Research: project a 96-output F17 demand and screen its retained-centre budget

research/qq16-f17-demand-projection/PREDECESSORS.json

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+{
+  "schema_version": 1,
+  "canonical_source_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "predecessors": [
+    {
+      "pr": 2512,
+      "author": "ywz65",
+      "head": "851dd3486a2d0549b51e85978a65ccb4eec619c0",
+      "role": "Actual96-output F17 demand and native-current-frame lineage. Original requires eight earlier T records."
+    },
+    {
+      "pr": 2707,
+      "author": "ywz65",
+      "head": "efa51a6c7ffec6edd556a98deedfe9deeba65809",
+      "role": "Source physical word and loader. replay.py explicitly adapts its replay: W-only ownership, Y-only borrowed inputs, ordinary output demand, selected temporary zeroing, only current B1 maps; removed unused future/F0/checkpoint branches."
+    },
+    {
+      "pr": 2681,
+      "author": "Arham-Tahir64 / Arham Tahir",
+      "head": "ea96706295631be10d92ae149b63c3e24acaeabc",
+      "role": "Retained routed algebra, phase functions, packet/archive source reconstruction and complete logical inverse, authenticated through PR2707. These are reused, not independently rederived here."
+    },
+    {
+      "pr": 3908,
+      "author": "1337isnot1337",
+      "head": "0d8880e38ed7c88d70eec6a48e5aa829d0fb22f3",
+      "role": "Fixed-profile obstruction and favorable rank8 waiver; new endpoint escapes that waiver but not the retained-eight model."
+    },
+    {
+      "pr": 3946,
+      "author": "Clear1nsight / Chris R",
+      "head": "8dec5c663ace6285aeee49ec3f8eeae9a8bc9a58",
+      "source_sha256": "e12f3d810a6f659e4b2453d251e323aa5e2c4693c4b28a9cec611796cc2dd94a",
+      "role": "budget.py explicitly extracts/adapts exact rational quadrature, price, profile expansion and moment functions; no unmerged source executable is needed at replay."
+    },
+    {
+      "pr": 3181,
+      "author": "dcharb78",
+      "head": "80fc72d14546088e9fce3c06dc12bc67270da0af",
+      "role": "Reported eight-rank8 profile premise; no universal claim that those copies survive the changed outer demand."
+    }
+  ],
+  "additional_credit": [
+    "ywz65 PR2492/2468 native read machinery",
+    "thakrarsagar PR2470 L2 identity",
+    "Ali Romman PR1969 and conserved QQ16/native lineage",
+    "starship-s original decoder",
+    "Ross Richardson retained-record lineage",
+    "Douglas Colkitt and Sagar Thakrar coverage/ceiling lineage",
+    "Nick Petalas numerical/consumer boundary guidance"
+  ],
+  "license": "New work Apache-2.0. Retained source notices remain in unchanged dependency files.",
+  "new_contribution": "Actual published demand binding, semantic projection with complete cleanup invoice, and changed budget exclusion/thresholds."
+}

research/qq16-f17-demand-projection/PROOF.md

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+# A projected F17 demand and its fixed-profile obstruction
+
+This is an exact local interface result under the retained QQ16 common-label
+cover contract. It is not a global controller, physical supplier, optimal
+consumer, or new multiplication bound.
+
+## 1. An actual demand, and the change of inputs
+
+PR2512 (`851dd3486a2d0549b51e85978a65ccb4eec619c0`, ywz65) explicitly
+ends with 96 consumer subtractions `Z_p -= X2_p`, ordinary ports p in U_ports,
+returning logical `y1_U` in `F_U1`. Its proof defines this frame as the product
+of C lines on coordinate axes 0 through 16, exactly PR2707's **F17**. The port
+set U_ports and the 17-dimensional coordinate subspace are distinct objects.
+The verifier authenticates the actual proof, full word and receipt, and checks
+the literal 96-event consumer epilogue and its named output contract.
+
+PR2512 reads 96 current X, 96 current Y and eight retained earlier T arrays.
