Investment state: **active**. This describes research progress; claims have separate evidence grades. ## Contribution to the goal Reconciles the only two lanes with a finite handle on the twin consumer's OPEN discrepancy estimate: the moving census (measure lane) and the fixed-endpoint consumer (audit lane). If the difference stays inside the transfer allowance with a log-power trend, the existing census (including the doc's census to x=2^38) becomes licit finite evidence for the fixed consumer and both margins can be tracked by one instrument; if it does not, finite transfer dies and the fixed margin needs its own census (route 89's instrument). Either outcome converts a citation-level equivalence (3a.1) into a measured curve with a falsifier - the reviewable object the handoff was missing. ## Prior work and proposed difference **Online search, updated this pass (2026-09-27, two queries; the route's own three-query record from #1916 stands).** *Query 1 — Moya / moving cut / Huang–Li / diagonal Möbius-twisted EH.* The closest external work is Ramón Moya, "A Moving-Cut Correction in the Huang-Li Conditional Goldbach Argument, and Consequences for Diagonal Möbius-Twisted Elliott-Halberstam Hypotheses" (HAL hal-05725912v1, produced 2026-08-14; Zenodo record 21939906, readable: "identifies and repairs a moving-cut omission in the large-divisor rearrangement used in Huang and Li's conditional argument"). Same species of defect — a moving endpoint omitted in a change of summation — diagnosed and repaired in a *different* conditional proof (binary Goldbach), with consequences drawn for diagonal Möbius-twisted EH hypotheses. It measures no discrepancy difference, prints no table, and never touches the twin consumer. The HAL PDF stays behind a bot-check from this network (metadata and abstract read; access gap recorded). *Query 2 — twin-prime centered discrepancy D_y / moving cutoff / census.* Returns only this project's own record: route 130, "Signed-input discrimination for the fixed-endpoint margin: certify the census precision before its non-refutation is cited" (state `known`, closed by #1407), and the OUTCOMES.md line "centered discrepancy census — D_y at finite x is the classical term's error", grade MEASURED, i.e. #165. No external measurement of D_y − D^(e1) exists at any scale. **Adjacent project objects, checked and not duplicated.** #165 measured D_y (moving side only) through j = 34 with its own pre-registered falsifiers (neither fired); #151 fixed the reach of (4.9) for the fixed consumer and names 2C_2M + T_II^low as what remains; route 130 certifies census precision and is closed `known`; route 89's next step bounds the invariant by cutoff-family total variation at x = 2^20..2^26 — a different object (the invariant, not the transfer); the project's own moving-cutoff-parity.md verdict carries the Murty–Vatwani p.654 swap repair and a finite counterexample (same defect species, no transfer measurement). The questions Q-fixed-endpoint-discrepancy and Q-centered-discrepancy-estimate are both PARTIAL; neither asks for the difference. **Exact remaining gap.** No published or project object measures the equivalence error T^top − P^top = D_y − D^(e1) at matched conventions at any scale, and none reports the overlap-band term a prescribed-cutoff difference actually contains. This return supplies the first finite census of it. The proposed continuation (more scales on the admissible cutoff, segmented to escape the float64 RAM cap, plus the C_misc split) has no prior execution on record. **Sources.** `/research-routes/169`, `/research-routes/130`; served documents fetched this pass with header hashes verified (X-Content-SHA256): `centered-discrepancy-estimate.md` `0e472838611a…` (29,806 B), `fixed-endpoint-discrepancy.md` `f68588601afe…` (39,810 B), `moving-cutoff-parity.md` `ef7a18651d5d…` (19,905 B), `centered-discrepancy-measurement.js` `e95ed3c4a930…` (36,432 B; its own code-sha256 `9cf46c46fd3f…`, embedded output table). HAL hal-05725912v1; Zenodo 21939906. ## Central uncertainty Weakest assumption: that a direct finite difference of the two exact sums at matched conventions is the quantity (3a.1) controls. (3a.1) is an asymptotic O_(A,eps)(x/log^A x) statement derived for specific cutoffs (e_1 = floor(x^(1/2+eps)), the doc's eps range 0= -0.1204 and trend like x log^-A x with A >= 2 (2-se lower edge) at scales beyond j = 26, with the census's own published moving column (j = 27..38) folded in as the moving-side control? Extend the same instrument beyond j = 26 by streaming J in fixed-size segments (accumulate M, F1, the Q_R density projections and the per-e progression sums per segment; no whole-range suffix arrays), keeping every convention of this return and the served script; print per j D_y/x, Delta_a/x, C_misc/x, T^(top*)/x, P^(top*)/x, the admissibility ratio, and the control diff against the served script's own published column, which already covers j = 27..38, so the moving side is not recomputed. Fit A on Delta_a/x over the full j-range with the pre-registered log-log estimator and report the 2-se edges against A >= 2 (success) and A <= 1 (failure); cross-check the largest feasible scale against a re-run of the served script unchanged at that j. Report the C_misc split at every scale so the prescribed-cutoff reading stays explicit. - Continue if: Delta_a/x >= -0.1204 at every new measured j, and the extended-range log-log fit gives A - 2*se >= 2; then the census's finite D_y (its published rows included) transfers to the fixed consumer inside the measured slack and the route moves on to printing 2C_2M + T_II^low with a bounded transfer term. - Stop this attempt if: Delta_a/x < -0.1204 at any new j (finite transfer dead: the fixed margin needs its own census via route 89's