Normalize the zero-retention QQ16 decoder with paid rank-one children

research/qq16-line-normalized-decoder/PREDECESSORS.json

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+{
+  "schema_version": 1,
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research/qq16-line-normalized-decoder/PROOF.md

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+# A charged line normalization for the zero-retention QQ16 decoder
+
+The predecessor is Arham Tahir's PR2681 at
+`ea96706295631be10d92ae149b63c3e24acaeabc`. Its logical inverse, source
+reconstruction, full-current observation contract, scalar schedule and
+two-chart routing are retained with credit. Full-current invertibility is
+already known. This result changes the physical implementation of that word.
+
+## Exact boundary
+
+At the completed B1 cut, the 112 current X fields have chart F17 and the 112
+current Y fields have chart F17 C_q^-1. Here F17 is the product of the signed
+Fourier line operators on address axes 0 through 16; q is the authenticated
+nine-bit normal at the corresponding port. All 224 current fields are borrowed
+and never written. The 224 eventual output banks are owned and may contain
+arbitrary dirt, which the same paid CLEAR operations remove. At termination
+they contain the original 224 logical input arrays, all in F17. No early
+values, banks or output availability before B1 are assumed. At most sixteen
+owned local scratch arrays are live. Their clearing/disposal contract is the
+predecessor's owned-scratch contract, not reversible uncomputation of dirt.
+
+The phase identities below are first stated on the same 73-dimensional
+binary coordinate space. For every actual owner coordinate d, substitute
+z -> d^T z in each character identity, as in the source's M(g,b) action.
+An identity for every character remains an identity after that substitution,
+and hence on every owner and every payload tensor factor. No owner coordinate
+or payload factor is dropped or sampled.
+The checker retains full routed operators on arbitrary arrays; constant
+payload samples would not suffice. Logical state is represented separately
+from its physical chart. Multiplying a physical array by a line operator
+changes its chart and preserves its represented logical value. A cover map
+changes the represented logical value by the authenticated address route and
+changes the chart by the explicit phase rule below.
+
+## Frame identity
+
+For a list of pairs (v,c), define its Fourier-character phase at z by
+
+    phi(z) = sum c * <v,z> mod 4,
+
+where each binary inner product is interpreted as 0 or 1. C_q contributes
+<q,z>; a physical XOR translation X_b contributes 2<b,z>. Thus an orthogonal
+involutive route g with its specified payload translation b takes a phase
+list Phi to
+
+    move(Phi,g,b) = [(g v,c) : (v,c) in Phi] + [(b,2)].
+
+The g at each port is reconstructed from the unchanged selected native source
+and checked against the actual QQ16 registry, in both stages. This is a
+physical payload alignment, not a substitution of a physical shift into the
+logical route algebra. The represented logical operator remains g.
+
+Let F16 denote the product of lines on axes 9 through 24. A stage-2 route swaps
+the eight local directions orthogonal to q with axes 17 through 24, fixes q,
+and leaves axes 9 through 16 unchanged. Consequently the image of the F17
+frame has the same underlying orthogonal directions as F16 C_q. Their phase
+polynomials may differ by an even linear character. Compute b_p from that
+difference, and verify the exact identities
+
+    move(F17,g_p,b_p)              = F16 C_q,
+    move(F16 C_q,g_p,g_p b_p)      = F17.             (1)
+
+Equality here means equality of complete phase polynomials, including the
+constant phase (both words have phase one at character zero). It is not
+equality only up to phase or equality of spanned binary subspaces.
+
+The constructor checks every one of the 112 actual ports. Independently, it
+evaluates the literal character sums on zero, all 73 basis characters and all
+2,628 pair sums. These determine these degree-at-most-two polynomials mod 4:
+expanding XOR in such a phase has only linear terms mod 4 and even quadratic
+terms; every term of higher degree is divisible by 4. This establishes (1)
+on every character of the full address space. The same two methods check
+the stage-1 maps preserving F17 with their own current-frame shifts. No
+claim that the predecessor's F25 shifts work for these new frames is made.
+
+## Literal lowering and restored intermediate frames
+
+Begin with the complete 4,047-event predecessor word, regenerated and compared
+with its retained WORD.json before lowering. Make only these physical changes:
+
+1. Delete all 224 input upgrades to F25 and all 224 final downgrades to F17.
