# QC wave 6, partition W — the three expensive natal-cap artifacts Files owned: `research/natal-cap-34-wrap-precision.js`, `research/natal-cap-35-x-multiplicity.js`, `research/natal-cap-37-at41-march.js`. No commits. No pushes. No `.md` edited. No `fold-profile-*.js` touched. Date of work: 2026-08-18. ## 0. THE FIRST STEP, AND WHAT IT OVERTURNED The brief warned that `research/wave7-logs/` might already hold output for two of the three. It holds output for two of the three — and the third's output was also on disk, in a place the brief did not name and no wave has cited: ~/Files/primeoire-runs/ (OUTSIDE the repo, untracked) at41/at41-run2.log 294 lines, 2026-08-16 03:29 — the COMPLETE @41 march at41/at41.log 116 lines, 2026-08-15 19:02 — the killed first attempt at41/audit.log 69 lines, 2026-08-15 18:14 at41/gates.log 79 lines, 2026-08-15 18:01 at41/cost.log 18 lines, 2026-08-15 18:03 at41/nc37-x{31,37,41}-of8-*.json 24 shard result files chain/cap34-verify.log 2026-08-15 21:42, 56.2 s, 88,520 checks chain/cap35-default.log 2026-08-15 21:27, 101.1 s chain/cap36-default.log, chain/cap36-at29.log, chain/chain.log lemmaV/lemmaV-full.log overnight-chain.sh the driver that produced the chain/ logs **`natal-cap-37`'s 6.16-hour @41 march had already been run to completion and its full output was sitting on disk.** `qc-scripts-S1.md`:194-196 records it as "NEEDS COMPUTE"; `MORNING-2026-08-16.md`:8 already knew the run finished. So the "needs 6 hours" reading was true of re-running and false of recovering. Anyone who had priced this partition off the script headers alone would have burned six hours reproducing a log that existed. This is the campaign's named trap in its exact predicted shape, and it was avoided only by listing directories. **Second finding from the same step, and it is a provenance error already in the repo:** `research/wave7-logs/cap34-cap27-custody.log` is **not cap-34 output**. Its text ("V. ENGINE VERIFICATION", "T. THE @13 FOURTH MOMENT", `[23 checks passed, 1202.5s]`) is printed by `research/natal-cap-27-t4-at13.js`:220, :255, :321 — it is a re-run of cap-34's custody TARGET, cap-27. `WAVE7-RESULTS-2026-08-15.md`:69-70 lists it as one of cap-34's two logs without saying so. Anyone pasting it into cap-34 as cap-34's output would have manufactured a false custody record. Severity MED, confidence HIGH (the format strings are unique to cap-27). ## 1. THE THREE-WAY TALLY | file | route | what landed | own custody? | |---|---|---|---| | `natal-cap-35-x-multiplicity.js` | **(a)+RE-RAN** | full 237-line run pasted, 80.3 s, produced today; third independent run, digit-identical to two archived logs | **YES, fully** | | `natal-cap-34-wrap-precision.js` | **RE-RAN the expensive stage** | `exact13` re-run today (10 workers), plus `verify`, `kurt`, `layers`, `c2`, `joint` | **YES, fully** | | `natal-cap-37-at41-march.js` | **(a) PASTED FROM LOG, plus own re-run of the cheap modes** | `audit`+`cost`+`at41` pasted from the 2026-08-15 logs with explicit provenance; `audit`, `smoke`, `gates` re-run today | **PARTIAL — the @41 march itself is log-only** | ## 2. PER FILE ### 2.1 `natal-cap-35-x-multiplicity.js` — ROUTE: re-ran it, 80.3 s **Cost basis: MEASURED, by running it.** `MORNING-2026-08-16.md`:109 priced it at 101 s and `WAVE7-RESULTS`:100 at 163 s. Both are right; it took 80.3 s today. Wave 5's "expensive, hours not minutes" pricing was wrong for this file by three orders of magnitude, and the two archived logs said so. **Provenance of the pasted output: my own run, today, on this machine.