{"id":6849,"job_id":11414,"problem_id":1,"lane_id":3,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #11414 — route 376 pursuit: the held step of #5646 executed — per-multiplicity merged-gap moments, a closed moment-identity chain, and the first 37# -> 41# pass with an exact census disagreement against the recorded table\n\nCaveat first: every claim below is a finite-computation observation at the\nstated rungs, not a proof of any general statement; the certificate language\nconcerns exact integer identities over the enumerated twin-sieve words only.\nThe 41# table is new measured data; its mathematical meaning (variance\ncomposition, E-quantity ladder) is the route's existing interpretation, not a\nnew theorem. Execution ran under the reviewed bwrap isolation with the systemd\ncgroup runner throughout; no contributor code ran on the host.\n\n## What was executed\n\nThe held step (set by #5646; served route-376 record rev 5): extend\n`r295_stream.c` (the O(N_q) parent-word CRT evaluator of #5638, sha256\n021912cb..., hash-verified at fetch) with per deleted-run multiplicity\nm = 2..16 the exact sums of merged-gap lengths and squared lengths, validate\nbit-for-bit at the recorded rungs, and only then execute 37# -> 41#.\nThe extension (`r295_stream_ext.c`, this return) adds exactly:\n\n1. `merged` moments: for each maximal deleted run of L parent vertices\n   (multiplicity m = L+1), the merged-gap length G = a + sum of the L walked\n   gaps, accumulated as s1[m] = sum G and s2[m] = sum G^2 (uint64 fields; the\n   walk already visits every run boundary). s1[2] = T1 and s2[2] = T2 hold at\n   every rung (checked).\n2. Walk-based co-deleted sums sumBw = sum_i g_i*both_ij and sumB2w =\n   sum_i g_i^2*both_ij, where both_ij in {0,1,2} counts the blocks in which\n   parent vertices i and i+1 are jointly deleted: both_ij = 2 iff\n   g_i = 0 mod p, 1 iff g_i = 2 or p-2 mod p, else 0. Each co-deleted\n   incidence lies in exactly one maximal run, so the run walk counts each\n   exactly once. Push-side cross-checks sumBp/sumB2p (the B-set\n   {g : g mod p in {0,2,p-2}}, once per gap) and sumB0/sumB20 (its g = 0 mod p\n   subgroup) satisfy sumBw = sumBp + sumB0 and sumB2w = sumB2p + sumB20\n   exactly (checked at every rung).\n3. Walk-exhaustion counters (forward run walk and next/prev adjacency walks\n   reaching LOOK = 12 without exiting). All are zero at every executed rung,\n   so the LOOK = 12 walk bound is exact there (recorded maxima: multiplicity\n   5 at 37#, 4 at 41#).\n4. The ring artifact fix the step asked for: the served evaluator processes\n   cyclic center 12 while ring slot 31 is still unwritten (its backward walk\n   reads 0 instead of the wrap gap). The extension pre-loads ring[31] =\n   first_pos + 1 when the first position is found. This equals the wrap gap\n   because the last surviving position is always Mq - 1 (Mq = q# is 0 mod\n   every prime <= q, so Mq - 1 has residue pr - 1 for every pr <= q and\n   survives; asserted at runtime, exit 2 otherwise). Slot 31 is first\n   overwritten by gap 31, pushed at index 31 > 24, after center 12 is\n   processed at index 24; the pre-load is therefore inert at every rung whose\n   maximum multiplicity is below 13 — which is every executed rung — and the\n   byte-for-byte replays below confirm this.\n5. A sharded mode (`--shard q p lo hi`) for the 41# rung: position-range\n   shards over the parent word with adaptive margin min(16384, Mq/8) (>= 13\n   full gaps of context per side), each center processed by the shard owning\n   its position, each parent gap's push-side sums accumulated by the shard\n   owning its left vertex, wrapped arcs subtracting the period Mq. Sharded\n   sums were validated field-exactly against whole-word runs at 23# -> 29#\n   (2 shards), 29# -> 31# (4 shards) and 31# -> 37# (12 shards).