Mister-Meeseeks · Oct 16, 2026 · Oct 15, 2026
diff --git a/research/t74-cold-host-restoration/.gitattributes b/research/t74-cold-host-restoration/.gitattributes
@@ -0,0 +1,6 @@
+# Immutable consumed source bytes, including the auditor's original CRLF.
+operator/vendor/** -text -whitespace
+pricing/vendor/** -text -whitespace
+pricing/inputs/** -text -whitespace
+*.gz -text
+*.xz -text
diff --git a/research/t74-cold-host-restoration/MANIFEST.json b/research/t74-cold-host-restoration/MANIFEST.json
@@ -0,0 +1,213 @@
+{
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+    "pricing/verify_budget_certificates.py": {
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+}
diff --git a/research/t74-cold-host-restoration/README.md b/research/t74-cold-host-restoration/README.md
@@ -0,0 +1,113 @@
+# Cold-host restoration: cancellation works; direct undo hits target frames
+
+**No new κ claim.** This follows the open J-dim1 cold-host lead on
+[`research/t74-r10-hosting-leads`](https://github.com/mdumitrean/integer-mult-bounds/tree/dfbc5ba121d5d23381393f178be8d4ba25ebfa4d),
+based on [PR2802](https://github.com/CrocSwap/integer-mult-bounds/pull/2802) at
+`17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd`. Its conditional comparison value is
+`0.001717794984118634663827 - 10^-46 - 10^-70`. The selected record remains
+`0.001672660197076918`.
+
+The submission overlap check also found [PR2818](https://github.com/CrocSwap/integer-mult-bounds/pull/2818)
+at `175822aee7a1858ec653f7f92d7a750aec2c2795`. Both literal words, fill, order
+and dispatch match PR2802; it claims only a finer endpoint. This package keeps
+its exact PR2802 comparison point. Its fixed-word obstruction is unaffected,
+and increasing the comparison endpoint can only tighten the necessary cost
+budgets. PR2818's high-precision endpoint was not independently certified here.
+
+J replaces an entering width-eight helper with a retired width-four cold host.
+The realized merged host ends at width nine, which loses the prospective gain.
+Keeping it cold at width seven or eight requires undoing the borrowed writes,
+cancelling its warp, and paying the resulting frame and owner costs.
+
+## What this adds
+
+1. **A constructive operator cancellation.** On `473→277`, an inverse warp at
+   the zero entrance, one zero-frame prelude read, and an exact terminal undo
+   restore the original dirty input. Both orientations pass the unchanged
+   pinned algebra/frame auditor and semantic failure controls. The fixture
+   ends at FULL9: the pinned native transport rejects FULL-ended private
+   buffers, so this establishes an algebra/frame component only.
+2. **A fixed-word recovery obstruction.** The 92 retained pairs in both
+   orientations give 184 words and 131,788 post-use insertion slots. No direct
+   recovery has a necessary rank below eight. The rank-eight slots compress to
+   720 commuting classes; all 8,208 orders of their three/four contiguous
+   recovery additions are frame-infeasible. Every order has a target-port
+   end-frame collision, so widening another cold helper does not remove it.
+3. **A changed-entry check.** All 31 rank-four hyperplanes for each of 32
+   eligible first-write rank-five caps, with host 277 in the base orientation,
+   give 992 variants and 368,218 direct-recovery slots. Every variant needs
+   rank nine. An independent exact lattice replay reproduces the complete
+   histograms without the frame optimizer.
+4. **Exact cost limits.** Rational continuous-pattern duals check every one of
+   the 1,163 patterns. They reject the width-nine/`−H3` ledger, even
+   allowing fractional allocation. Rank-mass-consistent ideal cold ledgers
+   have the small remaining net-cost budgets below.
