Mister-Meeseeks · Oct 20, 2026 · Oct 18, 2026 · Oct 18, 2026 · Oct 19, 2026
diff --git a/.github/workflows/p112-common-slice.yml b/.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

diff --git a/research/p104-caller-feasibility/README.md b/research/p104-caller-feasibility/README.md
@@ -0,0 +1,155 @@
+# P104 caller feasibility after PR3609
+
+**Two source-bound results, with no new supplier or selected bound claimed.**
+This package answers the changed-consumer and physical-format routes from the
+[PR3609 handoff](https://github.com/CrocSwap/integer-mult-bounds/pull/3609).
+The companion normalised-layer investigation is a different interface and
+does not supply a P104 cost credit.
+
+The first result is a sharp **425 rejected / 426 abstractly passing** threshold
+for rank-unit deletions from the actual new full dual, across every integer
+pair count in the named inherited coverage model. The second is a sharp
+**six / seven / six** fractional-bit contract for its entrance, full execution,
+and final outputs. A physical producer, legal owners, and an affordable full
+caller are still missing. Neither theorem makes unpriced costs zero.
+
+## Changed complete consumer
+
+[consumer/PROOF.md](consumer/PROOF.md) derives an exact whole-bill criterion for
+an arbitrary replacement dual profile, genuine unpaid coverage relief, and
+additional rank-normalised cost. It distinguishes a realised replacement from
+an optimistic relaxation.
+
+The retained forward has 1,646 children and rank mass 3,070. PR3609's new full
+dual has 1,742 children and rank mass 3,542. In the named all-pair consumer,
+there are p+1 forward calls and p dual calls, m=16p+9, W=208p, and the stated
+3,014 endpoint credit per call. Here p denotes the pair count, not precision.
+
+Deleting rank-one children is the most favourable integer rank-unit deletion
+at a fixed allowance. Strict convexity of the relaxed excess in p, together
+with exact outward rational evaluations at p=6,7,8, proves that deleting at
+most 425 units per dual fails for **every p>=1 and every finite number of
+fully paid auxiliary banks**. At 425, the global integer minimum is p=7 and
+is positive, approximately 1.6006864105095964.
+
+An abstract deletion of 426 rank-one children per dual passes at p=7 and
+a=1/596, whose outer ratio 1/597 exceeds the frozen selected benchmark. Its
+entire seven-pair bill has only about **4.557071360876949 rank-normalised cost
+units** of remaining slack. Adding four units passes; adding five fails.
+At fixed p=4, the corresponding boundary is 427/428. No such deletion network
+is constructed. Endpoint credits and coverage cannot be silently retained
+after a replacement that changes their premises.
+
+The independent calculator also reproduces two different providers' arithmetic.
+[PR3605](https://github.com/CrocSwap/integer-mult-bounds/pull/3605), at exact
+head `3efbb5de06a49ffeea6684482f2d3fe48cdca3fb`, has 23,953,011 children,
+rank mass 48,165,120, and the strict root bracket
+0.001730006549538841847005 < beta < 0.001730006549538841847006 in its own
+T740 model. The [PR3574](https://github.com/CrocSwap/integer-mult-bounds/pull/3574)
+1126/1127 hosting separator also agrees under its own native-channel law.
+These are comparisons, not substitute P104 bills. This package does not replay
+either historical physical release or establish its recursive assumptions.
+
+## Exact physical format
+
+[physical/FORMAT_PROOF.md](physical/FORMAT_PROOF.md) combines Gaussian-ideal
+valuation with the actual program's rational rows and a literal dependency
+cone. For arbitrary initial physical components on the 2^-f grid, one common
+fixed-point format needs the following added fractional bits.
+
+| Boundary | Sharp uniform guard | Scope |
+| --- | ---: | --- |
+| Standalone entrance | 6 | All 1,238 new operations |
+| Entrance plus retained projection | 7 | All 5,265 operations |
+| Required final outputs | 6 | All 358 physical fields |
+
+Refining the mantissa and its unit preserves the numerical input. The theorem
+computes the ideal Gaussian word exactly on the refined grid; it does not
+identify that result with a separately rounded coarse-grid execution outside
+the source's exactness domain. The six-bit entrance proof does not assert the
+false inclusion 64 Z[i]^512 in the stronger sufficient domain 4 B9.
