PROG-R4 unit E, THE H-HARD DIAGNOSTIC: is the obstruction the seed supply, or the realization?

Unit: PROG-R4 unit E (leg 380, wave 1), ORCHESTRATION.md §3g CONDUCTOR mode, Lane R. INSTRUMENT unit: it answers a gate about whether three diagnostics RETURN, not about whether anything converges. Mode: §3f SOLO. UNVERIFIED: produced and checked in one session, no paired verifier. Data of record: writeup/data/p2_prog_r4_e_v1.json; ledger experiments/programme_r4/e_hhard_ledger.json; converged fields experiments/programme_r4/e_hhard_converged_orbits.npz. Read-only inputs: experiments/programme_r4/u3_g1_ledger.json, u5_m3_ledger.json, u2_recurrence_library.json, writeup/data/p2_route_dsspb5_v1.json. Evidence: experiments/p2_prog_r4_e_evidence.py, 60/60, re-derives every number below from banked records, re-running no solve. Figure: fig109, 17/17 checks. Pre-registration: experiments/journal/prog_r4_e.md §§0–4, commit 70f3962, before the first attempt ran. Journal: experiments/journal/prog_r4_e.md.

G1 IS NOT RE-ANSWERED HERE. It stays UNDER-RESOURCED as banked in writeup/data/p2_prog_r4_g1_v1.json, which this unit does not write to. 0 of 16 is a count, pre-registered as such; it is not a no at G1, and no G1 re-open is raised.

1. The gate, and the answer

Do all three diagnostics return, each with a planted control that fires both ways?

YES. All three returned; each carries a planted control demonstrated firing in both directions. The gate is about the diagnostics returning, not about convergence: a clean non-convergence with working controls passes it.

Branch fired: E-iii: "converges to something else."

Ceiling: TIER 2. Nothing here is a proof. No L1 → L4 link moved. Clay stays ~0.05%.

2. What was planted, the E-iv discipline, stated before the run

A published Table IV row (arXiv:1406.1820v2) determines (T, s, m) and NOTHING ELSE. It does not determine a field. Every attempt therefore plants a field-plus-pinned-(T,s) seed, and no sentence in this unit calls that "seeding at the published orbit."

Two arms per row, one field each, no field reused: arm S "shift-matched field" (lowest R among candidates whose measured |s| is within 0.05 of published), arm Q "score-optimal field" (lowest R outright) the field U3 would have chosen).

The R < 0.25 Newton admission window is DELIBERATELY NOT APPLIED. U3 §5 measured it monotone in the very coordinate the targets are separated on; this is the unit entitled to ignore it, and neither U3 nor U5 ever ran a seed from outside it. One seed here (UPO35 arm S, R = 0.478) sits outside it.

Solver held at U5's values and imported rather than copied: Newton–GMRES–hookstep, tol = 1e-8, max_newton = 52, max_gmres = 140, gmres_rtol = 1e-3, fd_eps = 1e-6, U5's stall exit (k ≥ 20, window 10, threshold 0.5). Matching predicate is U3's, unchanged: a recovery requires both |ΔT| < 0.05 and |Δs|_{2π} < 0.05.

3. The prior: leg 353, stated up front, not rediscovered

Leg 353 attempted UPO37 (×2), UPO35, UPO9 and UPO22 and failed all five at line_search_failed, final ‖R‖ ∈ [22.5, 29.5]. This unit is a new measurement, not a re-walk, for two named reasons: leg 353 used a T_total = 2000 DNS against U2's T = 1e5, and plain-Newton line search, not the hookstep.

4. Diagnostic (1): PULL_TO_LOW_S

Over the 200 banked attempts (U3's 100 + U5's 100, read and never edited), 23 reached tol. All three pre-registered clauses hold:

Spearman(seed, converged) = 0.3205, the seed shift explains little of where a solve lands. 6 in-band seeds converged and 5 left the band.