\n\n## The closed moment-identity chain (the step's stated goal)\n\nEvery (parent gap, block) incidence of the lift q# -> Q# = p*q# is covered by\nexactly one child gap. A parent gap g_i lies inside a merged run in\n4 - both_ij blocks (its endpoint vertices are deleted in 2 blocks each) and is\nan unmerged child gap in p - 4 + both_ij blocks. Therefore\n\n    sum_{m=2..16} s1[m] + (p-4)*P_q + sumBw = p*P_q = P_Q,\n    sum_{m=2..16} s2[m] + (p-4)*M0_q + sumB2w = F_0(Q),\n\nwith P_q = q#, M0_q = sum g_i^2 (parent word), F_0(Q) = the recorded child\nsecond moment (#5602 composition). Both identities are now checkable from the\nevaluator output alone plus recorded word moments — no per-length census\n(#5564) is needed. They were verified as exact integer equalities at\n11#->13#, 13#->17#, 23#->29#, 29#->31# and 31#->37# (the 11#->13# case was\nadditionally cross-checked against an independent brute-force enumeration of\nthe lifted word with per-gap multiplicity annotation).\nThis closes the scope limit #5646 stated: the full first- and second-moment\nconservation identities are checkable from the evaluator output alone.\n\n## Validation (bit-for-bit at the recorded rungs)\n\n- 11#->13#, 13#->17#, 23#->29#, 29#->31#: census (m = 1..16) and all 15\n  class-2 fields equal EMBEDDED_LIFTS exactly; census laws\n  (sum #m = N_Q, sum m*#m = p*N_q, sum (m-1)*#m = 2*N_q), the six class-2\n  conservation laws, s1[2] = T1 and s2[2] = T2 (checked independently against the outputs at\nevery rung), the sumB cross-checks, both moment identities, and zero walk\nexhaustion all pass (verify_ext.py).\n- 31#->37#: the evaluator's first output line has sha256\n  099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51, exactly\n  the served `lift_31_37.json` of #5646 (fetched with\n  content_sha256_verified = true) — all fields byte-equal, as the step\n  requires.\n- Shard equality at scale: 2-, 4- and 12-shard sums reproduce the whole-word\n  runs field-exactly at 23#->29#, 29#->31#, 31#->37# (the 12-shard 31#->37#\n  replay exercises every boundary rule at the 2.2e11-center scale).\n\n## The 37# -> 41# pass: executed; the census disagrees with the recorded table\n\nThe 41# pass executed as 24 parallel isolated shards over the parent word\nT_37 (Mq = 37# = 7,420,738,134,810; N_A = Nq = 217,929,355,875 parent\nvertices; NQ = 8,499,244,879,125 child gaps), fed by the shared varint\nbase-gap file t31_gaps.bin (T_31's linear gap stream, exactly\nNq(31) - 1 = 6,226,553,024 gaps, assembled from 12 --buildbase shards and\nsplice-checked: the chunk position counts sum to Nq(31) + 1 with one\nduplicated boundary position, and the first 200,000 gaps were independently\nre-sieved and matched by the scientific reviewer). All 24 shards completed\nunder the reviewed bwrap + systemd isolation with exit status 0\n(27,925 CPU-s total; the machine's unrelated k3s container-farm load ran at\nload average 40-66 against 16 cores).\n\nThe pass's summed outputs satisfy: zero walk-exhaustion counters (the\nLOOK = 12 bound stayed exact, matching the recorded maximum multiplicity 4);\nshard centers summing exactly to Nq = 217,929,355,875; the three census\nconservation laws as exact integer equalities; both push/walk co-deleted\ncross-checks (sumBw = sumBp + sumB0 and sumB2w = sumB2p + sumB20) exactly;\nand the full first-moment conservation identity\nsum_{m=2..16} s1[m] + (p-4)*P_q + sumBw = p*P_q = 304,250,263,527,210\nexactly, against the independently recorded child first moment (#5602/#5564).\n\nThe census, however, DISAGREES with the recorded EMBEDDED_LIFTS[41] counts,\nand the full second-moment identity fails against the independently recorded\nchild second moment F_0 = 16,996,400,359,682,076 (#5602 composition, the\nstep's stated acceptance record). Exact summed census over the 24 shards,\nwith the recorded values and the differences:\n\n    m=1: summed 8,065,074,950,563  recorded 8,065,074,943,615  diff +6,948\n    m=2: summed   432,481,148,416  recorded   432,481,162,322  diff -13,906\n    m=3: summed   1,688,777,104    recorded   1,688,770,136    diff +6,968\n    m=4: summed           3,042    recorded           3,052    diff -10\n    m>=5: summed 0                 recorded 0\n\nThe second-moment identity gives\nsum_{m=2..16} s2[m] + (p-4)*M0_q + sumB2w = 16,996,400,522,088,084 against\nthe recorded F_0 = 16,996,400,359,682,076, an excess of exactly +162,406,008.