+Here the demand is supplied instead from **all 112 current Y arrays**, with no
+X read or early T record. The extra sixteen selected current Y reads are
+available under PR2707's 224-current-field contract; they are not available
+merely by assuming PR2512's narrower interface. Every Y is borrowed, physically
+in `F17 C_qp^-1`. The result needs 96 exclusively owned output arrays and sixteen
+owned full-cover temporaries. Arbitrary owned dirt is erased by paid CLEARs.
+No borrowed source is written. All sixteen temporaries and eight private scratch
+arrays finish at zero in identity frame. There is no storage/hosting admission.
+
+This pins a real published *local endpoint*, rather than inventing an ordinary
+frame tariff. It does not establish that a complete selected outer controller
+needs only these 96 values; other outputs may still be required there.
+
+## 2. The projected logical operator
+
+Use the actual ordered owner actions D_p in B1 and the pinned eight raw R rows.
+Define the query and ordinary injection in the normalization used by PR2681:
+
+    Q(Y)_k = sum_(p=0..111) R[k,p] D_p Y_p,
+    (K_U q)_p = (1/4) sum_k R[k,p] D_p^-1 q_k, p in U_ports.
+
+The retained complete B1 inverse first computes
+
+    u_U = Y2_U - K_U Q(Y2).
+
+Its future-logger reversal writes only selected A ports. Therefore it leaves
+u_U unchanged, and
+
+    y1_U = Y2_U - K_U Q(Y2).                       (1)
+
+This also follows from the conserved B1 equations: `Q(Y2)` is the old selected
+T query and `Y2_U = y1_U + K_U Q(Y2)`. The three conserved queries must not be
+interchanged. The source proof gives the identity over the ordered cover
+coefficient ring, so no owner matrices are silently commuted.
+
+The checker compares every demanded routed row of the new word with (1) on
+112 independent current Y symbols: 4,992 nonzero owner-labelled terms. It also
+forms B1 from 224 *independent x1/y1 symbols*, without imposing an F0 relation,
+and verifies that (1) recovers exactly those y1_U symbols. The latter replay
+checks the actual selected-row coefficients and future logger, rather than
+assuming a payload-constant or identity-owner special case.
+
+## 3. A legal native word
+
+`WORD.json` is regenerated deterministically from the complete authenticated
+3,823-event PR2707 word. It has 1,410 events:
+
+1. For every port, clear owned W_p in the Y hole frame, copy borrowed Y_p, and
+   apply the positive rank-one line C_qp. W now has F17 and logical Y2.
+2. Finish the source B1 alignment map on every W. With the actual source-derived
+   affine translation, `M_p F17 = F17 D_p`. All query operands have common F17.
+3. At each owner execute the entire private body: clear eight F_k, form all
+   eight Q rows from the complete 112-port W bank, subtract `R[k,p] F_k/4` from
+   ordinary W_p only, then clear all F_k in identity frame. Every query is
+   formed before any W output is overwritten. Finish the owner body before
+   visiting the next owner.
+4. Undo the alignment map on the 96 ordinary W outputs. Clear the sixteen
+   selected W temporaries directly in their existing frame, returning them
+   to zero in identity frame. Clearing owned dirt is a paid primitive; no
+   inverse map or native child is required to dispose of those owned values.
+
+The temporary disposal is an explicit addition to the projected prefix. It
+prevents an unreported dirty full-cover workspace liability. Every borrowed
+Y retains its exact initial content and frame, and every X is untouched.
+
+This projection is semantic: stage-2 map/line conjugations cancel on U because
+that logger writes only A. A naive instruction-liveness pass would retain
+conjugations on the demanded W fields. There is no reordering of native reads
+or private bodies, and no claim of shortest code or a universal 112-child floor.
+
+The phase checker uses complete modulo-four quadratic coefficients on all 73
+coordinates at every ADD and output. A line contributes parity, and parity has
+no terms above degree two modulo four. Thus these are full phase identities.
