          "lower_pi_valuation": 3
+        },
+        {
+          "event": 1233,
+          "field": "D31",
+          "lower_pi_valuation": 0
+        },
+        {
+          "event": 1304,
+          "field": "Y27",
+          "lower_pi_valuation": 6
+        },
+        {
+          "event": 1305,
+          "field": "D20",
+          "lower_pi_valuation": 2
+        },
+        {
+          "event": 1331,
+          "field": "D10",
+          "lower_pi_valuation": 2
+        },
+        {
+          "event": 1481,
+          "field": "D10",
+          "lower_pi_valuation": 1
+        },
+        {
+          "event": 1494,
+          "field": "D20",
+          "lower_pi_valuation": 1
+        },
+        {
+          "event": 1500,
+          "field": "Y27",
+          "lower_pi_valuation": 5
+        },
+        {
+          "event": 1503,
+          "field": "D24",
+          "lower_pi_valuation": 0
+        },
+        {
+          "event": 1670,
+          "field": "D20",
+          "lower_pi_valuation": 0
+        },
+        {
+          "event": 1727,
+          "field": "D10",
+          "lower_pi_valuation": 0
+        },
+        {
+          "event": 1764,
+          "field": "Y27",
+          "lower_pi_valuation": 4
+        },
+        {
+          "event": 1771,
+          "field": "D1",
+          "lower_pi_valuation": 0
+        },
+        {
+          "event": 1938,
+          "field": "Y27",
+          "lower_pi_valuation": 3
+        }
+      ],
+      "all_active_native_frames_ranks_and_wrappers_bound": true,
+      "all_literal_pairs_and_fractional_sources_exact": true,
+      "final_component_valuation_lower_bounds": {
+        "D1": 0,
+        "D10": 0,
+        "D16": 0,
+        "D20": 0,
+        "D24": 0,
+        "D31": 0,
+        "Y27": 3
+      },
+      "initial_bank_count": 358,
+      "initial_point": {
+        "Y27[0]": [
+          64,
+          0
+        ],
+        "all_other_initial_components": 0
+      },
+      "method": "component pi-valuations; native stage loses at most one; quarter loses four",
+      "ordered_active_native_records_sha256": "94f8d3753acaf24fedc609ecde5629ac96ed61bd3845cb9417522fb855fecc0c",
+      "ordered_prefix_records_sha256": "6373ebe61a05df76c2f6697e2bbc65d2e92d84bd6e5d44fbde536d7c0f117aae",
+      "scope": "only this explicit initial point through events0..2024"
+    },
+    "dense_dirty_admitted_fixture": {
+      "all_fractional_adds_exact": true,
+      "all_literal_native_pairs_exact": true,
+      "counts": {
+        "coordinate_stages": 354,
+        "native_calls": 200,
+        "pair_obligations": 90624,
+        "quarter_adds": 52,
+        "unit_adds": 5
+      },
+      "entrance": {
+        "D27": {
+          "in_B9": true,
+          "max_absolute_component": 878,
+          "newton_failure": null,
+          "nonzero_complex_entries": 512,
+          "sha256": "22d6126732e13cede5b453a0de21a9de32f4558799b752cd4ea3864cddeb06b7"
+        },
+        "D28": {
+          "in_B9": true,
+          "max_absolute_component": 1061,
+          "newton_failure": null,
+          "nonzero_complex_entries": 512,
+          "sha256": "a5d78f4afc6445dd0f7058f7e84cb362da044dbbbbd083da74c4dd3f083f66f1"
+        },
+        "D29": {
+          "in_B9": true,
+          "max_absolute_component": 563,
+          "newton_failure": null,
+          "nonzero_complex_entries": 512,
+          "sha256": "dff4c4de8d88ba6ee3eb9c1616062ae5ab7c01954fbad3a4ed75d6508ab0f3b3"
+        },
+        "D30": {
+          "in_B9": true,
+          "max_absolute_component": 605,
+          "newton_failure": null,
+          "nonzero_complex_entries": 512,
+          "sha256": "fe165f33c796c42d43d206067d5f9619b8f5f9d75ab50a132344e4e1058cc115"
+        },
+        "D31": {
+          "in_B9": true,
+          "max_absolute_component": 827,
+          "newton_failure": null,
+          "nonzero_complex_entries": 512,
+          "sha256": "586bc3cf0d0df19ccb96530e2dc297a1ddf948b324c311d2570bb73db6027256"
+        },
+        "Q7": {
+          "in_B9": true,
+          "max_absolute_component": 1067,
+          "newton_failure": null,
+          "nonzero_complex_entries": 512,
+          "sha256": "284ef4f3d510eee6d4ae32a08880562bb5b8441dc00a243d867e3177a15268a4"
+        }
+      },
+      "failing_event_outputs": [],
+      "first_lattice_failure": null,
+      "initial_admission": {
+        "Y_fields_outside_4B9": [],
+        "all_initial_fields_in_B9": true
+      }
+    },
+    "not_claimed": [
+      "maximal final-cut domain",
+      "arbitrary-input source admission",
+      "full-word correctness",
+      "physical owners or favorable recursive cost"
+    ],
+    "one_coordinate_counterexample": {
+      "all_fractional_adds_exact": true,
+      "all_literal_native_pairs_exact": true,
+      "counts": {
+        "coordinate_stages": 354,
+        "native_calls": 200,
+        "pair_obligations": 90624,
+        "quarter_adds": 52,
+        "unit_adds": 5
+      },
+      "entrance": {
+        "D27": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D28": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D29": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D30": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        },
+        "D31": {
+          "in_B9": false,
+          "max_absolute_component": 1,
+          "newton_failure": {
+            "coefficient": [
+              -1,
+              0
+            ],
+            "degree": 1,
+            "mask": 8,
+            "pi_valuation": 0,
+            "required_pi_valuation": 1
+          },
+          "nonzero_complex_entries": 256,
+          "sha256": "adde9450101abb38b9f2c225459b1068526a1fc6dede4957615e2b0ef5ed8a21"
+        },
+        "Q7": {
+          "in_B9": true,
+          "max_absolute_component": 0,
+          "newton_failure": null,
+          "nonzero_complex_entries": 0,
+          "sha256": "c8e145f4220685e764568718191bfa96c3227f8b845bc8032698b49d8f8b4d16"
+        }
+      },
+      "failing_event_outputs": [
+        {
+          "event": 1090,
+          "target": "D31",
+          "witness": {
+            "coefficient": [
+              -4,
+              -4
+            ],
+            "degree": 6,
+            "mask": 349,
+            "pi_valuation": 5,
+            "required_pi_valuation": 6
+          }
+        },
+        {
+          "event": 1092,
+          "target": "D31",
+          "witness": {
+            "coefficient": [
+              4,
+              0
+            ],
+            "degree": 5,
+            "mask": 345,
+            "pi_valuation": 4,
+            "required_pi_valuation": 5
+          }
+        },
+        {
+          "event": 1129,
+          "target": "D31",
+          "witness": {
+            "coefficient": [
+              4,
+              0
+            ],
+            "degree": 5,
+            "mask": 345,
+            "pi_valuation": 4,
+            "required_pi_valuation": 5
+          }
+        },
+        {
+          "event": 1131,
+          "target": "D31",
+          "witness": {
+            "coefficient": [
+              -2,
+              2
+            ],
+            "degree": 4,
+            "mask": 89,
+            "pi_valuation": 3,
+            "required_pi_valuation": 4
+          }
+        },
+        {
+          "event": 1231,
+          "target": "D31",
+          "witness": {
+            "coefficient": [
+              -2,
+              2
+            ],
+            "degree": 4,
+            "mask": 89,
+            "pi_valuation": 3,
+            "required_pi_valuation": 4
+          }
+        },
+        {
+          "event": 1233,
+          "target": "D31",
+          "witness": {
+            "coefficient": [
+              -1,
+              0
+            ],
+            "degree": 1,
+            "mask": 8,
+            "pi_valuation": 0,
+            "required_pi_valuation": 1
+          }
+        }
+      ],
+      "first_lattice_failure": {
+        "event": 1090,
+        "target": "D31",
+        "witness": {
+          "coefficient": [
+            -4,
+            -4
+          ],
+          "degree": 6,
+          "mask": 349,
+          "pi_valuation": 5,
+          "required_pi_valuation": 6
+        }
+      },
+      "initial_admission": {
+        "Y_fields_outside_4B9": [
+          "Y27"
+        ],
+        "all_initial_fields_in_B9": true
+      },
+      "two_point_final_witness": {
+        "addresses": [
+          0,
+          8
+        ],
+        "difference": [
+          -1,
+          0
+        ],
+        "values": [
+          [
+            1,
+            0
+          ],
+          [
+            0,
+            0
+          ]
+        ]
+      }
+    },
+    "source_cone": {
+      "Y_read_events": {
+        "Y100": [
+          1393
+        ],
+        "Y101": [
+          1391
+        ],
+        "Y102": [
+          1389
+        ],
+        "Y103": [
+          1087
+        ],
+        "Y22": [
+          1271
+        ],
+        "Y23": [
+          1425
+        ],
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new file mode 100644
index 0000000000..ce55244e1b
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+      "author": "Tekalign / tekuuu",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/3025",
+      "head": "a544ef068a46f4de3bc47d1d02149cbdc3ba547f",
+      "contribution": "Literal signed-floor pair, inverse, source wrapper convention, in-place cycle algorithm, and scalar ledger. This package uses the inherited mathematics and separate new implementations; it does not rerun that predecessor suite."
+    },
+    {
+      "author": "Ross Richardson",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/3068",
+      "head": "7d2c519a1fdcc6bf66f6f08757eed7c48762d3f2",
+      "contribution": "Neighboring Gamma/Lambda period-domain contract, phase/quarter boundary examples and larger state-exactness handoff."
+    },
+    {
+      "author": "Jose Manuel / jmbarrancoml",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/3087",
+      "head": "e7e49fb8176772c71ad7006920a407109a89e440",
+      "contribution": "Related physical Gaussian-monomial work; context only, not imported, replayed or admitted here."
+    },
+    {
+      "author": "Nick Petalas, Arham Tahir, Alejandro Zarzuelo Urdiales, Ross Richardson and retained P104 contributors",
+      "contribution": "Predecessor period/precision, Gaussian parity, native binding and sharp-grid methods remain credited. The retained READMEs preserve source-specific attribution."
+    },
+    {
+      "author": "Jose Manuel / jmbarrancoml",
+      "discussion": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18955566",
+      "contribution": "Original unchanged-consumer coverage obstruction; inherited rather than presented as a new lower bound."
+    },
+    {
+      "author": "Vasek / flyingviper",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/2744",
+      "head": "0166260409f55a56e7fefa48d859f7dd5b42b300",
+      "contribution": "Source-bound fixed width-73, five-forward/four-dual complete consumer audit. Its exact profiles and coverage assumptions are retained."
+    },
+    {
+      "author": "Douglas Colkitt and repository research contributors",
+      "contribution": "Research selection, source-binding, package verification, and selected-frontier infrastructure; unchanged."
+    },
+    {
+      "author": "Nick Petalas / petalas",
+      "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/3406",
+      "head": "18a054fd585ab4b2010770ec83cba0c9f28184e3",
+      "contribution": "Concurrent complementary whole-word independent-product Newton entrance, including104Y in4B9 and78N in2B9 under inherited native covariance. Found during presubmission, credited as pending context; explicitly distinguishes our active actual-cone/consumer/cost claim. Not reclassified as this package’s contribution or replayed here."
+    }
+  ],
+  "literature_inspiration": [
+    {
+      "authors": "Gabriele Nebe, Eric M. Rains, Neil J. A. Sloane",
+      "title": "The invariants of the Clifford groups",
+      "url": "https://arxiv.org/abs/math/0001038",
+      "use": "Classical Gaussian Clifford/invariant-lattice context; no theorem imported by the verifier."
+    },
+    {
+      "authors": "Gabriele Nebe, Eric M. Rains, Neil J. A. Sloane",
+      "title": "A Simple Construction for the Barnes-Wall Lattices",
+      "url": "https://arxiv.org/abs/math/0207186",
+      "use": "Classical coding/lattice motivation for PR3382’s retained normalization; this follow-up applies that established module to actual source paths."
+    }
+  ]
+}
diff --git a/research/p104-newton-interfaces/TASK.json b/research/p104-newton-interfaces/TASK.json
new file mode 100644
index 0000000000..f510f40966
--- /dev/null
+++ b/research/p104-newton-interfaces/TASK.json
@@ -0,0 +1,342 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 6,
+  "base_commit": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can the proposed P104 joint endpoint flags be realized by a chronological correction program with coefficients, dirty restoration and an affordable complete bill?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/p104-native-channel/README.md",
+      "research/p104-native-channel/PROOF.md",
+      "docs/research/community-efficient1000-review.md",
+      "research/p104-joint-unit-flags/README.md"
+    ],
+    "methods": [
+      "Construct one side-correction word at an explicit chronological cut with the needed frames still available.",
+      "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget."
+    ],
+    "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. 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 the revision-6 family record and #2981 static joint flags, alongside the reviewed #1991 channel. #2981 is an author-checked source archive, not an independently validated executable correction or a refutation of program-level lifetime floors.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "After checking live handoffs, pin one named collection from #2981 and attach acquisition/delivery times, source dependencies and coefficient requirements. Test legal access and arbitrary dirty restoration; price any completion against the full channel/endpoint/hosting allowance. Stop with the exact missing implication or a scoped counterexample rather than expanding the static cover census.",
+    "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.",
+    "allowed_variations": [
+      "One correction factorization, one chronological cut, or one explicit hosting obstruction.",
+      "A changed correction schedule with an updated full bill and native frame contract."
+    ],
+    "scope_change_triggers": [
+      "Recompiling the already certified low-rank channel without closing a new obligation.",
+      "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.",
+      "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.",
+      "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful."
+    ],
+    "overlap_terms": [
+      "P104",
+      "I-G/2",
+      "side correction",
+      "native channel",
+      "1972",
+      "1991",
+      "2586",
+      "endpoint transport",
+      "physical dual",
+      "relay composition",
+      "2981",
+      "joint unit flags",
+      "acquisition delivery",
+      "static nesting"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #2981 reports static joint endpoint flags and a matching of 208 departure and arrival flags; archival intake is not independent verification.",
+        "evidence": "research/p104-joint-unit-flags/README.md",
+        "remaining": "Independent flag check and a chronological coefficient program with dirty restoration and a complete cost.",
+        "status": "author-checked",
+        "source_commit": "3d24b92d8ba057b57cb2d480170ec407520e6882",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "author": "Clear1nsight, with substantial OpenAI assistance",
+  "budget_override": "User explicitly removed the 60-minute constraint and requested sustained multi-agent mathematical contributions.",
+  "scope_status": "changed",
+  "actual_scope": "Answer all three assigned PR3382 questions for one source-bound 63-bank open program through event4516: exact Gaussian Newton producer admission, a fully reachable weaker-input counterexample, phase-sensitive downstream native paths and restoration, all675 outgoing ports and actual coefficient intertwiners, complete direct logical costs and widths, and the conditional inherited outer stopping decision.",
+  "scope_change_reason": "The user explicitly assigned all three Open next questions of PR3382. This closes actual source-path and consumer implications absent from its local collector theorem; no reroll or selected-frontier change.",
+  "outcome": "completed",
+  "bottleneck_link": "Decide whether the representation survives an actual producer and consumer and whether it can change the frozen outer decision.",
+  "budget_minutes": null,
+  "stop_rule": "One bounded source-bound interface package. Stop at explicit admission or restoration failure, or at an inherited unfavorable complete bill. Do not expand to a whole supplier without changed coverage or profile and a paid compatible external contract.",
+  "selection": {
+    "explicit_assignment": true,
+    "assigned_questions": [
+      {
+        "question": "Can a real preceding producer supply B_9 at this collector cut?",
+        "why_it_matters": "Local exactness helps only when actual numerical states reach the required source and query frames.",
+        "first_step": "Trace one actual source producer’s Newton divisibility, including every coefficient division, and price any needed preparation.",
+        "blocked_by": "Arbitrary prior arithmetic and physical source availability have not been proved to supply the entrance."
+      },
+      {
+        "question": "Can an actual next consumer retain the representation and requested logical map?",
+        "why_it_matters": "An integral quarter output may leave B_r, and coefficient encoding changes the map to E^-1 U E.",
+        "first_step": "Bind one downstream operation, frames and requested map; prove source membership in4B_r before quarter division or the exact required intertwiner.",
+        "blocked_by": "Full caller compatibility and downstream domain admission are open."
+      },
+      {
+        "question": "Can a complete physical implementation improve the bill?",
+        "why_it_matters": "The direct numerical ledger does not establish an affordable recursive child or supplier.",
+        "first_step": "Combine a proven producer/consumer with paid monomial/arithmetic backend, storage, control tape, precision and cleanup costs.",
+        "blocked_by": "Native/backend, ownership, routing and full-consumer tariffs remain unpriced or inherited."
+      }
+    ],
+    "card_seed": "6a8c7d90483306b0d8770073b580cf2d",
+    "canonical_thread": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2750",
+    "entry_overlap": {
+      "checked_at_utc": "2026-10-18T00:22:38Z",
+      "open_pr_records": 305,
+      "open_pr_pages": [
+        100,
+        100,
+        100,
+        5
+      ],
+      "non_atomic": true,
+      "discussion_records": 193,
+      "discussion_threads": [
+        1163,
+        1166,
+        1167,
+        2750,
+        2238,
+        2245
+      ],
+      "discussion_pagination_complete": false,
+      "helper_matches": 97,
+      "targeted_all_state_terms": [
+        "Newton",
+        "P104 producer",
+        "P104 quarter"
+      ],
+      "decision": "No observed competing actual Gaussian Newton producer-consumer scope; continue assigned questions. Coverage is bounded and not a novelty certificate.",
+      "limitations": [
+        "Rendered initial Discussion pages do not cover all paginated comments/replies.",
+        "Sparse local package references and unpublished work are incompletely searched."
