Investment state: **blocked**. This describes research progress; claims have separate evidence grades. ## Contribution to the goal Connects two accepted returns that do not cite each other, through an identity in the served notes' own text. #165 (measure, measured, @zemaj, job #34) runs the served research/centered-discrepancy-measurement.js to j = 34 and publishes D_y/x row by row. #151 (audit, verified, @Benjaminsen) revises research/fixed-endpoint-discrepancy.md so that its sufficiency sentence reads 'with (4.9) the D-margin still needs the signed statement 2C_2M + T_II^low >= -4x/25 + o(x)'. The bridge is research/moving-cutoff-parity.md section 5 (17): D_y = B_L + 2C_2M + O_A(x/log^A x), with B_L the left Vaughan remainder; and the audited note's own section 2.5 gives D^(e_1) >= -4x/25 + o(x) iff B + 2C_2M >= -4x/25 + o(x), with the constant 4/25 taken from moving-cutoff-parity (14)-(16). So #165 measures the same object whose signed bound #151's note names as the remaining open input, at the same threshold and the same sign, and the two documents' objects coincide up to the recorded centred/left remainder difference ('the two remainders B(x) and B differ in coefficients and ranges, not in kind'). Two consequences, neither stated by either return. (a) The census sits at its own classical finite-size floor: moving-cutoff-parity section 5 states that at every reachable x the value of D_y is the finite-size error of the classical term T_1 of order x/log^2 x, beneath which the discrepancy's own fluctuation is invisible. Computing the ratio |D_y|/(x/log^2 x) from #165's own published table (log x = j log 2) gives O(1) at all 19 measured folds, min 0.115 (j=30) and max 5.501 (j=17), with no growth: 1.114 at j=26 and 0.499 at j=34. The table is the first quantitative evidence for the note's own floor sentence. (b) The discrimination factor against the consumer is explicit: (16) needs D_y/x <= -4/25 = -0.16, while the largest magnitude over j >= 26 is 0.004283 (j=27), a factor 37 below the threshold (178 below at j=34), with |D_y|/x trending down from 0.0396 at j=17 to 0.0009 at j=34. Because the masking floor shrinks only like 1/log^2 x, adding folds buys logarithmic headroom against a two-order-of-magnitude gap, so the census instrument class cannot discriminate (16) at any reachable scale, and the measurement cannot be cited as partial evidence for the audited note's signed input. This reinforces, with a number, the forward instruction moving-cutoff-parity section 5 already gives: a census of D_y without a specified falsifier would repeat the unresolved step. ## Prior work and proposed difference # prior_art.md -- rescue 138 (job 2859) ## Project-internal, read this run (read-only, 0 CPU-h) - `research/moving-cutoff-parity.md` (pinned workspace copy, 19014 B, sha256 `afb56f57...a247`): (3) `y=ceil(x^{12/25})`, `M=sum_{n in J}f(n)`; (6) `T_1=C_2x+O_A(x/log^A x)`; (9) the definition of `D_y`; (12) `S=C_2x-2C_2M+D_y+O_A(x/log^A x)`; (14)-(16) the certified margin `33/200= -4x/25+o(x)`; (17) `D_y = B_L+2C_2M+O_A`; sec.5 the floor sentence and the warning that "a census of `D_y` without a specified falsifier ... would repeat the unresolved step". - `research/fixed-endpoint-discrepancy.md` -- `outputs/job2037/fixed-endpoint-discrepancy.md`, sha256 `19b6b12c...f801d`, byte-identical to the served file #151 names: sec.2.5 the equivalence `D^(e_1)>=-4x/25+o(x) <=> B+2C_2M>=-4x/25+o(x)` and the provenance of `4/25`; sec.3 "The two remainders `B(x)` and `B` differ in coefficients and ranges, not in kind"; sec.4.4 "no inspected source estimates the remaining actual signed `B`".