** It is the THIRD run of the file. Diffed against both archived logs (`research/wave7-logs/cap35-x-multiplicity.log`, `~/Files/primeoire-runs/chain/cap35-default.log`) the only differing lines are the five wall-clock lines. Every figure is now reproduced three times. **Added:** a 237-line verbatim OUTPUT block and a 10-item READINGS block that grades the five predictions the header put on record and never graded. Findings, in the file and here: - **F-35-1 (MED, HIGH). P4 is REFUTED as stated, and refuted in the direction the file's own warning predicted.** Header:74-75 predicts "The m = 2 cell carries the sign change of X(0) − X̄ across the crossing". Output: the total X-gap flips sign between @11 and @13 (+8.74 → −4.18) while the m = 2 cell stays POSITIVE across that flip (+10.71 → +3.16); the flip is carried entirely by the m ≥ 3 cells (−1.96 → −7.34). The m = 2 cell only turns negative at @17. P4's second half ("m ≥ 3 cells carry large individual gaps that mostly cancel") holds: at @17 they are −751.28, +448.03, +60.68, +190.24 summing to −59.24. - **F-35-2 (MED, HIGH). P5 CONFIRMED**, the sharpest call in the file: X(0)/X̄ = 1.4541, 0.9908, 0.9482, **0.9558** — the descent breaks at @19 and breaks upward, exactly as predicted at header:80-83. - **F-35-3 (LOW-MED, HIGH). P2 is false at the level it was formed on.** "p_nat·Π_i to a few percent for i ≥ 2" reads 1.185 at @11 (18.5% out), then ≤3.7% at @13, ≤0.7% at @17, ≤0.5% at @19. - **F-35-4 (LOW, MED). P3 is unsupported.** The enhancement matrices show no cofactor-range structure in either direction; what they show instead is a level effect the prediction did not name — the j = 2 spread collapses to 1 (0.41..2.14 @11 → 0.87..1.01 @19), i.e. by @19 the pair channel is CRT and the whole departure has moved to j ≥ 3. - **F-35-5 (MED, HIGH). The @19 row is a MEANS row and carries no significance statistic.** Every `z(anch)` at @19 is NaN and there is no CUSTODY line at @19, because `part0` (the W-rotation sweep) runs only where cap-31 published a reference — `CAP31` at :106-108 holds x ∈ {11,13,17} only. cap-31's headline "pair statistics cannot see this" (z(X) = −2.71 vs z(P2) = −0.30 at @17) is therefore **NOT extended to @19 by this file**, though the @19 row is cited around the corpus as the fourth point of the X-channel story. - **F-35-6 (LOW, HIGH). The @19 ensemble column is not brute-force checked.** `[u-form vs sweep: PASS]` appears at @11/@13/@17 and is absent at @19, which is correct and honest (the sweep is what the u-form replaces) but means I1 at @19 rests on the identity holding three levels below. - **F-35-7 (LOW, MED). Cost of @23 is much lower than the corpus implies.** Of the 80.3 s total, @17 is 79.0 s and @19 is 0.96 s. The entire cost is the two things switched off above @17: the W-rotation custody sweep and the j = 3 census (`if(x<=17)part5(L,U,3)` at :347). `TODO.md`:280-281 says "Price the run, not the plumbing" without pricing it. Estimated, not measured: an @23 row through the u-form path is tens of seconds; an @23 custody sweep (2.2e8 rotations × 1,739 primes) is dead. I did **not** run @23, because adding to the hardcoded level array changes what the script computes and the brief forbids that. **Cross-partition correction applied (adjudicator handoff, verified before applying).