+   Normalization of the copied Y fields by the existing 112 positive C_q calls
+   is retained. The principal word therefore stays in F17.
+2. Implement each stage-1 map with its F17-preserving affine shift.
+3. At each stage-2 entry map on W_p, use (g_p,b_p), then a paid C_q^-1. This
+   gives chart F16. All 112 W fields and the eight active query scratch fields
+   are in that exact common frame throughout the future-query sweep.
+4. After that complete sweep, apply a paid C_q to each W_p and the inverse
+   affine map (g_p,g_p b_p). This returns every W field to F17. Z fields stay
+   in F17 throughout; no scalar ADD crosses the different intermediate charts.
+
+Every scalar ADD, CLEAR, private-scope event, logical route and its order are
+unchanged. In particular the noncommuting stage-1/stage-2 order is unchanged.
+Equation (1) proves that every changed map/line block implements the same
+logical route as its source counterpart. Common-chart induction then proves
+that every represented logical state at every scalar event is unchanged.
+Both complete inverse orders on 224 free input arrays are replayed, including
+the intermediate inverse-B1 checkpoint. The final physical chart is F17 for
+every output. Borrowed arrays are untouched rather than temporarily changed;
+all scratch ownership and disposal events are exactly the credited ones.
+
+## Native positive children and phase
+
+Each signed C_q is lowered using one positive rank-one child and two explicit
+monomial wrappers. Choose a binary basis with first vector q. The positive
+kernel has numerator 1+i at x and 1-i at x+q, common denominator two. For the
+negative sign, an output XOR by q swaps those coefficients. Equivalently
+C_q^-1 = X_q C_q; no negative child is declared free.
+
+The checker verifies all 512 basis columns for each of the 112 normals and
+both signs, including exact Gaussian coefficients and global phase. The
+wrappers act identically on the remaining 64 coordinates, so these are full
+73-coordinate operator identities. Every one of the 336 literal child
+occurrences is bound to its signed recipe. Cover maps are affine monomial
+permutations, with both translations retained. The phase operations are exact
+members of the inherited finite Gaussian-dyadic alphabet. Approximate child
+precision and physical address/control work require separate admission; an
+ideal unitary identity does not establish a rounded whole-caller guarantee.
+
+## Complete local comparison and bounded decision
+
+The transformed word has 3,823 events, 336 positive rank-one children and no
+rank-eight children. There are 672 native monomial wrappers, 464 full-cover
+maps, 1,808 signed unit ADDs, 896 signed quarter ADDs and 312 CLEARs. The
+inherited real scalar allowance is
+
+    8*1808 + 12*896 + 2*312 = 25840.
+
+These scalar coefficients and that allowance are unchanged from PR2681.
+Both words use 224 eventual output banks, at most sixteen local scratch banks
+and zero early retention. The old 448 H8 calls are replaced by 224 H1 calls;
+all 112 original line normalizations remain. The profile is a constructive
+finite upper bound, not an optimum or a placement/tape invoice.
+
+Against PR2540's same-endpoint 224 H1 + 16 H8 decoder, the numerator of the
+child-moment difference at the same parent width is
+
+    112 - 16*8^(1-a).
+
+For 0 <= a <= 1/16 this is strictly negative, because
+8^15 = 35184372088832 > 33232930569601 = 7^16. Raising positive numbers to
+the sixteenth power preserves order; hence 8^(15/16)>7. This includes the
+small saving parameters of the selected regime, without asserting a new
+selected bound. At a=0 the rank mass is 336 instead of 352.
+
+The comparison also has 192 more monomial wrappers, 256 more cover maps and
+8,368 more scalar primitive allowance than PR2540. These are real liabilities,
+not zero-cost terms. Whether their physical implementation is favorable is
+unknown. The newer output-bank coalescing of PR2651 changes the retained-bank
+comparison but still keeps sixteen values across B1; it does not erase these
+child and physical-cost distinctions.
+
+Revision-5 decision: retain one local module. The previous recipe's negative
+child-cost comparison is not a barrier to zero retention. Do not expand this
+construction into a supplier without a named consumer, complete physical
+map/wrapper/control prices, legal ownership/lifetimes and rounded precision.
+Inherited F0/B1 execution and output consumption also remain paid obligations.
+No new kappa, all-size supplier, native hosting or optimality claim follows.
+
+Arham Tahir/PR2681, ywz65/PR2540, the QQ16 authors and retained source/native
+lineage keep their attribution. New frame lowering and evidence prepared by
+ywz65 with substantial OpenAI Codex assistance. Apache-2.0.

