Realise the P104 omitted completion at the actual entrance

.github/workflows/p112-common-slice.yml

@@ -15,9 +15,9 @@ jobs:
     if: github.repository == 'CrocSwap/integer-mult-bounds'
     runs-on: ubuntu-24.04
     timeout-minutes: 20
-    env:
-      TMPDIR: ${{ runner.temp }}/p112-common-slice
     steps:
+      - name: Initialise P112 work directory
+        run: echo "TMPDIR=$RUNNER_TEMP/p112-common-slice" >> "$GITHUB_ENV"
       - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
         with:
           fetch-depth: 0

research/p104-inplace-entrance/COSTS.md

@@ -0,0 +1,180 @@
+# Exact local invoice and conditional consumer stop
+
+The in-place entrance completion reduces scalar ADD work and improves the
+native-only concave tariff. It still fails the retained five-forward/four-dual
+consumer model after substituting its **newly constructed** profile. This is a
+local construction with a conditional stopping result; it supplies no improved
+supplier or selected bound.
+
+Counts below are the source-derived outputs of [invoice.py](invoice.py), the
+actual wrapper census in [native.py](native.py), and the serialized
+[PROGRAM.json](PROGRAM.json). Source hashes and predecessor provenance are in
+[SOURCES.json](SOURCES.json). The cost units remain separate throughout.
+
+## Scalar work, return, and native children
+
+Each field has 512 Gaussian entries, hence 1,024 real components. A unit
+Gaussian bank ADD/SUB therefore costs 1,024 real ADD/SUB operations. Integer
+coefficients are expanded into repeated unit operations. Each fractional source
+read is implemented by exact componentwise halving, the signed ADD, and source
+restoration by doubling before the next original event. A quarter read uses two
+half passes and two restoring double passes. These are separately charged.
+
+| Scope | Unit Gaussian bank ADD/SUB | Real ADD/SUB | Exact real halves | Restoring real doubles |
+| --- | ---: | ---: | ---: | ---: |
+| Removed original events | 1,364 | 1,396,736 | 98,304 | 98,304 |
+| New entrance completion | 887 | 908,288 | 105,472 | 105,472 |
+| Original full word | 4,353 | 4,457,472 | 2,750,464 | 2,750,464 |
+| Changed full word | 3,876 | 3,969,024 | 2,757,632 | 2,757,632 |
+
+Thus the substitution saves 488,448 scalar real ADD/SUB operations and adds
+7,168 exact halves and 7,168 restoring doubles. The 787 weighted ADDs in the
+factor notation are **887 unit operations**: 247 for dirty preconditioning,
+393 for gathering, and 247 for scattering. Exactly 103 Y sources are halved
+and immediately restored; Y1 is unused by this completion.
+
+| Scope | Native calls | Native rank mass | Coordinate C pairs |
+| --- | ---: | ---: | ---: |
+| Removed original events | 473 | 889 | 227,584 |
+| New entrance completion | 145 | 889 | 227,584 |
+| Original full word | 2,070 | 3,542 | 906,752 |
+| Changed full word | 1,742 | 3,542 | 906,752 |
+
+The new profile is $52H_1+93H_9$. The 4,027-event retained projection and
+1,238-operation prelude together have 5,265 serialized operations. Removing
+the old complement removes 104 whole-bank sign events; 104 such signs remain
+in the projection and require their own 106,496 real negations. All eight
+original private-C zero/erase lifetimes remain. The prelude adds no private
+Gaussian bank: its eight dirty accumulators are required X outputs, and their
+original contributions are preserved. Literal native-pair arithmetic is not
+included in the scalar ADD table.
+
+## Wrappers and widths remain charges
+
+The actual 145 native occurrences have 290 monomial wrappers. Their 148,480
+address entries form 97,840 cycles. Direct cycle permutations require 50,640
+Gaussian SWAPs; the recorded phases additionally require 61,440 real SWAPs and
+148,480 real negations. A Gaussian SWAP exchanges two Gaussian entries, hence
+two pairs of real components. Its two-real-SWAP lowering would total 162,720
+real SWAPs including phase rotations.
+These are explicit operation inventories, not free relabelings or a completed
+machine tariff. The old omitted wrappers are outside this comparison; a
+difference of complete physical bills is not claimed.
+
+Let $H_X$ bound real and imaginary components after the singleton-to-empty
+entrance maps, and let $H_Y$ bound the **actual unhalved** common-frame Y
+fields. The fixed schedule's scalar row envelope is
+
+$$
+\max\{8H_X+95H_Y,\ 11H_X+64H_Y,\ 12H_X+49H_Y,\ 14H_X\}.
+$$
+
+Consequently $103H$, with $H=\max(H_X,H_Y)$, is a uniform bound. The
+equal-bound maximizing row has weights $(8,95)$ at prelude operation 929,
+equivalently scalar operation 877; indices are zero-based. Its
