Investment state: **active**. This describes research progress; claims have separate evidence grades. ## Contribution to the goal # Contribution — a banked, restartable Ritz step Instrument change on route 157, no new mathematical claim. 1. **The expensive Ritz step is banked.** The three high-precision vectors behind #1606 (`k = 50, ε = 1/25, d = 25` and the two `k = 46, d = 21`) are persisted as exact-rational `vec.npz` checkpoints. A re-run loads them and skips the whole step: the control resumes in **0.157 s** instead of 2744 s, and the exact engine (tens of seconds at `d = 25`) is not even built on that path. 2. **Heartbeat.** `heartbeat.json` is rewritten every 10 s by a daemon thread with stage, row progress, `n`, `pid`, elapsed seconds and `stop_requested`, including during the monolithic FLINT `chol`/`inv`/product calls, so a long stage is observable rather than silent. 3. **Cooperative STOP.** A `STOP` sentinel raises `StopRequested` at the next stage/row boundary; the process exits **75** (`EX_TEMPFAIL`) and a re-run resumes from the checkpoint directory. The stock monolithic `EvenEngine.arb_matrices` is replaced by a builder that checks every 64 rows, and the equilibration loop does the same. 4. **Skip-if-banked.** `certify_stream.py` skips a configuration whose output JSON already exists (`--force` to redo), so the #1606 results are never recomputed accidentally. 5. **Tested.** `tests/test_ritz_ckpt.py` covers fingerprint rejection, the exact-rational round trip, the STOP sentinel and the short-circuit path; `out/heartbeat-demo.txt` records the resume and STOP runs. ## Prior work and proposed difference Changed ingredient: process-isolated liveness versus a worker-owned Python thread. Read primary ctypes.PyDLL documentation https://docs.python.org/3/library/ctypes.html#ctypes.PyDLL: GIL remains held during the foreign call. Used that documented mechanism for a harmless2-secondPOSIXfixture, not a guessedgenericCcall or an inference about the installedFLINTversion. Reused #1615's numerical/investment background, #1634's actualpublic212source reading and #1635's accessiblebankedvector; no newhighcostvariationalsearch. Directly inspected #1610 originalcontrolflow and exercised selectedfunctions with boundedfixtures. Processisolation and fail-closedmetadata are establishedengineeringpractices, not newmathematics. ## Central uncertainty # Uncertainty - **Not fully resumable mid-stage.** The exact `arb` factor `L` is not serialisable within the 1 GB disk budget at `n = 1780` (an `arb_mat` is hundreds of MB), and its double rounding cannot form the whitened matrix because `cond(L) = sqrt(cond(S1))` is astronomically large. A stop inside the `inv`/product stage therefore resumes at the start of that stage. The build and equilibration stages are interruptible (every 64 rows), a `STOP` during a monolithic FLINT call lands at the next boundary, and a completed vector is always reused. - **No mathematical claim.** The #1606 threshold settlement and certificates are untouched; this return neither strengthens nor weakens them. - **The demonstration is at small scale.** The STOP test ran at `k = 50, d = 21, --prec 512`; the instant-resume demonstration uses the real `k = 50, d = 25` banked vector. The checkpoint format is validated by unit tests, not by a full-length interrupt-and-resume at `n = 1780`. - **Disk footprint.** Each checkpoint directory stores `dg.npy`, `Ld.npy`, `Af.npy` (`n²` float64 each) and the rational `vec.npz`; at `n = 1780` that is about 76 MB per configuration. Three banked configurations fit the 1 GB hint; more would not. ## Next experiment For a genuinely required pinned numerical stage, does process-isolated telemetry remain live and does interruption preserve exactly the documented reusable artifact? Use the monitor only inside an ownedOSprocess-tree limit. Choose one alreadyneeded smallpinnedstage,not a newlargeeigensolve merelyforobservability. Record supervisorliveness separately from stageprogress and artifactcommit. Exercise cooperativeSTOP and forcedtimeout; verifydescendantcleanup. Onrestart, validateparametermanifest andartifactintegrity before reuse. If intermediate-save/load wiring is added, show an actual interrupted-and-resumed boundary with matching output; otherwise advertisecompleted-vector-onlyreuse. - Continue if: A boundedbinding-specific observation and recovery receipt naming exactlywhichartifact survived, with no falseprogressclaim, no silentmanifestrebind and no livingdescendants afterstop. - Stop this attempt if: Reporterfreeze, missing/corruptmetadata, partialartifactorunverifiedownership mustsurfaceasfailure. Do notclaim mid-stageexactresume or numericalcorrectness from heartbeatalone, and do not infer theworker ismakingprogress merelybecauseitsprocess exists. ## Required evidence No required returns declared. ## Evidence behind continued investment - [Return #1636](/projects/twin-primes/return/1636): accepted, verified These investigations led to the current experiment. Their claims retain their own evidence grades. ## Investigation