research/qq16-line-normalized-decoder/README.md

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+# Zero-retention QQ16 decoding with paid line normalizations
+
+This implements PR2681's same logical decoder with **336 positive rank-one
+children and no rank-eight children**. Its published two-chart implementation
+uses 112 rank-one and 448 rank-eight children. A source-exact change of the
+intermediate physical frame replaces those 448 upgrades/downgrades with 224
+charged rank-one normalizations. All 224 original logical arrays still return
+in F17, all 224 current borrowed arrays remain untouched, and no value is
+retained across B1.
+
+The new step is the dynamic frame identity at every one of the 112 actual
+ports. The stage-2 route, with an explicitly computed affine translation,
+takes F17 to `F16 C_q`, where F16 uses address axes 9 through 24. A paid
+`C_q^-1` places the row in the common F16 frame for the query. A paid `C_q`
+and inverse affine map restore F17. The complete word and each native child
+occurrence are checked; the old scalar schedule is preserved.
+
+Full-current invertibility, the logical inverse and the scalar word are
+credited to [Arham Tahir's PR2681](https://github.com/CrocSwap/integer-mult-bounds/pull/2681)
+at `ea96706295631be10d92ae149b63c3e24acaeabc`, which answers
+[PR2540's comparison question](https://github.com/CrocSwap/integer-mult-bounds/pull/2540).
+They are not claimed as new. The retained checker supplies the authenticated
+source reconstruction and routed algebra. [PROOF.md](PROOF.md) proves the new
+frame identity, complete word refinement and exact child-moment comparison.
+
+| Added local charge | PR2540 | PR2681 | This word |
+|---|---:|---:|---:|
+| Values retained across B1 | 16 | 0 | 0 |
+| Positive rank-one children | 224 | 112 | 336 |
+| Positive rank-eight children | 16 | 448 | 0 |
+| Native rank mass | 352 | 3696 | 336 |
+| Native monomial wrappers | 480 | 1120 | 672 |
+| Full-cover maps | 208 | 464 | 464 |
+| Real scalar primitive allowance | 17472 | 25840 | 25840 |
+| Owned eventual outputs | 224 | 224 | 224 |
+| Peak owned local scratch | 16 | 16 | 16 |
+
+Against PR2540, the child-moment difference has numerator
+`112 - 16*8^(1-a)`, strictly negative for `0 <= a <= 1/16`. The proof uses
+the exact integer inequality `8^15 > 7^16`. **This is a child-cost comparison**:
+the extra 192 wrappers, 256 maps and 8,368 scalar allowance remain liabilities.
+Physical placement, movement, precision and a complete consumer invoice are
+unknown. The newer PR2651 output-bank coalescing retains sixteen early values
+without a separate bank; this result uses no early values at all.
+
+## Exact evidence
+
+The 3,823-event [WORD.json](WORD.json) has 336 line children, 464 cover maps,
+1,808 unit ADDs, 896 quarter ADDs and 312 CLEARs. All 224 input-array operators
+pass both inverse orders; the intermediate inverse-B1 checkpoint, arbitrary
+owned dirt, actual scalar frames, borrowed restoration and scratch disposal
+are checked. The output operator digest equals the exact retained predecessor.
+
+The new physical evidence checks:
+
+- Full phase-polynomial entry and exit identities at all 112 ports for both
+  stages, plus 1,210,496 separate literal character equalities determining
+  those degree-two phase polynomials on the full 73-coordinate space.
+- All 114,688 signed rank-one basis columns, including Gaussian coefficients,
+  global phase, negative-child XOR wrappers and all 336 literal occurrences.
+- Eleven semantic controls covering missing/wrong line normalization, wrong
+  normal, old frame shifts, wrong inverse shifts, failed restoration, owned
+  dirt, borrowed writes, scratch leaks, an inverse sign and a native wrapper.
+
+```sh
+python3.12 -I -O -B research/qq16-line-normalized-decoder/verify.py
+python3.12 -B scripts/research_package.py --package research/qq16-line-normalized-decoder
+```
+
+The default replay is read-only. `--write` requires both output receipts to be
+absent. Sources are authenticated with SHA-256 and Git blobs before compiling
+the captured predecessor verifier bytes; no imported `.pyc` is trusted.
+The predecessor's unchanged code, word, receipt and notices are retained in
+`vendor/pr2681/`, with complete pins in [PREDECESSORS.json](PREDECESSORS.json).
+Main scientific inputs are pinned in [SOURCES.json](SOURCES.json). A Git-free
+export is supported with those exact files.
+
+## Scope and expansion decision
+
+Milestone: **local module**. This is a changed physical implementation of one
+completed finite decoder. The favorable child moment reopens PR2681's local
+cost decision; it does not admit a complete supplier. The full inherited
+F0/B1 calls, all affine map and wrapper work, storage/ownership, rounded
+precision and output consumer remain separate paid obligations. Native line
+identities are ideal exact operators in the existing finite Gaussian-dyadic
+alphabet; they do not prove a rounded strict-zero or physical tape contract.
+No selected frontier, new kappa, optimality, formal-kernel or human-review
+claim is made.
+
+The verifier-engineering picker was preserved; TASK.json records the bounded
+pivot after nearby acceptance audits were already covered. Canonical main
+advanced to `1884c509efc004524786e9b7cfcc4aca572316d5` before this construction;
+revision-5 guidance and the selected record were unchanged. The canonical
+[advance claim](https://github.com/CrocSwap/integer-mult-bounds/pull/2681#issuecomment-6198194973)
+records the source, boundary, comparison and stopping condition. Do not expand
+without a pinned consumer and favorable complete physical allowance.
+
+## Open next questions
+
+1. Can an actual caller host the extra affine maps and wrappers, with all
+   movement, control and precision charges, within the child saving? Pin its
+   owner and output-consumer contracts before attempting that comparison.
+2. What precision suffices for this changed literal word under that caller's
+   completed-child error contract? Existing bounds for different words do not
+   transfer merely because their ideal endpoints agree.
+
+Credit Arham Tahir/PR2681, ywz65/PR2540, Ali Romman and the QQ16 contributors,
+starship-s/PR2443, thakrarsagar/PR2470, Ross Richardson/PR2480, and the retained
+PR2456/2468/2492/2512 source/native lineage. New work by ywz65 with substantial
+OpenAI Codex assistance. Apache-2.0. Validation and independent agent review
+are recorded in TASK.json; neither is independent human review.