** Header:8-10 read "proven PER LEVEL at @11, @13 and @17 **and nowhere else**, those being **the three levels** where the ensemble maximum of VR is enumerated". I confirmed the adjudicator's claim at the artifacts before touching the file: `natal-cap-19-calm-lemma.js`:505-511 enumerates the FULL @19 ensemble ("all 9699690 rotations") and returns V̄ = 8944.60 with `VR(W/2)=2.293 rank-from-top 0/9699690`, so max VR IS enumerated at @19; K = 435 from the same block; and S̄ = 49,238.76 comes from **my own run today**, not from a cited log. √(K·V̄·VRmax) = 2,987 < S̄ = 49,238.76, so the per-level inequality holds at @19 and the count is four, not three. Rewrote lines 8-10 to say four levels, to record the @19 evidence inline with its date, to name the old text as the false absence claim it was, and to KEEP the surviving clause that "from @13 upward" is still an extrapolation. Sites changed: **one** (`natal-cap-35-x-multiplicity.js`:8-10). I scanned my other two files for the same phrasing and for "nowhere else"/"enumerated" scope language: **no hits** in `natal-cap-34` or `natal-cap-37`. My new READINGS block does not restate the three-level scope anywhere. ### 2.2 `natal-cap-34-wrap-precision.js` — ROUTE: re-ran ALL SIX STAGES, ~25 min total **Cost basis: MEASURED, by running every stage.** This is the finding that most changes what the campaign believed. `qc-scripts-S1.md`:194-196 says cap-34's `exact13` is the "C(990,4) = 3.98e10 march. **NEEDS COMPUTE**, and the honest price is hours, not minutes." Measured on ten cores today: | stage | wall | note | |---|---|---| | `exact13` | **876.1 s (14.6 min)** | the full 39,782,707,965-quadruple march, 10 workers | | `layers` | 348.2 s | | | `c2` | 265.8 s | | | `verify` | 17.9 s | 88,520 checks, 2 workers | | `joint` | 3.8 s | | | `kurt` | 2.6 s | | | **all six** | **~25 min** | | The archived `wave7-logs/cap34-exact13.log` reads 1857.0 s because that run was sharing the machine with the @41 march. So "hours" was wrong by at least 4x, and the whole file is a coffee break. **Provenance: every byte pasted was produced by me today.** The two archived logs were used only as reproduction targets and both reproduce: - `exact13` is IDENTICAL digit for digit to `research/wave7-logs/cap34-exact13.log`. The only differing line in the whole block is the scratch path the truth JSON is written to. - `verify` is IDENTICAL to `~/Files/primeoire-runs/chain/cap34-verify.log` with timing prefixes stripped; 88,520 checks both times. The third archived log, `wave7-logs/cap34-cap27-custody.log`, is **cap-27 output** (see section 0) and is deliberately NOT pasted. **Added:** a six-stage verbatim OUTPUT block, a 12-item READINGS block grading all three predictions, a corrected PLAN-vs-CODE note, and a corrected predictions header. Findings: - **F-34-1 (HIGH, HIGH). P1 is now graded, and it is the answer the corpus has been missing.** Stage `layers` gives the -3.5e-5 as a measured per-layer budget: **Multi (model x CAL4 = 0.87) -4.531943e-5**, C2 instance +1.056084e-5, A k4-Monte-Carlo -1.597529e-9, C1 instance -2.265633e-13, C3 instance +6.720878e-14. The stage then rebuilds cap-32's whole instance pipeline and lands on 352241335.077, **REL -3.501681e-5**, reproducing cap-32's published -3.50e-5 to three digits. So P1's verdict (the multi layer, not C2 order-3) is CONFIRMED, and the published figure is a partial cancellation of a -4.53e-5 multi error against a +1.06e-5 C2 error. P1's own arithmetic was wrong twice in compensating directions: it assumed multi/G ~ 2e-4 (measured 6.795774e-4) and a ~13% calibration error (measured 6.7%). - **F-34-2 (HIGH, HIGH). The calibration constant is the entire error and its exact value is now known.** cap-32 used CAL4 = 0.87; the exact truth implies **0.932164**. The independence model fed with exact per-prime inputs returns 48083774.2789 against an exact 44821955.4433, so the model's shape is right to 7% and one hardcoded constant carries the whole published discrepancy. - **F-34-3 (HIGH, HIGH). The 1e-9 gate is missed by 2%, and by exactly one Monte-Carlo shape.