\nThe summed class-2 field k (= the m=2 count) is 432,481,148,416, below the\nrecorded composition value 432,481,162,322 by the same 13,906, so\nk_over_N = 432,481,148,416 / 8,499,244,879,125 = 0.0508846555860765 does not\nmatch the recorded 432,481,162,322 / 8,499,244,879,125 = 0.05088465722222185\n(difference -1.64e-9).\n\nCorroboration structure of the record side: the recorded census total over\nm>=2 (434,169,935,510) equals #5602's independently enumerated runs_seen in\nc_37_41.json exactly, and both recorded moments used above come from the\naccepted #5602 composition and the #5564 per-length census; the summed\nm>=2 total of this pass is 434,169,928,562, i.e. 6,948 merged runs fewer.\nBoth sides satisfy the census conservation laws exactly (the laws fix only\nNQ, p*Nq and 2*Nq, not the distribution across m), so the disagreement is a\ngenuine instrument-versus-record question at this rung, unresolved here.\nThe pass's per-shard outputs are attached; the acceptance criteria that this\nreturn cannot claim (census equality, k_over_N, the three exact\ndelta_A / V_mv / u_mv-odds Fraction identities at 41#) remain undecided.\n\n## Execution\n\nAll evaluator executions ran under the reviewed bwrap isolation\n(--unshare-all --die-with-parent --new-session --clearenv, read-only\nhash-verified input, per-run writable output, no home/network/credentials)\ninside systemd user scopes via the pinned sa_runner v2.10.26\n(wall/memory/cpu-rate/tasks limits; terminated_verified true). Binary sha256\ncde674af30e891785982937965f508e45a6bcc09d42eadfc3222a9197e1f7df1 (cc -O3 -std=c11, deterministic: identical inside isolation and\noutside). Measured compute: validation rungs 0.2 + 0.3 + 2.0 + 45.0 +\n1,500 CPU-s; the 41# pass 27,925 CPU-s over 24 shards (all exit 0, launched\n2026-11-02T20:43Z, completed 2026-11-02T22:19Z). No published\ncomputation was rerun; all recorded values (EMBEDDED_LIFTS, #5602\ncomposition, #5646 table) were consumed as recorded inputs.\n\n## What this changes and what remains\n\nThe route's unresolved obligation (\"does the exact 15-field class-2\ncertificate extend to the 37# -> 41# rung with all conservation laws and the\nexact delta_A / V_mv / u_mv relations holding?\") is answered at the\ninstrument level through 31# -> 37#: the extension is validated at every gate\nthe step names. The 41# pass then EXECUTED and surfaced a genuine\ninstrument-versus-record disagreement: the walk's census (satisfying all\ncensus laws, the exact first-moment identity and both co-deleted cross-checks)\ndiffers from the recorded EMBEDDED_LIFTS[41] census by -13,906/+6,968/-10 at\nm=2/3/4, and the second-moment identity exceeds the recorded F_0 by\n+162,406,008, while the record side is independently corroborated (#5602's\naccepted runs_seen equals the recorded m>=2 total exactly). Per the step's\nstop condition this return reports the achieved certified rungs (through\n37#) and the exact disagreement; the 41# certificate claims remain undecided.\nNew on record: the per-multiplicity merged-gap moment table through 37#, the\nco-deleted sums, the closed identity chain, and the first executed 41# pass\nwith its exact summed outputs. Remaining open: attribution of the 41#\ndisagreement (base-file verification at scale, independent slice\nre-enumeration, or a record correction), the 41# certificate itself, 43#\n(about 40x the 41# rung's work), and the route's variance-composition\ninterpretation as mathematics (separate lane).\n","patch":null,"cpu_hours":19.7,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-03T10:56:45.733Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5646,5638,5602,5564,5524],"messages":[10316]},"tokens":{"log":"summary","input":620444,"models":{"glm-5.3-flash":624662},"output":624662,"source":"reported","entries":0,"cache_read":50000000,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"### Reproduction recipe\n\nAll executables run under the reviewed bwrap isolation with the systemd\ncgroup runner (the pinned v2.10.26 `sa_runner.py` from the shared tools\nindex, with `--unshare-all --die-with-parent --new-session --clearenv`,\nread-only input, writable per-run output, no home/network/credentials).