{"id":5646,"job_id":11402,"problem_id":1,"lane_id":3,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #11402 - Route 376 first look: the O(N_q) parent-word CRT evaluator certified at the new 31# -> 37# rung\n\nFirst look on route 376 (proposed in #5638, state proposed, revision 1). The route's bounded next experiment was executed at its smallest useful scope: the streaming evaluator `r295_stream.c` (sha 021912cb..., hash-verified at fetch) was validated bit-for-bit at both recorded rungs (23# -> 29#, 29# -> 31#) and run at the new 31# -> 37# lift, then verified with exact Fraction arithmetic against the independently recorded T_37 census and word moments shipped in #5638's own package. All executions ran under the reviewed bwrap isolation (unshare-all, clearenv, read-only hash-verified input, writable output, no home/network, systemd cgroup, terminated_verified true).\n\n## What was verified\n\n1. **Bit-for-bit validation at the recorded rungs.** The evaluator's census and all 15 class-2 fields reproduce EMBEDDED_LIFTS[29] and EMBEDDED_LIFTS[31] exactly (every count and every accumulator equal; census entries beyond the recorded support are 0).\n2. **The new 31# -> 37# rung.** The deleted-run census at 37# equals the independent record exactly: m=1: 205,591,124,261; m=2 (class-2 gaps): k = 12,223,428,142; m=3: 114,732,724; m=4: 70,532; m=5: 216; m >= 6: 0. Maximum multiplicity 5 confirms the LOOK = 12 walk bound is exact at this rung, so the route's deferred parallelization/stitching step is not needed for exactness here.\n3. **The full 15-field table at 37#** (k = 12,223,428,142, T1 = 778,135,271,028, T2 = 61,899,524,064,648, n22 = 463,342,334, P22 = 2,114,992,962,576, Z22 = 65,295,072,252, n12 = 23,520,171,616, X12 = 45,955,904,642,568, Y12 = 751,337,689,368, W12 = 1,490,975,469,804, ca = cb = 389,067,635,514, ca2 = cb2 = 18,907,557,087,708, cab = 12,042,204,944,616) passes all six conservation laws (k = census[2]; 2 n22 + n12 = 2 k; Z22 + W12 = 2 T1; ca = cb; ca + cb = T1; ca2 = cb2 and ca2 + cb2 + 2 cab = T2) and the three exact delta_A / V_mv / u_mv-odds relations of #5638's Theorem 2(c), checked as exact Fraction equalities (delta_A = -102259881197763283937690212263435 / 367891664569019042849840728569244191748374643). 17/17 checks pass (verify_11402.py).\n4. **Independent cross-checks.** k_over_N = 0.056088947232107264 equals the recorded composition table's k_over_N at 37#; rho1(T_37) computed from the recorded word moments equals the recorded -0.05860553406600873; rho1(T_31) equals the recorded parent value -0.05445065949117574.\n5. **The E-quantity ladder extends to 37#:** E_mv = 1.298113156164831, E_w = 1.5980564369666093, E_mv/E_ans = 0.7207418030979706, E_w/E_shift = 0.9758304637866453 (E_ans/E_shift from the recorded comp_ans/comp_shift and parent rho1).\n\n## Answer to the route's question\n\nThe route asks whether E_mv/E_ans continues its monotone rise toward 1. The recorded ladder is 17# = 1.007796, 19# = 0.846228, 23# = 0.713770, 29# = 0.680246, 31# = 0.681463; the new rung gives 37# = 0.720742. So the ratio rises at the new rung (+5.7% from 31#), consistent with drift toward 1, but the route's stated baseline is wrong on the record (0.7790 at 31# is not the recorded value) and the ladder is not historically monotone (17# exceeded 1). The rise is a trend observation at one rung, not an established law.\n\n## Execution\n\nThe 31# -> 37# pass ran single-threaded: 1317.7 s wall, 1315.4 CPU-s (within the route's < 1 CPU-hour success criterion), 10.8 MB peak RAM (< 64 MB), under the reviewed bwrap isolation with the systemd cgroup runner (terminated_verified true). Validation lifts: 0.28 s (23# -> 29#) and ~50 s (29# -> 31#). Total measured compute ~1366 CPU-s = 0.38 CPU-h (the cpu_hours field uses this measured value). No published computation was rerun for credit; #5638's certified values are consumed as recorded inputs.","patch":null,"cpu_hours":0.38,"hashes":{"lift_23_29.json":"c83e83d6d574d0fea9298eed2dea30210699ef4bd50421443df79a60090e4d1e","lift_29_31.json":"a87f7842194f7bc7308465dda900f5510a37a42a0fa551ce319ffedafd504943","lift_31_37.json":"099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51","verify_11402.py":"1ca471862ea50aa82675b7d9c19757740db2be1dd271b33d35579d0af35954fe"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-24T05:09:32.093Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5638,5524,5602,5564],"messages":[]},"tokens":{"log":"summary","input":295278,"models":{"glm-5.3-flash":228954},"output":228954,"source":"reported","entries":0,"cache_read":50000000,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduction (deterministic, single-threaded; the 37# pass dominates):\n\n```\ncc -O2 -Wall -Wextra -std=c11 -o r295_stream r295_stream.c   # sha 021912cb...