** The best assembly `layers` can build — A(shapes + k4 by MC at n = 2e8) + C1,C3 instance + C2 factorised-exact + Multi EXACT — returns T4 = 352253669.51634955, **REL -1.021692e-9** against a 1e-9 gate, of which the k4 Monte Carlo alone is **8.290660e-10**. Every other layer in that assembly is exact to 1e-13 or better. The residual obstruction at @13 is neither the joint layer, nor C2, nor float: it is one MC shape whose exact value the same stage prints (60234.5044708). Honest caveat recorded in the file: k4_exact = A_exact - A_shapes needs the exact13 truth, so a cheap pipeline cannot help itself to it. - **F-34-4 (HIGH, HIGH). P3's precondition is six orders out of reach on the T4 road, and stage `kurt` prices it exactly.** @17 needs relT4 <= 3.055646e-8 for mu4 to 100%, 3.055646e-9 for 10%, **3.055646e-10 for 1%** (relT3 four times tighter). cap-32's @17 T4 is +-4e-4 relative. The corpus's standing plan ("meet the @13 gate, then rerun @17") is therefore not the cheap step it reads as: the @13 gate is 1e-9 and the @17 requirement is 3e-10 on a level whose T4 is known to 4e-4. The viable road is the kappa4 SIGN, not T4. - **F-34-5 (MED, HIGH). P3's arithmetic checks out and its multiplier is 3305, not "~3000".** `kurt`: @17 exact mu = 3245.512635440701, Var = 1062.3544031865895, Chebyshev 1.008562e-4, 3Var^2/mu^4 = 3.051595e-8. - **F-34-6 (MED, HIGH). A header CLI line that names a stage which does not exist.** BEFORE (line 59): `CLI: node natal-cap-34-wrap-precision.js [verify|exact13|layers|joint|at17]`. Running `at17` answers `unknown stage at17; have: verify ework exact13 layers c2 kurt joint`. The line both promises `at17`, which was never written, and omits `c2` and `kurt`, which exist and produce results. AFTER: the real dispatch list, plus a dated PLAN-vs-CODE note recording that the @13 gate which would have triggered stage [17] **was met by six orders**, so [17] is not a correctly skipped stage — it is the one piece of the file's own plan that its own result called for and nobody wrote. Fix is unambiguous (the dispatcher is the authority) and is documentation only; no computed value changed. - **F-34-7 (MED, HIGH). A header claim that had gone stale in the safe direction.** BEFORE (lines 12-17): "This file carries no pasted run output and no READINGS block, so the three predictions below are NOT graded inside the artifact." That was true when written and false the moment I pasted the output. AFTER: records the grading, the date, and what the header used to say. - **F-34-8 (MED, HIGH). The instance engine and the block engine differ by four to eleven orders and the corpus quotes "cap-32's C1" without saying which.** Per-layer error as relative error on T4: C1 instance -2.27e-13 vs block -1.796335e-4; C3 instance +6.72e-14 vs block -1.229796e-4; C2 instance +1.056084e-5 vs block +2.552517e-5. - **F-34-9 (MED, HIGH). The term cap-32 drops from C2 is a quarter of the layer.** Stage `c2`: factorised exact -184829668.852314 against truth -184829668.852342 (error 4.324244e-16 of G); without the s_kl term, -139150881.841113 (error 6.925684e-4 of G). The dropped piece is -45,678,787, **24.7% of the exact C2 layer** and 25x the whole published -3.5e-5. Price of exactness: 63.5 s + 69.3 s V4 against 5.6 s. - **F-34-10 (MED, HIGH). The joint road dies between @17 and @19, with exact operation counts.