{"id":6913,"job_id":13667,"problem_id":1,"lane_id":32,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job #13667 - route #207 step check: the Hcross estimate is still open; every post-setter return that mentions it is a screening or a different object\n\n**Outcome: `promising`, the step copied byte-exactly** (canonical sha256 `ac3080bc986b9a42665efb86f0c5a7de895ef3b3cdacd63ea52f3101e285e05f`). Route 207 is active at revision 15 with `last_return_id` 5789 and `updated_at` equal to #5789's `created_at`, so nothing has been written to the route since the step was set. Sweeping every return id from 5790 to 6940 served 810 records (341 absent, 0 throttled) and found **no route-207 return at all**; twelve records carry one of the step's tokens, five carry `Hcross`, and every one of them is either an applicability screening that says the block stays open or work on a different object.\n\nRead-only comparison; no experiment run, no computation reproduced, `cpu_hours 0`. `check_r207.py`: 12/12 gates, exit 0; four planted faults each name their own FAIL and exit 1.\n\n## 1. Step identity and route state\n\nThe brief's step block and the served `route 207.next_step` are one object, and its canonical sha256 equals #5789's `research.next_step` three ways (S01-S02). Setter context: #5789 (job 11734, route 207, `result`, accepted) proved `||H1_nonunit|| + ||H2_nonunit|| << x^(27/20)` for all 31 nonunit divisors `D | c` in #5571's five-prime family, which pays the `A T c x^(-1/100)` target there with `delta = 1/25`, and states in the same paragraph: \"Hcross, general moduli, the full restricted operator and the global theorem remain open\" (S10). It then set exactly this step as the remainder.\n\n## 2. What the step asks, and its inherited warnings\n\nThe question is whether the cross-coordinate block of `G = K*K`, `K(t,(a,b)) = S(t, theta(a e2 - b e1); c)`, satisfies `||Hcross|| <<_A T c x^(-1/100-delta)` for fixed `delta > 0`, on the actual full interval `I`, uniformly over every admitted harmonic subset `P` of `H x H`. Two constraints come from the predecessors and are preserved verbatim in the copied step: use #5540 §5's exact support (`a != a'` and `b != b'`, Hcross containing precisely the pairs differing in both coordinates, with the three supports disjoint and all four matrices Hermitian), and **do not** use the newly paid coordinate-collision blocks as a bound on Hcross. #5540 is explicit that its own price is an upper-bound price and not a lower bound, and that \"Hcross still needs its own estimate\" (S10) - so #5789's new `x^(27/20)` bound for H1/H2 buys nothing here, which is why the step forbids the shortcut.\n\n## 3. The record after the setter\n\nDirect probing of 5790..6940 (S05) found the route untouched (S06). The five `Hcross` carriers, all read:\n\n- **#5849** (job 11849, route 337, `promising`): a step check on route 337; Hcross appears only as part of route 337's own remainder list. Not an estimate.\n- **#5856** (job 11844, no research route): applicability screening of #5784. It restates #5784's scope and closes with \"cross-coordinate terms, H2, Hcross and the global theorem stay open\" (S08).\n- **#5859** (job 9791, route 337, `blocked`): the R-COR four-way off-diagonal partition on a different kernel (`e`-pair completed kernel); not the five-prime family's `Hcross`.\n- **#5860** (job 11851, no research route): applicability screening of #5789, which lists the 31 divisors, the CRT stratum identity, the Ramanujan weights and the `q`, `dq` and `a = d` bindings, then states \"Hcross, general moduli, the full operator and the global theorem stay open\" (S08). Its summary says the remaining piece is Hcross \"which the source names as its next experiment\".\n- **#5907** (job 11960, `upkeep`, no research route): trusted lane summary version 36, which records #5789 as folded and adds \"route 207's `Hcross` question is now the lane's first open item\" (S09).\n\nThe three comparisons named in the brief (#6701 route 395, #6149 route 287, #6080 route 395) contain none of the step's tokens (S11): they are ordinary step checks on other routes, and an unchanged-step comparison there is not evidence about this step.\n\nSo the record contains no proof, no partial saving and no counterexample for `Hcross`: the five mentions are two screenings asserting it is open, one lane summary naming it the first open item, and two returns about different objects. Under the step-check contract that is `promising` with the step unchanged.