The SECONDARY all-200 reading returns NO_PULL (median −0.0239, 120/80, p = 0.0057, but only 38.5% below 0.15 and Spearman 0.793) and is reported, not suppressed: a non-converged attempt has not landed anywhere, so its terminal |s| is mostly its seed |s|. The pull is a property of the solutions this realization reaches, not of every trajectory.

Controls: converged |s| := 0.10 → PULL_TO_LOW_S; converged |s| := seed ± 0.001 → NO_PULL (p = 1.0). Both ways.

5. Diagnostic (2): MIXED, and the ban

An accepted epoch is constrained if the accepted hookstep trial sits on the trust-region boundary (the minimisation chose the step) and unconstrained otherwise. Over 2,195 accepted epochs:

Observed rate difference −0.000853, within-attempt label permutation p = 0.9317 (20,000 perms, PERM_SEED = 380). The rates are indistinguishable, so the rule returns MIXED and this unit does not get to say the minimisation is dragging the solve. 98.0% of the descent is on constrained epochs because 97.1% of accepted steps are constrained at all, in this realization the full Newton step is almost never taken. corr(Δ‖R‖, d|s|) = +0.1954.

THE BAN, CONFIRMED. Because (2) did NOT return MINIMISATION_ATTRACTOR, the commissioned "the fix is in the SCORE" conditional does not fire and nothing is proposed. Independently, leg 349's ban is COMPLIANT and was never approached: every score touched is deterministic and pre-existing (U2's recurrence score R, the solver's extended residual). Nothing was fitted, learned, evolved or tuned to an outcome, and this unit proposes no learned or evolved seed-scoring fitness.

The score's own bias, re-derived from U2's library (1,153 m=0 candidates): Spearman(|s|, R) = 0.5012; admission fractions 43.79 / 20.19 / 11.53 / 2.86% across |s| ∈ [0,0.15) / [0.15,0.295) / [0.295,0.707) / [0.707,π]. The published band is the third cell. That reproduces U3 §5's 0.50 and 44/20/11/3 from the library rather than from U3's table.

Coverage limit, declared in the pre-registration: the per-epoch |s| path exists for U5's 100 attempts only, U3's ledger predates those fields. Cost to close: 122.1 core-hours. Not bought, not needed for this gate, not hidden.

6. Diagnostic (3): 16 attempts at the eight named rows

2 of 16 reached tol. 0 recovered their own named row. 0 recovered ANY named row. 0 secondary sign-agnostic |s| matches. Exits {stalled: 14, converged: 2}.

The two convergences are genuine solutions of this realization and neither is its row:

Both landed below diagnostic (1)'s 0.15 shelf, from seeds pinned at 0.707 and 0.295. That is the pull of diagnostic (1) reappearing at the strongest seed quality this programme can construct.

Closest approach: UPO35 arm S, ΔT = 0.0362, Δs = 0.0854, final ‖R‖ = 9.669: inside the box on T, just under 2× the tolerance out on s, and a STALLED attempt, not a solution.

No attempt hit the iteration cap. All 14 non-convergences stopped at the pre-registered stall exit at 20–31 of 52 available epochs, so "more Newton iterations" is not the obviously-missing resource.

Arm S starts closer and finishes further, 8 rows out of 8. The shift-matched field has the lower seed residual in every row, yet arm Q's mean final residual is 1.66 against arm S's 5.15, and both convergences are arm Q. The recurrence score, which knows nothing about the published rows, predicts Newton progress better than agreement with the published shift does.

Instrument fact (E-iv): the seed residuals here span [20.06, 54.94] against ≈14–19 for the mined seeds U3 and U5 ran. Planting at the published (T,s) yields a WORSE starting point than the repository's own mining: the direct cost of the row not supplying a field.

Controls. P (exact relative equilibrium in closed form, perturbed 0.1%) → converged, ‖R‖ = 7.75e-09, 33 epochs. N (phase-scrambled field at the same (T,s)) → did not converge, ‖R‖ = 51.46, 51 epochs, max_newton_hit. R (banked U5 convergence attempt007_P_UPO37, perturbed) → converged and matched back, ‖R‖ = 1.52e-10, 5 epochs, ΔT = 2.99e-07, Δs = 6.50e-08, harness_predicate_says_recovered = True. fired_as_planted = True, failures = [].