** WJ (w dropped, O(1) lookups) = 1.3198e+9 / 7.9777e+12 / 5.6899e+16 at @13/@17/@19; WJ4 (w kept) = 3.2818e+9 / 4.0689e+13 / **5.3882e+17**. Table building alone at @19 is 1391.5 s. And w cannot be dropped: doing so turns Multi's 44821955.4433 into 15975541.2041, -64.36% of the layer. So WJ4 is the real column and @19 is dead. - **F-34-11 (LOW-MED, HIGH). The multi layer is a two-prime object to four digits**: Multi 44821955.4433291 = 2-prime 45090019.6365043 + 3-prime -268718.409425233 + 4-and-up 654.216249991616. ### 2.3 `natal-cap-37-at41-march.js` — ROUTE: pasted from log (@41), re-ran the cheap modes **Cost basis: MEASURED, from the logs, and confirmed for the cheap modes by running them.** audit 9.3 s; cost 83.0 s; gates 450.1 s; at41 22,176.3 s = 6.160 h wall on ten cores. Only `at41` is genuinely hours, and it did not need re-running because its log is complete. **Provenance, stated in the file in the strongest terms I could write it.** The pasted `audit`/`cost`/`at41` blocks are copied byte for byte from `~/Files/primeoire-runs/at41/{audit,cost,at41-run2}.log` by a script, never retyped, and the block says at the top that none of it was produced today, gives each log's path and mtime, and marks both elisions in place with exact counts (49 repeated banner lines dropped, 145 progress ticks elided). I re-ran `smoke` (0.1 s, passes) and `audit` and `gates` myself for first-hand custody of everything except the march. Findings: - **F-37-1 (LOW-MED, HIGH). A cost figure in the code that the cost log does not support.** `natal-cap-37-at41-march.js`:606 prints `strike budget 4*M*sum_q 1/q = 5.916e13; projected 11 h at the measured 1.5e9 strikes/s aggregate.` `cost.log` never measured 1.5e9: its three 8-concurrent aggregates are 1185e6/s (13.9 h), **1357e6/s (12.1 h)** and 838e6/s (19.6 h). So "the measured 1.5e9" is not a measured number. The real run then delivered 6.035 h over the shards, i.e. ~2.7e9 aggregate — the probe under-predicted the march by 2×. Nothing depends on it; anyone pricing @43-class work off it will price high. - **F-37-2 (LOW, HIGH). Header runtime vs log.** The CLI block says `audit (~30 s)`; `audit.log` ends `[audit done in 9.3s]`. Only such disagreement I found between this header and these logs. - **F-37-3 (MED, HIGH). S(41) has ONE witness, and the corpus does not say so.** `paper/anchored-note.md`:485-492 states S(41) = 256,725,962,834 and β(41) = 0.8455 without noting the march ran once. The killed first attempt (`at41.log`) agrees digit-for-digit with run 2 at every shared progress tick (np=4686722957 S=349203305 at block 2000 through np=74987566147 S=4532204145 at block 32000), which covers ~10.6% of one shard of eight, i.e. ~1.3% of the tile, and establishes DETERMINISM, not correctness. The other 98.7% of S(41) has been computed exactly once, ever. Recorded in reading 5 and reading 10 of the new block. - **F-37-4 (INFO, HIGH). The gates have now been run three times**, identically: `gates.log` (18:01) and the gates inside `at41-run2.log` (19:19) differ only in timing lines, and I ran them again today. - **F-37-5 (LOW, HIGH). The logs are outside version control.** `~/Files/primeoire-runs/` is not in the repo and not in `.gitignore` either — it is simply elsewhere on the disk. The @41 march is the most expensive artifact in the corpus and until today its only record was an untracked file. Pasting it into the script is now the durable copy. - **F-37-6 (INFO, HIGH). The 2^53 ceiling is the level ladder's ceiling.** PART 0's binding path is F, the CRT anchor, bounded by y² ≤ W, so the engine is exact exactly while W < 2^53. @43 (43# = 1.45 × 2^53) dies at path A. The file's own @43 forecast (classical-raw 0.8393) is therefore on record and ungradeable by this engine. Worth a corpus-level note: the ladder stopped for ENGINE reasons at @41, not for cost reasons. ## 3. `.md` DISAGREEMENTS NOTICED — LOGGED, NOT EDITED (I edited no `.md` but this report) Each gives file:line, the exact text, and the contradicting evidence. 