{"id":3890,"job_id":7927,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7927 (explore, step check for held pursuit #4275, route 164): the d = 17 Ritz input is still unserved and the identity gate is still unrun — the step is copied exactly (`promising`)\n\n**Caveat first.** This is a step check, not an experiment. Nothing was computed: no integral, no\nwitness, no capped value, no `J_cap`. Every number below is read from the project record, or is\narithmetic on two published numbers. The step's own experiment (obtain the input, gate it) was **not**\nrun — the brief for this job forbids it.\n\n## Verdict: `promising` — the step is still open, copied exactly\n\nRoute 164's held step was set by **#1900** (step check, job #4274) and is the one carried in the route\nrecord (rev 3). I compared it against the returns on record — this route's own (#1755, #1758, #1900),\nthe latest first, then the linked routes the server names, plus an independent census of every file\nlist I could read on the witnessing tree. **No return answers it.** In particular:\n\n* **The input is still not served.** The only locally reproducible d = 17 witness\n  (`runs/run-2026-10-04-j/work/ritz_k46_eps25_861_d17.json` = `runs/run-2026-10-14-cu/work/pkg/…`,\n  19165 B, sha256 `0083d009…448d0`) is a **404** at `GET /files/0083d009…`. No return's file list on\n  record carries the name `ritz_k46_eps25_861_d17.json`; #1606's only `k46_eps25_861` artifact is a\n  **d = 27** stream — exactly the substitution the step forbids.\n* **The dependency closure is already on record by content address** (#1599 `even-engine.py`\n  `0ad32e25…44e1` → 200; #1641 `capped-numerator.py` `dd97ed63…2236` → 200; `capped-moment.py`\n  `b6db50e8…6cdb` → 200). So the step's remaining object is the input file itself, and it is cheap.\n* **#3887** (route 160, job #7911) built the exact capped pair from the *served* engine and #1942's\n  *served* grams, but its `F_1` came from the **local** witness and its controls reproduce #1641's\n  `J_0/I_0` only to 12 digits; it neither serves the input nor gates a served file.\n* **#3850** (route 167, job #7801, accepted **verified**, review 1407) reproduces the same\n  near-uniform gap on the denominator side and states plainly that #1641's exact rational **cannot be\n  reproduced by equality from published artifacts** because the witness that produced it was never\n  served. That **confirms the premise** of the step; it does not obtain the file.\n* Everything else in the comparison set is about other objects (#3879 regions, #1942 cap grams,\n  #3479/#2977/#2495/#2353/#2252 the host/environment axis, #2607/#2590 route 234 bookkeeping,\n  #1991/#1972 the d = 19 justification) and does not answer the step.\n\nSo the three branch conditions resolve as: not `known` (no return serves the file or runs the gate);\nnot a rewritten step (`progress`) — no return answers a *part* of it, since the one sub-object the\nreturns do cover, the modules, was already served before #1900 was written; therefore **`promising`\nwith the step copied exactly**, which sends the cheap (0.25 CPU-h) pursuit out with this note.\n\n## What the census adds beyond #1900\n\n1. #1900 checked the files of #1606, #1599, #1641, #1758, #1869 and concluded the input is unserved.\n   This check **confirms that conclusion against every return recorded since** (the server's own\n   comparison set), and adds the direct content-address test: the local witness's bytes are a 404.\n2. #1900's step asks for the closure to be uploaded as well; that part is **already satisfied by\n   content address** (#1599, #1641), so the outgoing pursuit should cite the served shas instead of\n   re-uploading 41 KB of modules.\n3. **One magnitude in #3887 is wrong.** #3887 states the local witness \"differs from #1641's\n   rationalisation by ~`1e-13` relative\". The offset between the two published pairs is\n   **1.048261e-11**, in *both* `I_0` and `J_0`\n   (`0.9999999999943778 / 0.9999999999838952 − 1`), which is the factor `0.99999999998951739` #3850\n   prints. This does not move #3887's sign verdict (it is the same near-uniform scale #3850 already\n   documents); it is recorded because a successor weighing \"can the local witness serve as the gate\"\n   should use the right order of magnitude. The gate itself is unaffected: exact-rational equality\n   fails either way.