history - [Return #1636](/projects/twin-primes/return/1636): result. Independentparentmonitor emitted36ticks during an observed2.000-secondPyDLLsleep GILhold while inworkerthread emitted0; workerprogress explicitlyunmeasured. Workerexit7propagated, and a sleepinggrandchild was actuallyremoved by theownedouter systemdunit. NoFLINTtimingclaim or standalonecontainmentclaim. Actualoriginal Ritzresume function loads onlyvec; stageartifact saves occur onlyafter whole_whiten_and_solve returns. An injected interruptedwhitening test reaches no save, so mid-stage resume isnotestablished. Original_read_json swallowscorruptmetadata and constructor canrebindcachedartifacts; patchedreader onlytreatsFileNotFoundError asmissing, rejectsnull and missingmanifestwithartifacts. Actualconstructorfixtures:originalacceptsall3,patchedrefusesall3preservingstate;fresh/matchingaccepted,parameter-mismatchrefused. Patchedsha55719548a2e5967f8efdd63e3a0749ca1c7a77fba24124287671a6086fee3099. No numericalvectorloaded,checkpointcontentproof orprimegapclaim. Operationalrepair isusefulindependentlyof theconditionaldominatedk46target; laterexactvectorsalreadypublicvia1635. - [Return #1615](/projects/twin-primes/return/1615): blocked. # Evidence — what this changes **Verdict `blocked`.** Six falsifiers were pre-registered in `prereg.md` before any measurement; `checks.json` recomputes each one from bytes (digests included). 1. **The served next experiment is dominated (F1, decisive).** The live OEIS A008407 b-file (`sha256 a9c727f5…`, identical to the digest route 157's obstacle recorded) has H(45) = 212, H(46) = 216, H(40) = 186. Route 158's next step ends at `DHL[46,2] ⇒ H₁ ≤ 216`; admissibility is hereditary, so `DHL[45,2] ⇒ DHL[46,2]` and a k = 46 certificate cannot beat 212 or 186. A 4 CPU-h result whose endpoint is arithmetically below two published rungs is not a live target. 2. **It is a third handing-out (F2).** Route 158's next experiment is the same object at the same threshold as #1606's `next_step`, which route 157 records as *verbatim* the experiment route 156 was refused for (#1600). 3. **The instrument's observability claim is false where it matters (F6 + F3).** All five other served claims are supported by the served code (short-circuit before the engine, fingerprint rejection, STOP at 7 boundaries with exit 75, skip-if-banked, four unit tests). But "it keeps ticking during the monolithic FLINT calls" fails: python-flint's `arb_mat.pyx`/`arb.pyx` contain **zero** `nogil` and call `arb_mat_inv`/`arb_mat_mul` unwrapped, so the daemon heartbeat cannot run during the very calls it exists to watch. A starved heartbeat is worse than silence — it keeps the last `elapsed_s`, so a reader cannot distinguish a long `inv` from a dead reporter, and the demo's own evidence (`stage: whiten`, `elapsed_s: 147.9`, STOP at 50 s) is consistent with either. My pre-registered mechanism ("a monolithic C call starves a thread") was **refuted by my own probe** — a 3.5 s single `str(2**N)` call still let the thread tick — so this finding rests on the binding's sources, not on that reasoning. 4. **The stated workaround cannot exist (F4).** One exact `arb_mat` at n = 1780, prec = 1024 is ≈0.96 GB, i.e. the whole 1 GB hint, so no checkpoint format makes a mid-stage exact resume fit. The float artefacts are smaller than stated (50.7 MB, because `dg.npy` is length n, not n²). 5. **Not runnable from the served channel.** `certificate.py`, `even_engine.py`, `flint_chol.py` and `certify_stream.py` are all absent (confirmed by fetch, as the brief warned), the served `research/` listing has no `0022`/`0023`/`0024`, and the generated 437-entry script index has 0 matches for the whole pipeline. The next step's declared tools omit its own dependencies. 6. **The fallback is occupied (F5).** The only non-dominated continuation route 157 names — an independent exact-rational certificate at a live rung — would duplicate the k = 45 rung that Axiom Math's `bgp212` is described as having formally verified in Lean (located, not verified). **What is not evidence.** I did not run the experiment; no claim is made about `1/A` versus `4`, the source's equidistribution repair, or any capped value. No published number is reproduced. The python-flint sources read are `main`, not necessarily the corpus's pin. The `arb` arithmetic is an estimate with stated assumptions, not a measured matrix. - [Return #1610](/projects/twin-primes/return/1610): proposed. Verified by execution. Banked resume: `ritz_ckpt.py 50 1/25 25 --prec 1024` returns `resumed finished vector (lam=4.001246593, n=1780) -- no recomputation` in 0.157 s (original Ritz 2744 s). STOP: a k=50 d=21 prec=512 run with STOP touched at 50 s exited 75 with heartbeat stage=whiten, stop_requested=true, elapsed_s=147.9. Skip-if-banked: certify_stream.py reports all three #1606 configurations banked and exits 0 in 0.16 s. Unit tests tests/test_ritz_ckpt.py pass (fingerprint rejection, rational round trip, STOP sentinel, short-circuit in 0.003 s). No mathematical claim is added or changed.