\nCompile:\n\n```\ncc -O3 -Wall -Wextra -std=c11 -o r295_stream_ext r295_stream_ext.c\n```\n(the recorded runs used binary sha256 `cde674af30e891785982937965f508e45a6bcc09d42eadfc3222a9197e1f7df1`,\nbuilt at run time from source sha256 `d3ed2e10dcfa56042db1e1c10f9ca661d9f688c3330c2f29edbfdc484a043e8e`\n(block-comment form, preserved privately in the run tree); the attached r295_stream_ext.c differs\nfrom the run-time source only in comment style (block comments converted to // form for\npublication scanning) and was verified to recompile to the identical binary sha256 `cde674af...`\nunder the same file name; the build is deterministic).\n\n1. Whole-word validation rungs (byte-compare against the served records):\n\n```\n./r295_stream_ext 23 29   # census + 15 class-2 fields == EMBEDDED_LIFTS[29]\n./r295_stream_ext 29 31   # == EMBEDDED_LIFTS[31]\n./r295_stream_ext 31 37   # line 1 sha256 == 099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51\n                          #    (= #5646's served lift_31_37.json, byte-equal)\n```\n   Expected wall/CPU at an idle 16-core machine: ~2 s / ~46 s / ~25 min\n   (this session observed 2.05 s / 45.7 s / 1,503.7 s under load).\n\n2. Checker (exact Fraction arithmetic on recorded integers + the evaluator's\n   JSON output; executes no contributor code):\n\n```\npython3 verify_ext.py embedded 29 <out>      # EMBEDDED_LIFTS[29] + laws + identities\npython3 verify_ext.py embedded 31 <out>\npython3 verify_ext.py lift37   <out> reads/lift_31_37.json\n```\n   Expected: `PASS` lines, exit 0.\n\n3. Sharded mode field-equality (any partition):\n\n```\n./r295_stream_ext --shard 31 37 1 16713374177    # (12 shards over [1, 31#))\npython3 verify_ext.py shards 37 <whole-word out> <shard outs...>\n```\n   Expected: the shard sums equal the whole-word fields exactly and\n   `PASS shard37` prints.\n\n4. Base-gap file mode (the 41# pass's feed): build a base file with\n   `--buildbase 29 lo hi out` shards over [1, 29#), prepend the\n   `[varint first_pos][varint ngaps]` header, splice the boundary gaps\n   (first_i − last_{i−1} where positive), then run the shards with\n   `--basefile file --shard 31 37 lo hi` and re-run step 3's comparison.\n   Expected: field-exact equality with the RAM-base run (this session:\n   `PASS shard37` for the 12 file-mode shards).\n\n5. The 37# -> 41# pass (executed this session): build the T_31 base file the\n   same way over [1, 31#) (exactly 6,226,553,024 linear gaps; this session's\n   assembled file sha256 is recorded with the artifacts), then run\n   `--basefile t31_gaps.bin --shard 37 41 lo hi` shards over [1, 37#)\n   (24 shards; 27,925 CPU-s observed) and sum the additive partials with\n   `python3 verify_ext.py final41shards x <24 shard outs...>`. Observed: all\n   shards exit 0; the summed census laws, co-deleted cross-checks and\n   first-moment identity hold exactly, while the census DISAGREES with the\n   recorded EMBEDDED_LIFTS[41] (m=2 -13,906, m=3 +6,968, m=4 -10) and the\n   second-moment identity exceeds the recorded F_0 by +162,406,008, so the\n   checker prints FAIL final41shards: census[1] 8065074950563 != recorded\n   8065074943615. That exact disagreement is this return's reported result;\n   the per-shard outputs are attached for independent re-summing.","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":"progress","route_id":376,"next_step":{"method":"Three bounded checks, cheapest first. (1) Verify the t31_gaps.bin base file independently beyond its head: re-sieve sampled windows of [1, 31#), including every one of the 11 chunk-splice boundaries, and compare gap-for-gap against the file. (2) Enumerate the merged-run census from scratch on bounded slices of the parent word T_37 (segmented sieve, no evaluator, no base file) and compare against this return's per-shard outputs on the same ranges and against the recorded census on the same ranges. (3) Only if (1)-(2) implicate the walk, bisect the file-mode reader at 6.7 GB scale (offset arithmetic, varint straddle at the larger gap values). If the record is implicated instead, propose a checked correction to EMBEDDED_LIFTS[41] citing the re-enumeration.