+By Fourier spanning they hold on arbitrary payload arrays; owner pullback and
+per-layer multiplication extend them to all owners and tensor layers under
+the inherited cover contract. The source kernels are lowered using a basis
+whose first column is q: one positive H1 child plus two inverse monomial
+wrappers realizes C_q. All 112 bases and 57,344 basis columns are checked;
+the other coordinates are spectators. This is not an execution on a huge
+physical tape, or a proof of child precision/placement.
+
+## 4. Complete local invoice and real removed work
+
+| Charge | New demand word | Complete PR2707 decoder | Difference removed |
+|---|---:|---:|---:|
+| Positive rank-one children | 112 | 336 | 224 |
+| Rank-eight children | 0 | 0 | 0 |
+| Native monomial wrappers | 224 | 672 | 448 |
+| Full-cover maps | 208 | 464 | 256 |
+| Unit ADD macros | 560 | 1,808 | 1,248 |
+| Quarter ADD macros | 384 | 896 | 512 |
+| CLEAR macros | 144 | 312 | 168 |
+| Real scalar primitive allowance | 9,376 | 25,840 | 16,464 |
+
+The scalar allowance is `8*560 + 12*384 + 2*144`. Its 144 clears include 112
+initial owned clears, sixteen private entry/exit clears and sixteen final
+full-cover temporary clears. There are 96 owned outputs, sixteen full-cover
+temporaries, eight owner-private scratch arrays, no early records and no X
+reads. All 112 borrowed Y fields are restored by remaining read-only.
+
+What disappears is the future logger reversal, the F0 inverse and unrelated
+X1/selected-output recovery, including the two complete future-frame line
+sweeps. The final output contract changes from all 224 original arrays to the
+96 published y1_U demand. These are actual deleted operations; no unchanged
+recursive child is assigned a lower tariff merely because its bit axis became
+cheaper. The comparison is not a same-output full-decoder improvement.
+
+Against PR2512's same logical *output* with different input/lifetime premises,
+this replaces `192 H1 + 16 H8` with `112 H1`, keeps 208 cover maps, and raises
+scalar allowance from 7,392 to 9,376. It removes early retention but needs the
+sixteen additional current Y fields, sixteen owned temporaries and eight
+private scratch arrays rather than one. No dominance or global memory saving
+follows from comparing child rank mass alone.
+
+## 5. What the changed budget proves, and what it does not
+
+Recounting the literal source F0/B1 words gives per-call average
+
+    n = {1:2428, 2:418, 3:432, 4:142, 5:82}.
+
+For the **same conditional pair-rate budget used by PR3908/PR3946**, allocate
+one demand word per two calls: add 56 H1 per call. Retaining the reported
+selected-profile eight H8 charges gives
+
+    n_full = {1:2484, 2:418, 3:432, 4:142, 5:82, 8:8}.
+
+The eight H8 charges are the retained profile premise, not new children in
+this demand word. This package does not prove that all eight remain needed
+by an outer controller with a changed demand. That is an explicit next audit.
+Likewise, this local pair amortization does not prove a full nine-call schedule
+or the number of decoder invocations required globally.
+
+Keep m=73, W=896/9, centre=64, and total mass T=72W+64=7232. The largest idle
+rank allowed by the outer halving guard is R=51 (`2*51^2 < 73^2 < 2*52^2`).
+For a>=0, price per rank-mass unit is `73^(a-1) r^(-a)`, nonincreasing in r.
+Every legal idle placement is therefore at least as expensive as fractional
+rank-51 idle work. If L=sum r*n_r and I=T-L, the favorable necessary screen is
+
+    G(a) = [sum_r n_r (r/73)^(1-a)
+            + (I/51) (51/73)^(1-a)] / W.
+
+For n_full, L=5658 and I=1574. For the rank-eight-waived variant, L=5594 and
+I=1638. All maps, wrappers, scalar operations, storage, movement, placement,
+precision and numerical-error costs are set favorably to zero in this screen.
+Thus failure already excludes the fixed profile; passing supplies no physical
+construction. The actual complete local invoice above remains a liability.