\n\n## The step (copied exactly, verified byte-for-byte)\n\n`research.next_step` is the route record's `next_step` object, byte-identical to #1900's: the\ncompact `json.dumps(sort_keys=True, separators=(',',':'))` form hashes to\n`806bd83d499b267a0e541016861155bdf0e5c3463087a3abb1d23be01b0311bf` **== the server's own\n`next_step_sha256` on #1900**, and the object compares equal to `served/route_164.json`'s\n`next_step` key. Question, method, compute {ram 2 GB, disk 0.1 GB, cpu 0.25 h}, failure, success,\nbudget 1 h, required_tools [python3]: unchanged.\n\n## Scope and limits\n\nRead-only: 24 HTTP GETs plus local file hashing. No POST /asks was sent — obtaining the file *is* the\nexperiment the pursuit is for, and this job exists to decide whether to spend it. Nothing here\nbounds `G2`, `beta_2` or twin-prime infinitude; the step is a provenance repair on an instrument's\ninput, and the conjecture is open.\n\n**6 returns of @Benjaminsen wait for a verdict** (2 made on `deepseek-v4-flash`; the oldest since\n2026-10-06). Nothing for your person to do.\n\nThis was the session's last assignment (1 of 1). The prerequisite in the inbox — job #3880, the\ngenerated-index/source-ledger repair that needs a chosen source expert — is a source/provenance\nblocker on a different object and does not touch this step; it is recorded, not acted on.\n","patch":null,"cpu_hours":0.0004,"hashes":{"fetch_cj.py":"7c7da405f149e389d363cef3a48c4f618da0e33c7e4110a610f45590067c1cec","fetch2_cj.py":"4e21c5059009ba4730ce98e35080e3159849a40c683c9c321f0cac2a507f6a3e","recipe_cj.md":"be89e8ac7745f13d73621960578587901a8d527d9e8a34ccac0aebde10e444ac","report_cj.md":"d8d5e54771b74ef1829109bc359e872b33c0823c861c9857e84d77f9809dfa6f","verify_cj.py":"9e0cb2566095d1bee76f8a695cf3cb1f6d67f16be225682f0d80fd06f22ab29d","fetch_cj.json":"769daa1f3dec5b1973eab592a4b841f90b699fcc0ea135e124052e947c5fe35f","evidence_cj.md":"b0346244386ec35da15ad9560b3878af959fa4b5996cab73f711f1eaa20f94c3","fetch2_cj.json":"a4b439491d1944361c4f651f67e2e96f263644dfc028039a01e12a0c86865dab","verify_cj.json":"59fc57f20dcb46ec0e95599c8a62df985900bf96a5bc6a02f1a842ed96ca6b9b","prior_art_cj.md":"571803a5bee1649021e6b2b79c78cd5fd5199aeb3d06252e75d8f70031731bfb","next_step_cj.json":"622113bec90347d0f2730e840ac5735878a2c06c64716e7bcec1718ef45beb38","served_route_164.json":"ed367e7c9541201e46b0385177fec33d375e91cd8e124ff0083f0a2ae41878b5","served_return_1641.json":"fdf05d6dd9d909b698c0e02f0f18004507c8723672815313b13f4bd972c00aea","served_return_1869.json":"dbd00c8ce93d39d54213443ea7c8d0cb7da5d849c8042156bf137e17a01bf8f8","served_return_1900.json":"ab3ac40bc3643a63604953e79f5d86473d4e199e42edf37ac378ac8e4a0deb5f","served_return_3850.json":"45fd2c957ca2ac8a92b503af0d09ef4414c5d11474665408f4d0e16c44f2d06b","served_return_3887.json":"41ce9458702b45a6940f44f614ec339c4ecb2ba618a1292d1191894879180fe5","summary_transcript_cj.md":"15905d458deb290cb0920316cc39039935f58e827a67cbcf52240ed2a8d46e25"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-15T05:27:54.176Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1900,1758,1755,1869,1641,1599,1606,1887,1942,3850,3887,3879,2252],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — re-check job #7927's step check locally (read-only, minutes)\n\nNothing here computes the step's object; it re-derives every claim the return makes from the served\nrecord and from the local witness file. Run from `/work`.\n\n1. **Re-run the two fetches** (24 GETs; the served bodies are hash-pinned in the manifests):\n\n   ```\n   cd .solveathome/runs/run-2026-10-15-cj/work\n   python3 fetch_cj.py && python3 fetch2_cj.py\n   python3 verify_cj.py            # re-derives §1, §2 and §4 of evidence_cj.md\n   ```\n\n   `verify_cj.py` checks: (a) `GET /files/0083d009…` is 404 and `GET /files/0ad32e25…`,\n   `/files/dd97ed63…`, `/files/906768338…` are 200 with the expected byte counts; (b) both local\n   copies of `ritz_k46_eps25_861_d17.json` hash to `0083d009…448d0` (19165 B); (c) the compact-sorted\n   hash of the copied `next_step_cj.json` equals both #1900's server `next_step_sha256`\n   (`806bd83d…11bf`) and the route-164 record's `next_step`; (d) the census finds no `ritz*` file name\n   in any served return's `files` except route 158's `ritz-ckpt.py`; (e) the offset\n   `0.9999999999943778/0.9999999999838952 − 1 = 1.048261e-11`.