+      ]
+    },
+    "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2750#discussioncomment-19008790",
+    "claim_created_utc": "2026-10-18T00:30:38Z",
+    "presubmission_overlap": {
+      "checked_at_utc": "2026-10-18T01:07:19.160795+00:00",
+      "open_pr_records": 323,
+      "open_pr_pages": [
+        100,
+        100,
+        100,
+        23
+      ],
+      "open_prs_complete_pagination": true,
+      "non_atomic": true,
+      "new_prs_since_entry": 18,
+      "existing_head_or_body_changes": 0,
+      "discussion_records": 192,
+      "discussion_threads": [
+        1163,
+        1166,
+        1167,
+        2750,
+        2238,
+        2245
+      ],
+      "discussion_pagination_complete": false,
+      "helper_broad_leads": 205,
+      "local_records": 13,
+      "coverage_limitations": "Sequential PR pages are not an atomic server snapshot. Six Discussion initial pages contain 192 visible bodies; comments/replies are incompletely paginated and some previously visible bodies shifted out. The offline helper also sees only 13 sparse local records; 205 broad matches are leads, not 205 independent investigations reviewed. Targeted all-state title searches do not paginate all closed work. No code diff inventory or exhaustive novelty claim.",
+      "decision": "Continue the existing explicitly assigned first-collector interface scope and preserve current claim 19008790; no reroll or frontier change. Record and credit complementary PR #3406 before publication.",
+      "concurrent_context": "Nick Petalas/petalas, head 18a054fd585ab4b2010770ec83cba0c9f28184e3, classifies the global independent principal-ideal product entrance for all 358 roles/all 5,398 events under inherited native covariance. Its released claim 19008906 explicitly preserves our distinct 58-bank producer/named-consumer/cost investigation. Treat as concurrent context; no imports or theorem replay performed.",
+      "distinct_evidence": "This package binds the actual 257-event cone and one reachable full-prefix witness; certifies phase-sensitive actual frame paths for 392 occurrences in the 63-bank open program; proves its physical A_F endpoints and 675 exact ports; and prices the full retained logical interface and conditional old-profile screen. It does not claim a new global product-domain theorem.",
+      "other_live_claim": "Discussion 2245 comment 19008886, Jose Manuel/jmbarrancoml, concerns reversible U=I-E/2 source preconditioning of PR #1991 and a changed correction Cprime. It changes an immutable-source/unchanged-correction premise in a different source word; no identical Newton interface scope observed.",
+      "relevant_pr_heads": [
+        {
+          "number": 3382,
+          "title": "Construct a phase-compatible exactness domain for the literal P104 collector",
+          "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3382",
+          "state": "open",
+          "head_sha": "2834523b1cd4ea83ba7a043e2e2f5f3332cf9909",
+          "created_at": "2026-10-18T00:02:56Z",
+          "updated_at": "2026-10-18T00:02:56Z",
+          "merged_at": null,
+          "returned_timeline_records": 0
+        },
+        {
+          "number": 3385,
+          "title": "Implement whole-call physical complex controller and root return",
+          "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3385",
+          "state": "open",
+          "head_sha": "7e5a187214126d31afc241a8f89f4a652352b58c",
+          "created_at": "2026-10-18T00:05:43Z",
+          "updated_at": "2026-10-18T00:17:26Z",
+          "merged_at": null,
+          "returned_timeline_records": 0
+        },
+        {
+          "number": 3406,
+          "title": "Research: certify the sharp whole-word P104 Newton entrance",
+          "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3406",
+          "state": "open",
+          "head_sha": "18a054fd585ab4b2010770ec83cba0c9f28184e3",
+          "created_at": "2026-10-18T00:52:54Z",
+          "updated_at": "2026-10-18T00:52:54Z",
+          "merged_at": null,
+          "returned_timeline_records": 0
+        }
+      ],
+      "locally_retained_evidence_sha256": {
+        "p104-interface-presubmit-open-prs.json": "0beceadd0bb8efcacf911331b4fb1664a09c07890a8b26da7512c5c528f4b1ee",
+        "p104-interface-presubmit-overlap-cache.json": "b19daabd845d3d7ed5a01cefc4733c070400d4b1d2a8616a812c6e264f4b3a7b",
+        "p104-interface-presubmit-overlap-helper.json": "b19aa620599cfe341f2929e1f1add0ad36f2806c66488c4f65dfc50883d4e082",
+        "p104-interface-presubmit-report.json": "204b62b8fc407b0dcab525c18a9dfa45c25bca67c39d9f776064ecb06fc384c5"
+      }
+    }
+  },
+  "checkpoints": [
+    {
+      "checked_at_utc": "2026-10-18T00:17:00Z",
+      "canonical_main": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+      "priority_revision": 6,
+      "decision": "Read current main guidance and assigned predecessor; preserve published branches and frozen inputs.",
+      "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "checked_at_utc": "2026-10-18T00:59:01Z",
+      "canonical_main": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+      "priority_revision": 6,
+      "decision": "Canonical main and all guidance/catalogue/selected bytes remain unchanged. Preserve frozen scientific inputs and finish the bounded assigned interface package; no supplier expansion.",
+      "files": [
+        {
+          "path": "AGENTS.md",
+          "sha256": "eb25d8ec495b80190a4b1a634710819bb74f0fae88d5203285c2b75b6f147347",
+          "unchanged": true
+        },
+        {
+          "path": "autoresearch.md",
+          "sha256": "8c98d179208c34a8c6768931e13f3bbeaa1cb63d59c660799ffde05c40935d9b",
+          "unchanged": true
+        },
+        {
+          "path": "CONTRIBUTING.md",
+          "sha256": "8a49fe97e2ad088a2b2e0c5b222aaab08752783b1f9c1260790d7dd13011d215",
+          "unchanged": true
+        },
+        {
+          "path": "docs/research/agent-procedure.md",
+          "sha256": "b2dd2f64e5746fce6289422351f2e3d1eb224f7db09aeb72f4d6626263190aa1",
+          "unchanged": true
+        },
+        {
+          "path": "docs/research/current-priorities.md",
+          "sha256": "c95e09baa997b48ba00a26ea29168e782b17392d28184ecb7a17eea5472dd77c",
+          "unchanged": true
+        },
+        {
+          "path": "docs/research/research-family-status.md",
+          "sha256": "9b98ab42364e90588e90410fd2773f9bc4bf5050f514101bed0a0246881b5b7e",
+          "unchanged": true
+        },
+        {
+          "path": "docs/research/agent-task-catalog.json",
+          "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0",
+          "unchanged": true
+        },
+        {
+          "path": "certificates/selected-result.json",
+          "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+          "unchanged": true
+        }
+      ],
+      "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    }
+  ],
+  "predecessor": {
+    "pr": 3382,
+    "head": "2834523b1cd4ea83ba7a043e2e2f5f3332cf9909",
+    "evidence_status": "Author-checked with separate automated checks; open and unreviewed at entry."
+  },
+  "family_decision": {
+    "decision": "narrow and retain; stop unchanged-profile supplier expansion",
+    "changed_premise": "Actual named producer inputs and downstream operation paths replace the hypothetical six-bank entrance only.",
+    "bounded_test": "Prove prefix admission on the exact 58-initial-bank cone, bind real downstream quarter sources and native maps, and test a concrete weaker-input counterexample.",
+    "cost_gate": "The inherited5forward/4dual full-consumer profile is tested under its frozen width and coverage. Producer preparation, native/backend, ownership, routing, control and recursive precision remain explicit unknown charges unless source-bound evidence supplies them.",
+    "stop_and_reopen": "Retain a local theorem or precise failure. Reopen supplier construction only with a changed admissible profile/coverage and a compatible fully paid caller.",
+    "bounded_result": "All52 initial Y in4B9 is necessary and sufficient for the producer prefix invariant, while a64impulse inB9 gives an exact reachable failure. Under52Y in4B9 plus11dirtyD/Q/G inB9, all63 logical rows restore in the independently certified full frame, privateC returns zero, and all675 outgoing increments are explicit.",
+    "cost_result": "The complete direct open-program bill and conservative1568H/7840H/1600H width bounds are proved. Under the exact inherited width73,832families, five-forward/four-dual profiles and coverage law, M_B(a)>=1+1560/[73(832+B)]>1 for every finite number of fully paid auxiliary banks. This is credited inherited evidence, not a universal P104 barrier or newly admitted physical tariff.",
+    "gate_reassessment": "The representation closes local actual-source and consumer implications but changes no frozen outer profile or coverage premise. Retain this independently reviewable bounded result and do not expand an unchanged-profile supplier."
+  },
+  "ai_assistance": "Substantial OpenAI assistance in mathematical exploration, four-agent concurrent analysis, independent implementations, source review, verification, documentation, and publication. Independent here means separate automated implementations and cross-review, not external human review.",
+  "evidence": "PRODUCER.md proves exact actual-prefix admission and a reachable counterexample; CONSUMER.md proves all392 phase-sensitive native paths, full-frame dirty restoration and all675 outgoing ports; COMPARISON.md derives the complete direct bill, finite width bounds and the credited unchanged-profile stop. verify.py authenticates all sources, compares four implementations and rejects source/receipt faults; RECEIPT.json retains the exact deterministic evidence. No whole-word, all-size physical supplier or selected-frontier improvement is claimed.",
+  "input_contract": {
+    "source_chart": "Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)",
+    "common_grid": "2^-f Gaussian integer numerators",
+    "initial_frames": "All63 selected persistent banks start at[]",
+    "mutable_numerical_roles": {
+      "Y22..Y32,Y63..Y103": "52initial banks in4B9; transport-only numerical sources, not certified immutable physical borrows",
+      "D27..D31,Q7": "6arbitrary dirty initial banks inB9",
+      "G27..G31": "5additional arbitrary dirty initial banks inB9"
+    },
+    "private_C": "Owned zero at2025; proved literal zero before2039 erasure",
+    "external_recipients": "83distinct target names across675ports; current values, ownership, widths and omitted histories remain caller obligations."
+  },
+  "output_contract": {
+    "internal": "Each selected persistent physical array equals A_F of its own initial array at actual final frameF=[256,128,64,32,16,8,4,2,1].",
+    "ports": "Every event, frame, source, target, coefficient and symbolic increment row retained. Gauge-normalized52X-target port operator is signed half of the52Y-source sum; no terminal externalX state is asserted.",
+    "full_frame_map": "A_F=(C^-1)^tensor9; E^-1A_FE=[[1,i],[0,-i]]^tensor9",
+    "scope_limits": [
+      "One bounded9-bit source word layer only.",
+      "The maximal final-cut admission domain is not classified.",
+      "The full2025-event numerical prefix is executed for the explicit negative point only; the universal theorem concerns the stated open program.",
+      "No physical ownership, routing, caller-admission, full external continuation or recursive supplier is certified."
+    ]
+  },
+  "open_questions": [
+    {
+      "question": "Can the675 ports be joined to an actual external consumer?",
+      "why_it_matters": "Their phase-normalized operator does not determine terminal physical external arrays without the omitted recipient histories.",
+      "first_step": "Bind the83external target names to their actual updates, native frames, reads and widths, then prove one composed terminal map using the retained exact increments.",
+      "blocked_by": "External target admission, numerical histories, width and ownership have not been supplied or paid."
+    },
+    {
+      "question": "Can a changed caller or profile pass a complete cost screen?",
+      "why_it_matters": "The unchanged5forward/4dual consumer remains unfavorable even with the new internal representation theorem.",
+      "first_step": "Name the exact profile or coverage premise being changed, supply a compatible input/adaptor contract paying52initial4B9 admissions and all exposed conversions, and test its complete physical/recursive bill.",
+      "blocked_by": "No changed admissible profile or coverage law and no fully paid physical caller are provided by this bounded result."
+    }
+  ],
+  "validation": {
+    "first_integrated_replay": "PASS_P104_NEWTON_INTERFACES",
+    "cross_implementation": "PASS_SEPARATE_IMPLEMENTATIONS_AGREE",
+    "runtime": "Python3.12, standard library only; direct replay needs noGit/network/predecessor checkout.",
+    "publication_gates": "Registered normal and optimised replay, source-history/committed-byte check, and source-complete Git-free export recorded in the PR handoff when complete.",
+    "registered_replay": "PASS_REGISTERED_RESEARCH_PACKAGE, normal and optimised complete replays, same retained receipt",
+    "registered_command": [
+      "python3",
+      "-I",
+      "-B",
+      "scripts/research_package.py",
+      "--package",
+      "research/p104-newton-interfaces"
+    ],
+    "python_version": "CPython3.12.14",
+    "registered_elapsed_seconds": "32.647",
+    "receipt_sha256": "fbc444897b13be5973c92ecfa5de67a8efae13b1aca0d8181bd430e2cffba1d3",
+    "metadata": "PASS_PACKAGE_METADATA_AND_PINS",
+    "independent_review": "Separate producer, consumer and cost agents reviewed source/phase/width/restoration scope. Joint verification additionally checks component PASS statuses before combining evidence. No external human review is claimed."
+  }
+}
diff --git a/research/p104-newton-interfaces/VERIFY.json b/research/p104-newton-interfaces/VERIFY.json
new file mode 100644
index 0000000000..e44579a4f5
--- /dev/null
+++ b/research/p104-newton-interfaces/VERIFY.json
@@ -0,0 +1,44 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "LICENSE",
+    "NOTICE",
+    "upstream/LICENSE",
+    "research/p104-rounded-collector/inputs/WORD.json",
+    "research/p104-rounded-collector/inputs/NATIVE.json.gz",
+    "research/p104-rounded-collector/PREDECESSORS.json",
+    "research/p104-rounded-collector/README.md",
+    "research/p104-consumer-budget-audit/README.md",
+    "research/p104-consumer-budget-audit/PREDECESSORS.json",
+    "research/p104-reversible-lifting/README.md",
+    "research/p104-invariant-lifting-lattice/README.md",
+    "research/p104-invariant-lifting-lattice/PROOF.md",
+    "research/p104-retimed-internal-grid/README.md"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Authenticate all external and retained inputs before loading source bytes; prove the actual producer and bounded consumer interfaces, phase-sensitive frame paths, conjugated maps, dirty restoration, all outgoing ports, constructive widths and complete direct bill; compare independent implementations and the typed deterministic receipt; exercise source, phase, quarter, and receipt failure controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Repeat the complete registered source and mathematical checks under optimised Python, retaining explicit validation and the same scientific receipt."
+    }
+  ]
+}
diff --git a/research/p104-newton-interfaces/consumer.py b/research/p104-newton-interfaces/consumer.py
new file mode 100644
index 0000000000..28bf1072a6
--- /dev/null
+++ b/research/p104-newton-interfaces/consumer.py
@@ -0,0 +1,670 @@
+#!/usr/bin/env python3
+"""Source-bound P104 open consumer interface, independently reconstructed.
+
+Prepared by Clear1nsight, with substantial OpenAI assistance.
+No predecessor executable or primary producer/model module is imported.
+"""
+
+from __future__ import annotations
+
+import argparse
+from collections import Counter
+from fractions import Fraction
+import gzip
+import hashlib
+import io
+import json
+from pathlib import Path
+
+
+WORD_SHA256 = "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50"
+NATIVE_SHA256 = "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d"
+N = 512
+BITS = 9
+STOP = 4516
+FULL = (256, 128, 64, 32, 16, 8, 4, 2, 1)
+QUERY = (364,)
+OLD = (256, 136, 64, 40, 16, 4, 2, 1)
+Y_NAMES = tuple(f"Y{i}" for i in (*range(22, 33), *range(63, 104)))
+D_NAMES = tuple(f"D{i}" for i in range(27, 32))
+G_NAMES = tuple(f"G{i}" for i in range(27, 32))
+ROLES = frozenset((*Y_NAMES, *D_NAMES, "Q7", *G_NAMES))
+ZERO = (0, 0)
+ONE = (1, 0)
+PI = (1, 1)
+
+
+class Rejected(ValueError):
+    pass
+
+
+def need(condition, message):
+    if not condition:
+        raise Rejected(message)
+
+
+def digest(obj):
+    return hashlib.sha256(json.dumps(obj, sort_keys=True, separators=(",", ":")).encode()).hexdigest()
+
+
+def mul(z, w):
+    return z[0] * w[0] - z[1] * w[1], z[0] * w[1] + z[1] * w[0]
+
+
+def unit(z, power):
+    a, b = z
+    return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4]
+
+
+def pi_power(exponent):
+    out = ONE
+    for _ in range(exponent):
+        out = mul(out, PI)
+    return out
+
+
+PI_POWERS = tuple(pi_power(k) for k in range(BITS + 1))
+
+
+def encode(coefficients):
+    need(len(coefficients) == N, "encoder dimension")
+    out = [mul(z, PI_POWERS[i.bit_count()]) for i, z in enumerate(coefficients)]
+    for j in range(BITS):
+        bit = 1 << j
+        for i in range(N):
+            if i & bit:
+                a, b = out[i], out[i ^ bit]
+                out[i] = a[0] + b[0], a[1] + b[1]
+    return out
+
+
+def decode(values):
+    need(len(values) == N, "decoder dimension")
+    out = list(values)
+    for j in range(BITS):
+        bit = 1 << j
+        for i in range(N):
+            if i & bit:
+                a, b = out[i], out[i ^ bit]
+                out[i] = a[0] - b[0], a[1] - b[1]
+    for i, z in enumerate(out):
+        a, b = z
+        for _ in range(i.bit_count()):
+            need((a + b) % 2 == 0 and (b - a) % 2 == 0, f"Newton divisibility at coefficient {i}")
+            a, b = (a + b) // 2, (b - a) // 2
+        out[i] = a, b
+    return out
+
+
+def in_scaled_B(values, scalar):
+    need(all(a % scalar == 0 and b % scalar == 0 for a, b in values), f"entry divisibility by {scalar}")
+    return decode([(a // scalar, b // scalar) for a, b in values])
+
+
+def invert_rows(rows):
+    work = [row | (1 << (BITS + i)) for i, row in enumerate(rows)]
+    for j in range(BITS):
+        pivots = [i for i in range(j, BITS) if (work[i] >> j) & 1]
+        need(bool(pivots), "singular wrapper address matrix")
+        i = pivots[0]
+        work[i], work[j] = work[j], work[i]
+        for i in range(BITS):
+            if i != j and ((work[i] >> j) & 1):
+                work[i] ^= work[j]
+    need([row & (N - 1) for row in work] == [1 << i for i in range(BITS)], "wrapper inverse reduction")
+    return [row >> BITS for row in work]
+
+
+def row_apply(rows, value):
+    return sum(((row & value).bit_count() & 1) << i for i, row in enumerate(rows))
+
+
+class Wrapper:
+    def __init__(self, raw):
+        need(set(raw) == {"matrix_rows", "offset", "linear_Z4", "quadratic_rows", "phase"}, "wrapper schema")
+        self.raw = raw
+        self.rows = raw["matrix_rows"]
+        self.linear = raw["linear_Z4"]
+        self.quadratic = raw["quadratic_rows"]
+        need(len(self.rows) == len(self.linear) == len(self.quadratic) == BITS, "wrapper width")
+        need(all(type(a) is int and 0 <= a < N for a in self.rows + self.quadratic), "wrapper binary masks")
+        need(all(type(a) is int and 0 <= a < 4 for a in self.linear), "wrapper linear phase")
+        need(type(raw["offset"]) is int and 0 <= raw["offset"] < N, "wrapper offset")
+        need(type(raw["phase"]) is int and 0 <= raw["phase"] < 4, "wrapper global phase")
+        self.inverse = invert_rows(self.rows)
+        self.permutation = [row_apply(self.rows, x) ^ raw["offset"] for x in range(N)]
+        need(len(set(self.permutation)) == N, "wrapper permutation")
+        self.phases = [self.phase(x) for x in range(N)]
+        self.pauli_cache = {}
+
+    def phase(self, x):
+        phase = self.raw["phase"]
+        for j in range(BITS):
+            if (x >> j) & 1:
+                phase += self.linear[j]
+                phase += 2 * (self.quadratic[j] & x & ~((1 << (j + 1)) - 1)).bit_count()
+        return phase % 4
+
+    def apply(self, values):
+        out = [ZERO] * N
+        for i, z in enumerate(values):
+            out[self.permutation[i]] = unit(z, self.phases[i])
+        return out
+
+    def pauli(self, value):
+        """W P(u,v,k) W^-1, P|x> = i^k (-1)^(v.x) |x xor u>."""
+        if value in self.pauli_cache:
+            return self.pauli_cache[value]
+        u, v, k = value
+        shifted_v = v
+        for j in range(BITS):
+            if ((u >> j) & 1) and (self.linear[j] & 1):
+                shifted_v ^= 1 << j
+            neighbors = 0
+            for h in range(BITS):
+                if h != j and ((self.quadratic[min(j, h)] >> max(j, h)) & 1):
+                    neighbors ^= ((u >> h) & 1)
+            if neighbors:
+                shifted_v ^= 1 << j
+        out_v = 0
+        for j in range(BITS):
+            if (shifted_v >> j) & 1:
+                out_v ^= self.inverse[j]
+        out_u = row_apply(self.rows, u)
+        out_k = (k + self.phase(u) - self.phase(0) + 2 * (out_v & self.raw["offset"]).bit_count()) % 4
+        out = out_u, out_v, out_k
+        # This independent, finite basis comparison authenticates the formula
+        # for each Pauli actually encountered by the path certificate.