+
+At the selected `a=836330098538459/499163669901461541`, exact rational bounds are:
+
+| Hypothesis | Enclosure for G |
+|---|---|
+| Eight reported H8 charges retained | [1.000023149708, 1.000023150305] |
+| All eight H8 charges waived into rank-51 idle mass | [0.999995759681, 0.999995760274] |
+
+The previous *rank-eight-waived* obstruction no longer applies to this changed
+endpoint. Carrying it over would be wrong. The retained-eight profile still
+fails even before physical overhead. With those eight charges fixed, at most
+61 integer decoder H1 calls per pair pass this relaxation; 62 fail. Our word
+has 112, so it needs at least 51 fewer pair calls, with no compensating charges,
+merely to pass the optimistic integer screen. There is no theorem that 61 is
+achievable, or that no different operator implementation can do better.
+
+Waiving all eight charges permits at most 121 integer pair calls; our 112 leaves
+only [0.000004239726, 0.000004240319] normalized allowance. Neither removing those
+children nor paying the remaining physical liabilities is constructed here.
+With 112 H1 fixed, retaining two H8 across the pair gives
+[0.999999183434, 0.999999184028], while three gives
+[1.000000895311, 1.000000895905]. Thus at least fourteen of the reported sixteen
+H8 charges across two calls must disappear, with no other new costs, to pass
+this integer relaxation. This is a repayment target, not a claim that a copy
+can be removed or that fractional per-call assignment is physically legal.
+The exact fixed-profile exclusion is the stopping result; it is not a global
+QQ16 obstruction and does not authorize construction expansion.
+
+The rational arithmetic is explicitly adapted from PR3946's independently
+checked midpoint/trapezoid logarithm and exponential remainder implementation.
+For convex 1/t on [1,y], midpoint sums are lower and trapezoid sums upper
+bounds on log(y). Scale arguments into [1,2], round outwards to 2^-80, and use
+the degree-six positive exponential sum with first omitted term divided by
+`1-hi/(degree+2)` as geometric tail. Every final decision compares Fractions;
+decimal formatting also rounds outward. Both sides of the 61/62 and 121/122
+thresholds are verified, rather than deriving a decision from rounded output.
+
+## 6. Bounded next question
+
+Audit the *actual eight H8 centre-copy outputs* in the retained supplier and
+whether their downstream uses survive this 96-output demand. First bind each
+copy's source, destination, frame and last use in the selected archive and a
+single real continuation. Either identify legal retirement and recompute the
+coverage mass (centre 64 cannot simply be kept or deleted by assertion), or
+prove all eight copies are still required under that continuation. This decides
+whether the relaxed opening has a valid premise before optimizing physical
+kernels. If retained, stop this recipe unless producer/consumer fusion deletes
+at least 51 genuine H1 pair charges or another priced premise changes.
+
+No new retained-query construction, further precision optimization or centre
+change is implemented. Full controller demand, copy lifetimes, both supplier
+caps, physical map/wrapper costs, numerical grids/dirty ranges, child placement
+and all-depth cleanup remain open.

research/qq16-f17-demand-projection/README.md

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+# A real F17 demand: 112-child projection and a conditional budget obstruction
+
+PR2512's published consumer demands 96 ordinary `y1_U` arrays in `F_U1=F17`.
+Projecting PR2707's zero-retention inverse onto this demand removes real work:
+**336 -> 112 rank-one children**, **464 -> 208 cover maps**, **672 -> 224 native
+wrappers**, and **25,840 -> 9,376 scalar primitive allowance**. The complete
+1,410-event word reads all 112 current Y fields, no X fields or early records;
+it returns 96 owned outputs, clears sixteen full-cover temporaries and eight
+owner-private scratch fields, and leaves all borrowed fields untouched.
+
+This changed demand **escapes PR3908's rank-eight-waived obstruction**. It does
+not yield an admitted supplier. Retaining the reported eight H8 profile charges
+still gives a favorable moment in **[1.000023149708, 1.000023150305]**, above one
+at the selected saving even with physical overhead free. The waived profile
+instead lies in **[0.999995759681, 0.999995760274]**, leaving only about
+0.00000424 normalized allowance. The fixed-eight profile requires at least
+51 fewer decoder H1 calls per pair just to pass the optimistic integer screen.