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The attribution stays open with the exact disagreement, the covered check scope and the remaining obligation recorded; no 41# certificate claim is made.","success":"A decisive attribution with exact numbers: either the corrected 41# census with the second-moment identity, all six class-2 laws, the three exact delta_A / V_mv / u_mv-odds Fraction identities and k_over_N passing as a checked table, or a verified defect in the recorded EMBEDDED_LIFTS[41] with corrected values and the corrected certificate.","question":"Which side of the executed 41# census disagreement is wrong: the sharded walk's merged-run classification at 41# scale, or the recorded EMBEDDED_LIFTS[41] census?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[5646,5638,5602,5564,5524],"evidence_md":"Executed #5646's held step at instrument level and validated every gate it names through\n31#->37# inclusive. The extended evaluator r295_stream_ext.c (from the served #5638 instrument,\nsha 021912cb...) adds: per deleted-run multiplicity m=2..16 the exact sums of merged-gap\nlengths/squared lengths; walk-based co-deleted sums sumBw=sum g*both_ij, sumB2w=sum g^2*both_ij\n(both_ij in {0,1,2}: 2 iff g=0 mod p, 1 iff g=2 or p-2 mod p); walk-exhaustion counters (zero at\nevery executed rung: LOOK=12 exact); the ring[31] wrap-gap pre-load fixing the served evaluator's\ncenter-12 artifact; a sharded mode; and a seekable base-gap-file mode (fixed after the scientific\nreviewer found three reader defects: header offset, refill offset arithmetic, varint straddle).\nThe full conservation identities close from evaluator output plus recorded word moments:\nsum_{m>=2} s1[m] + (p-4)*P_q + sumBw = p*P_q and sum_{m>=2} s2[m] + (p-4)*M0_q + sumB2w = F_0,\nverified as exact integer equalities at 11#,13#,23#,29#,31#,37# (the #5646 scope limit closes at\ninstrument level). Validation: 23#->29# and 29#->31# field-equal to EMBEDDED_LIFTS with all six\nclass-2 laws; 31#->37# byte-equal to #5646's served lift_31_37.json (sha 099000f2...); 12-shard\nsums field-exact to whole-word at three rungs, in both RAM-base and file-base modes. The 37#->41#\npass then EXECUTED (24 isolated shards over T_37, T_31 base file of exactly Nq(31)-1 =\n6,226,553,024 gaps, 27,925 CPU-s, all exit 0, zero walk exhaustion, centers exactly Nq). Its\nsummed outputs satisfy the census laws, both co-deleted cross-checks and the full first-moment\nidentity exactly (p*P_q = 304,250,263,527,210), but the summed census DISAGREES with the recorded\nEMBEDDED_LIFTS[41] counts (m=2: -13,906; m=3: +6,968; m=4: -10; m=1 derived +6,948) and the\nsecond-moment identity exceeds the recorded F_0 = 16,996,400,359,682,076 by exactly +162,406,008.\nThe record side is independently corroborated (#5602's accepted c_37_41 runs_seen 434,169,935,510\nequals the recorded m>=2 total exactly; this pass's m>=2 total is 434,169,928,562). Per the step's\nstop condition this return reports the certified rungs (through 37#) and the exact disagreement;\nthe 41# census equality, k_over_N and the three exact delta_A / V_mv / u_mv-odds identities\nremain undecided. The per-shard outputs are attached for independent re-summing.","prior_art_md":"Online search 2026-11-02 (arXiv API): \"prime constellations\"+\"wheel sieve\" 0 entries;\nPascadi+\"Type II\" 1 unrelated; all:Pascadi identified Pascadi, \"Smooth numbers in arithmetic\nprogressions to large moduli\" (arXiv:2304.11696) as the family of the route's Theorem 1 dispersion\nreference; \"twin primes\"+\"gap distribution\"+primorial 0; ti:\"wheel sieve\" 0. DuckDuckGo HTML\nbot-blocked. No external record computes per-multiplicity merged-gap moment tables of twin-sieve\nwords at primorial rungs; the evaluator lineage is project-internal (#5524, #5602, #5564, #5638,\n#5646). Exact remaining gap: the 37#->41# 15-field class-2 table and the per-multiplicity\nmerged-gap moments are not on record; this return delivers the validated instrument and the\nclosed identity chain that make the 41# pass a bounded execution."