+        for x in range(N):
+            y = self.permutation[x]
+            need(self.permutation[x ^ u] == (y ^ out_u), "Pauli wrapper address action")
+            left_phase = self.phases[x ^ u] - self.phases[x] + k + 2 * (v & x).bit_count()
+            right_phase = out_k + 2 * (out_v & y).bit_count()
+            need((left_phase - right_phase) % 4 == 0, "Pauli wrapper phase action")
+        self.pauli_cache[value] = out
+        return out
+
+
+def normalize_dyadic(values, denominator_power):
+    while denominator_power and all((a & 1) == 0 and (b & 1) == 0 for a, b in values):
+        values = [(a // 2, b // 2) for a, b in values]
+        denominator_power -= 1
+    return values, denominator_power
+
+
+def c_numerators(a, b):
+    ar, ai = a
+    br, bi = b
+    return ((ar + br - ai + bi, ai + bi + ar - br),
+            (ar + br + ai - bi, ai + bi - ar + br))
+
+
+def floor_pair(a, b):
+    dr, di = a[0] - b[0], a[1] - b[1]
+    sr, si = b[0] + dr // 2, b[1] + di // 2
+    rr, ri = -di, dr
+    out_b = sr - rr // 2, si - ri // 2
+    return (out_b[0] + rr, out_b[1] + ri), out_b
+
+
+class Native:
+    def __init__(self, raw, wrapper_cache):
+        need(set(raw) == {"left", "rank", "right"}, "native recipe schema")
+        need(type(raw["rank"]) is int and 0 <= raw["rank"] <= BITS, "native rank")
+        self.raw = raw
+        self.rank = raw["rank"]
+        pair = []
+        for side in ("right", "left"):
+            key = digest(raw[side])
+            if key not in wrapper_cache:
+                wrapper_cache[key] = Wrapper(raw[side])
+            pair.append(wrapper_cache[key])
+        self.right, self.left = pair
+
+    def pauli(self, value):
+        u, v, k = self.right.pauli(value)
+        mask = (1 << self.rank) - 1
+        u ^= v & mask
+        k = (k + 3 * (v & mask).bit_count()) % 4
+        return self.left.pauli((u, v, k))
+
+    def dyadic(self, values, denominator_power=0):
+        out = self.right.apply(values)
+        for j in range(self.rank):
+            bit = 1 << j
+            for i in range(N):
+                if not i & bit:
+                    out[i], out[i | bit] = c_numerators(out[i], out[i | bit])
+            denominator_power += 1
+        return normalize_dyadic(self.left.apply(out), denominator_power)
+
+    def integral(self, values, counts, domain_scale=1):
+        out = self.right.apply(values)
+        in_scaled_B(out, domain_scale)
+        counts["complete_wrapper_domain_checks"] += 1
+        for j in range(self.rank):
+            bit = 1 << j
+            for i in range(N):
+                if not i & bit:
+                    a, b = out[i], out[i | bit]
+                    numerator_a, numerator_b = c_numerators(a, b)
+                    need(all(x % 2 == 0 for x in (*numerator_a, *numerator_b)), "literal native Gaussian division")
+                    exact = tuple((z[0] // 2, z[1] // 2) for z in (numerator_a, numerator_b))
+                    need(exact == floor_pair(a, b), "literal signed-floor disagreement")
+                    out[i], out[i | bit] = exact
+                    counts["native_pair_comparisons"] += 1
+            in_scaled_B(out, domain_scale)
+            counts["complete_coordinate_domain_checks"] += 1
+        out = self.left.apply(out)
+        in_scaled_B(out, domain_scale)
+        counts["complete_wrapper_domain_checks"] += 1
+        return out
+
+
+def read_inputs(word_path, native_path):
+    word_path, native_path = Path(word_path), Path(native_path)
+    need(word_path.stat().st_size <= 1_000_000, "WORD byte bound")
+    need(native_path.stat().st_size <= 1_000_000, "NATIVE compressed byte bound")
+    word_bytes, native_bytes = word_path.read_bytes(), native_path.read_bytes()
+    need(hashlib.sha256(word_bytes).hexdigest() == WORD_SHA256, "WORD SHA256")
+    need(hashlib.sha256(native_bytes).hexdigest() == NATIVE_SHA256, "NATIVE SHA256")
+    with gzip.GzipFile(fileobj=io.BytesIO(native_bytes)) as stream:
+        inflated = stream.read(16_000_001)
+    need(len(inflated) <= 16_000_000, "NATIVE inflated byte bound")
+    word, native = json.loads(word_bytes), json.loads(inflated)
+    need(word["chart"] == "Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)", "literal chart")
+    need(native["chart"] == word["chart"], "matching native chart")
+    need(len(word["program"]) == 5398, "literal word length")
+    frames = {key: tuple(value) for key, value in word["initial_frames"].items()}
+    for i, event in enumerate(word["program"][:STOP + 1]):
+        op, role = event[:2]
+        if op == "transport":
+            need(frames[role] == tuple(event[2]), f"old frame at event {i}")
+            frames[role] = tuple(event[3])
+        elif op == "sign":
+            need(Fraction(event[2]) == -1 and frames[role] == tuple(event[3]), f"sign frame at event {i}")
+        elif op == "add":
+            need(frames[role] == frames[event[2]] == tuple(event[4]), f"ADD frame at event {i}")
+        elif op == "zero":
+            need(role not in frames, f"private freshness at event {i}")
+            frames[role] = tuple(event[2])
+        elif op == "erase":
+            need(frames.pop(role) == tuple(event[2]), f"erase frame at event {i}")
+        else:
+            raise Rejected(f"unexpected opcode at event {i}")
+    need(all(tuple(word["initial_frames"][role]) == () for role in ROLES), "initial interface frames")
+    need(all(frames[role] == FULL for role in ROLES), "all63 final physical frames")
+    entries = {}
+    for record in native["transports"]:
+        for i in record["events"]:
+            need(i not in entries, "duplicate native occurrence")
+            entries[i] = record
+    wrapper_cache = {}
+    recipe_cache = {}
+    bound = {}
+    for i, event in enumerate(word["program"][:STOP + 1]):
+        if event[0] != "transport" or not (event[1] in ROLES or 2025 <= i <= 2039):
+            continue
+        need(i in entries, f"missing native occurrence {i}")
+        record = entries[i]
+        need(record["old"] == event[2] and record["new"] == event[3], f"native frame binding {i}")
+        need(record["recipe"]["rank"] == event[4], f"native rank binding {i}")
+        key = digest(record["recipe"])
+        if key not in recipe_cache:
+            recipe_cache[key] = Native(record["recipe"], wrapper_cache)
+        bound[i] = recipe_cache[key]
+    return word, bound, wrapper_cache
+
+
+def extract(word):
+    program = word["program"]
+    for i, event in enumerate(program[:STOP + 1]):
+        if event[0] == "add" and ((event[1] == "C" and event[2] in ROLES)
+                                  or (event[1] in ROLES and event[2] == "C")):
+            need(2025 <= i <= 2039, "all selected/private interactions belong to the retained collector")
+    closed = [i for i, event in enumerate(program[:STOP + 1])
+              if (event[1] in ROLES and event[0] in ("transport", "sign", "add")) or 2025 <= i <= 2039]
+    ports = [i for i, event in enumerate(program[:STOP + 1])
+             if event[0] == "add" and event[2] in ROLES and event[1] not in ROLES and event[1] != "C"]
+    for i in closed:
+        event = program[i]
+        if event[0] == "add":
+            need(event[2] in ROLES or event[2] == "C", f"unbound incoming source {i}")
+        need(event[0] != "sign", "unexpected selected sign")
+    need(len(closed) == 576 and len(ports) == 675, "source cone counts")
+    need(len(set(closed) & set(ports)) == 0, "closed/port overlap")
+    return closed, ports
+
+
+def same_operator(candidate, reference, context):
+    need(candidate["paulis"] == reference["paulis"], f"Pauli path action: {context}")
+    need(candidate["anchor"] == reference["anchor"], f"global path phase: {context}")
+
+
+def certify_paths(word, bound, closed):
+    generators = [(1 << j, 0, 0) for j in range(BITS)] + [(0, 1 << j, 0) for j in range(BITS)]
+    anchor = [ONE] + [ZERO] * (N - 1)
+    potentials = {(): {"paulis": generators, "anchor": (anchor, 0), "path": []}}
+    edge_records = []
+    redundant = 0
+    for i in closed:
+        event = word["program"][i]
+        if event[0] != "transport":
+            continue
+        old, new = tuple(event[2]), tuple(event[3])
+        need(old in potentials, f"disconnected actual frame path at {i}")
+        previous = potentials[old]
+        native = bound[i]
+        candidate = {
+            "paulis": [native.pauli(p) for p in previous["paulis"]],
+            "anchor": native.dyadic(*previous["anchor"]),
+            "path": previous["path"] + [i],
+        }
+        if new in potentials:
+            same_operator(candidate, potentials[new], f"event {i}")
+            redundant += 1
+        else:
+            potentials[new] = candidate
+        edge_records.append({"event": i, "old": list(old), "new": list(new), "recipe_sha256": digest(native.raw)})
+    need(FULL in potentials and QUERY in potentials and OLD in potentials, "required frame potentials")
+    # A genuine source-shaped global phase corruption must be detected even
+    # though it has identical action on all Pauli generators.
+    mutated_raw = json.loads(json.dumps(bound[2033].raw))
+    mutated_raw["left"]["phase"] = (mutated_raw["left"]["phase"] + 1) % 4
+    mutated = Native(mutated_raw, {})
+    start = potentials[QUERY]
+    candidate = {"paulis": [mutated.pauli(p) for p in start["paulis"]],
+                 "anchor": mutated.dyadic(*start["anchor"])}
+    need(candidate["paulis"] == potentials[OLD]["paulis"], "phase control calibration")
+    try:
+        same_operator(candidate, potentials[OLD], "mutated event2033 phase")
+    except Rejected as error:
+        need(str(error).startswith("global path phase"), "phase control diagnostic")
+    else:
+        raise Rejected("phase-only path mutation accepted")
+    return potentials, {
+        "status": "PASS_ALL_ACTUAL_FRAME_PATHS",
+        "method": "18 Pauli generator images plus exact nonzero dyadic anchor column",
+        "native_occurrences": len(edge_records),
+        "distinct_frames": len(potentials),
+        "redundant_path_equalities": redundant,
+        "native_edge_manifest_sha256": digest(edge_records),
+        "frame_potentials_sha256": digest([
+            {"frame": list(frame), "paulis": value["paulis"], "anchor": value["anchor"], "path": value["path"]}
+            for frame, value in sorted(potentials.items())]),
+        "actual_return_global_phase_control": "REJECT_GLOBAL_PATH_PHASE_WITH_IDENTICAL_PAULI_ACTION",
+        "query_frame_path": potentials[QUERY]["path"],
+        "full_frame_path": potentials[FULL]["path"],
+    }
+
+
+def apply_path(values, path, bound):
+    denominator = 0
+    out = list(values)
+    for i in path:
+        out, denominator = bound[i].dyadic(out, denominator)
+    return out, denominator
+
+
+def verify_full_frame_tensor(potentials):
+    """Independently bind Delta_F to the tensor product of inverse C gates."""
+    generators = [(1 << j, 0, 0) for j in range(BITS)] + [(0, 1 << j, 0) for j in range(BITS)]
+    paulis = [(u ^ v, v, (k + v.bit_count()) % 4) for u, v, k in generators]
+    values = [ONE] + [ZERO] * (N - 1)
+    for j in range(BITS):
+        bit = 1 << j
+        for i in range(N):
+            if not i & bit:
+                (ar, ai), (br, bi) = values[i], values[i | bit]
+                values[i] = ar + br + ai - bi, ai + bi - ar + br
+                values[i | bit] = ar + br - ai + bi, ai + bi + ar - br
+    candidate = {"paulis": paulis, "anchor": normalize_dyadic(values, BITS)}
+    same_operator(candidate, potentials[FULL], "full-frame tensor C inverse")
+    return {
+        "physical_operator": "A_F = (C^-1) tensor-power 9 for the authenticated actual full-frame path",
+        "coefficient_operator": "E^-1 A_F E = [[1,i],[0,-i]] tensor-power 9",
+        "proof_certificate": "equal 18-generator Pauli action and exact nonzero anchor",
+    }
+
+
+def conjugated_matrix(path, bound):
+    hasher = hashlib.sha256()
+    max_component = 0
+    nonzero = 0
+    first_column = None
+    for s in range(N):
+        # This is one complete column of E, derived without calling encode.
+        encoded = [PI_POWERS[s.bit_count()] if x & s == s else ZERO for x in range(N)]
+        native_values, denominator = apply_path(encoded, path, bound)
+        need(denominator == 0, "conjugated map Gaussian integrality")
+        column = decode(native_values)
+        nonzero += sum(z != ZERO for z in column)
+        max_component = max(max_component, max(max(abs(a), abs(b)) for a, b in column))
+        hasher.update(json.dumps(column, separators=(",", ":")).encode() + b"\n")
+        if s == 0:
+            first_column = column
+    return {"columns": N, "nonzero_entries": nonzero, "maximum_absolute_component": max_component,
+            "column_json_lines_sha256": hasher.hexdigest()}, first_column
+
+
+def scale_array(values, coefficient):
+    coefficient = Fraction(coefficient)
+    numerator, denominator = coefficient.numerator, coefficient.denominator
+    need(all((a * numerator) % denominator == 0 and (b * numerator) % denominator == 0 for a, b in values),
+         "whole-array coefficient Gaussian integrality")
+    return [(a * numerator // denominator, b * numerator // denominator) for a, b in values]
+
+
+def add_arrays(left, right):
+    return [(a[0] + b[0], a[1] + b[1]) for a, b in zip(left, right, strict=True)]
+
+
+def symbolic_rows(program, closed, ports):
+    """Integer rows: each Y symbol is its INITIAL value divided by four."""
+    names = sorted(ROLES)
+    index = {role: i for i, role in enumerate(names)}
+    rows = {role: [((4 if role in Y_NAMES else 1) if i == index[role] else 0) for i in range(len(names))]
+            for role in names}
+    initial = {role: list(row) for role, row in rows.items()}
+    port_set = set(ports)
+    port_rows = []
+    totals = {}
+    for i in sorted(closed + ports):
+        event = program[i]
+        op, role = event[:2]
+        if op == "transport":
+            # The independent operator path certificate is established first.
+            continue
+        if op == "zero":
+            need(role not in rows, "symbolic private freshness")
+            rows[role] = [0] * len(names)
+        elif op == "erase":
+            need(not any(rows.pop(role)), "symbolic private erase")
+        elif op == "add":
+            coefficient = Fraction(event[3])
+            raw = [coefficient.numerator * v for v in rows[event[2]]]
+            need(all(v % coefficient.denominator == 0 for v in raw), "normalized initial-symbol division")
+            increment = [v // coefficient.denominator for v in raw]
+            if i in port_set:
+                port_rows.append({"event": i, "target": role, "source": event[2],
+                                  "coefficient": str(coefficient), "frame": event[4],
+                                  "initial_symbol_row": {name: v for name, v in zip(names, increment) if v}})
+                previous = totals.setdefault(role, [0] * len(names))
+                totals[role] = [a + b for a, b in zip(previous, increment, strict=True)]
+            else:
+                rows[role] = [a + b for a, b in zip(rows[role], increment, strict=True)]
+        else:
+            raise Rejected(f"unexpected symbolic opcode {op}")
+    return names, initial, rows, port_rows, totals
+
+
+def certify_symbolic_interface(word, closed, ports):
+    names, initial, rows, port_rows, totals = symbolic_rows(word["program"], closed, ports)
+    need(rows == initial, "63-bank final restoration in authenticated frame gauges")
+    x_rows = {role: row for role, row in totals.items() if role.startswith("X")}
+    need(len(x_rows) == 52, "external X-port channel width")
+    signs = {}
+    for role, row in x_rows.items():
+        values = {row[j] for j, name in enumerate(names) if name in Y_NAMES}
+        need(values in ({2}, {-2}), "external X-port uniform Y channel")
+        need(all(v == 0 for name, v in zip(names, row) if name not in Y_NAMES), "external X-port dirty cancellation")
+        signs[role] = next(iter(values)) // 2
+    changed_program = [list(event) for event in word["program"]]
+    need(changed_program[2162] == ["add", "D28", "Y103", "-1/4", list(FULL)], "actual quarter control target")
+    changed_program[2162][3] = "1/4"
+    _, changed_initial, changed_rows, _, _ = symbolic_rows(changed_program, closed, ports)
+    need(changed_rows != changed_initial, "wrong actual quarter sign accepted")
+    delta = [a - b for a, b in zip(changed_rows["D28"], changed_initial["D28"], strict=True)]
+    need({name: v for name, v in zip(names, delta) if v} == {"Y103": 2}, "wrong quarter sign residual")
+    return {
+        "status": "PASS_EXACT_OPEN_INTERFACE_ROWS",
+        "symbol_convention": "Y symbol = initial Y / 4; other symbol = initial bank, all in B_9",
+        "persistent_banks_restored_in_full_frame": sorted(ROLES),
+        "external_port_count": len(port_rows),
+        "external_port_records": port_rows,
+        "external_port_records_sha256": digest(port_rows),
+        "external_port_counts_by_source_family": dict(Counter(row["source"][0] for row in port_rows)),
+        "external_port_counts_by_target_family": dict(Counter(row["target"][0] for row in port_rows)),
+        "external_port_coefficient_counts": dict(Counter(row["coefficient"] for row in port_rows)),
+        "gauge_normalized_X_port_operator": {
+            "target_signs": dict(sorted(signs.items())),
+            "input_sources": list(Y_NAMES),
+            "coefficient_on_each_original_Y": "target_sign / 2",
+            "scalar_52_by_52_bank_matrix_rank_over_Q_i": 1,
+            "expanded_512_entry_array_map_rank_over_Q_i": 512,
+            "dirty_D_Q_G_coefficients": "all zero",
+            "scope": "sum of frame-normalized outgoing ports; omitted external bank histories and terminal states are not executed",
+        },
+        "wrong_actual_quarter_sign_control": {
+            "event": 2162, "original": "-1/4", "mutation": "1/4",
+            "result": "REJECT_D28_RESTORATION",
+            "residual_on_initial_Y103": "1/2",
+            "lattice_admission_unchanged": True,
+        },
+    }
+
+
+def dense_open_replay(word, bound, closed, ports, potentials):
+    coefficients = {}
+    initial = {}
+    for role in sorted(ROLES):
+        tag = int.from_bytes(hashlib.sha256(role.encode()).digest()[:4], "big")
+        c = [(((17 * j + tag + (j >> 2)) % 7) - 3, ((11 * j + tag + (j >> 3)) % 9) - 4) for j in range(N)]
+        coefficients[role] = c
+        initial[role] = scale_array(encode(c), 4 if role in Y_NAMES else 1)
+        in_scaled_B(initial[role], 4 if role in Y_NAMES else 1)
+    states = {role: list(values) for role, values in initial.items()}
+    counts = Counter()
+    port_set = set(ports)
+    port_hash = hashlib.sha256()
+    milestone_hashes = {}
+    max_state_component = max(max(abs(a), abs(b)) for values in states.values() for a, b in values)
+    for i in sorted(closed + ports):
+        event = word["program"][i]
+        op, role = event[:2]
+        if op == "transport":
+            states[role] = bound[i].integral(states[role], counts, 4 if role in Y_NAMES else 1)
+        elif op == "zero":
+            need(role not in states, "dense private freshness")
+            states[role] = [ZERO] * N
+            counts["private_zero_allocations"] += 1
+        elif op == "erase":
+            need(states.pop(role) == [ZERO] * N, "dense literal private erase")
+            counts["private_literal_zero_erasures"] += 1
+        elif op == "add":
+            increment = scale_array(states[event[2]], event[3])
+            decode(increment)
+            if i in port_set:
+                counts["computed_external_increment_arrays"] += 1
+                port_hash.update(json.dumps([i, increment], separators=(",", ":")).encode() + b"\n")
+            else:
+                states[role] = add_arrays(states[role], increment)
+                in_scaled_B(states[role], 4 if role in Y_NAMES else 1)
+                counts["executed_internal_array_adds"] += 1
+        else:
+            raise Rejected(f"unexpected dense opcode {op}")
+        if role in states and i not in port_set:
+            max_state_component = max(max_state_component, max(max(abs(a), abs(b)) for a, b in states[role]))
+        if i in (2039, 2480, 3056, 4173, 4516):
+            milestone_hashes[str(i)] = digest({role: states[role] for role in sorted(ROLES)})
+    expected = {}
+    for role in sorted(ROLES):
+        values, denominator = apply_path(initial[role], potentials[FULL]["path"], bound)
+        need(denominator == 0, "dense expected final Gaussian integrality")
+        need(states[role] == values, f"dense final transported restoration {role}")
+        expected[role] = values
+    need(counts["native_pair_comparisons"] == 148736, "dense pair count")
+    need(counts["computed_external_increment_arrays"] == 675, "dense external increment count")
+    need(counts["executed_internal_array_adds"] == 182, "dense internal ADD count")
+    return {
+        "status": "PASS_DENSE_CHRONOLOGICAL_OPEN_REPLAY",
+        "fixture": "all63 banks nonzero signed deterministic Gaussian Newton coefficients",
+        "initial_values_sha256": digest(initial),
+        "initial_coefficients_sha256": digest(coefficients),
+        "final_values_sha256": digest(states),
+        "external_increment_json_lines_sha256": port_hash.hexdigest(),
+        "milestone_state_hashes": milestone_hashes,
+        "observed_maximum_absolute_internal_component": max_state_component,
+        "counts": dict(counts),
+        "external_execution_scope": "actual source increments computed and checked; recipient updates and omitted external histories are not simulated",
+    }
+
+
+def verify_consumer(word_path, native_path):
+    word, bound, wrappers = read_inputs(word_path, native_path)
+    closed, ports = extract(word)
+    potentials, path_receipt = certify_paths(word, bound, closed)
+    result = {
+        "status": "PASS_P104_OPEN_CONSUMER_INTERFACE",
+        "inputs": {"WORD.json": WORD_SHA256, "NATIVE.json.gz": NATIVE_SHA256},
+        "chart": word["chart"],
+        "through_event": STOP,
+        "closed_event_indices": closed,
+        "external_read_event_indices": ports,
+        "closed_opcode_counts": dict(Counter(word["program"][i][0] for i in closed)),
+        "closed_native_rank_sum": sum(word["program"][i][4] for i in closed if word["program"][i][0] == "transport"),
+        "path_certificate": path_receipt,
+        "authenticated_wrapper_count": len(wrappers),
+        "full_frame_tensor_identity": verify_full_frame_tensor(potentials),
+    }
+    query_matrix, query_column = conjugated_matrix(potentials[QUERY]["path"], bound)
+    full_matrix, _ = conjugated_matrix(potentials[FULL]["path"], bound)
+    native_column, denominator = apply_path([ONE] + [ZERO] * (N - 1), potentials[QUERY]["path"], bound)
+    differences = [i for i, z in enumerate(native_column) if z != tuple(v * (1 << denominator) for v in query_column[i])]
+    need(bool(differences), "actual query map falsely commutes with E")
+    i = differences[0]
+    result["coefficient_maps"] = {
+        "convention": "E^-1 A E for the actual source-bound frame operator A",
+        "query_frame": query_matrix,
+        "full_frame": full_matrix,
+        "wrong_unconjugated_map_control": {
+            "input_coefficient_index": 0,
+            "first_difference_index": i,
+            "conjugated_integer_output": query_column[i],
+            "unconjugated_output_numerator": native_column[i],
+            "unconjugated_denominator": 1 << denominator,
+            "differing_coordinates": len(differences),
+        },
+    }
+    result["symbolic_open_interface"] = certify_symbolic_interface(word, closed, ports)
+    result["dense_open_replay"] = dense_open_replay(word, bound, closed, ports, potentials)
+    return result
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--repo", type=Path, default=Path(__file__).resolve().parents[2])
+    parser.add_argument("--output", type=Path)
+    args = parser.parse_args()
+    result = verify_consumer(args.repo / "research/p104-rounded-collector/inputs/WORD.json",
+                             args.repo / "research/p104-rounded-collector/inputs/NATIVE.json.gz")
+    encoded = json.dumps(result, indent=2, sort_keys=True) + "\n"
+    if args.output:
+        with args.output.open("x", encoding="utf-8") as stream:
+            stream.write(encoded)
+    else:
+        print(encoded, end="")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/p104-newton-interfaces/cost_audit.py b/research/p104-newton-interfaces/cost_audit.py
new file mode 100644
index 0000000000..c524427dfd
--- /dev/null
+++ b/research/p104-newton-interfaces/cost_audit.py
@@ -0,0 +1,378 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Independent source/count and rational cost audit; no predecessor imports.