+
+[PROOF.md](PROOF.md) gives the operator identity, exact input/frame/ownership
+contract, complete counts, rational bounds and limits. This is one source-bound
+local endpoint and a conditional fixed-profile exclusion, not a shortest word,
+whole-controller result, physical six-tape admission, net storage saving or new
+kappa. The full 224-output decoder and its obstruction remain valid for their
+original contract. PR2512's input contract differs: its eight retained T arrays
+are replaced by sixteen additional selected current Y reads here.
+
+## Reproduce
+
+Standard library, CPython 3.12; from repository root:
+
+```sh
+python3 -I -Werror -B research/qq16-f17-demand-projection/verify.py
+python3 -I -O -Werror -B research/qq16-f17-demand-projection/test_verify.py
+python3 -B scripts/research_package.py --package research/qq16-f17-demand-projection
+```
+
+`verify.py` checks the complete committed word and receipt without writing.
+Expected marker: `PASS_QQ16_F17_DEMAND_PROJECTION no_new_kappa`. Its replay uses
+explicitly adapted, source-authenticated predecessor operator primitives;
+it is not a code-disjoint reimplementation of all inherited algebra.
+Evidence includes independent x1/y1 B1 symbols, 4,992 demanded routed terms,
+full 73-coordinate phases, 57,344 native basis columns, nine semantic mutants,
+the complete local invoice and both sides of the budget thresholds. Seven
+boundary test groups include a read-only Git-free export, pre-execution source
+failure and complete word/typed receipt rejection. See VERIFICATION.json for
+actual commands and publication checks. No huge payload, selected cold replay,
+Lean/formal-kernel check or independent human review is claimed.
+
+## Scope and workflow
+
+Explicit assigned continuation of #3946/#3908; no task reroll. Canonical main
+`20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority revision 6; exact inputs and
+original task card in SOURCES.json/TASK.json. Only this scoped package is added.
+Frozen sources and selected frontier are unchanged. The [advance claim and
+canonical update](https://github.com/CrocSwap/integer-mult-bounds/pull/3946#issuecomment-6260950964)
+records the stop rule. Live targeted PR searches and the overlap helper found
+the named adjacent packages; the helper lacks gh, so remote coverage is partial,
+not a novelty guarantee. PREDECESSORS.json retains exact heads and code reuse.
+
+## Open next questions
+
+The next useful audit is **the eight reported rank-eight centre copies under
+this actual reduced demand**. Bind their literal source/destination/frame and
+last uses to one real continuation; decide whether they can legally retire (at least fourteen of sixteen pair H8 charges must disappear with this 112-H1 word under unchanged centre 64),
+and recompute coverage and physical costs. If they remain, this word is
+excluded in the fixed model and needs at least 51 genuinely removed H1 pair
+charges before further implementation is warranted. A hypothetical free centre
+or arbitrary waiver is not that audit. Structured questions, first steps and
+blockers are in TASK.json; the full stopping rule is in PROOF.md section 6.
+
+## Credit
+
+Chris R / Clear1nsight, with substantial OpenAI assistance in source inspection,
+derivation, implementation, verification and writing. Apache-2.0.
+
+Credit ywz65's #2512/#2492/#2468 for the actual demand, L2 native maps and read
+machinery; thakrarsagar/#2470 for L2; Arham Tahir/#2681 for the complete logical
+inverse and routed/phase primitives; ywz65/#2707 for the line-normalized physical
+word; 1337isnot1337/#3908 for the budget obstruction; dcharb78/#3181 for its
+profile premise; Clear1nsight/#3946 for the independent budget arithmetic;
+Ali Romman/#1969, starship-s, Ross Richardson and retained QQ16/native lineage;
+Douglas Colkitt, Sagar Thakrar and coverage-ceiling contributors. Source notices
+remain intact. The new result is the demanded projection, its complete local
+invoice and the changed budget conclusion, not those predecessor identities.