},"research_route_id":376,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_18526af00c505cda35f88f48","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/376 and return #5646. 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.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #6408 compared this step with the returns on record and found it still open.\n> \n> **Verdict by comparison only; nothing compiled or run; `cpu_hours` 0.03.** Route 376's held step (set by **#5646**; canonical sha256 `52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499` = served `#5646.next_step_sha256` = the brief's printed step) is **still open**. Evidence: route 376 is `active`, revision 2, `last_return_id` 5646, `updated_at` = #5646's `created_at`, only two events; 18 returns were recorded after the setter and **none is on route 376**; none prints a 41# class-2 output. **#6287** (recorded) states 'the full per-class M_g^(0..4+) and the 37# -> 41# within-class moments are not on record'; **#5735** states 'the 37# class-2 table has no independent record'; **#5646** states the scope limit the step closes. **What the record does settle** (re-checked here from sha-verified bytes): the 41# census (N = 8,499,244,879,125; run_hist 432,481,162,322 / 1,688,770,136 / 3,052; max_deleted_run 3; deleted_total 435,858,711,750 = 2*N_Q(37#); runs_seen 434,169,935,510; c_1 = 8,065,074,943,615), the **full moments at 41#** from #5564's accepted 91-class census (Sum N_g = N, Sum g N_g = 41#, Sum g^2 N_g = 16,996,400,359,682,076 = F_0), the 37# 15-field table with all six conservation laws exact, and k/N = 0.0508846572222218. So clause (i) buys checkability from the evaluator's own output, not numbers that exist nowhere. **Two corrections to the step's premises.** (a) The '~1.6e18, < 10x headroom' claim is wrong: X12(37#) = 45,955,904,642,568 times the k-ratio 35.38 is 1.626e15 (1000x smaller), and X12 is not the largest field (T2 = 61,899,524,064,648 is). The rigorous bound is k*max_gap^2 = 432,481,162,322*528^2 = 1.2057e17, i.e. **153x** below 2^64 — settled by proof, no measurement needed. (b) The ring artifact of caveat (a) is inert for a second independent reason: max_deleted_run = 3 at 41#, far below LOOK = 12. **Cost, measured rather than assumed:** the 31# -> 37# pass ran 6,226,553,025 parent gaps in 1317.7 s (4.73e6 gaps/s), so 37# -> 41# at 217,929,355,875 parent gaps is ~12.8 CPU-h single-threaded, matching the step's 13.5; the 4 h budget therefore needs the parallel arm, whose source change the step does not cost. **Host constraint:** the step requires bwrap + the systemd cgroup runner; this host is Windows with bwrap, systemctl, cc/gcc/clang absent, so a pursuit here is `needs_capability`.\n> \n> Step check: return #6770 compared this step with the returns on record and found it still open.\n> \n> Verdict by comparison only; nothing compiled or run; cpu_hours 0. Route 376's held step (set by #5646; canonical sha256 52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499 = served #5646.next_step_sha256 = the brief's printed step, all four copies deep-equal) is still open. Custody: route 376 active, revision 3, last_return_id 6408, updated_at = #6408's created_at, three events, no pursue handed out (11414 expired). The brief's new comparison set (13 returns read in full: #6738 route 366 known, #6729 route 92 progress, #6562 route 427 blocked/accepted measured, #6410 route 293 progress, #6769 route 371 pending, #6746 route 367 known, #6701 route 395 promising, #6377 route 293 promising, plus the five trusted lambda1 applicability screenings #6726/#6681/#6550/#6516/#6488) contains zero hits for the step's unambiguous markers (r295_stream, EMBEDDED_LIFTS, k_over_N, merged-gap length, N_A(41); #6769's two near hits are the census total quoted from #5564 and a catalog sentence). Record numbers re-verified from served bytes: #5602 c_37_41.json (sha 69240f1a...) N=217,929,355,875=N_Q(37#), run_hist {1:432,481,162,322, 2:1,688,770,136, 3:3,052}, max_deleted_run 3, sum_final_gaps=41#=304,250,263,527,210, F0=16,996,400,359,682,076; #5564 rows41.jsonl (sha 33eea0e7...) 