\n\n## 4. What would move it, stated so the next worker inherits the real obstacle\n\nThe step is a source-and-algebra obligation with no numeric content, and the two candidates it names are (i) #5540 §5's exact two-coordinate support and (ii) #5784's common-prime Gram comparison plus #5789's weight classification (`D = d^i q^j f`, the 31-divisor partition, Ramanujan weights `c_D(r)`, the PSD per-stratum trace bound). The obstruction that must be faced is that the common-prime method in #5784 works when a reduced prime factor is independent of the harmonic column; on `Hcross` both coordinates vary, so the column and the modulus move together, and the `H1`/`H2` bookkeeping (a single spike at `a = d`, one coordinate fixed) has no direct analogue. A proof must therefore either exhibit a degeneracy that reduces part of `Hcross` to a paid configuration before any Gram estimate - which is what \"separate genuine local degeneracies\" in the copied method asks - or produce the correlation input for genuinely two-coordinate pairs.\n\n## 5. Limits\n\n- Token screening is lexical: a return that proved an `Hcross` bound without the word would be missed. The five hits were read in full at the relevant sections, and the sweeping statement here is bounded by ids 5790..6940.\n- 341 ids in the probed range are absent (404); a return there is unread, not shown irrelevant. Nothing was probed outside that range, and no listing endpoint exists (`/returns` is 404), so coverage is by id only.\n- I did not re-derive #5789's `x^(27/20)` or #5784's `x^(269/200) log x`; they enter as the setter's own accepted statements, and the step forbids using them for `Hcross` anyway.","patch":null,"cpu_hours":0,"hashes":{"check_r207.py":"2036dd5ffd8c8ebfd70369df53cf52ad7e6807ceb4d2e14469bd9dae8c3583c3","r207_gates.out":"aa3f005c076e33008e83369e765a5798dd4e0e74232df36d94f9bc0b00c62b12","r207_step.json":"9a55e7f1eeec0044007071c14c09b644bbf1b65bc69b9152b673ef86938797eb","r207_sweep.jsonl":"3991415d849677a8b7b4c48b63e9dd9fb68cac94cced69ce030def4fee55e28a","r207_gates.sweep.out":"be18d0fa484344c09c0680d23c5230d9a7b0b2728319cf7ee19deceb80045679","r207_gates.stepsha.out":"5720f1a4da6e2c8d3bed58289ff8e2970f67c4b3c5ff5cd5805b5778568aac56"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T20:10:08.008Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5789,5540,5571,5784,5856,5860,5907,5849],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"Freebuff Desktop 0.0.198 keeps no per-turn token record for this session on this machine: the project database's messages table has 0 rows and the bound thread's harness_state carries only a cloud thr","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Verification recipe\n\nStandard library only; no network in the checker.\n1. Place under `state/work/r207/`: `route207.json`, `step.json` (the brief's step block), `return_5789.json`, `return_5540.json`, `return_5856.json`, `return_5860.json`, `return_5907.json`, `return_6701.json`, `return_6149.json`, `return_6080.json`, `sweep.jsonl`.\n2. `python check_r207.py` -> 12/12 PASS, exit 0, identical to `check_r207.out`.\n3. `python check_r207.py --corrupt stepsha|routemoved|sweep|carriers` -> each names its own FAIL and exits 1 (`stepsha` and `sweep` uploaded).\n4. Re-derive the sha: canonical JSON, sorted keys, separators (',',':'), ensure_ascii=False, sha256 -> ac3080bc...\n5. Reproduce the screen: probe ids 5790..6940 against `/return/<id>` and filter on the three tokens (about 3 min, 8 threads).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":207,"next_step":{"method":"Use5540Section5's exact Hcross support a!=a' and b!=b'. Retain all t rows, the actual interval and harmonic subset P. Separate genuine local degeneracies before any Gram or Fourier estimate; test whether the common-prime method of5784 and this return's weight classification helps the two-coordinate correlations. Do not use the newly paid coordinate-collision blocks as a bound on Hcross. No numerical experiment.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0},"failure":"Identify an exact remaining correlation term or violated source hypothesis; a failed upper-bound method is not a lower bound, counterexample or route closure.","success":"Prove the displayed Hcross estimate uniformly within this five-prime family, with any coefficient or coprimality hypotheses explicit and compatible with the actual matrix.","question":"In this same five-prime family and every admitted P subset H x H, does the cross-coordinate part Hcross of G=K* K, K(t,(a,b))=S(t,theta(a e2-b e1);c), satisfy ||Hcross|| <<A T c x^(-1/100-delta) for some fixed delta>0, on the actual full interval I?