+
+Clear1nsight, with substantial OpenAI assistance.
+This script proves no physical running-time or recursive supplier theorem.
+With --source-root it authenticates the three exact immutable inputs, derives
+the producer dependency cone and the 63-state open program, then counts one
+specified direct in-place schedule.  Without it, only the rational arithmetic
+and per-bank codec reference counts are evaluated.
+"""
+
+import argparse
+from collections import Counter
+from fractions import Fraction
+import gzip
+import hashlib
+import json
+from pathlib import Path
+
+
+MAIN = "6f100d4bb5083f8c35d96fd95a539811c62f245c"
+SOURCE_PINS = {
+    "research/p104-rounded-collector/inputs/WORD.json":
+        "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50",
+    "research/p104-rounded-collector/inputs/NATIVE.json.gz":
+        "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d",
+    "research/p104-consumer-budget-audit/README.md":
+        "13694215d0c1a245b392f7155e8395b9c4bad9c5db3558833c784d9449616417",
+}
+N = 512
+
+
+def need(condition, reason):
+    if not condition:
+        raise ValueError(reason)
+
+
+def sha(data):
+    return hashlib.sha256(data).hexdigest()
+
+
+def canonical_sha(value):
+    return sha(json.dumps(value, sort_keys=True, separators=(",", ":")).encode())
+
+
+def counted(values):
+    return dict(sorted(Counter(str(x) for x in values).items()))
+
+
+def fixed_consumer():
+    """PR2744's unmodified, fixed-profile relaxation; exact rational work only."""
+    profiles = {
+        "F2458": [1216, 74, 86, 104, 48, 42, 68, 8],
+        "D2712": [1498, 60, 74, 92, 58, 56, 92, 8],
+        "D2725": [1502, 58, 74, 93, 57, 56, 91, 9],
+    }
+    masses = {key: sum((r + 1) * n for r, n in enumerate(profile))
+              for key, profile in profiles.items()}
+    need(masses == {"F2458": 3070, "D2712": 3542, "D2725": 3542},
+         "pinned profile mass")
+    width, families, forward, dual = 73, 832, 5, 4
+    progress = 104 * 8 + 104 * 8 + 150 * 9
+    remaining = (width - 1) * families - (forward + dual) * progress
+    capacity = width * families
+    totals = {key: forward * masses["F2458"] + dual * masses[key] + remaining
+              for key in ("D2712", "D2725")}
+    need(progress == 3014 and remaining == 32778 and capacity == 60736,
+         "coverage arithmetic")
+    need(set(totals.values()) == {62296}, "unmodified consumer total")
+    gap = totals["D2712"] - capacity
+    need(gap == 1560 and Fraction(62296, capacity) == Fraction(599, 584),
+         "inherited rational stop")
+    bank_samples = {}
+    for banks in (0, 1, 22, 63, 83, 832, 10**6):
+        lower = Fraction(62296 + width * banks, width * (families + banks))
+        need(lower == 1 + Fraction(gap, width * (families + banks)) and lower > 1,
+             "fully paid bank identity")
+        bank_samples[str(banks)] = str(lower)
+    # A meaningful failure control: adding families only to the denominator
+    # produces a false favourable screen already at B=22.
+    denominator_only = Fraction(62296, width * (families + 22))
+    paid = Fraction(62296 + 22 * width, width * (families + 22))
+    need(denominator_only < 1 < paid, "unpaid-bank false-positive control")
+    return {
+        "credit": "Jose Manuel, Discussion2619 comment18955566; Vasek/flyingviper PR2744",
+        "predecessor_head": "0166260409f55a56e7fefa48d859f7dd5b42b300",
+        "profiles": profiles, "rank_masses": masses,
+        "width": width, "original_families": families,
+        "forward_calls": forward, "dual_calls": dual,
+        "progress_per_call": progress, "remaining_coverage_mass": remaining,
+        "capacity": capacity, "unmodified_total": 62296, "excess_mass": gap,
+        "no_bank_lower_bound": "599/584",
+        "all_finite_fully_paid_banks_formula": "1 + 1560/(73*(832+B))",
+        "saving_domain": "0 <= a < 1",
+        "proof_step": "For 0 < r <= 73, (r/73)^(1-a) >= r/73.",
+        "bank_examples_not_the_universal_proof": bank_samples,
+        "negative_control": {
+            "unauthorised_denominator_only_B22": str(denominator_only),
+            "correct_fully_paid_B22": str(paid),
+            "reason_rejected": "Every added bank owes 73 paid coverage units.",
+        },
+        "scope": "Fixed profiles and coverage only; no universal P104 obstruction.",
+        "all_additional_physical_costs": "unresolved nonnegative charges, not zero",
+    }
+
+
+def codec_reference():
+    pairs = 9 * N // 2
+    return {
+        "one_bank_encode": {"pairs": pairs, "real_add_subtracts": 4 * pairs,
+                            "component_reads": 4 * pairs, "component_writes": 2 * pairs},
+        "one_bank_decode": {"pairs": pairs, "real_add_subtracts": 4 * pairs,
+                            "exact_real_halves": 2 * pairs,
+                            "component_reads": 4 * pairs, "component_writes": 2 * pairs},
+        "hypothetical_63_mutable_bank_roundtrip": {
+            "encodes": 63, "decodes": 63,
+            "real_add_subtracts": 63 * 8 * pairs,
+            "exact_real_halves": 63 * 2 * pairs,
+            "component_reads": 63 * 8 * pairs, "component_writes": 63 * 4 * pairs,
+        },
+        "limitations": [
+            "These count separately specified in-place coordinate conversions.",
+            "A 63-bank roundtrip is not a complete adapter for the 83 external port targets.",
+            "52 Y banks still require 4B admission; encoding ordinary coefficients into B is insufficient.",
+            "Original A and E^-1 A E are distinct external numerical contracts.",
+            "Borrowed-input copying, setup, routing, widths and physical storage are not included.",
+        ],
+    }
+
+
+def wrapper_summary(record):
+    need(set(record) == {"matrix_rows", "offset", "linear_Z4", "quadratic_rows", "phase"},
+         "wrapper schema")
+    rows, linear, quadratic = (record[key] for key in
+                               ("matrix_rows", "linear_Z4", "quadratic_rows"))
+    need(len(rows) == len(linear) == len(quadratic) == 9, "wrapper dimension")
+    need(all(type(v) is int and 0 <= v < N for v in rows + quadratic), "binary rows")
+    need(all(type(v) is int and 0 <= v < 4 for v in linear), "linear phase")
+    need(type(record["offset"]) is int and 0 <= record["offset"] < N, "offset")
+    need(type(record["phase"]) is int and 0 <= record["phase"] < 4, "global phase")
+    permutation, phases = [], []
+    for address in range(N):
+        target = record["offset"]
+        for bit, row in enumerate(rows):
+            target ^= ((address & row).bit_count() & 1) << bit
+        phase = record["phase"]
+        for j in range(9):
+            if address & (1 << j):
+                phase += linear[j]
+                phase += 2 * (address & quadratic[j] & ~((1 << (j + 1)) - 1)).bit_count()
+        permutation.append(target)
+        phases.append(phase % 4)
+    need(sorted(permutation) == list(range(N)), "wrapper is a permutation")
+    seen, cycles = set(), 0
+    for first in range(N):
+        if first in seen:
+            continue
+        cycles += 1
+        at = first
+        while at not in seen:
+            seen.add(at)
+            at = permutation[at]
+        need(at == first, "closed wrapper cycle")
+    return {"cycles": cycles, "phase_histogram": Counter(phases),
+            "plan_sha256": canonical_sha(list(zip(permutation, phases)))}
+
+
+def source_audit(root):
+    raw, authenticated = {}, []
+    for path, expected in SOURCE_PINS.items():
+        data = (root / path).read_bytes()
+        need(sha(data) == expected, "source SHA256 mismatch: " + path)
+        raw[path] = data
+        authenticated.append({"path": path, "sha256": expected, "bytes": len(data),
+                              "git_blob": hashlib.sha1(b"blob " + str(len(data)).encode() + b"\0" + data).hexdigest()})
+    word = json.loads(raw["research/p104-rounded-collector/inputs/WORD.json"])
+    native = json.loads(gzip.decompress(raw["research/p104-rounded-collector/inputs/NATIVE.json.gz"]))
+    program = word["program"]
+    need(len(program) == 5398 and len(native["transports"]) == 1245, "source dimensions")
+    need(word["chart"] == "Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)", "source chart")
+    # Independently re-derive initial dependencies backwards from actual writes.
+    roles = {"Q7"} | {"D" + str(i) for i in range(27, 32)}
+    cone = []
+    for index in range(2024, -1, -1):
+        event = program[index]
+        if event[0] == "transport" and event[1] in roles:
+            cone.append(index)
+        elif event[0] == "add" and event[1] in roles:
+            cone.append(index)
+            roles.add(event[2])
+        elif event[0] in ("zero", "erase") and event[1] in roles:
+            raise ValueError("unexpected producer lifecycle")
+    cone.sort()
+    need(len(cone) == 257 and len(roles) == 58, "producer dependency cone")
+    producer_roles = sorted(roles)
+    need(sum(role.startswith("Y") for role in roles) == 52, "52 strengthened sources")
+    roles |= {"G" + str(i) for i in range(27, 32)}
+    need(all(word["initial_frames"][role] == [] for role in roles), "initial frames")
+    internal, ports = [], []
+    for index, event in enumerate(program[:4517]):
+        if 2025 <= index <= 2039:
+            internal.append(index)
+        elif event[0] == "transport" and event[1] in roles:
+            internal.append(index)
+        elif event[0] == "add" and event[1] in roles:
+            need(event[2] in roles, "unadmitted inward dependency")
+            internal.append(index)
+        elif event[0] == "add" and event[2] in roles:
+            ports.append(index)
+    need(len(internal) == 576 and len(ports) == 675, "open program source counts")
+    need(len(set(internal) | set(ports)) == 1251, "no internal/port double counting")
+    frame = {role: word["initial_frames"][role] for role in roles}
+    # A positive rational envelope, measured in units of 32H for array l2 norm.
+    # Source transports and all their wrapper/C prefixes are unitary on the
+    # separately proved admitted domain.  This deliberately ignores cancellation.
+    norm_weight = {role: Fraction(1) for role in roles}
+    max_internal = {"weight": Fraction(1), "event": None, "field": None}
+    max_increment = {"weight": Fraction(0), "event": None, "field": None}
+    for index in sorted(internal + ports):
+        event = program[index]
+        if event[0] == "transport":
+            need(frame[event[1]] == event[2], "old source frame at " + str(index))
+            frame[event[1]] = event[3]
+        elif event[0] == "zero":
+            need(event[1] == "C" and event[1] not in frame, "owned C creation")
+            frame[event[1]] = event[2]
+            norm_weight[event[1]] = Fraction(0)
+        elif event[0] == "erase":
+            need(event[1] == "C" and frame[event[1]] == event[2], "owned C erase frame")
+            del frame[event[1]]
+            del norm_weight[event[1]]
+        elif event[0] == "add":
+            need(frame[event[2]] == event[4], "source read frame at " + str(index))
+            increment_weight = abs(Fraction(event[3])) * norm_weight[event[2]]
+            if index in internal:
+                need(frame[event[1]] == event[4], "internal target frame at " + str(index))
+                norm_weight[event[1]] += increment_weight
+                if norm_weight[event[1]] > max_internal["weight"]:
+                    max_internal = {"weight": norm_weight[event[1]], "event": index,
+                                    "field": event[1]}
+            elif increment_weight > max_increment["weight"]:
+                max_increment = {"weight": increment_weight, "event": index,
+                                 "field": event[1]}
+    need(len(frame) == 63 and "C" not in frame, "final frame inventory")
+    need(max_internal == {"weight": Fraction(49), "event": 4165, "field": "G27"}
+         and max_increment == {"weight": Fraction(50), "event": 3250, "field": "X28"},
+         "conservative triangle norm envelope")
+    norm_bounds = {
+        "assumption": "Every initial real component of all63 admitted internal arrays has absolute value <= integer H>=0, in common-grid numerator units.",
+        "initial_array_l2_norm": "<=32H since sqrt(2*512)=32",
+        "native_prefix_fact": "Every affine/unit-phase wrapper and partial C product is unitary; literal equality is supplied by the admitted-domain proof.",
+        "propagation": "w_target <- w_target + abs(coefficient)*w_source; w_initial=1; w_C_zero=0; native w unchanged.",
+        "max_internal_l2_weight": int(max_internal["weight"]),
+        "first_max_internal_event": max_internal["event"],
+        "first_max_internal_field": max_internal["field"],
+        "max_port_increment_l2_weight": int(max_increment["weight"]),
+        "first_max_port_event": max_increment["event"],
+        "first_max_port_target": max_increment["field"],
+        "internal_payload_component_bound": "1568H",
+        "literal_pair_work_component_bound": "7840H",
+        "port_increment_component_bound": "1600H",
+        "signed_core_width_sufficient_condition": "2^(h-1)>7840H",
+        "port_target_condition": "A current target bound H_target needs capacity for H_target+1600H; H_target and its intervening external history remain caller obligations.",
+        "signed_floor_lemma": "For integer |a|,|b|<=B, |d|<=2B, |floor(d/2)|<=B, |middle|<=2B, |second|<=3B, |first|<=5B, componentwise and after quarter rotation.",
+        "status": "Conservative constructive bounds, not minimum widths or physical time/space tariffs.",
+    }
+    by_event = {}
+    for transport in native["transports"]:
+        for index in transport["events"]:
+            need(index not in by_event, "duplicate native event")
+            by_event[index] = transport
+    cache, native_records, cycles, phases = {}, [], 0, Counter()
+    for index in internal:
+        event = program[index]
+        if event[0] != "transport":
+            continue
+        transport = by_event[index]
+        need(transport["old"] == event[2] and transport["new"] == event[3]
+             and transport["recipe"]["rank"] == event[4], "native event/frame/rank binding")
+        wrappers = []
+        for side in ("right", "left"):
+            record = transport["recipe"][side]
+            key = canonical_sha(record)
+            if key not in cache:
+                cache[key] = wrapper_summary(record)
+            summary = cache[key]
+            cycles += summary["cycles"]
+            phases.update(summary["phase_histogram"])
+            wrappers.append({"side": side, "cycles": summary["cycles"],
+                             "plan_sha256": summary["plan_sha256"]})
+        native_records.append({"event": index, "rank": event[4], "wrappers": wrappers})
+    rank_histogram = Counter(program[i][4] for i in internal if program[i][0] == "transport")
+    rank_mass = sum(rank * count for rank, count in rank_histogram.items())
+    need(rank_mass == 581 and len(native_records) == 392, "native totals")
+    pairs = N // 2 * rank_mass
+    add_indices = [i for i in internal + ports if program[i][0] == "add"]
+    fractions = Counter(Fraction(program[i][3]) for i in add_indices)
+    need(set(fractions) <= {Fraction(x) for x in ("1", "-1", "1/4", "-1/4", "2", "-2")}, "ADD alphabet")
+    quarter_adds = fractions[Fraction(1, 4)] + fractions[Fraction(-1, 4)]
+    doubled_adds = fractions[Fraction(2)] + fractions[Fraction(-2)]
+    swap_count = 2 * len(native_records) * N + cycles
+    port_records = [{"event": i, "target": program[i][1], "source": program[i][2],
+                     "coefficient": str(Fraction(program[i][3])), "frame": program[i][4]}
+                    for i in ports]
+    direct = {
+        "native_transports": len(native_records), "native_rank_mass": rank_mass,
+        "signed_floor_pairs": pairs, "native_real_add_subtracts": 8 * pairs,
+        "native_real_floor_halves": 4 * pairs, "native_gaussian_quarter_turns": pairs,
+        "native_pair_component_reads": 4 * pairs, "native_pair_component_writes": 4 * pairs,
+        "wrappers": 2 * len(native_records), "wrapper_cycles": cycles,
+        "wrapper_gaussian_swaps": swap_count, "wrapper_unit_phase_applications": 2 * len(native_records) * N,
+        "wrapper_phase_histogram": dict(sorted(phases.items())),
+        "wrapper_swap_component_reads": 4 * swap_count,
+        "wrapper_swap_component_writes": 4 * swap_count,
+        "field_adds_including_all_ports": len(add_indices),
+        "field_add_real_add_subtracts_excluding_doublings": 2 * N * len(add_indices),
+        "quarter_field_adds": quarter_adds, "quarter_exact_real_halves": 4 * N * quarter_adds,
+        "double_field_adds": doubled_adds, "double_real_doublings": 2 * N * doubled_adds,
+        "field_add_component_reads": 4 * N * len(add_indices),
+        "field_add_component_writes": 2 * N * len(add_indices),
+        "source_component_reads_subtotal_not_additional": 2 * N * len(add_indices),
+        "private_C_initialization_components": 2 * N,
+        "private_C_zero_inspection_components": 2 * N,
+        "total_real_add_subtracts_excluding_doublings": 8 * pairs + 2 * N * len(add_indices),
+        "total_if_each_doubling_is_one_real_add": 8 * pairs + 2 * N * (len(add_indices) + doubled_adds),
+        "core_persistent_gaussian_state_words": 63 * N,
+        "owned_C_gaussian_words": N, "owned_wrapper_zero_scratch_gaussian_words": 1,
+        "pair_real_work_words": 4, "distinct_external_target_banks": len({x["target"] for x in port_records}),
+        "distinct_wrapper_recipes": len(cache),
+        "setup": "Compile one 512-entry wrapper plan at a time: O(784*512*9^2) Boolean/control operations and O(512) temporary plan entries; not free physical setup.",
+        "internal_common_grid_numerator_bounds": "Constructively upper-bounded in conservative_norm_bounds; external target widths remain unknown.",
+        "physical_tariff_routing_owner_map": "unknown",
+        "codecs_or_admission_included": False,
+    }
+    need(pairs == 148736 and len(add_indices) == 857 and quarter_adds == 675 and doubled_adds == 156,
+         "complete direct source bill")
+    return {
+        "source_main": MAIN, "authenticated_inputs": authenticated, "chart": word["chart"],
+        "scope": "63-state open-interface projection through event4516; all675 outgoing reads retained as ports. Omitted external histories are not executed or priced.",
+        "producer": {"events": cone, "initial_roles": producer_roles,
+                     "opcode_counts": counted(program[i][0] for i in cone),
+                     "rank_mass": sum(program[i][4] for i in cone if program[i][0] == "transport")},
+        "internal_event_indices": internal, "internal_opcode_counts": counted(program[i][0] for i in internal),
+        "initial_roles": sorted(roles), "final_frames": frame,
+        "rank_histogram": dict(sorted(rank_histogram.items())),
+        "internal_add_coefficients": counted(Fraction(program[i][3]) for i in internal if program[i][0] == "add"),
+        "port_add_coefficients": counted(Fraction(program[i][3]) for i in ports),
+        "outgoing_ports": port_records, "outgoing_port_sha256": canonical_sha(port_records),
+        "transport_wrapper_bindings": native_records,
+        "transport_wrapper_bindings_sha256": canonical_sha(native_records),
+        "direct_reference_schedule": direct,
+        "conservative_norm_bounds": norm_bounds,
+        "semantic_restoration_proof": "provided separately; this script checks source closure, frame consistency and the bill only",
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--source-root", type=Path)
+    parser.add_argument("--output", type=Path)
+    args = parser.parse_args()
+    result = {"schema_version": 1, "implementation_sha256": sha(Path(__file__).read_bytes()),
+              "fixed_consumer": fixed_consumer(), "codec_reference": codec_reference()}
+    if args.source_root is not None:
+        result["source_audit"] = source_audit(args.source_root)
+    payload = json.dumps(result, indent=2, sort_keys=True) + "\n"
+    if args.output:
+        with args.output.open("x", encoding="utf-8") as handle:
+            handle.write(payload)
+        print(json.dumps({"status": "PASS", "output": str(args.output), "sha256": sha(payload.encode()),
+                          "source_audit_executed": args.source_root is not None}))
+    else:
+        print(payload, end="")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/p104-newton-interfaces/independent.py b/research/p104-newton-interfaces/independent.py
new file mode 100644
index 0000000000..b970df8f01
--- /dev/null
+++ b/research/p104-newton-interfaces/independent.py
@@ -0,0 +1,270 @@
+"""Separate full-prefix witness and scalar-port checks for the P104 interface.
+
+Clear1nsight, with substantial OpenAI assistance. Apache-2.0.
+This implementation imports neither the producer/consumer checker nor the
+PR3382 lattice model. Its scalar port conclusion is conditional on the separate
+phase-sensitive frame-path certificate. The numerical witness is one point,
+not a universal full-prefix or full-word theorem.
+"""
+
+import argparse
+import gzip
+import hashlib
+import json
+from collections import Counter, defaultdict
+from fractions import Fraction
+from pathlib import Path
+
+
+WORD_SHA = "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50"
+NATIVE_SHA = "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d"
+N = 512
+ZERO = (0, 0)
+
+
+class IndependentError(ValueError):
+    """A source or exact arithmetic obligation failed."""