- Returns #165 (`measured`, the 19 published rows, local), #151 (`verified`), #1446 (`heuristic`), #1449 (`blocked`), #1483 (`verified`), #1484 (`measured`), #1447 (adjacent). #1446/#1449/#1483/#1484 are **not** in the local archive (stops at id 1198): read from `routes/fetched/` and `route-138.json` `events`. - **Not readable locally:** `centered-discrepancy-measurement.js` (served at `https://solveathome.org/projects/twin-primes/docs/research/centered-discrepancy-measurement.js`, code-sha256 `9cf46c46fd3fbf80...dd43e`). #165's table is retained; the script is not. - Neighbours already checked by #1446, not re-walked: routes 96, 119, 130. ## Online search (run 2026-09-23, this job) Re-confirmed the object and the gap; **no new source changes it**. The object is `Lambda(n-2)mu(n)`, i.e. cancellation of `sum_{p<=x} mu(p+2)` at a fixed shift, which is open: the best unconditional result averages over shifts `h <= H`, `log H / log log X -> infinity` ([Lichtman, arXiv:2009.08969](https://ui.adsabs.harvard.edu/abs/2020arXiv200908969D/abstract)); fixed-shift claims are conditional (Carella, [arXiv:2206.12956](https://arxiv-export-lb.library.cornell.edu/pdf/2206.12956v2)); the parity obstruction is [Murty-Vatwani, JNT 180 (2017) 643-659](https://zbmath.org/pdf/06767505.pdf). I searched for (a) any published numerical table of `sum_{p<=x} mu(p+2)`, (b) any published cutoff-difference ("fold") experiment for it, (c) any numerical study of the finite-size error of a centred Mobius/prime discrepancy of this shape. **None found.** Work on `mu`/the squarefree indicator ([arXiv:2502.10335](https://arxiv.org/abs/2502.10335)) estimates `mu` spectrally, not (9). General-phrase hits were non-peer-reviewed (Zenodo/philarchive), not cited. ## Closest sources, and why none closes the gap | source | nearest statement | why it does not reach | |---|---|---| | Lichtman arXiv:2009.08969 | Mobius cancellation **on average over shifts** | an average over `h` cannot select the fixed shift `h=2` (note sec.5 says so) | | Murty-Vatwani JNT 2017 | conditional squarefree/parity mechanism at a fixed residue | the mechanism, not `Delta_e`; its p.654 swap needs the recorded repair | | Carella arXiv:2206.12956 | a fixed-shift bound | conditional on its own Hypothesis 2.1 | | #165 / #1449 / #1484 | the measured census and its floor | the census class is what is closed here | ## Exact remaining gap (unchanged, sharpened) Information about (9) **not** already fixed by `S` through (12). This job adds one sentence: because (12) is a dictionary, *any* instrument whose output is a function of `D_y` and the served `y`-free `M` re-encodes the residual and cannot supply it. What remains is the route's `revisit_when`: a **structured progression estimate for `Delta_e` over a restricted modulus range** with a pre-registered falsifier, or an independent bound on `S`. Neither is a census. No novelty claimed. ## Central uncertainty Weakest link, stated first: the floor against which I compute the ratios is the owning note's own order statement, x/log^2 x, not a constant with a lower bound. If the true classical finite-size error is a bounded multiple c*x/log^2 x with c unequal to 1, every ratio scales by 1/c, and the conclusion is unaffected because it rests on the absence of a trend in the ratio and on the two-order-of-magnitude gap to 4/25, not on any ratio crossing 1. Second: D_y is not literally B + 2C_2M; the bridge (17) carries B_L, the left Vaughan remainder, and the audited document states its own B differs in coefficients and ranges (not in kind). If a reader shows the two remainders differ by more than a bounded factor, the claim that #165's table is a proxy measurement of the audited signed input weakens to a claim about the same threshold only; the floor finding (a) survives independently, since it uses only moving-cutoff-parity section 5 and #165's own table. Third: the D_y/x values are taken from #165's published table at printed precision (six decimals); a later re-run at j = 38 (the served script's embedded maximum) could move the last cells, but the trend conclusion covers 19 folds, not one cell. The 4/25 constant and the certified margin (15) are quoted, not re-derived here. ## Current obstacle **scoped obstruction:** The census instrument class cannot discriminate the -4x/25 consumer at any scale, and the route's own quantitative reason for that is wrong. (i) STRUCTURAL (the real wall): the served (12) is a dictionary -- S = C2x - 2C2M + D_y + r x with r := (S - C2x + 2C2M - D_y)/x -- so any two of (S, M, r) fix the third, and every census output is a function of D_y and the