1. **`TODO.md`:220-223 (MED, HIGH) — two different runs welded into one custody claim.** Text: *"(natal-cap-34, verified by clean re-run, 88,520 checks): the exact decomposition returns T₄ = 352,253,669.87624460 against cap-27's certified value, relative 3.4e-16."* The 88,520 checks are the **`verify`** stage (`~/Files/primeoire-runs/chain/cap34-verify.log`, 56.2 s, `[88520 checks passed]`), which does @7, @11 and a 120-slot @13 subset and never touches all C(990,4) quadruples. The T₄ figure is the **`exact13`** stage (`research/wave7-logs/cap34-exact13.log`, 1857 s), which prints `[4 checks passed]`. The "clean re-run" of `MORNING-2026-08-16.md`:112 was `verify` only. So the sentence attaches exact13's number to verify's check count and to verify's re-run. **As of my run today the underlying claim is now true** — exact13 has been re-run and reproduces — but the sentence's evidence chain was wrong when written. 2. **`MORNING-2026-08-16.md`:123-124 (MED, HIGH) — an over-retirement.** Text: *"The provenance warning in `WAVE7-RESULTS-2026-08-15.md` can be retired for cap-34, cap-35 and cap-36, whose numbers are now reproduced from clean runs."* For cap-34 only `verify` was in the overnight chain (`overnight-chain.sh` step 4/4); `exact13`, which produced every number cap-34 is cited for, was NOT re-run. True for cap-35 and cap-36; false for cap-34 until today. 3. **`research/history/staging/qc-scope-T.md`:1283 (LOW, HIGH) — a recomputed number that does not reproduce.** Text: *"κ₄ is negative at both certified levels (recomputed: @11 −1.14, @13 −0.48)"*. Running `natal-cap-34 kurt` today: κ₄ = **−1.1063** at @11 and −0.4850 at @13. The @13 figure is right; @11 rounds to −1.11, not −1.14. 4. **`research/SCRIPTS.md`:12 (LOW, HIGH) — a stale generated count.** Text: *"Scripts: **128**. Cited by at least one document: **128**."* `research/` holds **132** `.js` files today (wave 5 counted 131; `natal-cap-38` landed this morning and is not in the index at all). The file's own banner says regenerate with `node research/gen-scripts-index.js`; nobody has. 5. **`research/history/WAVE7-RESULTS-2026-08-15.md`:167-175 (LOW-MED, HIGH) — a document frozen mid-flight.** Text: *"**Running now.** Eight shards launched detached at 18:16 … That claim is NOT independently confirmed here, because the agent died before writing its OUTPUT block; the gates should be re-run and the result checked against the log when the march finishes."* The march finished at 03:29 on 2026-08-16, the gates ARE in the log, and everything the paragraph asks for has been done — but the paragraph still reads as if @41 is in flight. Same file :69, :99, :167 give line counts 655 / 356 / 565 against 660 / 359 / 622 before my edits today. 6. **`paper/anchored-note.md`:490 (LOW, HIGH) — a runtime that double-counts.** Text: *"6.16 hours over eight shards, after reproducing @7 through @29 digit-for-digit and S(31) and S(37) exactly through the same sharded code path."* `at41-run2.log`: the eight shards took **6.035 h**; the 6.160 h is the whole job and INCLUDES the 450.1 s of gates the sentence describes as coming before it. 7. **`research/history/MORNING-2026-08-16.md`:106 (LOW, MED) — not my partition, flagged only.** *"natal-cap-36 --at29 (781 s)"*. `qc-scope-T.md`:1270-1277 already has three other figures for the same pass (header 11.3 min, printed `[658s]`, `wave7-logs/cap36-at29.log` 1111.9 s). MORNING's 781 s is a **fourth**. I did not chase it; cap-36 is another agent's file. 8. **Confirming two findings already on the books, not new.