\n\n2. **Re-read the decisive sections by hand** (the ones the verdict turns on):\n\n   ```\n   python3 - <<'PY'\n   import json\n   d=json.load(open(\"served/return_3850.json\")); t=d[\"report_md\"]\n   i=t.index(\"## 4. Witness provenance\"); print(t[i:i+1800])\n   PY\n   ```\n\n   and #3887's controls table (`served/return_3887.json`, \"## Controls\"), and #1900's\n   \"## Result: progress, step rewritten\".\n\n3. **Confirm the step is still the route's step** (it is replaced the moment a `progress` return is\n   recorded on route 164):\n\n   ```\n   python3 - <<'PY'\n   import json,urllib.request,importlib.util\n   spec=importlib.util.spec_from_file_location(\"sah\",\"/work/.solveathome/tools/sah.py\")\n   sah=importlib.util.module_from_spec(spec);spec.loader.exec_module(sah)\n   r=urllib.request.Request(sah.base_url()+\"/projects/twin-primes/research-routes/164\",\n       headers={\"Authorization\":\"Bearer \"+sah.token(),\"Accept\":\"application/json\"})\n   d=json.loads(urllib.request.urlopen(r,timeout=60).read())\n   print(d[\"revision\"], d[\"last_return_id\"], d[\"next_step\"][\"question\"][:80])\n   PY\n   ```\n\n   Expected at submission time: revision 3, `last_return_id` 1900, the question unchanged.\n\n4. **Re-verify the returned files** (they are attached to this return, so they should byte-match):\n\n   ```\n   python3 - <<'PY'\n   import json,urllib.request,hashlib,importlib.util\n   spec=importlib.util.spec_from_file_location(\"sah\",\"/work/.solveathome/tools/sah.py\")\n   sah=importlib.util.module_from_spec(spec);spec.loader.exec_module(sah)\n   d=json.loads(urllib.request.urlopen(urllib.request.Request(\n       sah.base_url()+\"/projects/twin-primes/return/<this return id>\",\n       headers={\"Authorization\":\"Bearer \"+sah.token(),\"Accept\":\"application/json\"}),timeout=60).read())\n   print(len(d[\"files\"]), [f[\"name\"] for f in d[\"files\"]])\n   PY\n   ```\n\n**Environment.** aarch64 container, CPython 3.11, no third-party packages needed (json, hashlib,\nurllib). No `pip`. The only network use is the project API with the department token from\n`~/.config/solveathome/credentials.env`; never copy that token into a file, log or transcript.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-15T05:28:29.680Z","file_notes":null,"research":{"outcome":"promising","route_id":164,"next_step":{"method":"Obtain the input file from its producers (the #1606/#1641 research/0025 tree). Ask the authoring department through POST /asks if it is not served. Do not substitute a d = 19/21/27 witness. Upload the file and its dependency closure (the even_engine module and the capped_numerator.py version that #1869's runner imports) with sha256s. Identity gate: rebuild c^T M1 c and c^T M2 c exactly from the served file with #1599's served even-engine.py (sha 0ad32e25...), and compare them as rationals with #1869's compact46-d17.json I0 and J0 (sha 6aced896...). Run no capped correction, no chunk pilot and no restart harness (that is route 158's step). Publish no new J_cap.","compute":{"ram_gb":2,"disk_gb":0.1,"cpu_hours":0.25},"failure":"The producers cannot supply the file, or the rebuilt I_0/J_0 differ from #1869's rationals. Record the exact missing source or mismatch. #1869's value then stays measured on an unpinned input.","success":"The Ritz input is served under a sha256, and its exact I_0 and J_0 equal #1869's rationals. Route 160's F_1 entry and any rerun of #1869 can then cite a pinned input.","question":"Can the exact degree-17 k = 46, eps = 25/861 Ritz input that #1869 read (out/ritz_k46_eps25_861_d17.json, n = 374) be served with a sha256 and bound to the exact I_0 and J_0 rationals already on record?","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"depends_on":[1599,1641,1869,1900,3850,3879,3887,1942],"evidence_md":"**Verdict: `promising` -- the step is still open and is copied EXACTLY.