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[5789,5540,5784,5856,5860],"evidence_md":"Route 207's step (set by #5789, canonical sha256 ac3080bc986b9a42665efb86f0c5a7de895ef3b3cdacd63ea52f3101e285e05f, identical in the brief, the served route and #5789.research.next_step) is still open, so it is copied unchanged. Route 207 is active at revision 15 with last_return_id 5789 and updated_at equal to #5789.created_at, so no route-207 return follows the setter. An exhaustive id probe of 5790..6940 served 810 records (341 absent, 0 throttled) with no route-207 return; twelve carry a step token and five carry Hcross, and all five were read: #5856 (applicability screening of #5784) and #5860 (applicability screening of #5789) both state that Hcross, the general moduli, the full operator and the global theorem stay open; #5907 (lane upkeep v36) records route 207's Hcross as the lane's first open item; #5849 is a route-337 step check and #5859 is route 337's R-COR work on a different completed-pair kernel. The brief's three comparisons (#6701, #6149, #6080) carry no step token. #5789 pays all 31 nonunit coordinate-collision strata at x^(27/20) (delta = 1/25) and explicitly leaves Hcross open; #5540 section 5 fixes Hcross's exact support (a != a', b != b', disjoint from H1/H2, all Hermitian) and warns that its coordinate-collision price is an upper-bound price, not a lower bound - which is why the step forbids using those blocks. No proof, partial saving or counterexample for Hcross is on record. Boundaries: lexical token screening over ids 5790..6940 only, 341 unserved ids unread, no recomputation of the predecessors' exponents."},"research_route_id":207,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"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":"maxime-fleury","job_brief":"Step check before pursuit. Route #207's next experiment was set by return #5789, 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\":\"Use5540Section5's exact Hcross support a!=a' and b!=b'. Retain all t rows, the actual interval and harmonic subset P. Separate genuine local degeneracies before any Gram or Fourier estimate; test whether the common-prime method of5784 and this return's weight classification helps the two-coordinate correlations. Do not use the newly paid coordinate-collision blocks as a bound on Hcross. No numerical experiment.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Identify an exact remaining correlation term or violated source hypothesis; a failed upper-bound method is not a lower bound, counterexample or route closure.\",\"success\":\"Prove the displayed Hcross estimate uniformly within this five-prime family, with any coefficient or coprimality hypotheses explicit and compatible with the actual matrix.\",\"question\":\"In this same five-prime family and every admitted P subset H x H, does the cross-coordinate part Hcross of G=K* K, K(t,(a,b))=S(t,theta(a e2-b e1);c), satisfy ||Hcross|| <<A T c x^(-1/100-delta) for some fixed delta>0, on the actual full interval I?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2455, #2458, #2538, #2539, #3261, #3289, #3304, #4837, #4861, #5519, #5540, #5552, #5571, #5784, #5789 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6701 (route 395, promising, recorded, recorded): # Evidence - job #13360 (route 395 step check, outcome `promising`) Read-only; no experiment run; no K(m) evaluated; the only recomputation is slope arithmetic on #5880's served JSON (as #6080 did). **Custody.** Route 395 active, rev 3, `last_return_id` **6080**, `updated_at` = #6080.created_at (2026-10-26T17:33:48.314Z); served `next_step` canonical sha256 `103b164ab7597f49c6a21f50fcb1c56b68e71d\n- Return #6149 (route 287, result, accepted, measured): What the evidence changes for route 287, and its exact scope. 1. The obligated band shape is answered for `chi_w`. Step's success clause: \"min_w chi_w >= x^(7/400) at every band rung with the minimum at T = c/M\". Measured at x = 1e8, M = 30199, c in [25,902,002, 39,810,717] (c/M in 862-1304), full two-cosine weight, r = 1: min_w chi_w = 8.2868, 9.3636, 9.2742 (omega 2), 9.2981 (omega 3), 12.9550 \n- Return #6080 (route 395, progress, recorded, recorded): # Evidence — job #12234 (route 395 step check, outcome `progress`) Read-only; no experiment run. Every number is a served field, a re-hashed artifact, or arithmetic on published values (`stepcheck_u2.py` -> `stepcheck_u2.json` + `.out`, exit 0). **Custody.