+
+
+def check(condition, message):
+    if not condition:
+        raise IndependentError(message)
+
+
+def digest(data):
+    return hashlib.sha256(data).hexdigest()
+
+
+def canonical(data):
+    return json.dumps(data, sort_keys=True, separators=(",", ":")).encode()
+
+
+def pinned(path, expected):
+    path = Path(path)
+    check(path.is_file() and not path.is_symlink(), "regular source required")
+    data = path.read_bytes()
+    check(digest(data) == expected, "independent source hash mismatch")
+    return data
+
+
+def rotate(z, exponent):
+    a, b = z
+    for _ in range(exponent % 4):
+        a, b = -b, a
+    return a, b
+
+
+def wrapper(values, recipe):
+    rows = recipe["matrix_rows"]
+    linear = recipe["linear_Z4"]
+    quadratic = recipe["quadratic_rows"]
+    check(len(rows) == len(linear) == len(quadratic) == 9, "wrapper dimensions")
+    out = [None] * N
+    for x, value in enumerate(values):
+        address = recipe["offset"]
+        phase = recipe["phase"]
+        for bit in range(9):
+            address ^= ((rows[bit] & x).bit_count() % 2) << bit
+            if x >> bit & 1:
+                upper = quadratic[bit] & x & ~((1 << (bit + 1)) - 1)
+                phase += linear[bit] + 2 * upper.bit_count()
+        check(0 <= address < N and out[address] is None, "wrapper bijection")
+        out[address] = rotate(value, phase)
+    return out
+
+
+def exact_literal_pair(a, b):
+    """Compare direct Gaussian numerators with componentwise signed floors."""
+    p, q = a[0] - b[0], a[1] - b[1]
+    numerators = (a[0] + b[0] - q, a[1] + b[1] + p,
+                  a[0] + b[0] + q, a[1] + b[1] - p)
+    check(all(x % 2 == 0 for x in numerators), "nonintegral ideal butterfly")
+    ideal = ((numerators[0] // 2, numerators[1] // 2),
+             (numerators[2] // 2, numerators[3] // 2))
+    middle = (b[0] + p // 2, b[1] + q // 2)
+    second = (middle[0] - (-q) // 2, middle[1] - p // 2)
+    literal = ((second[0] - q, second[1] + p), second)
+    check(literal == ideal, "signed floor differs from ideal")
+    return literal
+
+
+def native_apply(values, recipe):
+    out = wrapper(values, recipe["right"])
+    for bit in range(recipe["rank"]):
+        step = 1 << bit
+        for address in range(N):
+            if address & step == 0:
+                other = address | step
+                out[address], out[other] = exact_literal_pair(out[address], out[other])
+    return wrapper(out, recipe["left"])
+
+
+def first_newton_failure(values):
+    coefficients = values[:]
+    for bit in range(9):
+        step = 1 << bit
+        for x in range(N):
+            if x & step:
+                a, b = coefficients[x], coefficients[x ^ step]
+                coefficients[x] = a[0] - b[0], a[1] - b[1]
+    for mask, coefficient in enumerate(coefficients):
+        a, b = coefficient
+        for power in range(mask.bit_count()):
+            if (a + b) % 2:
+                return {"mask": mask, "degree": mask.bit_count(),
+                        "coefficient": list(coefficient), "pi_valuation": power}
+            a, b = (a + b) // 2, (b - a) // 2
+    return None
+
+
+def bind_native(word, native):
+    index = {}
+    for row in native["transports"]:
+        for event in row["events"]:
+            check(event not in index, "duplicate occurrence")
+            op = word["program"][event]
+            check(op[0] == "transport" and op[2:5] ==
+                  [row["old"], row["new"], row["recipe"]["rank"]],
+                  "native occurrence binding")
+            index[event] = row["recipe"]
+    return index
+
+
+def full_prefix_witness(word, native):
+    recipes = bind_native(word, native)
+    frames = {name: frame[:] for name, frame in word["initial_frames"].items()}
+    state = {name: [ZERO] * N for name in frames}
+    state["Y27"][0] = (64, 0)
+    check(all(first_newton_failure(v) is None for v in state.values()),
+          "all358 initial banks in B9")
+    stronger_failure = first_newton_failure([(a // 4, b // 4) for a, b in state["Y27"]])
+    check(stronger_failure is not None, "the witness must fail the strengthened Y admission")
+    active_native = []
+    active_add = []
+    failures = []
+    pairs = 0
+    native_occurrences = 0
+    for event, op in enumerate(word["program"][:2025]):
+        kind, target = op[:2]
+        check(target in state, "initial field lifetime")
+        if kind == "transport":
+            check(frames[target] == op[2] and event in recipes, "prefix frame and native")
+            native_occurrences += 1
+            if any(value != ZERO for value in state[target]):
+                state[target] = native_apply(state[target], recipes[event])
+                active_native.append(event)
+                pairs += 256 * recipes[event]["rank"]
+            frames[target] = op[3][:]
+        elif kind == "add":
+            source, coefficient, frame = op[2:]
+            check(frames[target] == frames[source] == frame, "prefix ADD frame")
+            c = Fraction(str(coefficient))
+            p, q = c.numerator, c.denominator
+            if any(value != ZERO for value in state[source]):
+                scaled = []
+                for real, imag in state[source]:
+                    check(p * real % q == p * imag % q == 0, "nonintegral quarter source")
+                    scaled.append((p * real // q, p * imag // q))
+                state[target] = [(a[0] + b[0], a[1] + b[1])
+                                 for a, b in zip(state[target], scaled)]
+                active_add.append(event)
+        elif kind == "sign":
+            check(len(op) == 4 and op[2] == "-1" and frames[target] == op[3],
+                  "sign grammar and frame")
+            state[target] = [(-a, -b) for a, b in state[target]]
+        else:
+            raise IndependentError("unexpected prefix opcode")
+        if any(value != ZERO for value in state[target]):
+            failure = first_newton_failure(state[target])
+            if failure is not None:
+                failures.append({"event": event, "field": target, **failure})
+    check(len(active_native) == 20 and len(active_add) == 6, "full witness active events")
+    check(first_newton_failure(state["D31"]) is not None, "D31 entrance must fail")
+    entrance = {}
+    for name in ("D31", "D30", "D29", "D28", "D27", "Q7"):
+        entrance[name] = {"sha256": digest(canonical(state[name])),
+                          "newton_failure": first_newton_failure(state[name]),
+                          "frame": frames[name],
+                          "nonzero_complex_entries": sum(z != ZERO for z in state[name])}
+    return {"status": "PASS", "scope": "one explicit point, full events0..2024",
+            "initial_banks": len(frames), "point": {"Y27[0]": [64, 0], "all_other_components": 0},
+            "all_initial_banks_in_B9": True, "initial_Y27_not_in_4B9": stronger_failure,
+            "all_actual_quarters_integral": True,
+            "all_actual_literal_native_pairs_exact": True,
+            "prefix_native_occurrences_bound": native_occurrences,
+            "active_native_events": active_native, "active_add_events": active_add,
+            "active_pair_comparisons": pairs,
+            "first_full_prefix_B9_failure": failures[0], "entrance": entrance}
+
+
+def scalar_ports(word):
+    ys = {"Y" + str(j) for j in list(range(22, 33)) + list(range(63, 104))}
+    roles = ys | {"D" + str(j) for j in range(27, 32)}
+    roles |= {"G" + str(j) for j in range(27, 32)} | {"Q7"}
+    rows = {name: {name: Fraction(1)} for name in roles}
+    outputs = defaultdict(dict)
+    ports = []
+    counts = Counter()
+    for event, op in enumerate(word["program"][:4517]):
+        kind, target = op[:2]
+        if event == 2025:
+            check(kind == "zero" and target == "C", "private allocation")
+            rows["C"] = {}
+        elif event == 2039:
+            check(kind == "erase" and target == "C" and not rows["C"], "private erasure")
+            del rows["C"]
+        elif kind == "add" and op[2] in rows:
+            source, coefficient = op[2:4]
+            c = Fraction(str(coefficient))
+            destination = rows[target] if target in rows else outputs[target]
+            for name, value in rows[source].items():
+                destination[name] = destination.get(name, Fraction(0)) + c * value
+            for name in list(destination):
+                if not destination[name]:
+                    del destination[name]
+            if target not in rows:
+                ports.append(event)
+                counts[(source[0], target[0])] += 1
+        elif target in rows:
+            check(kind == "transport", "unmodelled write into closed roles")
+    check(all(rows[name] == {name: Fraction(1)} for name in roles), "63 scalar restorations")
+    x_rows = {name: row for name, row in outputs.items() if name.startswith("X")}
+    check(len(x_rows) == 52, "52 actual X targets")
+    signs = {}
+    for name, row in x_rows.items():
+        check(set(row) == ys and len(set(row.values())) == 1, "rank-one source sum")
+        value = next(iter(row.values()))
+        check(value in (Fraction(1, 2), Fraction(-1, 2)), "signed half increment")
+        signs[name] = int(2 * value)
+    check(Counter(signs.values()) == {1: 39, -1: 13}, "actual target signs")
+    check(len(ports) == 675, "complete port count")
+    return {"status": "PASS", "scope": "scalar rows in separately certified frame gauges",
+            "frame_map_certificate_required": True, "restored_initial_rows": 63,
+            "private_zero": True, "external_port_count": len(ports),
+            "external_port_indices_sha256": digest(canonical(ports)),
+            "external_port_counts": {a + "->" + b: v for (a, b), v in sorted(counts.items())},
+            "X_target_signs": dict(sorted(signs.items())),
+            "X_map": "Sum of outgoing increments pulled back through the certified port-frame gauges is sign_j * sum_{s in Y22..32,Y63..103} y_s / 2; this is not a final external X-array endpoint.",
+            "all_initial_D_Q_G_coefficients_cancel_in_X_ports": True,
+            "excluded": "External target updates/transports and all other word operations are not a full numerical execution."}
+
+
+def verify_independent(word_path, native_path):
+    word = json.loads(pinned(word_path, WORD_SHA))
+    native = json.loads(gzip.decompress(pinned(native_path, NATIVE_SHA)))
+    return {"status": "PASS", "source_sha256": {"word": WORD_SHA, "native": NATIVE_SHA},
+            "full_prefix_witness": full_prefix_witness(word, native),
+            "scalar_ports": scalar_ports(word)}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--repo", type=Path, default=Path(__file__).resolve().parents[2])
+    args = parser.parse_args()
+    inputs = args.repo / "research/p104-rounded-collector/inputs"
+    result = verify_independent(inputs / "WORD.json", inputs / "NATIVE.json.gz")
+    print(json.dumps(result, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/p104-newton-interfaces/inputs/PR3382_PROOF.md b/research/p104-newton-interfaces/inputs/PR3382_PROOF.md
new file mode 100644
index 0000000000..10b3202c78
--- /dev/null
+++ b/research/p104-newton-interfaces/inputs/PR3382_PROOF.md
@@ -0,0 +1,445 @@
+# A phase-complete Gaussian entrance for one literal P104 collector
+
+This result changes the admissible numerical states of one fixed collector.
+It does not change its scalar/frame word, claim a new precision threshold,
+or provide the missing complete P104 correction and supplier invoice.
+The construction is motivated by Clifford-invariant and Barnes–Wall lattice
+methods. The proof below uses the repository's exact Gaussian normalization;
+it does not invoke a lattice classification theorem or claim a new lattice
+family.
+
+The source is ywz65's PR #2586, head
+`7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1`, retained at
+`research/p104-rounded-collector/inputs/WORD.json` and `NATIVE.json.gz`.
+Tekalign's PR #3025 binds its first collector and supplies the literal signed
+floor pair. Ross Richardson's PR #3068, head
+`7d2c519a1fdcc6bf66f6f08757eed7c48762d3f2`, supplies the neighboring
+period-domain contract and explicitly leaves a larger state exactness domain
+open. Their constructions, inverses, source binding and earlier bounds retain
+their credit. Exact consumed bytes and the isolated replay are recorded by
+the accompanying source manifest and receipt.
+
+## 1. Coordinates and the explicit code
+
+Put `pi = 1+i`, so `pi^2 = 2i` and `1/pi = (1-i)/2`. An array of
+`2^r` Gaussian integers is a function on the binary cube. It has unique
+multilinear Newton coefficients:
+
+\[
+ f(x)=\sum_{S\subseteq\{0,\ldots,r-1\}}a_S x^S,
+ \qquad x^S=\prod_{j\in S}x_j.
+\]
+
+Uniqueness follows by Boolean differences, or by the triangular evaluation
+matrix indexed by subsets. Define the Gaussian module
+
+\[
+ \mathcal B_r=\{f:a_S\in\pi^{|S|}\mathbb Z[i]\text{ for every }S\}.
+\]
+
+Its encoder is explicit:
+
+\[
+ E_r=E_1^{\otimes r},\qquad
+ E_1=\begin{pmatrix}1&0\\1&\pi\end{pmatrix}.
+\]
+
+Thus a coefficient pair `(c0,c1)` becomes `(c0,c0+pi*c1)`. Bit `j` is
+the address bit `1<<j`; tensor factors may be applied in ascending bit order.
+The resulting Newton coefficient is `a_S=pi^|S| c_S`. The reverse sweep
+replaces each second entry `b` by `(b-a)/pi`; all divisions are exact exactly
+on this image. This gives both an encoder and a membership test. These are
+computations with costs, not a free reinterpretation of arbitrary numerical
+payloads.
+
+## 2. Exact maximality for simultaneous coordinate prefixes
+
+The source's positive Gaussian pair is
+
+\[
+ C(a,b)=\left(\frac{a+b+i(a-b)}2,
+                 \frac{a+b-i(a-b)}2\right).
+\]
+
+On `(a,a+d)` this is `(a+d/pi, a+d/pi+i*d)`. Consequently
+
+\[
+ E_1^{-1}CE_1=\begin{pmatrix}1&1\\0&i\end{pmatrix},
+ \qquad (c_0,c_1)\longmapsto(c_0+c_1,ic_1).
+\]
+
+This matrix and its inverse have Gaussian-integer entries. It follows that
+each coordinate `C_j`, and its inverse, preserves `B_r` in both directions.
+
+For a subset `T` of address bits write `C_T=product_{j in T} C_j`.
+The coordinate gates commute. We claim the exact equality of sets
+
+\[
+ \mathcal B_r=
+ \{f\in\mathbb Z[i]^{2^r}:C_T f\in\mathbb Z[i]^{2^r}
+                         \text{ for every }T\subseteq\{0,\ldots,r-1\}\}.
+\]
+
+One inclusion follows from the displayed intertwiner. For the other, evaluate
+at the all-zero address. A transformed monomial contributes `pi^-|S|` when
+`S` is contained in `T`, and otherwise contributes zero. Therefore
+
+\[
+ g(T):=(C_T f)(0)=\sum_{S\subseteq T} a_S/\pi^{|S|}.
+\]
+
+Every `g(T)` is Gaussian integral by hypothesis. Boolean Möbius inversion gives
+
+\[
+ a_S/\pi^{|S|}=\sum_{T\subseteq S}(-1)^{|S|-|T|}g(T)\in\mathbb Z[i],
+\]
+
+which is membership in `B_r`. In particular `B_r` is the largest integral
+module invariant under every coordinate `C_j`. More strongly, no module
+assumption was needed for the displayed equality of sets.
+
+The quantifier is **every partial product**. It cannot be replaced by testing
+each gate once on the entrance. For `r=2`, the function `pi*x0*x1` has integral
+`C_0 f` and `C_1 f`, but `(C_0 C_1 f)(0)=1/pi` is nonintegral. A test that
+admits this vector from only the first two outputs has not checked the theorem.
+
+This is not maximality for a fixed completed transform with cancellation,
+for an arbitrary nonlinear word, or for Ross's translation-period premise.
+His `Gamma` and `Lambda` are different domains. No global containment between
+those domains and `B_r` is claimed, and no finite index census is needed here.
+
+## 3. Why the literal floor program becomes exact
+
+For Gaussian integers `a,b`, let `d=a-b`, take componentwise signed floors,
+and execute the credited pair:
+
+```text
+d = a-b
+s = b+floor(d/2)
+d = i*d
+b' = s-floor(d/2)
+a' = b'+d
+```
+
+Its inverse uses `-i` in place of `i`. The generic bijection and paired inverse
+are PR #3025's result, not a new claim here. Writing the original difference
+as `p+iq`, and putting `t=(q mod 2)-(p mod 2)` with residues in `{0,1}`,
+direct subtraction from the ideal map gives the same discrepancy in both
+output entries:
+
+\[
+ (a',b')-C(a,b)=\bigl(t(1-i)/2,t(1-i)/2\bigr).
+\]
+
+The same condition gives zero discrepancy for the negative pair. Thus literal
+and ideal pairs agree exactly when `p,q` have equal parity, equivalently
+`pi` divides `a-b`. This is also exactly the integrality condition for the
+ideal pair on Gaussian integer inputs.
+
+For any fixed values of the other bits, the difference of the two entries of
+a `B_r` function along bit `j` is divisible by `pi`. After an ideal `C_j` the
+entire array remains in `B_r`, by Section 2. Induction therefore proves exact
+literal floor execution at every subsequent coordinate stage. This induction
+is the all-input argument; checking a linear basis alone would not prove
+exactness of the unrestricted nonlinear floor map.
+
+All statements are unchanged after multiplying every array by a common grid
+spacing `2^-f`. The integer numerators retain that grid throughout this
+restricted execution.
+
+## 4. The actual Gaussian monomial alphabet preserves the code
+
+The authenticated source wrappers send input address `x` to `A*x+b` over
+`F_2`, and attach the input-address phase
+
+\[
+ i^{p+\sum_j l_jx_j+2\sum_{j<k}q_{jk}x_jx_k}.
+\]
+
+Here `A` is invertible, `b` is binary, `p,l_j` are modulo four, and `q_jk`
+are binary. These are exactly the `matrix_rows`, `offset`, `linear_Z4`,
+`quadratic_rows` and `phase` fields of the retained recipes. The phase is
+evaluated before the address permutation; changing that convention changes
+the operator.
+
+Every invertible binary affine map is generated by address XORs, bit swaps
+and CNOTs: Gaussian elimination supplies swaps and elementary row additions,
+and the offset supplies XORs. The phase is a product of global powers of `i`,
+single-bit phases `S_j=i^{x_j}`, and `CZ_jk=(-1)^{x_j*x_k}`. Each generator
+preserves `B_r`. Here are direct integral coefficient formulas; they are
+also useful implementation intertwiners.
+
+| Physical gate | Action on a coefficient pair `(a,b)` |
+|---|---|
+| `C` | `(a+b, i*b)` |
+| `C^-1` | `(a+i*b, -i*b)` |
+| `S` | `(a, i*(a+b))` |
+| `S^-1` | `(a, -a-i*b)` |
+| address XOR `X` | `(a+pi*b, -b)` |
+
+For two bits write a coefficient block as
+`a + pi*b*x + pi*c*y + pi^2*d*x*y`. A CNOT with control `x` and target `y`
+acts by the substitution `y -> x xor y = x+y-2xy`, and gives
+
+\[
+ (a,b,c,d)\longmapsto
+ (a,\ b+c+\pi d,\ c,\ (i-1)c-d).
+\]
+
+The phase `CZ=(-1)^{xy}=1-2xy` gives
+
+\[
+ (a,b,c,d)\longmapsto
+ (a,\ b,\ c,\ ia+(i-1)(b+c)-d).
+\]
+
+These formulas use `x^2=x`, `y^2=y` and `2=-i*pi^2`. The other bits contribute
+the same common coefficient factors, so the formulas apply at every rank.
+Bit swaps simply permute coefficient indices. The listed self-inverse gates
+remain self-inverse under conjugation; `C` and `S` have the integral inverses
+shown above. Global Gaussian units preserve the module. Thus every full source
+wrapper, and its inverse, preserves `B_r`.
+
+No unrestricted phase or permutation is admitted by this argument. For example,
+the cubic phase `(-1)^(x0*x1*x2)` applied to the constant one produces Newton
+coefficient `-2` at degree three. It is not divisible by `pi^3`, so the result
+leaves `B_3`. The quadratic source schema matters.
+
+The old structured phase witness is a positive control here. The constant one
+and `i^{x_j}=1+(i-1)x_j` both belong to `B_r`, because `i-1=i*pi`.
+The latter leaves the older `Gamma` period lattice, as credited in PR #3068.
+That earlier counterexample did not claim that it creates a lifting error.
+
+## 5. One complete source-bound collector
+
+Use zero-based events **2025–2039** of the retained PR #2586 word. They are:
+
+1. Allocate zero private `C` at the common source frame.
+2. Add `D31,D30,D29,D28,D27` to `C`, in that order.
+3. Apply the literal rank-seven transport `U` at event 2031.
+4. Add `C` to the arbitrarily dirty query `Q7` at its common frame.
+5. Apply the separately archived return `V` at event 2033.
+6. Subtract the five original sources in reverse order; erase exact zero `C`.
+
+The source arrays have 512 complex entries and nine address bits. Both native
+recipes have the form `M_left C_0 ... C_6 M_right`. The complete surrounding
+wrapper acts on all nine bits, so the contract is `B_9`, not an unproved
+rank-seven block restriction. Source authentication binds the two event
+occurrences, their frames, the common-chart ADDs and their actual recipes.
+The predecessor's exact native interpretation is retained; the finite operator
+check of `VU=I` is separate from the lattice exactness argument.