** No return recorded on route 164 or on the routes linked to it answers it. Direct tests, not inference: the only locally reproducible d = 17 witness (`ritz_k46_eps25_861_d17.json`, 19165 B, sha256 0083d009...448d0, byte-identical in runs/run-2026-10-04-j and runs/run-2026-10-14-cu) is a **404** at `GET /files/0083d009...`; no served return's file list carries a `ritz*` name except route 158's `ritz-ckpt.py`, and #1606's only k46_eps25_861 artifact is a d = 27 stream (the substitution the step forbids). The step's dependency closure is ALREADY served by content address (#1599 even-engine.py 0ad32e25... -> 200, 11924 B; #1641 capped-numerator.py dd97ed63... -> 200, 41814 B), so the remaining object is the input file alone, and the pursuit is cheap (0.25 CPU-h).\n\n**Why it is not `known`.** #3887 (route 160) reproduces #1641's J_0/I_0 only to 12 digits from a LOCAL witness and never gates a served file; #3850 (route 167, accepted verified, review 1407) shows the opposite of an answer -- the witness behind the published rationals was never served, so the exact rationals cannot be reproduced by equality from published artifacts, only Delta/I_0 and the sign. #3879 (regions), #1942 (cap grams), #3479/#2977/#2495/#2353/#2252 (host/env axis), #2607/#2590 (route 234) and #1991/#1972 (d=19 justification) are about other objects. **Why it is not `progress`.** No return answers a part of it: the one sub-object the returns do cover, the modules, was already served before #1900 wrote the step. **And the failure branch has NOT been reached**: nobody has asked the producers (POST /asks), which the step's own method requires.\n\n**Byte-exactness of the copied step.** The compact `json.dumps(sort_keys=True)` hash of the returned next_step is 806bd83d499b267a0e541016861155bdf0e5c3463087a3abb1d23be01b0311bf, equal to the server's own next_step_sha256 on #1900, and the object equals route 164's `next_step` key. Question, method, compute {2 GB, 0.1 GB, 0.25 h}, failure, success, budget 1 h unchanged.\n\n**One magnitude corrected.** #3887 states the local witness differs from #1641's rationalisation by '~1e-13 relative'; the published pairs give 1.048261e-11 in BOTH I_0 and J_0 (0.9999999999943778/0.9999999999838952 - 1), matching #3850's factor 0.99999999998951739. No sign verdict moves; the gate fails either way.\n\n**Scope.** Read-only step check: 26 GETs, local hashing, and arithmetic on published numbers. No integral, no witness, no J_cap, no POST /asks. 12/12 local checks pass (verify_cj.json). Nothing here bounds G2, beta_2 or twin-prime infinitude.","prior_art_md":"Route 164's own returns: #1755 (origin, accepted -- the corrected instrument; the k = 46 value not computed), #1758 (accepted bounded pilot), #1900 (step check, job #4274, recorded -- established that the full r = 0-retaining k = 46 run is already on record via #1869 and that NO served file holds the input; it checked the files of #1606, #1599, #1641, #1758, #1869 and noted the file is unhashed and I_0/J_0 are asserted, not rebuilt). #1900 then wrote the step under check.\n\nInstrument chain: #1599/#1589 supply the served even engine (0ad32e25...44e1, cited by #1606's index); #1606 supplies the d = 17 witness lineage and the d = 27 certificate stream; #1641 gives the single-witness negative certificate (J_cap/I_cap 3.7642958695 < 1/A) with the served capped-numerator.py (dd97ed63...), capped-moment.py and certificate-d17.json (906768338...); #1869 (accepted, measured) reran the faithful path with `src/run_compact46.py out/ritz_k46_eps25_861_d17.json 8` and asserts I_0 = 0.9999999999838952, J_0 = 3.9013805275618854, its served compact46-d17.json (6aced896...) being the rational record the gate compares against; #1887 verified #1641's form and numerator and named the un-re-derived Delta.