** Route 395 `active`, rev **2**, `last_return_id` **5880**, `updated_at` = `#5880.created_at` (`2026-10-25T16:13:40.858Z`); served `next_step\n- Return #5914 (route 270, progress, recorded, recorded): # Evidence — job #10091, route 270 (inline digest; full files attached) **Instrument.** `route270_ext.py` imports `route270_ek.py` verbatim (sha256 `cedbe6c1cfb83a109224f4a15e77e9c0189b60da6e764ecae5272abe488e7e98`, the attachment of #5103) and adds sections G (gates), T (obligation (ii)), E (census to 4000), F (family to p=499), H (fits, crossing, clause). Reference copies of #5103's own `p2_m1_\n- Return #5880 (route 395, promising, recorded, recorded): ### Decisive Experimental & Algebraic Evidence (`src_m_11890.py`) 1. **Exact Anchor & Identity Verification (`Gates V1, V2, V4`)**: - Reproduces all 13 `#5863` published $|\\sum_m K|/M_{\\text{dist}}$ values to $\\le 3.94\\times 10^{-4}$ relative error, all 4 `#5859` published $\\operatorname{mean}_m |K(m)|^2$ values to $2.07\\times 10^{-16}$, and verifies the closed-form geometric-series evaluator \n- Return #5865 (route 395, proposed, recorded, recorded): ### 1. Validation (before any new number) Re-implementation of #5863's kernel reproduces its 13 published |sum_m K|/Mdist values, 13/13 within 5e-3 relative. Pair-space identity `sum_m K = 1^T M 1`, M_{h,h'} = sum_m u_h v_{h'} with u_h = a_h e_c(2 l2 h mbar), v_h = b_h e_c(-2 l1 h mbar): relative error <= 8.7e-15 on 17 points. All 9 probe rungs are in the binding regime Mdist > sqrt(c); the pair k\n- Return #5863 (route 337, progress, recorded, recorded): ### 1. Ledger audit of `#5859` (exact rational, reproduces its table) The transfer table is generated by `moment = per-class + E^2 - A^2 + Q` and `block = (moment + M + Q)/2` with `M=14/25, Q=1/20, E=9/20, A=3/50, c=19/20, T=c-M=39/100`. It reproduces `407/400` (per-class `A^2*sqrt(c)=119/200`), `424/400` (`M*A^2=17/25`), `412/400` (`M*A=31/50`), `407/400` (unit diagonal) and `463/400` (unit-pair\n- Return #5859 (route 337, blocked, recorded, recorded): ### 1. Exact Four-Way Partition & Extended Scale Probe (`|H|=4..64`, Tasks 1 & 4) - **Anchor reproduction (`C1`):** `derive_9791.py` reproduces `#4880`'s 4 corpus blocks (`B2=4.842074789, B3=5.487934900, B6=3.822041417, B7=3.949777717`) and probe values `|H|=4..16` (`4.470373, 3.620510, 6.476353, 2.810555, 4.728646`) to `1e-9`. - **Extended probe (`|H|=24, 32, 48, 64`):** Extending `#4880`'s `2M <\n- Return #5823 (route 335, progress, recorded, recorded): ### Evidence — job #11807 (route 335) All arithmetic is exact (`fractions.Fraction`) or a checked float against a published digit; no experiment was re-run and nothing was measured. Instrument: `check_11807.py --served served` (15/15 gates, exit 0, ~0.05 s), outputs `check_11807.out` and `check_11807.json`, which carries the `report_sha256` of every return read so a reviewer can re-fetch and comp\n\nReturn the ordinary report and transcript plus research: {route_id: 207, 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. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"5540","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5784","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5789","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"5856","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5860","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":6927,"handle":"maxime-fleury","status":"recorded"},{"id":6932,"handle":"maxime-fleury","status":"recorded"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/207","transcript_url":"/projects/twin-primes/return/6913/transcript","files":[{"sha256":"2036dd5ffd8c8ebfd70369df53cf52ad7e6807ceb4d2e14469bd9dae8c3583c3","name":"check_r207.py","bytes":4934},{"sha256":"aa3f005c076e33008e83369e765a5798dd4e0e74232df36d94f9bc0b00c62b12","name":"r207_gates.out","bytes":990},{"sha256":"5720f1a4da6e2c8d3bed58289ff8e2970f67c4b3c5ff5cd5805b5778568aac56","name":"r207_gates.stepsha.out","bytes":1113},{"sha256":"be18d0fa484344c09c0680d23c5230d9a7b0b2728319cf7ee19deceb80045679","name":"r207_gates.sweep.out","bytes":1093},{"sha256":"9a55e7f1eeec0044007071c14c09b644bbf1b65bc69b9152b673ef86938797eb","name":"r207_step.json","bytes":1192},{"sha256":"3991415d849677a8b7b4c48b63e9dd9fb68cac94cced69ce030def4fee55e28a","name":"r207_sweep.jsonl","bytes":96350}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"45ddc0f99138076f56cf8a4e775416bef00d7d80bd93b8d99a9928ad2d0137be","next_step_sha256":"ac3080bc986b9a42665efb86f0c5a7de895ef3b3cdacd63ea52f3101e285e05f","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}