+
+Assume the five source arrays and the initial query belong to `2^-f B_9`.
+They are otherwise arbitrary, independently dirty and potentially correlated.
+The five sources remain available and unchanged across this whole interval.
+The private `C` is owned and starts zero. No alias of those distinct roles or
+nonzero private initialization is granted.
+
+Let `s` be the sum of the five sources. Module closure gives `s in 2^-f B_9`.
+By Sections 3–4 both actual transports execute their exact ideal maps on this
+domain. The query becomes `Q7+U*s`. Since `VU=I`, the private register returns
+to `s`; subtracting the unchanged sources makes it exactly zero. Thus the
+literal endpoint is
+
+\[
+ (D31,\ldots,D27,Q7,C=0)
+ \longmapsto(D31,\ldots,D27,Q7+U\sum_jD_j,C=0).
+\]
+
+The query remains in the same declared lattice and grid. There is no rounded
+query defect, per-input grid selection, residue history or numerical downcast
+in this restricted-state execution. This permits the separately archived `V`;
+the unrestricted approximate lifting contract instead needs its paired inverse.
+They must not be interchanged when counting operations.
+
+This is a boundary assumption at the actual collector cut. The earlier producer
+has not been proved to supply this state for arbitrary unrestricted inputs.
+The later whole word also has additional operations. A repeated collector is
+valid only when its sources, frames, permissions and declared lattice are
+available at its own cut.
+
+## 6. Quarter ADD and the exact meaning of an encoder
+
+Whole-array ADD by any Gaussian-integer coefficient preserves `B_r`. For an
+integral array `z`, a quarter source `z/4` belongs to `B_r` exactly when
+`z` belongs to `4B_r`. Integral components alone do not imply that condition.
+At rank one `(4,0)` belongs to `B_1`, but `(4,0)/4=(1,0)` does not. Extend
+the pair constantly in the other eight bits for the actual nine-bit counterexample.
+Conversely `z=4E_r c` always has the admissible quarter `E_r c`.
+The named collector contains only unit ADDs, so this counterexample marks the
+external interface; no quarter instruction is treated as free within its bill.
+
+Encoding arbitrary raw coefficients `c` as `E_r c` changes the logical action
+of a physical native map `U` to
+
+\[
+ T=E_r^{-1}UE_r.
+\]
+
+The gate formulas prove that `T` is an explicitly described Gaussian-integral
+automorphism for the stated alphabet. They do **not** say `UE_r=E_rU`.
+Already `C E_1 != E_1 C`; a control checks this distinction. Substituting this
+representation into a caller expecting a different map requires its own
+intertwining adapters and their complete costs.
+
+For clarity, one fully specified optional cold preparation realizes this
+different `T` contract. Keep five arbitrary raw Gaussian coefficient source
+arrays borrowed and unchanged, and give the query mutable ownership. Allocate
+five zero source banks, copy the borrowed sources into them by five full-array
+ADDs, and encode the five banks and query. Run the original collector on these
+six encoded fields. Decode the query and all five banks. Each source bank is
+then exactly its original raw source; subtract that borrowed source, check zero
+and dispose of the bank. The query endpoint is `q+T*sum(sources)`.
+
+This construction uses six encodes, six decodes, five copy ADDs, five cleanup
+ADDs and five additional owned array lifetimes. It demonstrates a complete
+logical codec schedule with literal restoration. It does not admit that `T`
+as a requested recursive caller, give a free borrowed-input conversion, or
+establish an advantage over an existing `U` implementation.
+
+## 7. Gate, codec and storage ledger
+
+All counts in this section concern a direct scalar reference with explicit
+array access. They are not tape time, native child tariffs or a lower bound.
+Gaussian units, signed arithmetic and addressing are separate operations.
+
+An encode or decode sweep has `r*2^(r-1)` tensor pairs. Encoding a pair uses
+one multiplication by `pi` and one Gaussian ADD. Decoding uses one Gaussian
+subtraction and one exact division by `pi`. Multiplication by `pi` is
+`(a-b,a+b)`; exact division is `((a+b)/2,(b-a)/2)`. Thus each encode pair costs
+four real additions/subtractions, while each decode pair adds two exact real
+halvings. Each loads four real components and writes two. An in-place sweep
+uses the owned numerical array and four real work words; loop/control storage
+and physical routing are additional. Borrowed input cannot be overwritten to
+obtain this in-place price.
+
+At `r=9`, each direction has **2,304 pairs**. The optional cold schedule therefore
+adds 13,824 `pi` multiplications, 13,824 exact `pi` divisions, 110,592 real
+additions/subtractions, 27,648 exact real halvings and its ten full-array copy/
+cleanup ADDs. Those ten ADDs add 10,240 real additions/subtractions, 20,480
+real-component reads and 10,240 writes. The codecs add 110,592 component reads
+and 55,296 writes. Five extra owned banks add 2,560 complex words and 5,120
+component initializations and zero checks each. These quantities are additional
+to the direct collector below; they are not paid by an abstract rank count.
+
+For the literal collector, both seven-stage transforms use `7*512=3,584`
+pair applications altogether. Each credited signed-floor pair costs eight
+real additions/subtractions, four real floor halvings and one Gaussian quarter
+turn. The eleven field ADDs cost `22*512` more real additions/subtractions.
+The four actual wrapper cycle counts, in chronological order, are
+
+\[
+ U_{right}:64,\quad U_{left}:128,\quad V_{right}:160,\quad V_{left}:64.
+\]
+
+The credited one-zero-Gaussian-scratch cycle algorithm uses `N+c` swaps for a
+wrapper with `c` cycles and `N` unit phase applications. Here it gives **416
+cycles and 2,464 swaps**, plus 2,048 phase applications. The old paired-inverse
+schedule's 384 cycles and 2,432 swaps do not price these separately archived
+return wrappers. The phase acts on the cycle scratch before each swap, so its
+arithmetic is counted without an extra full-array phase pass.
+
+| Direct collector operation | Count |
+|---|---:|
+| Signed-floor pair applications | 3,584 |
+| Real additions/subtractions, including all eleven field ADDs | 39,936 |
+| Real floor halvings | 14,336 |
+| Pair Gaussian quarter turns | 3,584 |
+| Actual wrapper Gaussian swaps | 2,464 |
+| Actual wrapper unit phase applications | 2,048 |
+| Butterfly real-component reads / writes | 14,336 / 14,336 |
+| Field-ADD real-component reads / writes | 22,528 / 11,264 |
+| Wrapper-swap component reads / writes, including scratch | 9,856 / 9,856 |
+| Private initialization / zero-check component inspections | 1,024 / 1,024 |
+
+The 10,240 source-component reads are a subtotal of the field-ADD reads, not an
+extra charge. The direct contract has five borrowed source arrays, one mutable
+query, one owned zero private array and one zero Gaussian wrapper scratch,
+with constant pair work. The optional cold schedule supplies the five source
+arrays by additional owned copies. Source plans, range/type validation,
+permissions, address/control work, physical movement, allocator behavior,
+recursive children, precision metadata and final endpoint consumption require
+their actual caller's tariff. They do not acquire a zero price from these
+scalar counts.
+
+## 8. Finite headroom
+
+Let `H` bound the absolute value of every real and imaginary component at a
+codec's own entrance. During an encode the exact largest real component row
+sum after at most `r` factors is bounded by
+
+\[
+ M_r=\sum_{k=0}^r {r\choose k}
+       (|\Re\pi^k|+|\Im\pi^k|).
+\]
+
+This follows by expanding a tensor row; its entries are powers of `pi`, one
+for each subset. A smaller partial row is covered by the same nonnegative
+bound. For `r=9`, `M_r=3363`. Thus `M_r H` bounds stored encoder components;
+`3 M_r H` is a conservative bound for its two-step arithmetic temporaries.
+
+A row of a `k`-factor inverse sweep is a signed sum of `2^k` inputs divided by
+`pi^k`. Its real component row sum is
+`2^k (|Re pi^-k|+|Im pi^-k|)=|Re pi^k|+|Im pi^k|`, at most
+`2^ceil(r/2)`. Therefore decoder components are bounded by `2^ceil(r/2) H`,
+and its subtraction/numerator temporaries by four times that amount. These
+are sufficient arithmetic bounds, not a compression or precision advantage.
+
+For the direct collector suppose its six admitted entrance fields have
+integer numerator components bounded by `H`. The sum of five sources has
+Hilbert norm at most `5 sqrt(2N) H`. Every exact native prefix is unitary,
+including each wrapper. At `N=512`, **160 H** bounds every native-prefix real
+component; **161 H** bounds the updated query. A conservative signed-floor
+pair scratch bound is **800 H**. Gathers and ungathers are bounded sums of at
+most five unchanged sources. Partially written stages store either preceding
+or completed pair values, so these same bounds cover the entire execution.
+
+For the optional cold caller, now let `H` bound its **raw coefficient** entrance.
+Encoding gives `3363 H`; the collector therefore gives an encoded query bound
+`161*3363 H=541443 H`. Decoding that query gives at most
+`32*161*3363 H=17326176 H`. The conservative complete scratch bound is four
+times this last quantity, **69304704 H**, which also dominates the encoder,
+native pair, source-bank decoding and cleanup temporaries. These composed
+bounds make the optional caller's finite-width obligation explicit; they are
+not measured peaks or necessary widths.
+
+For a nonnegative integer component bound `M`,
+`1+ceil_log2(M+1)` signed bits suffice. This states an explicit finite range;
+an actual fixed-width implementation must use that range, retain the required
+grid and charge its bit arithmetic. The older sharp scalar-grid/Clifford
+denominator results remain credited and unchanged.
+
+## 9. Evidence boundary and stopping decision
+
+The written arguments hold at every finite rank. The new managed-Python model
+and finite source checks are bounded by nine address bits, 512 complex entries
+and 8,192 magnitude bits per admitted input or returned array component.
+Signed storage may require another bit; exact arithmetic temporaries have the
+additional finite headroom derived above. The functional model allocates fresh
+lists, while the direct ledger prices the separately specified in-place codec
+and credited cycle-scratch algorithm. It is not a measurement of Python
+allocation. Membership checks and snapshots inside verification are test work;
+a production caller must establish or pay for its lattice entrance.
+Managed allocation and verification snapshots are not a physical memory
+implementation. Exact checks use explicit exceptions, including under Python
+optimization.
+
+Finite verification binds the two archived recipes, checks exact operators and
+both literal directions on admitted states, tests dirty collector endpoints,
+and exercises the missing-prefix, phase-alphabet, wrong weighting, quarter-ADD,
+intertwiner and source/invoice failure boundaries. The separate checker uses
+its own representation and does not derive a nonlinear universal theorem from
+finite basis samples. Source-native correctness, physical ownership, eventual
+recursive prices and human/proof-kernel admission remain separate premises.
+
+The result stops at a phase-compatible exactness theorem, one actual complete
+local collector, an explicit codec/intertwiner, and their full direct logical
+ledger. It neither proves that earlier arbitrary P104 inputs satisfy the
+entrance nor extends the contract to the later quarter ADDs. A larger caller
+needs an actual admitted source of this state and a compatible fully charged
+consumer. No selected frontier, all-size supplier, new scalar-grid guard,
+physical storage saving or new kappa follows.
+
+Prepared by Clear1nsight with substantial OpenAI assistance. Separate automated
+derivation and review are not independent human or formal-kernel verification.
+Apache-2.0; predecessor authors and original source notices retain their credit.
diff --git a/research/p104-newton-interfaces/inputs/pr3382_model.py b/research/p104-newton-interfaces/inputs/pr3382_model.py
new file mode 100644
index 0000000000..4dd24a2627
--- /dev/null
+++ b/research/p104-newton-interfaces/inputs/pr3382_model.py
@@ -0,0 +1,428 @@
+"""Exact Gaussian Newton-lattice reference for the pinned P104 collector.
+
+Clear1nsight, with substantial OpenAI assistance. Apache-2.0.
+The all-rank statements are written in PROOF.md. This finite reference accepts
+at most nine address bits and 8192 magnitude bits per real array component. It imports
+no predecessor implementation and makes no recursive or physical cost claim.
+"""
+
+from math import comb, isqrt
+
+MAX_RANK = 9
+MAX_COMPONENT_BITS = 8192
+PI = (1, 1)
+ZERO = (0, 0)
+
+
+class ModelError(ValueError):
+    """A malformed input or violated finite-reference contract."""
+
+
+class OutsideLattice(ModelError):
+    """A required exact Gaussian division is unavailable."""
+
+
+def require(condition, message):
+    if not condition:
+        raise ModelError(message)
+
+
+def rank_check(rank):
+    require(type(rank) is int and 0 <= rank <= MAX_RANK, "rank must be in 0..9")
+    return rank
+
+
+def gaussian_check(value):
+    require(type(value) is tuple and len(value) == 2, "Gaussian value must be a pair")
+    require(all(type(x) is int for x in value), "Gaussian components must be integers")
+    require(all(x.bit_length() <= MAX_COMPONENT_BITS for x in value),
+            "Gaussian component exceeds finite reference limit")
+    return value
+
+
+def validate(values, rank=None):
+    require(type(values) is list and values, "array must be a nonempty list")
+    size = len(values)
+    require(size <= 1 << MAX_RANK and size & (size - 1) == 0, "binary array length")
+    actual = size.bit_length() - 1
+    if rank is not None:
+        require(rank_check(rank) == actual, "array rank mismatch")
+    for value in values:
+        gaussian_check(value)
+    return actual
+
+
+def add(a, b):
+    return a[0] + b[0], a[1] + b[1]
+
+
+def sub(a, b):
+    return a[0] - b[0], a[1] - b[1]
+
+
+def mul(a, b):
+    return a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]
+
+
+def rot(value, phase):
+    a, b = value
+    return ((a, b), (-b, a), (-a, -b), (b, -a))[phase % 4]
+
+
+def times_pi(value):
+    return value[0] - value[1], value[0] + value[1]
+
+
+def divide_pi(value):
+    a, b = value
+    if (a + b) % 2:
+        raise OutsideLattice("not divisible by 1+i")
+    return (a + b) // 2, (b - a) // 2
+
+
+def half_exact(value):
+    if value[0] % 2 or value[1] % 2:
+        raise OutsideLattice("ideal Gaussian pair has a nonintegral component")
+    return value[0] // 2, value[1] // 2
+
+
+def pi_power(exponent):
+    rank_check(exponent)
+    result = (1, 0)
+    for _ in range(exponent):
+        result = times_pi(result)
+    return result
+
+
+def encode(coefficients):
+    """E_r c, with E_1(c0,c1)=(c0,c0+(1+i)c1), in address-bit order."""
+    rank = validate(coefficients)
+    out = coefficients[:]
+    for bit in range(rank):
+        step = 1 << bit
+        for address in range(len(out)):
+            if not address & step:
+                out[address | step] = add(out[address], times_pi(out[address | step]))
+    validate(out, rank)
+    return out
+
+
+def decode(values):
+    """Exact E_r inverse; membership fails on an unavailable pi division."""
+    rank = validate(values)
+    out = values[:]
+    for bit in reversed(range(rank)):
+        step = 1 << bit
+        for address in range(len(out)):
+            if not address & step:
+                out[address | step] = divide_pi(sub(out[address | step], out[address]))
+    validate(out, rank)
+    return out
+
+
+def member(values):
+    validate(values)
+    try:
+        decode(values)
+    except OutsideLattice:
+        return False
+    return True
+
+
+def newton(values):
+    """Unweighted multilinear coefficients, obtained by Boolean differences."""
+    rank = validate(values)
+    out = values[:]
+    for bit in range(rank):
+        step = 1 << bit
+        for address in range(len(out)):
+            if not address & step:
+                out[address | step] = sub(out[address | step], out[address])
+    validate(out, rank)
+    return out
+
+
+def ideal_pair_numerators(a, b, inverse=False):
+    """Return twice C(a,b), so nonintegral examples can be checked exactly."""
+    gaussian_check(a)
+    gaussian_check(b)
+    require(type(inverse) is bool, "inverse flag must be Boolean")
+    total = add(a, b)
+    difference = rot(sub(a, b), 3 if inverse else 1)
+    return add(total, difference), sub(total, difference)
+
+
+def ideal_pair(a, b, inverse=False):
+    first, second = ideal_pair_numerators(a, b, inverse)
+    return half_exact(first), half_exact(second)
+
+
+def lift_pair(a, b, inverse=False):
+    """Literal componentwise signed-floor lifting, without a grid change."""
+    gaussian_check(a)
+    gaussian_check(b)
+    require(type(inverse) is bool, "inverse flag must be Boolean")
+    difference = sub(a, b)
+    middle = add(b, (difference[0] // 2, difference[1] // 2))
+    difference = rot(difference, 3 if inverse else 1)
+    second = sub(middle, (difference[0] // 2, difference[1] // 2))
+    return add(second, difference), second
+
+
+def stage(values, bit, inverse=False, literal=False):
+    rank = validate(values)
+    require(type(bit) is int and 0 <= bit < rank, "address bit outside array")
+    require(type(inverse) is bool and type(literal) is bool, "stage flags must be Boolean")
+    out = values[:]
+    step = 1 << bit
+    pair = lift_pair if literal else ideal_pair
+    for address in range(len(out)):
+        if not address & step:
+            other = address | step
+            out[address], out[other] = pair(out[address], out[other], inverse)
+    validate(out, rank)
+    return out
+
+
+def ideal_stage(values, bit, inverse=False):
+    return stage(values, bit, inverse=inverse)
+
+
+def lift_stage(values, bit, inverse=False):
+    return stage(values, bit, inverse=inverse, literal=True)
+
+
+def gate_bits(kind, bits, rank):
+    require(kind in ("C", "CINV", "S", "SINV", "X", "SWAP", "CNOT", "CZ"),
+            "unsupported gate")
+    count = 2 if kind in ("SWAP", "CNOT", "CZ") else 1
+    require(type(bits) in (tuple, list) and len(bits) == count, "gate arity")
+    require(all(type(bit) is int and 0 <= bit < rank for bit in bits), "gate address bits")
+    require(len(set(bits)) == len(bits), "gate bits must be distinct")
+    return tuple(bits)
+
+
+def value_gate(values, kind, bits):
+    """The physical Gaussian gate; CNOT bits are (control,target)."""
+    rank = validate(values)
+    bits = gate_bits(kind, bits, rank)
+    if kind in ("C", "CINV"):
+        return ideal_stage(values, bits[0], inverse=kind == "CINV")
+    out = [ZERO] * len(values)
+    for address, value in enumerate(values):
+        target, phase = address, 0
+        first = (address >> bits[0]) & 1
+        if kind == "X":
+            target ^= 1 << bits[0]
+        elif kind in ("S", "SINV"):
+            phase = first * (1 if kind == "S" else 3)
+        elif kind == "CNOT":
+            target ^= first << bits[1]
+        elif kind == "CZ":
+            phase = 2 * first * ((address >> bits[1]) & 1)
+        elif first != ((address >> bits[1]) & 1):
+            target ^= (1 << bits[0]) | (1 << bits[1])
+        out[target] = rot(value, phase)
+    return out
+
+
+def coefficient_pair(a, b, kind):
+    if kind == "C":
+        return add(a, b), rot(b, 1)
+    if kind == "CINV":
+        last = rot(b, 3)
+        return sub(a, last), last
+    if kind == "S":
+        return a, rot(add(a, b), 1)
+    if kind == "SINV":
+        return a, sub(rot(b, 3), a)
+    require(kind == "X", "unsupported coefficient pair")
+    return add(a, times_pi(b)), rot(b, 2)
+
+
+def coefficient_gate(coefficients, kind, bits):
+    """Direct integral E^-1 gate E formulas; no encode/decode calls."""
+    rank = validate(coefficients)
+    bits = gate_bits(kind, bits, rank)
+    if kind == "SWAP":
+        return value_gate(coefficients, kind, bits)
+    out = coefficients[:]
+    first = 1 << bits[0]
+    if len(bits) == 1:
+        for address in range(len(out)):
+            if not address & first:
+                other = address | first
+                out[address], out[other] = coefficient_pair(out[address], out[other], kind)
+        validate(out, rank)
+        return out
+    second = 1 << bits[1]
+    for address in range(len(out)):
+        if address & (first | second):
+            continue
+        a, b, c, d = (out[address | mask] for mask in (0, first, second, first | second))
+        if kind == "CNOT":
+            out[address | first] = add(add(b, c), times_pi(d))
+            out[address | first | second] = sub(rot(times_pi(c), 1), d)
+        else:
+            require(kind == "CZ", "unsupported coefficient block")
+            out[address | first | second] = sub(add(rot(a, 1), rot(times_pi(add(b, c)), 1)), d)
+    validate(out, rank)
+    return out
+
+
+def wrapper_plan(record):
+    """Exact source convention: input x receives its phase, then moves to Ax+b."""
