[codyw912]

Change and mathematical scope

Adds the five-file research/r437-root-step-handoff/ package answering #4685/#4682's actual Program/capsule handoff.

For the real carrier-D early SOURCE87 MOVE (stage 0, replica 0, position 22397, common view), the checker connects an original-root Program with zero STEPs at e=n=2048,h=0 to an actually emitted GOOD child boundary, a literal generated 2048→64 STEP, and all eight Machine.prepare_child capsule channels. It independently checks serialized history, source identity, modulus, width/depth grants, exact row quotient and spectator conservation.

Conditional metadata correspondence only. This is not a proof that execution of the numerical root payload reaches the cut. Count ports and huge spectator powers use explicit symbolic arithmetic; the directory contains one justified prefix specimen, not a complete produced directory; the source payload tape is empty and is not represented as executed. Complete compiler/root execution, child return/restoration, physical tariffs, supplier admission and a new κ are unclaimed.

The genuine new edge starts from a root-only Program, unlike the predecessor fixture with pre-existing 2048→64 history followed by generated 64→2. Nick Petalas's #3246 already proves the one-factor stock divisor; that theorem is credited and not claimed anew. Mihir Srivastava's #4685 supplies the arithmetic-path handoff.

Source and adapter boundaries

Canonical base b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, priority revision 7; selected #4470 κ=0.00302015 unchanged. Only the five new package files change. No environment setup or frozen/shared source edits.

An authenticated 154-file historical runtime closure already on main is materialized in a private temporary tree, with current carrier inputs and retained pooled sources. Loader guards are preserved. Historical selection provenance is explicitly separate from current orientation; the old loader's rejection of the live newer selection is not bypassed.

The common-view q127 low class requires an exact prefix-count/binary-search ordinal adapter instead of enumerating q entries. Its written equivalence proof, finite-q comparison controls, q127 roundtrip and independently reported executed-adapter hash distinguish it from the unchanged source-codebook identity. The production regional emitter is executed from its unchanged authenticated AST; complete enclosing compiler execution is not claimed.

Validation

Executed by the orchestrator on Linux x86_64, CPython 3.12.13:

python3.12 -I -B research/r437-root-step-handoff/verify.py --write
python3.12 -B scripts/research_package.py --package research/r437-root-step-handoff
python3.12 -B -m unittest discover -s tests -p 'test_research_*.py' -v

• Explicit initial run recorded the actual deterministic receipt in TASK.json.
• Ordinary and optimized registered replays both passed, comparing that receipt and retaining explicit exception checks under -O.
• 27 rejection controls cover wrong replica/view/catalogue/source, false Program object identity, event/serialized STEP/root mutations, doubled rows, leading-versus-unused, missing spectator factors and below-cutoff false recursion.
• 191 source/provenance pins; all 188 live inputs declared. Original source authentication remains active.
• Shared onboarding suite: 331 tests, 11 Windows-only skips, no failures.
• Separate Astra code/scientific-boundary review found no substantive blocker. No independent human, proof-kernel or hosted CI approval claimed.
• Publication preflight passed for commit 4c1a746590ec97fa84537da43dc662775a5b72e7: exact 193 package/input files and source-history ancestry. The committed export passed integrity checking. Both registered commands also passed in a fresh git clone --no-local --single-branch with its own reachable-history object store. The Git-dependent checker is not claimed portable as a standalone tarball.

Task and overlap

Task r437-carrier-integration, refined to the one original-root edge correspondence. Latest recorded overlap covers 469 open PR bodies and 3,624 discussion records, with complete pagination, plus all 5,860 tracked local notes. Arbitrary diffs, closed remote PR bodies and unpublished work remain outside coverage. #4685 head ca336bd72aff54e025a8ddbb1f3c8b756d9b9631 is unchanged. Public claim posting failed; no reservation is claimed.

Credit

Chris R/Clear1nsight (#4067/#4176), unpaidmoon (#4147), Jose Manuel/jmbarrancoml (#2809), David Arias (#2753), Nick Petalas (#3246), Mihir Srivastava (#4685), Ross Richardson, Tekalign, Rohan Arun, ai-nanachi, ywz65 and the retained source/hosting lineage. Prepared for codyw912 with substantial OpenAI Codex (GPT-6 Astra) assistance and separate AI review. Apache-2.0; inherited source notices retained.

Open next questions

Connect the complete root packet/directory producer and preceding routed payload to this conditional metadata cut; separately establish child return/restoration and physical tariffs. README/TASK explain the smallest next step and blocker. These obligations are not silently assigned zero cost.