+
+The checker traces every scalar row, scalar product, and final frame. A
+36-event dependency cone gives the actual seven-bit obstruction at original
+event 2142, combined event 3000. A required X0 endpoint proves the six-bit lower
+bound. Full seven-bit sufficiency uses the credited Newton module and native
+covariance theorems. Those historical theorems are inherited, not re-certified
+by the bounded witness.
+
+If each original real and imaginary component has magnitude at most H, a
+sufficient stored-field bound is **3296H**, and the declared literal scalar
+schedule's scratch bound is **6592H**. With b magnitude bits in the original
+mantissa, sufficient full-word signed widths are b+20 for fields and b+21 for
+scratch. These include integer headroom as well as the seven fractional bits.
+No minimal magnitude-width or arbitrary recursive-depth claim is made.
+
+[physical/CALLER_AUDIT.md](physical/CALLER_AUDIT.md) records the named source
+interfaces inspected and the exact producer, borrowing, conversion, routing,
+and cost obligations. Source preparation and output-format conversion remain
+paid operations or explicit producer/consumer contracts.
+
+## Evidence and reproduction
+
+Use Python 3.12 and the standard library. From this directory, including a
+Git-free source export, run
+
+```sh
+python3.12 -I -Werror -B verify.py
+python3.12 -I -O -Werror -B verify.py
+```
+
+Each component authenticates its retained source bytes, recomputes its receipt,
+and compares it with strict JSON types. Default replay is read-only. Arithmetic
+signs use outward rational intervals, not floating-point approximations.
+See [consumer/RESULT.json](consumer/RESULT.json) and
+[physical/FORMAT_RESULT.json](physical/FORMAT_RESULT.json) for the deterministic
+receipts. [VERIFY.json](VERIFY.json) registers both Python modes. These commands
+do not launch a historical native census, full selected replay, physical owner
+implementation, or formal proof kernel.
+
+From a complete repository checkout, run
+
+```sh
+GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/p104-caller-feasibility --check-only
+GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/p104-caller-feasibility
+GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/check_research_commit.py --package research/p104-caller-feasibility --check-source-history
+```
+
+[SOURCES.json](SOURCES.json) binds the unchanged task catalogue and selected
+record at main `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. Exact pending-source
+bytes are retained in this PR's own ancestor history. The component manifests
+record original public paths, commits, blobs, and SHA256s. This preserves
+provenance without requiring unrelated unmerged branches in a clean checkout.
+The selected frontier is unchanged.
+
+## Open next questions
+
+[TASK.json](TASK.json) gives structured questions, first steps, and blockers.
+Useful P104 reopening evidence is a realised replacement profile or changed
+coverage law that passes its own full bill, with legal field access and actual
+source/return contracts. The 426 sensitivity witness is a rejection screen for
+proposals, not a reason to expand an unpriced construction.
+
+A concrete caller must supply writable/restored Y access, owned private-zero
+lifetimes, the stated frames and width, and paid conversion, routing,
+controller, and recursion. Those costs must enter the same complete inequality.
+For work aimed at the stronger existing T740 candidate, the distinct next step
+is an independent audit of PR3605's complete release and retained implications,
+not transplanting its profile into P104.
+
+## Credit
+
+Prepared by Clear1nsight with substantial OpenAI assistance from a root agent
+and three concurrent specialists, including cross-review. This is same-session
+independent implementation and review, not independent human acceptance.
+New work is Apache-2.0; original notices are retained with the source inputs.
+
+Credit PR3609 for the actual entrance and full profile; Jose Manuel's p=4
+consumer and Nick Petalas's all-pair budget for the inherited model; Vasek and
+PR2458/2744 for the forward; ywz65 and Arham Tahir for the original physical
+word and native data; the PR3382/3406/3416 lineage and Ross Richardson's
+Clifford-grid work for module and precision premises; and Dumas and Grenet
+for the earlier dirty-accumulation method. PR3605's T740 construction is Ross
+Richardson's work. PR3574 is jwr's work, retaining Nick Petalas's budget,
+Rohan Arun's native channel, and its lineage. Detailed attribution remains in
+the component proofs and manifests.
diff --git a/research/p104-caller-feasibility/SOURCES.json b/research/p104-caller-feasibility/SOURCES.json
@@ -0,0 +1,187 @@
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+    }
+  ],
+  "retention_note": "These exact bytes were retained in this PR own ancestor 35cf06a9d35b20701550b5517f4d69afd43c0ca7. Original public origins and notices remain in consumer/SOURCES.json and physical/SOURCE_MANIFEST.json. No source algorithm is rewritten; no pending foreign Git object is needed for replay."
+}