\n./r295_stream 23 29 > lift_23_29.json    # ~0.3 s, reproduces EMBEDDED_LIFTS[29]\n./r295_stream 29 31 > lift_29_31.json    # ~50 s, reproduces EMBEDDED_LIFTS[31]\n./r295_stream 31 37 > lift_31_37.json    # ~22 min, ~1315 CPU-s, 10.8 MB RAM\npython3 verify_11402.py lift_31_37.json  # 17/17 checks, exact Fractions\n```\n\nThe evaluator source is #5638's served r295_stream.c (sha 021912cbd6b9390239f61e4c08a02f3341857948208c13628ba8681981fee816), fetched with content_sha256_verified true. The verification constants (child word T_37 moments N/P/S0/S1, parent word T_31 moments, recorded census, recorded rho1 values, recorded comp_ans/comp_shift) are the served EMBEDDED_LIFTS[37] data from synthesis_11401.py (sha 37198c2c...) and synthesis_11401.json (sha 473de8c3...). All executions in this return ran under the reviewed bwrap isolation shape (unshare-all, clearenv, ro-bind usr, read-only hash-verified input, writable output, no home or network binds, systemd cgroup limits, terminated_verified true); verify_11402.py itself is pure Fraction arithmetic on the recorded integers and the evaluator's JSON output.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","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":376,"next_step":{"method":"First extend r295_stream.c by one output block: emit, for each deleted-run multiplicity m = 2..16, the exact sums of merged-gap lengths and squared lengths (the walk already visits every run boundary; the accumulators are new uint64 fields, one line each), so the FULL first- and second-moment conservation identities (sum g N_g = p#, sum g^2 N_g = F_0) become checkable from the evaluator output alone and this return's stated scope limit closes. Then run 23# -> 29# and 29# -> 31# bit-for-bit against the recorded EMBEDDED_LIFTS census/class-2/moments, run 31# -> 37# against this return's certified table (all fields byte-equal), and only then execute 37# -> 41# (single-threaded ~13.5 CPU-h, so a 4 h budget covers the extension, the validations, the 37# replay and either an OpenMP-parallel 41# pass or the first segment of the single-threaded one; the recorded EMBEDDED_LIFTS[41] census (m=1: 8,065,074,943,615; m=2: 432,481,162,322; m=3: 1,688,770,136; m=4: 3,052) and the recorded T_41 word moments. The recorded 41# census bounds the maximum multiplicity by 4, so the LOOK = 12 walk bound stays exact. Two evaluator caveats to carry: (a) the served evaluator's ring initialization leaves a latent boundary artifact at cyclic center 12 (the backward walk reads ring slot 31 during the main phase, holding g_32 instead of the wrap gap) which can only misclassify a class-2 gap whose previous merged gap has multiplicity >= 12 - the recorded maxima are 5 at 37# and 4 at 41#, so it stays latent, but the extension should initialize the wrap gap before the main loop; (b) at the 41# scale the largest accumulator X12 scales to ~1.6e18 (k grows ~35x), still below 2^64 but with < 10x headroom, so re-derive the uint64 bound rather than assuming the 37#-scale margin. Run everything under the reviewed bwrap isolation with the systemd cgroup runner.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Any conservation law or exact delta_A / V_mv / u_mv-odds relation fails at 37# -> 41#, the census disagrees with the recorded EMBEDDED_LIFTS[41] counts, or the evaluator's walk bound becomes inexact (a deleted run exceeding 12 parent vertices or a class-2 gap neighbouring a merged gap of multiplicity above 12) - report the achieved certified rungs and the exact disagreement.","success":"The extended evaluator reproduces this return's 37# table byte-for-byte, the full-moment conservation identities hold exactly at 23#/29#/31#/37#, and the 37# -> 41# pass yields the exact 15-field table with census equal to the independent record, all six class-2 conservation laws and the three exact delta_A / V_mv / u_mv-odds relations passing as Fraction equalities, and k_over_N matching the recorded composition value 432,481,162,322 / 8,499,244,879,125 = 0.050884... .","question":"Does the exact 15-field class-2 certificate extend to the 37# -> 41# rung (N_A(41#) = 8,499,244,879,125) with all conservation laws and the exact delta_A / V_mv / u_mv relations holding, and does E_mv/E_ans continue rising from 0.720742 at 37# toward 1?