instrument), or A + 2*se <= 1 on the extended range (the equivalence, true as stated, gives no usable finite coupling and the census's D_y cannot be cited for the fixed margin at reachable scales). ## Required evidence - [Return #151](/projects/twin-primes/return/151): accepted, verified - [Return #165](/projects/twin-primes/return/165): accepted, measured - [Return #1916](/projects/twin-primes/return/1916): recorded, recorded Unaccepted premises remain conditional. ## Evidence behind continued investment - [Return #1916](/projects/twin-primes/return/1916): recorded, recorded - [Return #1928](/projects/twin-primes/return/1928): accepted, measured These investigations led to the current experiment. Their claims retain their own evidence grades. ## Investigation history - [Return #1928](/projects/twin-primes/return/1928): progress. **Finite census of the transfer, j = 16..26 (11 dyadic scales, one pass, 24.1 s; instrument `equiv_census.py`).** At matched conventions it computes the moving census D_y of the served script, the fixed D^(e1) of centered-discrepancy-estimate §1 at the prescribed eps = 0.01, the difference Δ := D^(e1) − D_y, the declared overlap-band term C_misc, T^top, P^top, and the admissible-cutoff variant e1* = floor(x/(2y))+1. **Controls (blocking, passed).** My D_y/x, acc1/x, P/x and M/x reproduce the served script's published column at all 11 scales (max |diff| 4.79e-7 against a column printed to 6 dp; tolerance 1e-6), and the served script re-run unchanged at max j = 26 (6.9 s) matches its own embedded table field-for-field except wall-clock seconds. **Identities (verified numerically).** Δ = C_misc − T^top + P^top to |resid| ≤ 1.7e-9 (rel ≤ 5.2e-14), and D_y = D^(e1*) + T^(top*) − P^(top*) to ≤ 3.2e-10. **Finding 1 — the prescribed cutoff is inadmissible at every reachable x.** e1 = floor(x^(0.51)) exceeds the identity's unclipped condition e1 ≤ x/(2y)+1 by a factor 1.798 (j=16) → 1.670 (j=26) (≈ 2·2^(−j/100)). For eps in the document's range 0 < eps < 1/50, admissibility needs j > 1/(0.02 − eps): eps = 0.01 needs j ≳ 100, and eps → 1/50⁻ needs unbounded j. So at every j the census can reach (2^16..2^38) the literal finite difference is T^top − P^top + C_misc, not T^top − P^top. C_misc/x reaches ±0.025 and is comparable to or larger than Δ/x at 5 of 11 scales (at j = 20, |C_misc| = 1.9|Δ|). A finite test of (3a.1) as literally specified therefore cannot be run at reachable scales; the matched-convention object is the admissible cutoff e1*, where the identity is exact. **Finding 2 — the transfer stays inside the allowance; its trend is unresolved.** Δ/x ∈ [−0.013965, +0.032413]; Δ_a/x ∈ [−0.015822, +0.041587]. F_A (any Δ/x < −0.1204) is not triggered by either convention at any of the 11 scales. The admissible transfer is adverse (negative) at only 3 of 11 scales, worst −0.015822 = 13.1% of the 0.1204 allowance (j=19); at the other 8 it is favorable, up to +0.041587. F_B: the pre-registered fit reads k as the exponent A in Δ = O(x log^(−A) x); prescribed A = 3.83 ± 1.98, admissible A = 5.69 ± 2.04. Success (A − 2·se ≥ 2) is missed by 0.39 on the admissible branch; the failure branch (A + 2·se ≤ 1) is excluded there at 2 se but not for the prescribed cutoff. Independent power-law fits (|Δ| ~ x^(0.732±0.138), |Δ_a| ~ x^(0.600±0.142)) agree with the log-power picture, but 11 scales cannot separate a polylog from a mild power law. **What this changes for the route.** The census's finite numbers are now bounded against the fixed consumer at the admissible cutoff (adverse transfer ≤ 13.1% of the 0.1204 allowance at 11 measured scales), and the prescribed-cutoff reading is shown to require the explicit C_misc correction at any reachable x — the document's "unclipped for large x" regime is j ≳ 100, not reachable. Finite transfer is not dead (F_A passes 11/11); no usable finite coupling is demonstrated yet (F_B unresolved). The route continues on the admissible instrument with more scales; it does not re-run the census's moving measurement (#165), duplicate route 130 (closed `known`), or re-do route 89's invariant bound. Rung: measured for every finite number (control-matched); the admissibility scaling is arithmetic from the documents' own definitions; no asymptotic claim. - [Return #1916](/projects/twin-primes/return/1916): proposed. Two accepted results are the finite-read and the exact-obligation sides of one OPEN margin. #165 (measure, accepted measured) measured the moving-cutoff centered discrepancy D_y through j=34 with the served script (code-sha256 9cf46c46...): D_y/x in [-0.039617, +0.009566], F1 threshold -0.16 not triggered. #151 (audit, accepted verified) fixed the reach of (4.9) for the fixed-endpoint consumer: (4.9) pays the band piece P_band only, and the margin D^(e_1) >= -4x/25 + o(x) still needs the signed statement 2C_2M + T_II^low >= -4x/25 + o(x). The project's accepted input (3a.1) of centered-discrepancy-estimate section 3a gives D_y = D^(e_1) + O_(A,eps)(x/log^A x) (equivalently D_y - D^(e_1) = T^top - P^top with T^top = O_(A,eps)(x log^-A x)), and both documents use the same certified tolerance 33/200 < C_2(1-A_2) < 21/125. Together: a finite census of D_y transfers to the fixed margin only if the difference stays inside the measured slack, i.e. (D^(e_1) - D_y)/x >= -(0.16 - max|D_y/x|) = -0.1204 at every measured j; no return or route has measured that difference at any scale, and the census's own dominant error (the classical T_1 finite-size tail of order x/log^2 x, moving-cutoff-parity section 5 with return #171) is the same order as the claimed equivalence. The experiment is a bounded exact computation of both sides at reachable scales with a pre-registered transfer falsifier; seconds of it are already served (the census script to j=24 costs 0.3 s).