** `qc-scope-T.md`:1284 says `natal-cap-32-wrap-identity.md` carries no reference to cap-34 — confirmed, `grep` returns zero hits, though cap-34 exists solely to grade cap-32's engines. `qc-scope-T.md`:1289-1293 says cap-31 carries no pointer to cap-35 — confirmed. ## 4. EDITS MADE, IN FULL `research/natal-cap-34-wrap-precision.js` (660 → 953 lines) - header lines 12-17 rewritten: the "carries no output, predictions ungraded" paragraph replaced by the grading verdict, dated, with what it used to say. - header lines 57-59 rewritten: PLAN-vs-CODE note added; the CLI line replaced with the real dispatch list. - appended: OUTPUT block (six stages, all run today), READINGS block (12 items). - **no executable line changed.** `node --check` passes. `research/natal-cap-35-x-multiplicity.js` (359 → 720 lines) - header lines 8-10 rewritten: X-limitation scope corrected from three levels to four, with the @19 evidence and its date inline (adjudicator handoff, verified at the artifacts first — see 2.1). - appended: OUTPUT block (237 lines, run today), READINGS block (10 items). - **no executable line changed.** `node --check` passes. `research/natal-cap-37-at41-march.js` (622 → 974 lines) - appended: OUTPUT block (audit + cost + at41, pasted from the 2026-08-15 logs with provenance and marked elisions), READINGS block (10 items), CUSTODY ADDENDUM recording the three modes I re-ran today. - **nothing in the existing header or code changed.** F-37-1 (the "measured 1.5e9" that was not measured) and F-37-2 (audit "~30 s" vs 9.3 s) were deliberately left in place and reported here, because both sit inside a printed line whose bytes are quoted in the pasted OUTPUT block: editing line 606 would put the source out of step with its own pasted output. The adjudicator should decide whether to change the line and re-paste, or annotate. - `node --check` passes. `research/history/staging/qc-wave6-W.md` — this report. No other `.md` touched. Custody check run after every paste: each pasted block was re-read out of the finished `.js` and string-compared against the log it came from. All eight blocks (six cap-34, one cap-35, audit+cost+at41 for cap-37) verified VERBATIM. ## 5. COVERAGE — what I did not reach, and how much to trust what I did **Trust the numbers; the cost estimates are the soft part.** WHAT I DID NOT REACH. 1. **The @41 march was not re-run and S(41) still has one witness.** This is the single biggest gap in the partition. 6 h of ten cores. The ~1.3%-of-tile agreement with the killed first attempt is determinism, not correctness. If one number in this corpus deserves a second independent run, it is S(41) = 256,725,962,834, because `paper/anchored-note.md` builds the fifth residual collapse on it. 2. **Stage `at17` was not written and I did not write it.** Writing it would be new work, not QC, and reading 5 of cap-34 says the T4 road it would take is six orders short anyway. The kappa4-sign road at @17 is unattempted by anyone. 3. **cap-35 at @23 was not run.** It needs an edit to the hardcoded level array, which the brief forbids. My "tens of seconds" price for it is an ESTIMATE from the @19 u-form cost (0.96 s) scaled by W (23x) — **low-to-medium confidence**. The O(W log log W) legs should scale that way; part3/part4 factor the natal set and may not. Nobody should quote it as measured. 4. **I did not verify every figure in the pasted blocks.** cap-37's at41 block alone prints hundreds. I verified: every figure a READING quotes, every figure a citing `.md` quotes, and the shard-fold arithmetic. Figures printed and never quoted were not independently recomputed. 