Control R is what makes the zero a measurement: the same predicate that returned 0 recoveries can return a recovery, on this solver, at this tolerance, in this harness.

The stall rule was re-validated before use: replayed against both banked ledgers it kills zero of U3's 14 and zero of U5's 9 convergences (worst 10-epoch ratios 0.0724 and 0.0606 against 0.5).

7. The branch, E-iii, with E-ii's antecedent recorded

E-iii fired: "converges to something else." Two convergences at 1e-9 and 1e-10, neither its row, both at low |s|, distances quantified in §6 and drawn in fig109 panel D where the matching box is empty.

E-ii's antecedent is also literally satisfied, 0 of 16 recovered any named row, and is recorded, not suppressed: on this evidence the obstruction sits in the realization rather than the search, which would be the first evidence in this programme that what G1 has been measuring is the realization rather than the budget. E-iii is reported because it is the more specific of the two: E-ii names an absence, E-iii names what happened instead. E-i did not fire. No fifth branch is constructed.

8. Leg 353 (agreement and disagreement

AGREEMENT: under a bigger DNS, a better solver and twice the row coverage, this unit also recovered none of the named rows.

DISAGREEMENT, three: (i) line_search_failed does not occur once and cannot) the hookstep always accepts a step, so plain Newton's failure mode is unreachable; every attempt exited at the stall rule or at tol. (ii) Final ‖R‖ spans [0.80, 10.32] against [22.5, 29.5], from worse seeds. The bigger realization gets strictly further into the problem and still recovers no named row. (iii) It converged at all: twice, to other solutions.

9. §3d: cost, and the scale at which the question is properly posed

This is a measurement of THIS realization at THIS budget. It is NOT a no about the named rows and may not be quoted as one.

Spent: 5.687 core-hours banked (0.569 h wall on 10 workers) plus 0.806 h of controls; the sum of per-attempt wall over all 16 attempts is 9.088 core-hours, and one unattended launch was killed by the host after ~2 h with nothing banked.

The commissioned model was ~0.0713 h/attempt; the true figure is ~0.57 h/attempt: an ~8× under-estimate, structurally so: mined-seed attempts stall early, while an attempt planted at a published (T,s) runs 20–31 epochs before the stall rule fires. A plausible seed is expensive precisely because it does not fail fast.

None were bought and none are proposed as work. No new DNS, no new seed mining, no new solver construction, no re-run of U5, and no proposal of more seed supply for PROG-R4. The numbers exist so the next person knows the price instead of rediscovering it.

10. Lesson 91, what this negative names

Realization: 2-D Kolmogorov flow, N = 24, Re = 60, n = 4, dt = 0.01, 2/3-rule dealiasing, RK4 with an exact viscous integrating factor in a Lie–Trotter split that is globally FIRST order in time; fields from U2's single T = 1e5 trajectory. Trial space: 16 field-plus-pinned-(T,s) seeds (8 rows × 2 arms, one field each, from the 1,153 m = 0 candidates anchored by |T_c − T_pub| ≤ 1.0, with the R < 0.25 window deliberately not applied. Basis: real vorticity on a 24 × 24 grid; extended residual with continuous x-shift and period, two phase rows; m is not carried and the m ≠ 0 class cannot be expressed) which bites the instrument's generality, not these eight m_pub = 0 rows. Budget: hookstep, tol = 1e-8, max_newton = 52, U5's stall exit, 9.1 core-hours. Determinism: fixed recorded seeds (PERM_SEED = 380, N_PERM = 20000); every field a bit-for-bit re-integration of a recorded snapshot index; the sign of s measured, not drawn.

Scale is not evidence. The T = 1e5 trajectory buys candidates, not truth, and this unit's own headline is that the bigger realization got further and still recovered nothing.

Produced and checked in a single session with no independent reviewer, and therefore labelled UNVERIFIED under this project's own rules. Verification is a fresh pair of eyes or it is not verification.