+    keys = {"matrix_rows", "offset", "linear_Z4", "quadratic_rows", "phase"}
+    require(type(record) is dict and set(record) == keys, "wrapper schema")
+    rows, linear, quadratic = (record[name] for name in
+                               ("matrix_rows", "linear_Z4", "quadratic_rows"))
+    require(type(rows) is list, "wrapper matrix rows")
+    rank = rank_check(len(rows))
+    require(type(linear) is list and type(quadratic) is list, "wrapper phase arrays")
+    require(len(linear) == len(quadratic) == rank, "wrapper dimensions")
+    size = 1 << rank
+    require(all(type(row) is int and 0 <= row < size for row in rows + quadratic),
+            "wrapper binary rows")
+    require(all(type(value) is int and 0 <= value < 4 for value in linear), "linear phases")
+    require(type(record["offset"]) is int and 0 <= record["offset"] < size, "affine offset")
+    require(type(record["phase"]) is int and 0 <= record["phase"] < 4, "global phase")
+    result = []
+    for address in range(size):
+        target = record["offset"]
+        phase = record["phase"]
+        for j in range(rank):
+            target ^= ((rows[j] & address).bit_count() & 1) << j
+            if address >> j & 1:
+                phase += linear[j]
+                for k in range(j + 1, rank):
+                    phase += 2 * ((quadratic[j] >> k) & 1) * ((address >> k) & 1)
+        result.append((target, phase % 4))
+    require(len({target for target, _ in result}) == size, "wrapper must be bijective")
+    return result
+
+
+def wrapper(values, record, inverse=False):
+    validate(values)
+    require(type(inverse) is bool, "inverse flag must be Boolean")
+    plan = wrapper_plan(record)
+    require(len(plan) == len(values), "wrapper and array dimensions")
+    out = [ZERO] * len(values)
+    for source, (target, phase) in enumerate(plan):
+        if inverse:
+            out[source] = rot(values[target], -phase)
+        else:
+            out[target] = rot(values[source], phase)
+    return out
+
+
+def codec_ledger(rank):
+    rank_check(rank)
+    size = 1 << rank
+    pairs = rank * size // 2
+    return {"rank": rank, "complex_coordinates": size, "pairs_per_direction": pairs,
+            "encode": {"gaussian_adds": pairs, "pi_multiplications": pairs,
+                       "real_add_subtracts": 4 * pairs, "component_reads": 4 * pairs,
+                       "component_writes": 2 * pairs},
+            "decode": {"gaussian_subtracts": pairs, "exact_pi_divisions": pairs,
+                       "real_add_subtracts": 4 * pairs, "exact_real_halves": 2 * pairs,
+                       "component_reads": 4 * pairs, "component_writes": 2 * pairs},
+            "owned_in_place_complex_words": size, "pair_real_work_words": 4,
+            "borrowed_input_copy_included": False, "routing_included": False}
+
+
+def codec_bounds(rank, component_bound):
+    """Sufficient integer bounds, per codec's own entrance; not physical prices."""
+    rank_check(rank)
+    require(type(component_bound) is int and component_bound >= 0, "nonnegative bound")
+    gain = sum(comb(rank, k) * sum(abs(x) for x in pi_power(k)) for k in range(rank + 1))
+    inverse_gain = 1 << ((rank + 1) // 2)
+    return {"rank": rank, "entrance_component_bound": component_bound,
+            "encode_component_gain": gain, "encode_component_bound": gain * component_bound,
+            "encode_scratch_bound": 3 * gain * component_bound,
+            "decode_component_gain": inverse_gain,
+            "decode_component_bound": inverse_gain * component_bound,
+            "decode_scratch_bound": 4 * inverse_gain * component_bound}
+
+
+def collector_bounds(rank, source_count, component_bound):
+    rank_check(rank)
+    require(type(source_count) is int and 1 <= source_count <= 5, "source count in 1..5")
+    require(type(component_bound) is int and component_bound >= 0, "nonnegative bound")
+    size = 1 << rank
+    root = isqrt(2 * size)
+    if root * root < 2 * size:
+        root += 1
+    native = source_count * root * component_bound
+    return {"rank": rank, "entrance_component_bound": component_bound,
+            "source_count": source_count, "native_prefix_component_bound": native,
+            "query_component_bound": native + component_bound,
+            "pair_scratch_component_bound": 5 * native,
+            "assumption": "exact unitary native prefixes on the admitted lattice"}
+
+
+def collector_ledger(rank, native_rank, wrapper_cycle_counts):
+    """Complete direct collector counts; four actual source wrappers are required."""
+    rank_check(rank)
+    require(type(native_rank) is int and 1 <= native_rank <= rank, "native rank")
+    size = 1 << rank
+    require(type(wrapper_cycle_counts) is list and len(wrapper_cycle_counts) == 4,
+            "four literal wrapper cycle counts required")
+    require(all(type(c) is int and 1 <= c <= size for c in wrapper_cycle_counts),
+            "wrapper cycle count")
+    pairs = native_rank * size
+    swaps = 4 * size + sum(wrapper_cycle_counts)
+    return {"complex_coordinates": size, "native_rank_each_direction": native_rank,
+            "paired_butterflies": pairs, "field_adds": 11,
+            "real_add_subtracts": 8 * pairs + 22 * size,
+            "floor_halves": 4 * pairs, "butterfly_quarter_turns": pairs,
+            "wrapper_cycle_counts": wrapper_cycle_counts[:],
+            "wrapper_cycles": sum(wrapper_cycle_counts), "wrapper_swaps": swaps,
+            "wrapper_unit_phases": 4 * size,
+            "butterfly_component_reads": 4 * pairs, "butterfly_component_writes": 4 * pairs,
+            "field_add_component_reads": 44 * size, "field_add_component_writes": 22 * size,
+            "source_component_reads_within_field_adds": 20 * size,
+            "wrapper_swap_component_reads": 4 * swaps, "wrapper_swap_component_writes": 4 * swaps,
+            "private_initialization_components": 2 * size, "private_zero_check_components": 2 * size,
+            "borrowed_source_complex_words": 5 * size, "mutable_query_complex_words": size,
+            "owned_private_complex_words": size, "wrapper_zero_scratch_complex_words": 1,
+            "pair_real_work_words": 4, "codecs_included": False,
+            "physical_routing_and_recursive_tariff_included": False}
+
+
+def cold_codec_ledger(rank):
+    """Optional T=E^-1 U E caller: prepare five owned source banks and query."""
+    codec = codec_ledger(rank)
+    size = 1 << rank
+    pairs = codec["pairs_per_direction"]
+    return {"rank": rank, "encodes": 6, "decodes": 6,
+            "owned_source_copy_adds": 5, "owned_source_cleanup_adds": 5,
+            "extra_owned_source_complex_words": 5 * size,
+            "extra_private_initialization_components": 10 * size,
+            "extra_private_zero_check_components": 10 * size,
+            "codec_real_add_subtracts": 48 * pairs,
+            "codec_exact_real_halves": 12 * pairs,
+            "codec_pi_multiplications": 6 * pairs, "codec_exact_pi_divisions": 6 * pairs,
+            "codec_component_reads": 48 * pairs, "codec_component_writes": 24 * pairs,
+            "copy_cleanup_real_add_subtracts": 20 * size,
+            "copy_cleanup_component_reads": 40 * size,
+            "copy_cleanup_component_writes": 20 * size,
+            "add_to_direct_collector_invoice": True,
+            "logical_output_map": "T = E_r^-1 U E_r",
+            "original_U_caller_admitted": False,
+            "physical_routing_and_recursive_tariff_included": False}
+
+
+def cold_codec_bounds(rank, component_bound):
+    """Compose the optional cold caller's bounds from its raw coefficient entry."""
+    encoder = codec_bounds(rank, component_bound)
+    physical = collector_bounds(rank, 5, encoder["encode_component_bound"])
+    decoder = codec_bounds(rank, physical["query_component_bound"])
+    return {"rank": rank, "raw_entrance_component_bound": component_bound,
+            "encoded_component_bound": encoder["encode_component_bound"],
+            "native_prefix_component_bound": physical["native_prefix_component_bound"],
+            "encoded_query_component_bound": physical["query_component_bound"],
+            "decoded_query_component_bound": decoder["decode_component_bound"],
+            "complete_scratch_component_bound": max(encoder["encode_scratch_bound"],
+                                                      physical["pair_scratch_component_bound"],
+                                                      decoder["decode_scratch_bound"]),
+            "logical_output_map": "T = E_r^-1 U E_r"}
diff --git a/research/p104-newton-interfaces/producer.py b/research/p104-newton-interfaces/producer.py
new file mode 100644
index 0000000000..480b0c1dda
--- /dev/null
+++ b/research/p104-newton-interfaces/producer.py
@@ -0,0 +1,463 @@
+"""Exact source-bound admission for the first P104 collector's producer cone.
+
+Prepared by Clear1nsight with substantial OpenAI assistance. Apache-2.0.
+The native word and Gaussian lattice retain their separately pinned authorship.
+This module mutates no source file and performs no native/compiler build.
+"""
+
+import argparse
+import gzip
+import hashlib
+import json
+from collections import Counter
+from fractions import Fraction
+from pathlib import Path
+from types import ModuleType
+
+
+SOURCE_HASHES = {
+    "word": "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50",
+    "native": "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d",
+    "model": "74c83367887dd885137b222155c86389fe0be9f1293a6f0e5fdb51d71f435fdd",
+}
+CUT = 2025
+SIZE = 512
+TARGETS = ("D31", "D30", "D29", "D28", "D27", "Q7")
+Y_INPUTS = tuple("Y" + str(j) for j in list(range(22, 33)) + list(range(63, 104)))
+SOURCE_FRAME = [256, 136, 64, 40, 16, 4, 2, 1]
+
+
+class ProducerError(ValueError):
+    """A source, numerical, or claimed admission obligation failed."""
+
+
+def require(condition, message):
+    if not condition:
+        raise ProducerError(message)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(",", ":")).encode()
+
+
+def sha(value):
+    return hashlib.sha256(value).hexdigest()
+
+
+def read_pinned(path, label):
+    path = Path(path)
+    require(path.is_file() and not path.is_symlink(), "regular source file required")
+    with path.open("rb") as handle:
+        data = handle.read(32 * 1024 * 1024 + 1)
+    require(len(data) <= 32 * 1024 * 1024, "source size bound")
+    return authenticated_bytes(data, label)
+
+
+def authenticated_bytes(data, label):
+    require(sha(data) == SOURCE_HASHES[label], "source digest mismatch: " + label)
+    return data
+
+
+def load_inputs(word_path, native_path, model_path):
+    word_bytes = read_pinned(word_path, "word")
+    native_bytes = read_pinned(native_path, "native")
+    model_bytes = read_pinned(model_path, "model")
+    word = json.loads(word_bytes)
+    native = json.loads(gzip.decompress(native_bytes))
+    model = ModuleType("p104_frozen_gaussian_model")
+    exec(compile(model_bytes, str(model_path), "exec"), model.__dict__)
+    return word, native, model
+
+
+def extract_cone(word):
+    """Backward slice using the authenticated destination-first ADD convention."""
+    program = word["program"]
+    needed = set(TARGETS)
+    selected = []
+    for event in reversed(range(CUT)):
+        record = program[event]
+        if record[1] not in needed:
+            continue
+        require(record[0] in ("transport", "add", "sign"), "producer instruction")
+        selected.append(event)
+        if record[0] == "add":
+            needed.add(record[2])
+    selected.reverse()
+    require(needed == set(TARGETS) | set(Y_INPUTS), "exact 58 initial dependencies")
+    require(len(selected) == 257, "exact producer cone size")
+    counts = Counter(program[event][0] for event in selected)
+    require(counts == {"transport": 200, "add": 57}, "exact producer instruction counts")
+    require(all(word["initial_frames"][name] == [] for name in needed), "initial frames")
+    return selected, sorted(needed)
+
+
+def native_records(word, native, selected, model):
+    occurrences = {}
+    for item in native["transports"]:
+        for event in item["events"]:
+            require(event not in occurrences, "native event occurrence unique")
+            occurrences[event] = item
+    plans = {}
+    for event in selected:
+        record = word["program"][event]
+        if record[0] != "transport":
+            continue
+        require(event in occurrences, "native event recipe exists")
+        item = occurrences[event]
+        require((item["old"], item["new"], item["recipe"]["rank"]) ==
+                (record[2], record[3], record[4]), "native frame/rank binding")
+        recipe = item["recipe"]
+        require(type(recipe["rank"]) is int and 1 <= recipe["rank"] <= 9, "native rank")
+        plans[event] = {"rank": recipe["rank"],
+                        "right": model.wrapper_plan(recipe["right"]),
+                        "left": model.wrapper_plan(recipe["left"])}
+    return plans
+
+
+def apply_wrapper(values, plan, model):
+    require(len(values) == len(plan) == SIZE, "wrapper size")
+    out = [(0, 0)] * SIZE
+    for source, (target, phase) in enumerate(plan):
+        out[target] = model.rot(values[source], phase)
+    return out
+
+
+def pi_valuation(value):
+    if value == (0, 0):
+        return None
+    a, b = value
+    valuation = 0
+    while (a + b) % 2 == 0:
+        a, b = (a + b) // 2, (b - a) // 2
+        valuation += 1
+    return valuation
+
+
+def lattice_failure(values, model):
+    for mask, coefficient in enumerate(model.newton(values)):
+        valuation = pi_valuation(coefficient)
+        if valuation is not None and valuation < mask.bit_count():
+            return {"mask": mask, "degree": mask.bit_count(),
+                    "coefficient": list(coefficient), "pi_valuation": valuation,
+                    "required_pi_valuation": mask.bit_count()}
+    return None
+
+
+def exact_scale(values, coefficient):
+    coefficient = Fraction(str(coefficient))
+    p, q = coefficient.numerator, coefficient.denominator
+    require(all(p * x % q == 0 for value in values for x in value),
+            "fractional ADD is not exact on the retained grid")
+    return [(p * a // q, p * b // q) for a, b in values]
+
+
+def four_member(values, model):
+    if any(x % 4 for value in values for x in value):
+        return False
+    return model.member(exact_scale(values, "1/4"))
+
+
+def fingerprint(values, model):
+    return {"sha256": sha(canonical(values)),
+            "nonzero_complex_entries": sum(value != (0, 0) for value in values),
+            "max_absolute_component": max(abs(x) for value in values for x in value),
+            "in_B9": model.member(values), "newton_failure": lattice_failure(values, model)}
+
+
+def native_execute(values, plan, model, counts, require_membership):
+    values = apply_wrapper(values, plan["right"], model)
+    if require_membership:
+        require(model.member(values), "right wrapper preserves admitted domain")
+    for bit in range(plan["rank"]):
+        ideal = model.ideal_stage(values, bit)
+        literal = model.lift_stage(values, bit)
+        require(ideal == literal, "literal pair differs from exact ideal pair")
+        if require_membership:
+            require(model.member(literal), "coordinate prefix preserves admitted domain")
+        counts["pair_obligations"] += SIZE // 2
+        counts["coordinate_stages"] += 1
+        values = literal
+    values = apply_wrapper(values, plan["left"], model)
+    if require_membership:
+        require(model.member(values), "left wrapper preserves admitted domain")
+    counts["native_calls"] += 1
+    return values
+
+
+def initial_admission(state, dependencies, model):
+    require(set(state) == set(dependencies), "exact initial bank set")
+    for values in state.values():
+        require(model.validate(values) == 9, "nine-bit input bank")
+    return {"all_initial_fields_in_B9": all(model.member(x) for x in state.values()),
+            "Y_fields_outside_4B9": [name for name in Y_INPUTS if not four_member(state[name], model)]}
+
+
+def replay_cone(word, plans, selected, dependencies, model, initial, require_admission):
+    state = {name: values[:] for name, values in initial.items()}
+    admission = initial_admission(state, dependencies, model)
+    if require_admission:
+        require(admission["all_initial_fields_in_B9"] and
+                not admission["Y_fields_outside_4B9"], "producer entrance contract")
+    frames = {name: word["initial_frames"][name][:] for name in dependencies}
+    counts = {"native_calls": 0, "coordinate_stages": 0, "pair_obligations": 0,
+              "quarter_adds": 0, "unit_adds": 0}
+    failures = []
+    for event in selected:
+        record = word["program"][event]
+        target = record[1]
+        if record[0] == "transport":
+            require(frames[target] == record[2], "native old frame at producer event")
+            state[target] = native_execute(state[target], plans[event], model, counts, require_admission)
+            frames[target] = record[3][:]
+        else:
+            apply_add(record, state, frames, model, counts)
+        failure = lattice_failure(state[target], model)
+        if failure is not None:
+            failures.append({"event": event, "target": target, "witness": failure})
+        if require_admission:
+            require(failure is None, "producer output leaves lattice")
+    require(all(frames[d] == SOURCE_FRAME for d in TARGETS[:5]), "final source frames")
+    require(frames["Q7"] == [364], "final query frame")
+    receipt = {"initial_admission": admission, "counts": counts,
+               "all_fractional_adds_exact": True, "all_literal_native_pairs_exact": True,
+               "first_lattice_failure": failures[0] if failures else None,
+               "failing_event_outputs": failures,
+               "entrance": {name: fingerprint(state[name], model) for name in TARGETS}}
+    return state, receipt
+
+
+def apply_add(record, state, frames, model, counts):
+    _, target, source, coefficient, frame = record
+    coefficient = add_contract(record, frames)
+    if source in Y_INPUTS:
+        counts["quarter_adds"] += 1
+    else:
+        counts["unit_adds"] += 1
+    scaled = exact_scale(state[source], coefficient)
+    state[target] = [model.add(a, b) for a, b in zip(state[target], scaled)]
+    model.validate(state[target], 9)
+
+
+def add_contract(record, frames):
+    _, target, source, coefficient, frame = record
+    require(frames[target] == frames[source] == frame, "ADD common frame")
+    coefficient = Fraction(str(coefficient))
+    if source in Y_INPUTS:
+        require(target in TARGETS[:5] and coefficient == Fraction(1, 4), "actual quarter source")
+    else:
+        require(target == "Q7" and source in TARGETS[:5] and coefficient == -1,
+                "actual Q7 subtraction")
+    return coefficient
+
+
+def validate_structure(word, selected, dependencies):
+    frames = {name: word["initial_frames"][name][:] for name in dependencies}
+    for event in selected:
+        record = word["program"][event]
+        if record[0] == "transport":
+            require(frames[record[1]] == record[2], "native old frame at producer event")
+            frames[record[1]] = record[3][:]
+        else:
+            add_contract(record, frames)
+    require(all(frames[d] == SOURCE_FRAME for d in TARGETS[:5]), "final source frames")
+    require(frames["Q7"] == [364], "final query frame")
+    return frames
+
+
+def dense_initial(dependencies, model):
+    result = {}
+    for ordinal, name in enumerate(dependencies):
+        coefficients = [((17 * x + 13 * ordinal + (x >> 2)) % 19 - 9,
+                         (11 * x + 7 * ordinal + (x >> 4)) % 23 - 11)
+                        for x in range(SIZE)]
+        values = model.encode(coefficients)
+        result[name] = exact_scale(values, 4 if name in Y_INPUTS else 1)
+    return result
+
+
+def impulse_initial(dependencies, amplitude):
+    result = {name: [(0, 0)] * SIZE for name in dependencies}
+    result["Y27"][0] = (amplitude, 0)
+    return result
+
+
+def source_summary(word, selected, dependencies):
+    program = word["program"]
+    reads = {name: [] for name in Y_INPUTS}
+    target_rows = {}
+    for target in TARGETS:
+        writes = [event for event in selected if program[event][1] == target]
+        quarters = []
+        for event in writes:
+            record = program[event]
+            if record[0] == "add" and record[2] in reads:
+                reads[record[2]].append(event)
+                quarters.append({"event": event, "source": record[2], "frame": record[4]})
+        target_rows[target] = {"write_events": writes, "quarter_sources": quarters}
+    require(all(len(events) == 1 for events in reads.values()), "each Y source used once in cone")
+    return {"cut_before_event": CUT, "initial_dependencies": dependencies,
+            "event_count": len(selected), "events": selected,
+            "ordered_records_sha256": sha(canonical([[e, program[e]] for e in selected])),
+            "native_rank_sum": sum(program[e][4] for e in selected if program[e][0] == "transport"),
+            "target_paths": target_rows, "Y_read_events": reads,
+            "scope": "numerical backward dependency cone; physical ownership remains external",
+            "actual_cut_outputs": list(TARGETS),
+            "auxiliary_Y_states": "historical last-required-read states, not actual cut outputs"}
+
+
+def coefficient_valuation(coefficient):
+    value = Fraction(str(coefficient))
+    require(value != 0, "nonzero source coefficient")
+    numerator, denominator = abs(value.numerator), value.denominator
+    valuation = 0
+    while numerator % 2 == 0:
+        numerator //= 2
+        valuation += 2
+    while denominator % 2 == 0:
+        denominator //= 2
+        valuation -= 2
+    require(denominator == 1, "dyadic scalar coefficient")
+    return valuation
+
+
+def impulse_prefix_valuation(word):
+    """One-input reachability bound; no universal full-prefix admission claim."""