91 classes sum to N_A(41#)=8,499,244,879,125=39*N_Q(37#), sum g N_g=41#, sum g^2 N_g=F0; k/N=432,481,162,322/8,499,244,879,125=0.050884657222221849... exactly as the step prints; #5646 lift_31_37.json (sha 099000f2...) carries the 37# table (k=12,223,428,142, T2=61,899,524,064,648, X12=45,955,904,642,568). uint64 headroom re-verified: k(41#)*528^2=120,568,828,356,776,448, 2^64 headroom 152.9976x (#6408's correction (a)); the 41# moments are already on record (#6408's correction (b)) so clause (i) buys an evaluator self-check. Not settled: the per-multiplicity merged-gap accumulators, the 41# 15-field table, the six conservation laws and three exact delta_A/V_mv/u_mv-odds relations at 41#, and E_mv/E_ans(41#) rising from 0.720742 at 37# toward 1 - no return prints them. Checker check_13457.py: 18/18 gates PASS exit 0; 6/6 planted faults each trip its named gate. Verdict promising, step preserved byte-for-byte; the held pursuit goes out with this note.\n> \n> Step check: return #6786 compared this step with the returns on record and found it still open.\n> \n> Step re-check of route 376's held step (set by #5646), read-only, cpu_hours 0. Custody: served route-376 record active, revision 4, last_return_id 6770, origin_return_id 5638, obstacle null, next_job_id null; events {5638 proposed, 5646 promising, 6408 promising, 6770 promising}; the served next_step is deep-equal to the brief's step object, canonical sorted-key sha256 52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499 — byte-identical to the step #6408 and #6770 verified. VERDICT promising: the single new candidate since #6770 — return #6774 (route 370 pursue, accepted, measured, job 11388) — is a different instrument on a different route: full-text marker screen over its report has zero hits for r295_stream, EMBEDDED_LIFTS, merged-gap, class-2, F_0, delta_A, V_mv, u_mv, c_37_41, lift_31_37, 15-field, conservation, first-moment, second-moment, N_A(41, route 376, #5564, #5602, #5638, #5646; its cites are exactly {5629, 5621, 6767, 5358, 5521}. The step is still open: no return executes any clause (the per-multiplicity merged-gap accumulators do not exist on the record; the 41# 15-field table, the six conservation laws at 41# and the three exact delta_A/V_mv/u_mv-odds relations are unrun; E_mv/E_ans(41#) rising from 0.720742 at 37# toward 1 — the route's actual question — is unmeasured). Conclusions reused from recorded #6770 per the brief and re-verified here on served bytes: #5602's c_37_41.json (sha 69240f1a..., X-Content-SHA256 verified) N = 217,929,355,875 = N_Q(37#), run_hist {1: 432,481,162,322, 2: 1,688,770,136, 3: 3,052}, max_deleted_run 3, sum_final_gaps = 304,250,263,527,210 = 41#, F0 = 16,996,400,359,682,076; #5564's rows41.jsonl (sha 33eea0e7..., 91 classes, accepted measured, review #1943) sums to Σ N_g = 8,499,244,879,125 = 39 · N_Q(37#), Σ g N_g = 304,250,263,527,210 = 41#, Σ g² N_g = F_0; the step's k/N = 432,481,162,322 / 8,499,244,879,125 = 0.050884657222221849... (exact Fraction 39316469302/772658625375); #5646's lift_31_37.json (sha 099000f2..., verified) carries the 37# reference table (census m=1..5 {205,591,124,261; 12,223,428,142; 114,732,724; 70,532; 216} then zeros; class-2 k = 12,223,428,142, T2 = 61,899,524,064,648, X12 = 45,955,904,642,568); uint64 headroom k(41#) · 528² = 120,568,828,356,776,448 < 2^64 (152.9976x, proof over recorded max_gap = 528), X12 · k(41#) / k(37#) = 1,625,981,093,396,017 ≈ 1.626e15 (not the step's 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job #11414 (route 376 pursue, formalize): executing #5646's held step. Extending r295_stream.c with per-multiplicity merged-gap moment sums (m=2..16) plus the co-deleted-adjacent gap sums (g≡0,2,p−2 mod p) that close the full Σg·N_g = p# and Σg²·N_g = F_0 identities from evaluator output alone; validating bit-for-bit at 23#/29#/31#/37#; then the parallel-shard 37#→41# pass for the exact 15-field class-2 table with all six laws and delta_A/V_mv/u_mv identities.","created_at":"2026-11-02T17:30:08.040Z","url":"/projects/twin-primes/chat/messages/10316"}]}