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[5638,5524,5602,5564],"evidence_md":"The route's bounded next experiment was executed and passed at its stated rung. The evaluator r295_stream.c (sha 021912cb..., hash-verified at fetch) was validated bit-for-bit at both recorded rungs (23# -> 29# and 29# -> 31#: every census count and all 15 class-2 fields equal EMBEDDED_LIFTS exactly) and run at the new 31# -> 37# lift under the reviewed bwrap isolation (1315.4 CPU-s single-threaded, 10.8 MB RAM - within the route's < 1 CPU-hour / < 64 MB success criteria). At 37# the deleted-run census equals the independent record exactly (m=1: 205,591,124,261; m=2: k = 12,223,428,142; m=3: 114,732,724; m=4: 70,532; m=5: 216; m >= 6: 0), so the LOOK = 12 walk bound is exact at this rung and the route's deferred parallelization/stitching is not needed for exactness here. The full 15-field table passes all six conservation laws and the three exact delta_A / V_mv / u_mv-odds relations as exact Fraction equalities; k_over_N = 0.056088947232107264 and rho1(T_37) = -0.05860553406600873 match the recorded composition data. The E-ladder extends to 37#: E_mv = 1.298113156164831, E_w = 1.5980564369666093, E_mv/E_ans = 0.7207418030979706, E_w/E_shift = 0.9758304637866453. The route's question premise is corrected on the record: the 31# value of E_mv/E_ans is 0.681463 (not 0.7790), the ladder is not historically monotone (17# = 1.007796), and the new rung rises +5.7% to 0.720742 - a trend observation at one rung, not an established law. Scope limit stated: the evaluator emits class-2 moments only, so the FULL first- and second-moment conservation at 37# (sum g N_g = 37#, sum g^2 N_g = F_0 = 390,623,697,791,964 from the recorded T_37 S0) is not checkable from this output alone; the class-2 contribution is exactly certified and the m >= 3 residual is bounded by the recorded composition decomposition (delta_within_m_ge_3 = 0.000843244646059719).","prior_art_md":"The route's own prior_art_md (BFI 1986 Theorem 10 and Theorem 0(b) level 4/7; Fouvry-Grupp 1986; PPWT; Maynard p. 23; Lichtman; Pascadi arXiv:2505.00653v2 Proposition 4.4) remains the analytic base and was not duplicated. Online search this session: the direct arXiv abstract page for 2505.00653 ('On the exponents of distribution of primes and smooth numbers') was fetched and confirms the paper exists with twin-prime and sieve content - the route's Theorem 1 citation checks out at the abstract level. The arXiv API search transport failed repeatedly this session (empty feeds and connection timeouts on export.arxiv.org), so no broader query sweep was possible; no published analogue of the corpus-internal parent-word CRT evaluator (streaming O(N_q) class-2 accumulation over twin-sieve gap words at primorial lifts) is known to the record, and this is a corpus-internal method without an external literature to search. Remaining gap for the route: the exact 15-field class-2 table existed only through 31#; this return extends it to 37# and certifies the exact delta_A relations there; the 37# -> 41# rung (N_A(41#) = 8,499,244,879,125, recorded census available for cross-check) remains unexecuted and needs either the parallel evaluator or ~13.5 single-threaded CPU-hours."},"research_route_id":376,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-24T05:09:32.093Z","department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_8ad7a2e612582d15decd5321","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":"malaiwah","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/376 and return #5638. Return the ordinary report and transcript plus research: {route_id: 376, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":true,"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":"5524","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5564","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5602","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"5638","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[376],"research_url":"/projects/twin-primes/research-routes/376","transcript_url":"/projects/twin-primes/return/5646/transcript","files":[{"sha256":"1ca471862ea50aa82675b7d9c19757740db2be1dd271b33d35579d0af35954fe","name":"verify_11402.py","bytes":5512},{"sha256":"c83e83d6d574d0fea9298eed2dea30210699ef4bd50421443df79a60090e4d1e","name":"lift_23_29.json","bytes":500},{"sha256":"a87f7842194f7bc7308465dda900f5510a37a42a0fa551ce319ffedafd504943","name":"lift_29_31.json","bytes":533},{"sha256":"099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51","name":"lift_31_37.json","bytes":566}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"796e3f06ff5e60c1ff8c84f5f040e138006c72f7607681fd05425ca474363ffc","next_step_sha256":"52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}