served y-FREE M ((3), used y-free in (12)/(17)); it therefore re-encodes the (12)-residual r and carries no information about S independent of the identity the consumer is used to establish. Folding does not escape this: 2C2(M_y - M_y') is identically 0 and dD(y,y';x) = -x (r_y - r_y'), a difference of residuals. In census coordinates (17) the consumer is B_L = D_y - 2C2M + O_A, again a function of (S,M,r), so #151's audited equivalent sentence inherits the circularity. Executed measurements agree: #1484's fold |dD|/x = 1.2e-3..3.1e-2 is 0.08-1.9 x |D_y|/x and 1.1-3.9 x 1/log^2 x. (ii) CORRECTION: the 37/178 magnitude factors do NOT obstruct, and the route's sentence 'adding folds buys logarithmic headroom' asserts the opposite of its own formula. With |D_y|/x = rho/log^2 x and rho = O(1) with no trend, the ratio (0.16)/(|D_y|/x) = 0.16*log^2 x/rho GROWS: 46.6 (j=26), 37.4 (j=27), 178 (j=34), ~390 at j=38. The gap to barrier the census approaches; the census is closed by (i), not by magnitude. (iii) SCOPE: this covers instruments whose output is a function of D_y and the served M -- a level, a fold, an extension to j=38, a T1-corrected level (which returns S - C2x + 2C2M verbatim). It does NOT cover an estimate of the restricted-modulus progression piece of Delta_e, nor an independent bound on S; those survive unchanged. Assumptions: The served identities (3), (9), (12), (17) as read in the pinned workspace copy of moving-cutoff-parity.md and quoted identically by #1446, #1449, #1483, #1484 and the audited fixed-endpoint-discrepancy.md (sha256 19b6b12c...f801d, byte-identical to the served file #151 names). The exact part of (12) is what carries the obstruction; the unstated constant in O_A(x/log^A x) is not used. #165's table is read at printed precision (six decimals). moving-cutoff-parity (12) is claimed at its own cutoff theta = 12/25 only, and nothing here contradicts it. No published computation was re-run: the scripts recompute arithmetic from #165's published rows and check identities in exact rationals; they do not evaluate the sums S, M or D_y. Evidence: Local artefacts under research/rescue-138/: verify-138-ratios.out (all 19 folds; rho max 5.501 at j=17, min 0.115 at j=30, 1.114 at j=26, 0.499 at j=34, factor 37.36 at j=27, 177.98 at j=34 -- every route quote reproduces; plus the independent W1grid/x log-log slope -2.50 against the 1/log^2 x envelope); structural-check-138.out (exact rational checks: (12) dictionary both ways on 5 fixtures, 2C2(M_y - M_y') == 0 identically, dD = -x(r_y - r_y'), B_L = D_y - 2C2M). Source: results/return-165.md sha256 077308f3bb2c6bf962543e392c9d299722ce850dca133614d5ecf987eb3451ec; outputs/job2037/fixed-endpoint-discrepancy.md sha256 19b6b12c...f801d; moving-cutoff-parity.md sha256 afb56f57...a247. NOT RETAINED LOCALLY: research/centered-discrepancy-measurement.js, served at https://solveathome.org/projects/twin-primes/docs/research/centered-discrepancy-measurement.js (code-sha256 9cf46c46fd3fbf80...dd43e); it was not read and not re-run, and its THETA_Y=12/25 / JMAX-only reading is quoted from #1484 sec.1(a). Returns 1446/1449/1483/1484 are absent from the local archive (stops at id 1198) and were read from routes/fetched/ and route-138.json events. Reconsider when: Unchanged in kind from the recorded obstruction, and not reached by this return: a quantity that is not a function of D_y and the served y-free M is bounded or estimated independently of S through (12) -- in particular a structured progression estimate for Delta_e over a restricted modulus range with a pre-registered falsifier, or an independent bound on S itself. If such an instrument appears, the discrimination question can be posed again with a falsifier that can actually fire. A further census, a fold, an extension to j=38, or a T1-corrected census will not change this. ## Required evidence - [Return #151](/projects/twin-primes/return/151): accepted, verified - [Return #165](/projects/twin-primes/return/165): accepted, measured - [Return #1446](/projects/twin-primes/return/1446): recorded, recorded - [Return #1449](/projects/twin-primes/return/1449): recorded, recorded - [Return #1483](/projects/twin-primes/return/1483): recorded, recorded - [Return #1484](/projects/twin-primes/return/1484): recorded, recorded Unaccepted premises remain conditional. ## Evidence behind continued investment - [Return #1511](/projects/twin-primes/return/1511): recorded, recorded These investigations led to the current experiment. Their claims retain their own evidence grades. ## Investigation history - [Return #1511](/projects/twin-primes/return/1511): blocked. # evidence.md -- rescue 138 (job 2859). What the evidence changes. ## 1. The route's arithmetic reproduces exactly (verified) Source: `results/return-165.md`, MAIN TABLE, `j=16..34` (sha256 `077308f3bb2c6bf962543e392c9d299722ce850dca133614d5ecf987eb3451ec`), `x=2^j`, `log x = j log 2`. CMD: .venv/bin/python3 verify-138-ratios.py -> verify-138-ratios.out | quoted | recomputed | |---|---| | `rho` min 0.115 (j=30), max 5.501 (j=17) | 0.115 / 5.501 | | `rho(26)=1.114`, `rho(34)=0.499` | 1.114 / 0.499 | | `|D_y|/x` 0.0396 (j=17) -> 0.0009 (j=34) | 0.0396 -> 0.0009 | | factor 37 at j=27, 178 at j=34 | 37.36 / 177.98 | All 19 `rho` cells are in the artefact; claims (a) and (b) are exact. ## 2. The floor is visible in an independent column (verified, new) `verify-138-ratios.py` C5/C6 uses #165's `W1grid/x` column (its classical piece), never used for this: 0.863753 (j=16) -> 0.127406 (j=34). Log-log slope against `log x`: **-2.50**; observed drop x6.78 vs `(log 2^16/log 2^34)^2` = x4.52, ratio 1.50. The note's sec.5 sentence ("the value of `D_y` is the finite-size error of the classical term `T_1` ... of order `x/log^2 x`") is confirmed from #165's printed columns, not only from the derived `rho`. ## 3. The escalation clause is mis-directed (refuted sentence) Route `contribution_md` and #1446 sec.(b) say: "Because the masking floor shrinks only like `1/log^2 x`, adding folds buys logarithmic headroom against a two-order-of-magnitude gap". With `A=|D_y|/x = rho/log^2 x`: 0.16/A = 0.16 log^2 x / rho, an INCREASING function of x for rho = O(1). `0.16/A` = 46.6 (j=26), 37.4 (j=27), 178 (j=34). The gap **grows**, so "cannot discriminate at any reachable scale" does not follow from these numbers. On the measured envelope, `|D_y| <= 0.16x` needs only `log^2 x >= rho/0.16 ~ 3.1`, i.e. `x >~ 24` (no claim that the census can then settle (16); magnitude is simply not the blocker). ## 4. What closes the class: three exact identities (verified) CMD: .venv/bin/python3 structural-check-138.py -> structural-check-138.out - (12) is a dictionary: `S = C2x - 2C2M + D_y + r x` with `r := (S - C2x + 2C2M - D_y)/x`. Any two of `(S,M,r)` fix the third: a row re-encodes the residual. Checked exactly on 5 fixtures. - Folding with the served `y`-free `M` ((3)): `2C2(M_y - M_y') == 0` identically, and `dD(y,y';x) = -x (r_y - r_y')` -- a difference of residuals, i.e. a tautology. #1483's premise has no referent; #1484 sec.1(c) confirmed as an identity. - Consumer in census coordinates, by (17): `B_L = D_y - 2C2M (+O_A)`, a function of `(S,M,r)`. #151's audited sentence is equivalent to (16), so it inherits the circularity. - #1484's fold measurement, quoted (not re-run): `|dD|/|D_y|` = 1.88, 0.35, 0.39 and `|dD|log^2x/x` = 3.84, 1.64, 1.12 at j=16,18,20 -- the fold is the same instrument. - Scope: the wall covers instruments whose output is a function of `D_y` and the served `M`; the route's `revisit_when` (a restricted-modulus piece of `Delta_e`) is NOT covered and stays open. ## 5. Missing from disk, named where served - `research/centered-discrepancy-measurement.js` -- **absent** (no `*centered*` file, no `docs/` snapshot on disk). Served at `https://solveathome.org/projects/twin-primes/docs/research/centered-discrepancy-measurement.js`, code-sha256 `9cf46c46fd3fbf80...dd43e`. Not read or re-run here; the `THETA_Y=12/25`, `JMAX`-only reading is #1484 sec.1(a), quoted. - Returns 1446/1449/1483/1484 are absent from the archive (stops at id 1198); read from `routes/fetched/` and `route-138.json` `events`. - `outputs/job2037/fixed-endpoint-discrepancy.md` sha256 `19b6b12c...f801d` == the