5. ~~The eight `nc37-x41-of8-*.json` shard files were not opened.~~ **DONE after first drafting this section.** Summed in BigInt outside `combineReport`: sum S = 256,725,962,834 (== published S(41)), sum np = 5,666,163,252,750 (== published N(41)), and the eight kA..kB ranges are contiguous from 0 to M = 10,141,675,450,907 with no gap and no overlap. That independently confirms the FOLD and the PARTITION, and confirms nothing about the march, since the JSONs are the same run's own output. F-37-3 stands unchanged. Recorded as ADDENDUM 2 in the artifact. 6. **`~/Files/primeoire-runs/lemmaV/lemmaV-full.log` (16 KB) and `chain/cap36-*.log` were listed but not read.** They belong to other partitions. Whoever owns cap-36 and Lemma V should know these exist: the directory `~/Files/primeoire-runs/` is untracked and is not in the brief for any partition I know of. **It should be swept by someone.** 7. **I did not audit the `.md` companions** of these three scripts (cap-34, cap-35 and cap-37 have none) or the wider corpus. Section 3's list is what I tripped over while chasing numbers, not a sweep. 8. **`natal-cap-38-loudness-driver.js` landed this morning and I read only the four lines of it I needed** to check the adjudicator's claim. I did not audit it. It is not in `SCRIPTS.md`. HOW MUCH I TRUST MY COST FIGURES. - **exact13 876.1 s, layers 348.2 s, c2 265.8 s, gates 440.5 s, audit 5.3 s, smoke 0.1 s, cap-35 80.3 s: HIGH confidence, these are stopwatch readings from runs I started.** They will move with machine load; the archived exact13's 1857.0 s against my 876.1 s is a 2.1x load factor on the same machine, so treat any single figure as +-2x. - **at41 6.160 h and cost's 83.0 s: HIGH confidence in the log, but I did not produce them.** The 6.035 h shard figure and the 6.160 h total are two different numbers and the corpus quotes them interchangeably (F-37-6). - **@23 for cap-35: LOW-MEDIUM, as above.** - **The claim "@43 is unreachable by this engine": HIGH.** It is computed inside PART 0 from 43# = 1.45 x 2^53, and I reproduced PART 0 today. WHAT I SUSPECT AND COULD NOT PROVE. - **The CAL4 = 0.87 constant is probably wrong at @17 too, by more than at @13.** Implied CAL4 at @13 is 0.932164. Nothing measures it at @11 or @17, so I have one point and no trend. If CAL4 drifts with level, cap-32's @17 T4 = 4,616,850,623,332 +- 4e-4 may be biased rather than merely imprecise, and the +-4e-4 would be an understatement. **Cheap test: run the same implied-CAL4 extraction at @11, where `bruteTG` gives the exact truth in seconds.** I did not, because it needs a new stage and the brief forbids changing what the script computes. - **The k4 Monte-Carlo error may be the reason cap-32's @17 figure carries +-4e-4 rather than something smaller.** At @13 k4-by-MC alone is 8.29e-10 of T4 at n = 2e8; the shape count grows fast with N. Unproven; I have one level. - **`wave7-logs/` may hold other mis-attributed logs.** `cap34-cap27-custody.log` was one. I checked only the three in my partition. The naming convention ("cap34-cap27-custody") is ambiguous by construction: it reads as "cap-34's cap-27 custody log" and is in fact "cap-27's output, run as cap-34's custody target". **Someone should check `cap36-cap30-repro.log` and `lemmaV-pilot-rerun.log` for the same shape.** I did not. - **The corpus has no convention for logs living outside the repo.** Three partitions' worth of primary evidence sits in `~/Files/primeoire-runs/`. There is no `.gitignore` entry, no README pointer, and `SCRIPTS.md` does not mention it. That is a structural risk, not a finding, and it is above my pay grade.