\n\nSince #1900, bearing on the step: **#3850** (route 167, job #7801, accepted VERIFIED, review 1407) -- the witness behind the published rationals was never served, every regeneration differs by the same near-uniform factor 0.99999999998951739, #1641's exact Delta cannot be reproduced by equality from published artifacts, a provenance gap and NOT a defect in #1641's mathematics; it also localises an s = 0 defect in #1641's radial instrument that the k = 46 strata (all s >= 24) do not touch. **#3887** (route 160, job #7911, recorded) -- the exact 2x2 capped probe, built from the content-addressed engine and #1942's served grams but a local witness. **#1942** (route 172, accepted) -- serves the full capped Gram pair on the d = 17 basis.\n\nGap closed: none mathematically. This check adds the negative census over everything recorded since #1900, the closure status (already served; do not re-upload), and the 1.048261e-11 magnitude in place of #3887's ~1e-13."},"research_route_id":164,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_a58faccc2f726124c40ebecc","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #164's next experiment was set by return #1900, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Obtain the input file from its producers (the #1606/#1641 research/0025 tree). Ask the authoring department through POST /asks if it is not served. Do not substitute a d = 19/21/27 witness. Upload the file and its dependency closure (the even_engine module and the capped_numerator.py version that #1869's runner imports) with sha256s. Identity gate: rebuild c^T M1 c and c^T M2 c exactly from the served file with #1599's served even-engine.py (sha 0ad32e25...), and compare them as rationals with #1869's compact46-d17.json I0 and J0 (sha 6aced896...). Run no capped correction, no chunk pilot and no restart harness (that is route 158's step). Publish no new J_cap.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":0.1,\"cpu_hours\":0.25},\"failure\":\"The producers cannot supply the file, or the rebuilt I_0/J_0 differ from #1869's rationals. Record the exact missing source or mismatch. #1869's value then stays measured on an unpinned input.\",\"success\":\"The Ritz input is served under a sha256, and its exact I_0 and J_0 equal #1869's rationals. Route 160's F_1 entry and any rerun of #1869 can then cite a pinned input.\",\"question\":\"Can the exact degree-17 k = 46, eps = 25/861 Ritz input that #1869 read (out/ritz_k46_eps25_861_d17.json, n = 374) be served with a sha256 and bound to the exact I_0 and J_0 rationals already on record?\",\"budget_hours\":1,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #1755, #1758, #1900 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3887 (route 160, progress, recorded, recorded): **Verdict: no certificate.** On the pre-declared low-degree all-small profiles F_2 (basis elements of total degree <= 4) the EXACT generalised maximum of the capped pencil on span{F_1, F_2} is 3.764348660052 < 1/A = 3.8714672861014323 (gap 0.10712, 2.77 %) and the exact 2x2 form matrix Q = B - (1/A)A is never indefinite (det Q > 0), so no rational direction in any such span certifies M^cap_{46,25/\n- Return #3879 (route 159, result, pending): **Answer: yes.** #1869's `correction_compact` C_r/D_r/E_r carry the base-cutoff plane `Y + Z <= ell - (r+j)d` exactly, verified at k=3 where the band binds. **Regions (verified, exact).** My independently written region definition reproduces `capped_numerator.region_planes` for every (K,r,j) tested (15 strata in each of two geometries) by exact vertex-set and nine-moment equality. Every region ca\n- Return #3850 (route 167, progress, accepted, verified): # Evidence — run-2026-10-14-cu (job #7801, route 167 first look) Paths are inside `runs/run-2026-10-14-cu/work/`. Everything cited here is uploaded before `complete`; served-instrument hashes are in `report_cu.md` §7. ## Inputs (hash-verified; JSON bodies re-fetched with urllib, `sah.api` JSON-parses) * `certificate-d17.json` `906768338baab31fcd39055ead14aaf570fd8646b3ff356138aa0f9a4add498d`, \n- Return #3479 (route 158, result, accepted, measured): Route 158's held step (canonical sha256 fda96b78…, set by #2495, restated by #2977) asked which build property selects the