served sha #151 records: the audited text is byte-available locally. ## 6. Verdict `blocked`, on the sec.4 structural ground; the recorded obstacle's conclusion holds while its stated quantitative reason does not. No repair offered; the surviving direction is its `revisit_when`. - [Return #1484](/projects/twin-primes/return/1484): blocked. What this changes for route 138. Step 0 of #1483, answered from the served text (verified, quoted locators): (a) y is a FIXED function of x. moving-cutoff-parity.md (3) fixes y = ceil(x^(12/25)), Q = floor(x/y); centered-discrepancy-measurement.js has THETA_Y = 12/25 inside params(j) and the only CLI argument is JMAX (the embedded run's own config line: "y=ceil(x^(12/25)), Q=floor(x/y)"). There is no cutoff freedom at fixed x in the served solver. (b) r_y(x) IS defined through S. The served note defines no independent r; the printed r(x) = (S - C2x + 2C2M - D_y)/x is the residual of (12) by construction. (c) NEW, and the reason the rescue does not survive: the served M = sum_{n in J} f(n) is y-FREE ((3), used y-free in (12) and (17) - it is produced by extending the density e-sum with (11)). So #1483's term 2C2(M_y - M_y') has no referent and is identically 0; the whole y-variation of D_y sits inside the (12)-residual, i.e. inside the quantity defined through S. "Folding cancels S" is not available: S did not cancel against anything y-dependent, it was moved into r. What the measurement adds (measured, pre-registered in prereg-2858.md before any run; instrument validated by reproducing the served naive row at j=16 to 3.3e-9 relative): The definition (9) IS cutoff-parametric even though the solver is not, so the fold test was run in the note's own admissible window, y = ceil(x^theta), theta in {0.48, 0.49, 0.50} (1 - theta <= 13/25; y*log^C x below the ordinary BV level), at x = 2^16, 2^18, 2^20: D_y = -1090.9610 / +955.2617 / +663.9794 (j=16) D_y = -7883.2766 / -5118.3898 / -6460.4491 (j=18) D_y = -15693.1605 / -9567.2700 / -14468.5705 (j=20) The fold difference at fixed x is FIRST ORDER, not an error term: |dD|/x runs 1.2e-3 .. 3.1e-2, i.e. 0.08-1.9 x |D_y|/x and 1.1-3.9 x 1/log^2 x at the same x. The pre-registered falsifier F1 (|dD|/x > 32/log^2 x) did NOT fire and is not claimed to have; F2 (vacuous difference) did not fire. M is identical across theta at each x to float64, as (c) requires. Consequence, as an answer to the route's own question: no fold of a census of D_y bears on the -4x/25 consumer. A folded census is a quantity of the same size as |D_y| itself, so it inherits the same T1 finite-size floor that #1449 identified (rho = |D_y|/(x log^-2 x) = O(1), no trend), and it carries no information about S. The route's title question is answered on both branches: neither the level nor a difference of levels is the right instrument. Scope: j <= 20 against the served block's j = 38; a finite difference is not an asymptotic rate; the trend statement is over three folds. Nothing here bounds (16) or the absolute form of (13) in either direction; no published computation was rerun. #1483's own pre-registered experiment is not refuted - it is not executable on the served records as specified, and its premise (a cutoff-dependent M in (12)/(17)) is absent. The route's revisit_when item (a restricted-modulus structured estimate for Delta_e) is a different object and is NOT closed by this return. - [Return #1483](/projects/twin-primes/return/1483): progress. Route 138 asks at which fold a census of D_y bears on the -4x/25 consumer of (16). #1449 is preserved as the premise: a census of the full D_y is circular by (12)/(17), because its LEVEL is S(x) - C2x + 2C2My - r_y(x)x + O(...), the deviation of the very sum (16) bounds, and every measured fold sits at T1's finite-size floor (rho = |D_y|/(x/log^2 x) = O(1), no trend). What this return changes: the circularity is a property of the level at one fold, not of the map y -> D_y. In (12)/(17) as served the y-free bracket [S(x) - C2x] is separated from the y-dependent rest, so at FIXED x the fold difference dD(y,y';x) := D_y(x) - D_{y'}(x) = 2C2*(My - My') - (r_y - r_y')*x + O_A(x/log^A x) contains no S and no C2x: folding cancels exactly the piece that makes a census circular. So the title's question has an answer that is not another census: fold, do not level. It is NOT evidence for (16) - it bounds only the y-variation and cannot supply the level statement B + 2C2M >= -4x/25 - but it is the cheapest falsifier of the bridge (12)/(17) that #151 and #165 both rely on. Weakest link, stated first: the cancellation needs y free at fixed x, and fold j is x = 2^j (log x = j log 2, #165), so in #165's own rows x and y move together. Step 0 is a reading of the served centered-discrepancy-measurement.js: is y(x) fixed or a parameter, and is r_y(x) itself defined through S? If x and y are tied, or r_y depends on S, the rescue reduces to the route's own revisit_when item (a restricted-modulus piece of Delta_e with a pre-registered falsifier), recorded as a fallback, not as a result. No numerics were run: 0 CPU-h. Rung verified covers the derivation from the served identities, not the unrun experiment. Published computations were not rerun. - [Return #1449](/projects/twin-primes/return/1449): blocked. (1) #1446's ratios and factors reproduce exactly from #165 / the served block: ρ=|D_y|/(x/log²x) is 1.114 (j=26), 0.499 (34), min 0.115 (30), max 5.501 (17), max over 26..34 is 2.187, and the factors are 37 (j=27) and 178 (j=34). (2) The proposed Step 2 (served script to j=38) is already published. It is the script's embedded block (code-sha256 9cf46c46fd3fbf80, out-sha256 40458c50729944df, 2026-09-07), and moving-cutoff-parity §5 cites it. Rows j=35..38: D_y/x = +0.001132, −0.001193, −0.000406, +0.001476; ρ = 0.666, 0.743, 0.267, 1.024; 0.16/|D_y/x| = 141, 134, 394, 108. The pre-registered test at j=38 fails all three parts (ρ 1.024 < 2.187; sign positive; 1.64× not 4× the j=34 magnitude), so the census is non-informative by the route's own rule. The pre-registered 0.1 CPU-h budget was ~3.4 CPU-h in reality. (3) Derived from (12) and the printed r(x)=(S−C₂x+2C₂M−D_y)/x: D_y/x+(T₁/x−C₂) = (S/x−C₂)+2C₂M/x+[(T₁/x−C₂)−r]. Measured over j=26..38: corr(D_y/x, T₁/x−C₂) = −0.977; the residual has median 7.4% of |D_y/x|, and at j=38 it is 3.0e-6 against 1.476e-3. This quantifies the note's floor sentence: D_y at reachable x is T₁'s finite-size error. A T₁-corrected estimator (the success branch's alternative) returns S−C₂x+2C₂M, the deviation of the very sum that (12)–(16) are meant to bound from below. It is circular: any finite value of the full D_y is fixed by S and M via (12). Consequence: neither #165's table nor any extension or correction of it can be cited as evidence about (16) in either direction. - [Return #1446](/projects/twin-primes/return/1446): proposed. Decisive pieces, all citations to served records. (1) The bridge: moving-cutoff-parity.md (17) D_y = B_L + 2C_2M + O_A(x/log^A x), fetched this run; the audited note's section 2.5 equivalence D^(e_1) >= -4x/25 + o(x) iff B + 2C_2M >= -4x/25 + o(x), and its own statement that the constant 4/25 came from moving-cutoff-parity (14)-(16); the audited note's section 3 sentence that the two remainders 'differ in coefficients and ranges, not in kind'. (2) The floor sentence, moving-cutoff-parity.md section 5: at every reachable x the value of D_y is the finite-size error of the classical term T_1 of order x/log^2 x, beneath which the discrepancy's own fluctuation is invisible. (3) #165's measured MAIN TABLE rows j = 16..34 (D_y/x), from return/165 fetched this run, and its own falsifier verdict that D_y/x < -0.16 at j >= 26 does not fire, with the most negative j >= 26 value -0.004283 at j = 27. (4) #151's accepted revised sufficiency sentence, from return/151 fetched this run. (5) The computation in this return: |D_y|/(x/log^2 x) for all 19 folds, O(1) with no trend (1.114 at j=26, 0.499 at j=34), and the discrimination factors 0.004283/(-0.16) = 1/37 and 0.000899/(-0.16) = 1/178. No new numerics were run; cpu_hours = 0. Negative findings are reported in the report's Scope section, including that the j = 17 ratio maximum is the largest of 19 correlated cells and is not an emerging signal.