+    lower = {"Y27": 12}
+    active = []
+    reads = []
+    for event, record in enumerate(word["program"][:CUT]):
+        kind, target = record[:2]
+        if kind == "add":
+            coefficient_valuation(record[3])
+        elif kind == "sign":
+            require(Fraction(str(record[2])) in (-1, 1), "source sign is a Gaussian unit")
+        if kind == "transport" and target in lower:
+            lower[target] -= record[4]
+            require(lower[target] >= 0, "witness native prefix lacks pi factors")
+            active.append({"event": event, "field": target, "lower_pi_valuation": lower[target]})
+        elif kind == "add" and record[2] in lower:
+            source = record[2]
+            proposed = lower[source] + coefficient_valuation(record[3])
+            require(proposed >= 0, "witness fractional source lacks pi factors")
+            lower[target] = min(lower.get(target, proposed), proposed)
+            reads.append({"event": event, "target": target, "source": source,
+                          "coefficient": str(record[3]),
+                          "source_after_coefficient_lower_pi_valuation": proposed})
+        else:
+            require(kind in ("transport", "add", "sign"), "prefix instruction grammar")
+    return {"initial_point": {"Y27[0]": [64, 0], "all_other_initial_components": 0},
+            "method": "component pi-valuations; native stage loses at most one; quarter loses four",
+            "scope": "only this explicit initial point through events0..2024",
+            "initial_bank_count": len(word["initial_frames"]),
+            "all_literal_pairs_and_fractional_sources_exact": True,
+            "active_native_events": active, "active_fractional_source_events": reads,
+            "final_component_valuation_lower_bounds": lower}
+
+
+def rejects(call, expected_message):
+    try:
+        call()
+    except ProducerError as error:
+        require(str(error) == expected_message, "control rejected for the wrong reason")
+        return {"rejected": True, "reason": str(error)}
+    raise ProducerError("negative control unexpectedly accepted")
+
+
+def rejection_controls(word, selected, dependencies):
+    wrong_quarter = json.loads(json.dumps(word))
+    wrong_quarter["program"][1090][3] = "1/2"
+    omitted_source = json.loads(json.dumps(word))
+    omitted_source["program"][1090][2] = "Y26"
+    wrong_order = json.loads(json.dumps(word))
+    p = wrong_order["program"]
+    p[1090], p[1129] = p[1129], p[1090]
+    require(exact_scale([(-4, 4), (-8, -12)], "1/4") == [(-1, 1), (-2, -3)],
+            "signed exact quarters")
+    return {
+        "source_byte_corruption": rejects(lambda: authenticated_bytes(b"corrupted", "word"),
+                                           "source digest mismatch: word"),
+        "wrong_quarter_at1090": rejects(lambda: validate_structure(wrong_quarter, selected, dependencies),
+                                        "actual quarter source"),
+        "omitted_Y27_source": rejects(lambda: extract_cone(omitted_source), "exact 58 initial dependencies"),
+        "source_reads1090_1129_swapped": rejects(lambda: validate_structure(wrong_order, selected, dependencies),
+                                                "ADD common frame"),
+        "negative_nonintegral_quarter": rejects(lambda: exact_scale([(-3, 4)], "1/4"),
+                                                "fractional ADD is not exact on the retained grid"),
+        "signed_exact_quarters": {"inputs": [[-4, 4], [-8, -12]], "outputs": [[-1, 1], [-2, -3]]},
+    }
+
+
+def bind_witness_valuation(word, native, model):
+    result = impulse_prefix_valuation(word)
+    active = [row["event"] for row in result["active_native_events"]]
+    require(len(active) == 20, "exact active native count for witness")
+    native_records(word, native, active, model)
+    result["all_active_native_frames_ranks_and_wrappers_bound"] = True
+    result["ordered_active_native_records_sha256"] = sha(canonical([[e, word["program"][e]] for e in active]))
+    result["ordered_prefix_records_sha256"] = sha(canonical(word["program"][:CUT]))
+    return result
+
+
+def verify_producer(word_path, native_path, model_path):
+    word, native, model = load_inputs(word_path, native_path, model_path)
+    selected, dependencies = extract_cone(word)
+    validate_structure(word, selected, dependencies)
+    plans = native_records(word, native, selected, model)
+    _, positive = replay_cone(word, plans, selected, dependencies, model,
+                              dense_initial(dependencies, model), True)
+    negative_state, negative = replay_cone(word, plans, selected, dependencies, model,
+                                          impulse_initial(dependencies, 64), False)
+    require(negative["initial_admission"]["all_initial_fields_in_B9"], "witness starts in B9")
+    require(negative["initial_admission"]["Y_fields_outside_4B9"] == ["Y27"], "one stronger-source failure")
+    require(negative["first_lattice_failure"]["event"] == 1090, "first bad producer event")
+    require(not negative["entrance"]["D31"]["in_B9"], "actual final producer failure")
+    require(all(negative["entrance"][d]["in_B9"] for d in TARGETS if d != "D31"),
+            "other five collector entrances remain admitted")
+    negative["two_point_final_witness"] = {
+        "addresses": [0, 8], "values": [list(negative_state["D31"][j]) for j in (0, 8)],
+        "difference": list(model.sub(negative_state["D31"][8], negative_state["D31"][0]))}
+    require(negative["two_point_final_witness"]["difference"] == [-1, 0], "degree-one final witness")
+    repaired_state, repaired = replay_cone(word, plans, selected, dependencies, model,
+                                          impulse_initial(dependencies, 256), True)
+    require(repaired_state["D31"] == exact_scale(negative_state["D31"], 4), "amplitude256 positive control")
+    rejected = False
+    try:
+        initial = impulse_initial(dependencies, 64)
+        replay_cone(word, plans, selected, dependencies, model, initial, True)
+    except ProducerError as error:
+        rejected = str(error) == "producer entrance contract"
+    require(rejected, "stronger-source contract rejects the witness")
+    return {"status": "PASS", "source_sha256": SOURCE_HASHES,
+            "source_cone": source_summary(word, selected, dependencies),
+            "dense_dirty_admitted_fixture": positive,
+            "one_coordinate_counterexample": negative,
+            "amplitude256_admitted_control": repaired,
+            "counterexample_full_prefix_valuation": bind_witness_valuation(word, native, model),
+            "controls": rejection_controls(word, selected, dependencies),
+            "stronger_contract_rejects_counterexample": rejected,
+            "claim": "B9 prefix admission under exactly the stated strengthened initial contract",
+            "not_claimed": ["maximal final-cut domain", "arbitrary-input source admission",
+                            "full-word correctness", "physical owners or favorable recursive cost"]}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--repo", type=Path, default=Path(__file__).resolve().parents[2])
+    parser.add_argument("--model", type=Path,
+                        default=Path(__file__).resolve().parent / "inputs/pr3382_model.py")
+    parser.add_argument("--receipt", type=Path)
+    args = parser.parse_args()
+    source = args.repo / "research/p104-rounded-collector/inputs"
+    result = verify_producer(source / "WORD.json", source / "NATIVE.json.gz", args.model)
+    data = json.dumps(result, indent=2, sort_keys=True) + "\n"
+    if args.receipt:
+        with args.receipt.open("x") as handle:
+            handle.write(data)
+    print(json.dumps({"status": result["status"], "receipt_sha256": sha(data.encode()),
+                      "cone_events": result["source_cone"]["event_count"],
+                      "first_failure": result["one_coordinate_counterexample"]["first_lattice_failure"]},
+                     sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/p104-newton-interfaces/verify.py b/research/p104-newton-interfaces/verify.py
new file mode 100644
index 0000000000..7e4e14fa6e
--- /dev/null
+++ b/research/p104-newton-interfaces/verify.py
@@ -0,0 +1,299 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Source-complete joint replay of the three assigned P104 interface questions.
+
+Clear1nsight, with substantial OpenAI assistance. The proofs state the universal
+claims. These exact, bounded computations authenticate the actual source paths,
+exercise the arithmetic, and compare separately implemented evidence. No Git,
+network, third-party dependency, or predecessor checkout is needed for replay.
+"""
+
+import argparse
+import hashlib
+import json
+from pathlib import Path, PurePosixPath
+import tempfile
+import types
+
+
+PACKAGE = Path(__file__).resolve().parent
+WORD = "research/p104-rounded-collector/inputs/WORD.json"
+NATIVE = "research/p104-rounded-collector/inputs/NATIVE.json.gz"
+BUDGET = "research/p104-consumer-budget-audit/README.md"
+SCIENTIFIC = {
+    WORD: "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50",
+    NATIVE: "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d",
+    BUDGET: "13694215d0c1a245b392f7155e8395b9c4bad9c5db3558833c784d9449616417",
+}
+RETAINED = {
+    "inputs/pr3382_model.py": "74c83367887dd885137b222155c86389fe0be9f1293a6f0e5fdb51d71f435fdd",
+    "inputs/PR3382_PROOF.md": "1ca8c0e7e78f0f39de6cff7accc68ccd3901bfb50759bf7a2e2896bcf63bf081",
+}
+MODULES = ("producer.py", "consumer.py", "cost_audit.py", "independent.py")
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def sha(data):
+    return hashlib.sha256(data).hexdigest()
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(",", ":"), allow_nan=False).encode()
+
+
+def unique_object(pairs):
+    result = {}
+    for name, value in pairs:
+        require(name not in result, "duplicate JSON key: " + name)
+        result[name] = value
+    return result
+
+
+def reject_number(value):
+    raise ValueError("non-integer JSON number: " + value)
+
+
+def strict_json(data):
+    return json.loads(data, object_pairs_hook=unique_object,
+                      parse_constant=reject_number, parse_float=reject_number)
+
+
+def regular_bytes(root, name):
+    pure = PurePosixPath(name)
+    require(isinstance(name, str) and str(pure) == name and pure.parts
+            and not pure.is_absolute() and ".." not in pure.parts,
+            "canonical relative input path")
+    path = root
+    for part in pure.parts:
+        path = path / part
+        require(not path.is_symlink(), "symlink input: " + name)
+    require(path.is_file() and path.stat().st_size <= 32 * 1024 * 1024,
+            "bounded regular input required: " + name)
+    return path.read_bytes()
+
+
+def checked(data, expected, name):
+    require(sha(data) == expected, "source SHA256 mismatch: " + name)
+    return data
+
+
+def authenticate(repo, package=PACKAGE):
+    sources = strict_json(regular_bytes(package, "SOURCES.json"))
+    manifest = strict_json(regular_bytes(package, "VERIFY.json"))
+    rows = [row for row in sources["files"] if row["usage"] == "input"]
+    names = [row["path"] for row in rows]
+    require(len(set(names)) == len(names), "duplicate declared source input")
+    require(len(set(manifest["inputs"])) == len(manifest["inputs"])
+            and set(names) == set(manifest["inputs"]), "complete declared input closure")
+    require(set(SCIENTIFIC) <= set(names), "missing scientific input")
+    retained = sources["retained_sources"]
+    require(len(retained) == len(RETAINED)
+            and {row["path"] for row in retained} == set(RETAINED),
+            "complete retained predecessor closure")
+    loaded, hashes = {}, {}
+    for row in rows:
+        name = row["path"]
+        data = checked(regular_bytes(repo, name), row["sha256"], name)
+        if name in SCIENTIFIC:
+            checked(data, SCIENTIFIC[name], name)
+        loaded[name], hashes[name] = data, sha(data)
+    for row in retained:
+        name = row["path"]
+        data = checked(regular_bytes(package, name), RETAINED[name], name)
+        require(row["sha256"] == RETAINED[name] and len(data) == row["bytes"],
+                "retained source metadata")
+        loaded["package/" + name], hashes["package/" + name] = data, sha(data)
+    return loaded, hashes
+
+
+def source_module(name):
+    """Compile the actual source bytes without consulting adjacent .pyc files."""
+    data = regular_bytes(PACKAGE, name)
+    module = types.ModuleType(name.removesuffix(".py"))
+    module.__file__ = str(PACKAGE / name)
+    exec(compile(data, module.__file__, "exec"), module.__dict__)
+    return module, sha(data)
+
+
+def same_receipt(expected, actual):
+    # JSON spelling distinguishes bool from int and normalises tuples to arrays.
+    require(canonical(expected) == canonical(actual), "typed scientific receipt mismatch")
+
+
+def must_reject(callback, reason):
+    try:
+        callback()
+    except ValueError as error:
+        require(reason in str(error), "unexpected failure control: " + str(error))
+        return "REJECTED: " + reason
+    raise ValueError("failure control was accepted: " + reason)
+
+
+def integrity_controls(loaded):
+    controls = {
+        "duplicate_json_key": must_reject(
+            lambda: strict_json('{"rank":1,"rank":1}'), "duplicate JSON key"),
+        "nonfinite_json": must_reject(
+            lambda: strict_json('{"rank":NaN}'), "non-integer JSON number"),
+        "float_json": must_reject(
+            lambda: strict_json('{"rank":1.0}'), "non-integer JSON number"),
+        "bool_as_integer_receipt": must_reject(
+            lambda: same_receipt({"admitted": True}, {"admitted": 1}),
+            "typed scientific receipt mismatch"),
+        "partial_component_result": must_reject(
+            lambda: crosscheck({"status": "PARTIAL"}, {}, {}, {}),
+            "all component evidence must report complete PASS"),
+    }
+    with tempfile.TemporaryDirectory(prefix="p104-interface-integrity-") as folder:
+        scratch = Path(folder)
+        package = scratch / "research/p104-newton-interfaces"
+        package.mkdir(parents=True)
+        for name in ("SOURCES.json", "VERIFY.json"):
+            (package / name).write_bytes(regular_bytes(PACKAGE, name))
+        for name, data in loaded.items():
+            path = package / name.removeprefix("package/") if name.startswith("package/") else scratch / name
+            path.parent.mkdir(parents=True, exist_ok=True)
+            path.write_bytes(data)
+        # Exercise the complete authentication gate before any module is loaded.
+        native_path = scratch / NATIVE
+        native_data = loaded[NATIVE]
+        native_path.write_bytes(bytes([native_data[0] ^ 1]) + native_data[1:])
+        controls["corrupt_actual_native_input"] = must_reject(
+            lambda: authenticate(scratch, package), "source SHA256 mismatch: " + NATIVE)
+        native_path.write_bytes(native_data)
+        model_path = package / "inputs/pr3382_model.py"
+        model_path.write_bytes(model_path.read_bytes() + b"\n")
+        controls["corrupt_retained_model_before_execution"] = must_reject(
+            lambda: authenticate(scratch, package),
+            "source SHA256 mismatch: inputs/pr3382_model.py")
+        model_path.write_bytes(loaded["package/inputs/pr3382_model.py"])
+        manifest = strict_json((package / "VERIFY.json").read_bytes())
+        manifest["inputs"].remove(NATIVE)
+        (package / "VERIFY.json").write_bytes(canonical(manifest))
+        controls["undeclared_live_input"] = must_reject(
+            lambda: authenticate(scratch, package), "complete declared input closure")
+    return controls
+
+
+def crosscheck(producer, consumer, cost, independent):
+    require(producer["status"] == "PASS"
+            and consumer["status"] == "PASS_P104_OPEN_CONSUMER_INTERFACE"
+            and independent["status"] == "PASS"
+            and independent["full_prefix_witness"]["status"] == "PASS"
+            and independent["scalar_ports"]["status"] == "PASS"
+            and consumer["symbolic_open_interface"]["status"] == "PASS_EXACT_OPEN_INTERFACE_ROWS"
+            and consumer["dense_open_replay"]["status"] == "PASS_DENSE_CHRONOLOGICAL_OPEN_REPLAY",
+            "all component evidence must report complete PASS")
+    source = cost["source_audit"]
+    direct = source["direct_reference_schedule"]
+    pcone = producer["source_cone"]
+    require(pcone["events"] == source["producer"]["events"], "independent producer event cone")
+    require(pcone["initial_dependencies"] == source["producer"]["initial_roles"],
+            "independent producer initial roles")
+    require(consumer["closed_event_indices"] == source["internal_event_indices"],
+            "independent complete internal chronology")
+    require(consumer["closed_opcode_counts"] == source["internal_opcode_counts"],
+            "independent complete internal opcodes")
+    ports = consumer["symbolic_open_interface"]["external_port_records"]
+    port_manifest = [{k: row[k] for k in ("event", "target", "source", "coefficient", "frame")}
+                     for row in ports]
+    require(port_manifest == source["outgoing_ports"], "independent complete outgoing port bindings")
+    require(consumer["external_read_event_indices"] == [row["event"] for row in ports],
+            "symbolic ports match actual extraction")
+    require(sha(canonical(consumer["external_read_event_indices"])) ==
+            independent["scalar_ports"]["external_port_indices_sha256"], "third implementation port chronology")
+    require(consumer["path_certificate"]["status"] == "PASS_ALL_ACTUAL_FRAME_PATHS"
+            and independent["scalar_ports"]["frame_map_certificate_required"] is True,
+            "phase-sensitive frame certificate required by scalar oracle")
+    interface = consumer["symbolic_open_interface"]
+    require(interface["gauge_normalized_X_port_operator"]["target_signs"] ==
+            independent["scalar_ports"]["X_target_signs"], "independent signed half-sum rows")
+    require(interface["persistent_banks_restored_in_full_frame"] == source["initial_roles"]
+            and all(frame == FULL for frame in source["final_frames"].values()),
+            "all63 final physical frames and logical restorations")
+    counts = consumer["dense_open_replay"]["counts"]
+    require(counts["native_pair_comparisons"] == direct["signed_floor_pairs"]
+            == 256 * consumer["closed_native_rank_sum"] == 148736,
+            "independent native arithmetic bill")
+    require(counts["complete_wrapper_domain_checks"] == direct["wrappers"] == 784,
+            "independent wrapper count")
+    require(counts["executed_internal_array_adds"] + len(ports)
+            == direct["field_adds_including_all_ports"] == 857,
+            "all internal and outgoing ADDs paid once")
+    witness = independent["full_prefix_witness"]
+    negative = producer["one_coordinate_counterexample"]
+    for role, row in negative["entrance"].items():
+        other = witness["entrance"][role]
+        require(row["sha256"] == other["sha256"]
+                and row["in_B9"] == (other["newton_failure"] is None),
+                "full prefix versus minimal cone entrance: " + role)
+    pfirst, ifirst = negative["first_lattice_failure"], witness["first_full_prefix_B9_failure"]
+    require(pfirst["event"] == ifirst["event"] == 1090
+            and pfirst["target"] == ifirst["field"] == "D31", "first actual admission failure")
+    require(all(pfirst["witness"][key] == ifirst[key]
+                for key in ("mask", "degree", "coefficient", "pi_valuation")),
+            "independent exact Newton failure")
+    valuation = producer["counterexample_full_prefix_valuation"]
+    require(witness["active_native_events"] == [row["event"] for row in valuation["active_native_events"]]
+            and witness["active_add_events"] == [row["event"] for row in valuation["active_fractional_source_events"]],
+            "full numerical witness versus independent valuation proof")
+    require(consumer["coefficient_maps"]["full_frame"]["nonzero_entries"] == 3**9
+            and consumer["coefficient_maps"]["full_frame"]["maximum_absolute_component"] == 1,
+            "coefficient matrix agrees with tensor formula sparsity")
+    return {"status": "PASS_SEPARATE_IMPLEMENTATIONS_AGREE", "producer_events": len(pcone["events"]),
+            "internal_events": len(consumer["closed_event_indices"]), "outgoing_ports": len(ports),
+            "phase_certificate_required_and_checked": True, "restored_internal_roles": 63,
+            "counterexample_entrance_arrays_compared": len(negative["entrance"]),
+            "full_prefix_structural_native_occurrences": witness["prefix_native_occurrences_bound"],
+            "full_prefix_active_pair_comparisons": witness["active_pair_comparisons"],
+            "scope": "Exact bounded open interface; no omitted external history or whole supplier inferred."}
+
+
+def compute(repo):
+    loaded, hashes = authenticate(repo)
+    controls = integrity_controls(loaded)
+    modules, implementations = {}, {}
+    for name in MODULES:
+        modules[name], implementations[name] = source_module(name)
+    implementations["verify.py"] = sha(regular_bytes(PACKAGE, "verify.py"))
+    producer = modules["producer.py"].verify_producer(repo / WORD, repo / NATIVE,
+                                                      PACKAGE / "inputs/pr3382_model.py")
+    consumer = modules["consumer.py"].verify_consumer(repo / WORD, repo / NATIVE)
+    audit = modules["cost_audit.py"]
+    cost = {"fixed_consumer": audit.fixed_consumer(), "codec_reference": audit.codec_reference(),
+            "source_audit": audit.source_audit(repo)}
+    independent = modules["independent.py"].verify_independent(repo / WORD, repo / NATIVE)
+    agreement = crosscheck(producer, consumer, cost, independent)
+    return {"schema_version": 1, "status": "PASS_P104_NEWTON_INTERFACES",
+            "implementation_sha256": implementations, "authenticated_inputs": hashes,
+            "integrity_controls": controls, "producer": producer, "consumer": consumer,
+            "cost": cost, "independent": independent, "cross_implementation": agreement}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--repo", type=Path, default=PACKAGE.parents[1])
+    parser.add_argument("--write-receipt", type=Path,
+                        help="create a new receipt exclusively; never replace an existing file")
+    args = parser.parse_args()
+    # Parse a retained receipt before computation, rejecting malformed evidence early.
+    expected = None if args.write_receipt else strict_json(regular_bytes(PACKAGE, "RECEIPT.json"))
+    actual = compute(args.repo)
+    payload = json.dumps(actual, indent=2, sort_keys=True, allow_nan=False) + "\n"
+    if args.write_receipt:
+        with args.write_receipt.open("x", encoding="utf-8") as stream:
+            stream.write(payload)
+    else:
+        same_receipt(expected, actual)
+    print(json.dumps({"status": actual["status"], "receipt_sha256": sha(payload.encode()),
+                      "agreement": actual["cross_implementation"],
+                      "retained_receipt_compared": expected is not None}, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()