+$8H_X+95H_Y$ value alone is not a uniform bound for independently varying
+inputs. Entrance/exit native growth and signed-floor temporaries require
+additional bounds.
+
+The dense physical fixture's observed peak, 11,232, measures stored field
+values after complete operations. It does not measure internal native-pair
+temporaries or prove a universal width allowance. Python oracle arrays,
+dictionaries and temporary vectors are verification storage, not claimed
+physical workspace.
+
+## New profile substituted into the named consumer
+
+Jose Manuel's original stopping insight and Vasek's
+[PR2744 consumer audit](../p104-consumer-budget-audit/README.md) concern fixed
+predecessor profiles. Their theorem does not automatically cover this
+resynthesis. `invoice.consumer_stop` performs a new substitution, retaining
+the same explicit coverage assumptions:
+
+- Width $m=73$, $W=832$ original families, five fixed forward calls and four
+  calls of this newly constructed dual word.
+- Favorable persistent credit $P=3014$ per call, leaving
+  $I=72\cdot832-9\cdot3014=32778$ paid coverage units.
+- Up to 416 integer rank units forgiven per dual, with the new decomposition
+  otherwise fixed; other positive children have rank at most 73.
+- Every auxiliary bank adds 73 paid coverage units and one family; all other
+  charges are nonnegative.
+
+The unchanged forward mass is 3,070. The nine-call profile, after favorable
+H1 forgiveness, has H1 count 9,680 and total mass 27,854. The certified bounds
+
+$$
+\log 73>4,\qquad \log(73/r)>2\quad(2\le r\le9)
+$$
+
+give the new slope
+
+$$
+L=4(9680)+2(27854-9680)=75068.
+$$
+
+For every finite number $B\ge0$ of fully paid auxiliary banks and primitive
+saving $0<a<1$, the favorable moment satisfies
+
+$$
+M_B(a)>1+\frac{75068a-104}{73(832+B)}.
+$$
+
+At the retained benchmark
+
+$$
+\kappa=\frac{836330098538459}{500000000000000000},\qquad
+75068\kappa-104=
+\frac{2695406959271260053}{125000000000000000}>0.
+$$
+
+With no auxiliary banks this gives the exact lower bound
+
+$$
+M_0(\kappa)>
+\frac{7594695406959271260053}{7592000000000000000000}>1.
+$$
+
+The retained transfer requires primitive saving greater than this tested
+multiplication saving. The lower bound increases with $a$, so this consumer
+fails already under the more favorable test. Additional resynthesis, changed
+coverage, or a different consumer requires a new calculation.
+
+The native-only gain is real: concavity gives the old omitted tariff at least
+
+$$
+421+52\,9^s,
+$$
+
+while the new tariff is $52+93\,9^s$. Their difference is at least
+
+$$
+41(9-9^s)>0\quad(0\le s<1),
+$$
+
+with equal rank mass at $s=1$. This gain does not discharge the consumer's
+remaining coverage or physical charges.
+
+## Obligations and stopping decision
+
+| Boundary | Established here or explicitly inherited | Remaining obligation |
+| --- | --- | --- |
+| Local operator | Exact scalar matrix, dirty preservation, source return, 53 native certificates and dense literal comparison | Actual supplier invocation with these fields |
+| Source domain | Local 93 dirty fields in B9 and Y in 4B9; common full-word sufficient domain: 104 Y in 4B9, 78 N in 2B9, 176 other inputs in B9 | Paid preparation from a named upstream input |
+| Storage | No added Gaussian bank; eight inherited private-C lifetimes retained | Owners, allowed source mutation, component scratch and legal erasure implementation |
+| Width and addressing | Scalar envelope and explicit wrapper inventory | Finite caller widths, temporary headroom, routing and controller lowering |
+| Recursive supplier | Exact conditional model rejection | All-size/rounded-child transfer and a different favorable complete bill |
+
+Stop dependent owner or supplier construction aimed at beating the selected
+target with this exact five-forward/four-dual model. The local identity remains
+useful evidence; the failed favorable model does not justify further physical
+construction along that route.
+
+Credit Jose Manuel (`jmbarrancoml`) first for the consumer-budget observation,
+then Vasek (`flyingviper`)/PR2744 for its conditional audit; Ross Richardson's
+PR2458 forward binding and PR2445 word; ywz65's P104/native/dual lineage;
+Hiroki Kumazaki's PR3446 retained projection; Nick Petalas's PR3462 factor,
+PR3469 adapters and PR3416 covariance; Jeremy Kothe's retained compiler lineage;
+and Tekalign's PR3218 phase-sensitive criterion and the earlier compiler authors
+retained in [SOURCES.json](SOURCES.json). This package contributes the
+dirty-basis entrance schedule and its new profile substitution, with substantial
+OpenAI assistance. Predecessor credit and notices remain in force.