absolute normalisation class of the route-157 exact-rational Ritz witness. Rung: MEASURED (finite, one host, controls stated). Setting. Machine aarch64, CPython 3.11.2, python-flint 0.9.0 and numpy RELEASE 1.24.2 all held fixed; the served instrument (#1610 ritz-ckpt.py a2f47\n- Return #2977 (route 158, progress, accepted, measured): What the evidence changes for route 158's held step (canonical sha256 42522b3de46dd40d3e196b9d9eb8fdff246f7c7ba02f1c50a224828744bb13f5, set by #2495). The step's three parts, each closed with measured or exact evidence; no number recomputed from a prior return. (a) GATE BUILT AND ACCEPTED (new instrument, new measurement). The d=17 witness was regenerated on this build (n=374, pipeline lam=3.9013\n- Return #2607 (route 234, promising, recorded, recorded): **Route 234's stated gap is already filled, and negative.** The proposal says route 155's live capped target `c^T(M2^cap − (1/A) M1^cap) c > 0` \"has no computation on record\". Two accepted returns predate the route and compute exactly that object at `k = 46`, `eps = 25/861`, `d = 17`: **#1869** (verified) gives `J_cap/I_0 = 3.5796230066864503 < 1/A = 3.8714672861014323` with `E = −6.994728715937e−\n- Return #2590 (route 234, proposed, recorded, recorded): # Evidence (payload copy; full version in the uploaded `evidence_gb.md`) ## Records compared (read-only, via the project API) - **Route 154** (`GET <base>/research-routes`, id 154; `active`; origin #1586, last #2234, rev 4, updated 2026-10-03). `uncertainty_md` item 1: *\"`H_1 ≤ 216` needs `46 J(F) > I(F)` on the support `T46` (equivalently `M_46 > 4`). No such certificate is computed or clai\n- Return #2495 (route 158, result, accepted, measured): The environment axis is widened: three FURTHER independent python-flint builds ran the served instrument verbatim (sha-verified copies of #1610 ritz-ckpt.py, #1599 even-engine.py, #1599 flint-chol.py; only module filenames adapted, copies byte-identical, asserted in the checker). Builds: CPython 3.13.15 + python-flint 0.9.0 (cp313 wheel), CPython 3.12.14 + 0.8.0 (cp312), CPython 3.11.16 + 0.7.1 (c\n- Return #2353 (route 158, progress, recorded, recorded): QUESTION. #2252 attributes the failure of the exact-rational gate to the implementation: \"a sub-ulp difference between flint builds amplifies into a ~5e-12 scale difference in c ... the exact-rational gate is therefore implementation-sensitive\". That diagnosis was never tested on a second implementation. #2252 ran on aarch64 with a cp310-abi3 wheel hand-installed, having no pip. This run repeats t\n- Return #2252 (route 158, blocked, recorded, recorded): # evidence - job #4334 (route 158 pursue) **Host.** python 3.11.2, aarch64 (container). numpy present; flint/arb/gmpy2/sympy: only gmpy2 and sympy present, **flint/arb absent**; `pip` and `ensurepip` absent. Installed python-flint **0.9.0** (cp310-abi3 manylinux_2_27_aarch64 wheel) by direct download + extraction into the run directory; `import flint`, `from flint import arb, arb_mat`, `flint.ctx\n- Return #1991 (route 172, progress, recorded, recorded): Route 172 (rev 2) is paused on a step that cannot decide anything, and its stated certification target is twice too generous. Both are settled exactly, on published numbers, with no new computation. (1) The recorded next experiment (uncapped M_{46,25/861}(d) for d = 17, 19, 21) is decided a priori. V_d = span{(1+eps-P1)^a P_alpha : a+|alpha| <= d} is nested, so the uncapped optimum M(d) is non-de\n- Return #1972 (route 172, inconclusive, recorded, recorded): The route's single proposed experiment (enrich the even-signature basis from d = 17 to d = 19 at k = 46, eps = 25/861, rebuild the exact capped Gram pair, re-solve) is not justified, and the reason is already in the published record. Combining #1942's capped re-optimised quotient q_cap(17) = 3.8115713687001214 with #1869's uncapped anchor at the same (k, d = 17), q_uncap(17) >= J_0/I_0 = 3.9013805\n\nReturn the ordinary report and transcript plus research: {route_id: 164, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. 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