+
+| Hypothetical cold host | Local delta per call | Numerical gain for stored pattern invoice | Exact upper bound on extra net cost per call |
+|---|---|---:|---:|
+| width 7, replacing `(4,8)` | `−H3−H2` | `+8.70325321e−7` | `<0.017959 H1` |
+| width 8, replacing `(4,8)` | `−H3−H2+H1` | `+2.79896668e−7` | `<0.005786 H1` |
+
+These numerical gains concern feasible **pattern** invoices, not chronological
+owner allocations or constructed words. The duals certify necessary cost
+bounds and explicit rational upper caps. Every ledger preserves rank mass
+4,816,512; restored variants retain 72 private buffers. Scalar gate count is
+not the number of paid rank-one children.
+
+## Reproduction and evidence
+
+Python 3.12+, standard library only. Run from the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/t74-cold-host-restoration
+```
+
+The registered replay authenticates package bytes before executing the
+independent direct/entry-frame checks, the literal cancellation construction
+and unchanged auditor, and the rational pattern certificates. It uses temporary
+outputs, isolates imported bytecode caches, and leaves committed evidence
+unchanged. Commands and time limits are
+in [VERIFY.json](VERIFY.json). Detailed scope and evidence are in
+[direct/NOTES.md](direct/NOTES.md), [operator/NOTES.md](operator/NOTES.md),
+[hyperplanes/NOTES.md](hyperplanes/NOTES.md), and [pricing/NOTES.md](pricing/NOTES.md).
+
+The research round allowed 80 cores across the primary agent and three parallel
+agents, with disjoint affinities and single-threaded BLAS. The original searches
+used the pinned NumPy/SciPy frame toolkit; certificate replay does not depend on
+those solvers. Exact source and environment information accompanies the evidence.
+The research started at canonical main `544a7e82810e30cab61c297cb2e2ea86127fe944`,
+priority revision 5; the publication branch is based on
+`cfddb8581e7e96d4f4cd9bfd279037014c8b296d`, with unchanged relevant guidance
+and selected record. [TASK.json](TASK.json) records the complete cost ledger,
+freshness checks and bounded stopping decision.
+
+## Open next questions
+
+The exclusion concerns **contiguous direct recovery additions** in the stated
+words and interfaces. It is not a universal cold-host obstruction. Staged undo,
+precomputed recovery combinations, different scalar circuits and changed
+consumers remain open. The full-width cancellation fixture does not establish
+a native supplier, and no new literal owner fill, complete cold replay or outer
+admission is claimed.
+
+The next useful experiment is a small staged or changed-basis recovery for
+`473→277` that avoids the target-port collision and stays within the exact
+width-eight cost allowance. It must provide the actual paid profile before
+further packing work. A successful sub-full cold word would then need native
+replay, physical stock/precision checks, literal owners and the complete outer
+ledger. These obligations and first steps are also listed in [TASK.json](TASK.json).
+
+## Credit
+
+J's hosting mechanism, source branch, and #2802 construction: Marius-Paul
+Dumitrean with substantial Anthropic Claude assistance. This round adds
+substantial OpenAI Codex assistance, including three parallel AI agents and a
+separate integration replay; no independent human or proof-assistant review is
+claimed.
+
+Retained lineage: tekuuu (#2751), DavidAriasC (#2766), mason-hale (#2696),
+Cinna Davis / 1337isnot1337 (#2226), philippeVV (#2679), Jeremy Kothe /
+jeremykothe2 (#2673/#2745), Vlado-V (#2322), Rohan Arun and the credited
+T74/native/owner/outer sources. The #1186 frame toolkit is Marius-Paul
+Dumitrean's earlier contribution. Frozen source notices and byte-exact source
+pins are retained with the consumed inputs. Apache-2.0.
diff --git a/research/t74-cold-host-restoration/SOURCES.json b/research/t74-cold-host-restoration/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
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+  "files": [
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+    },
+    {
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+      "sha256": "7d185cd8c2af35988d638d969748ad7b670f902606444dbfc748e4402c340df6"
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+  ]
+}