# RUN-025 — Round 22: the legality rules and the lift pilot rebuild exactly; with dense cores the Pareto map's volume axis inverts, and the "cheap" harmonics cannot close their cell **Arm:** 懸衡 (Xuán Héng) / AMRAL Research Lab **Date:** 2026-09-25 **Subject:** `AMRAL_Lebesgue_Finite_Closure_Round_22_Fourier_Pareto_v0.1.md` (AMRAL-LUC-FC-R22, dated 2026-09-19) and its package, read from the archive: - `FOURIER_ORACLE_SPEC.json`, `PARETO_SUMMARY.json`, `VALIDATION.json`, `State_Crystal`; - `AMRAL_LUC_FC_Round_22_repro.py`, read only after this tree's reconstruction, and never run; - from earlier packages: Round 20's mixed-shard manifest (the four marked cells), and Round 21's synthesis summary (its image of q† and B7's placement there). **Tools:** [`run025_round22_fourier_pareto.py`](../code/run025_round22_fourier_pareto.py) — the mixture 0.92 B7 + 0.08 B3 as exact arcs; smooth witnesses (the pure harmonics, the recorded multi-mode candidate) bracketed between the hull of their contact points and a support polygon that includes the hull's bridging normals; RUN-023's B_n lift; a harmonic lift with the pilot's 40-direction cores or dense ones, and with the pilot's motion bound or the support's own **Logs:** [`run025-round22-fourier-pareto.json`](../data/gate-logs/run025-round22-fourier-pareto.json) **Verdict: PASS for the legality rules, the full-orientation rule and its example, the recorded multi-mode candidate and its verdict, and the lift pilot as computed; PARTIAL for the search minima of B7 and of the harmonics, which sit on both sides of the true ones; FAIL for the proof-cost Pareto map's volume axis — with dense cores the ranking inverts, and the two "cheap" witnesses cannot close the cell at all.** - **The legality rules are right.** - Odd modes keep the width at 1: to 2×10⁻¹⁶ on the recorded candidate. - |q + q''| ≤ Σ(k² − 1)√(a_k² + b_k²) is the triangle inequality, so the budget λ/2 is sufficient. On 48 random draws at the full budget, the radius of curvature stays ≥ 0. - The budget is also sharp. One mode at 1.02 times its budget, its trough on a vertex's normals, goes negative for every k from 3 to 11. - The recorded candidate spends 0.0339507 of 0.0369363 (91.9%). Its least radius of curvature is 0.00516, above the 0.00299 the budget guarantees. - For the pure harmonics, |a| ≤ 1/(2(k² − 1)) is exact: ρ reaches 0 at the bound and goes negative 0.1% past it. σ is 0.05 at 90% and 0.0025 at 99.5%, for every k. The package's amplitudes and its ratios 7/k are these. - The symmetry order is gcd(7, S). Measured: 1, 7, 7, 7, 1 for S = {5}, {7}, {21}, {7, 21}, {3, 7}. - **The mixture example rebuilds, on Round 21's image of q†.** - 0.92 B7 + 0.08 B3 is 18 exact arcs: support to 2×10⁻¹⁶, width 1, no rotational symmetry. - Its least hull area over the whole circle is 0.8358390980, at φ ≈ −0.077, outside [0, 2π/7). A second basin at φ ≈ 2.171 is 7.7×10⁻¹⁰ higher. The package's 0.83583910 is 4.4×10⁻⁹ above the least. - The package's "optimistic" 0.83742146 is the basin reached from B7's own minimising placement there: 0.8374213467, with the package's value 1.1×10⁻⁷ above it. - A search held to [0, 2π/7) does better than that basin, but stops on the domain's edge, φ = 0, at 0.8368710. The true basin lies just outside. - **The multi-mode candidate rebuilds — once B7 is turned to put a vertex at θ = π.** - The package records λ and all ten coefficients, but not which way h_B7 faces. - With a vertex at θ = 0, the four-cell minima miss the package's by up to 3.9×10⁻⁵. Mirrored, they miss by up to 2.8×10⁻⁵ and 1.2×10⁻⁵. - With a vertex at θ = π, they agree to 3.6×10⁻⁶, and the worst cell to 2×10⁻⁸. - B7 beats it on every cell, by 2.3–2.5×10⁻⁴, as §7 says. It also needs 7 times the orientation domain. - **The searched minima are off in both directions.** - B7, with the exact area and 28 starts per cell. The package's values sit 1.9×10⁻⁹, 1.0×10⁻⁷ and 3.3×10⁻⁶ above the minima on cells 03, 02 and 00. - On cell-01, its 0.83714197 is the other channel's local minimum (3.9×10⁻⁷ above it), 1.2×10⁻⁴ above the true 0.8370211. The worst cell — the one §7 quotes — is right. - The harmonics at 90%, bracketed to 2×10⁻⁹. The coarse scan sits 3.6–5.0×10⁻⁵ below the true four-cell minima for k = 9, 11, 15, 17 and 19. For k = 7 and 13 it sits 1.2×10⁻⁵ and 2.5×10⁻⁵ above them: it missed the worst cell's basin. - H11: the package's 0.83574698 is 1.7×10⁻⁵ below the true 0.8357638. Its "dense bracket at the found worst placement", [0.83578614, 0.83581539], lies 2.2×10⁻⁵ above the true minimum: that placement was not the worst. - H13: the package's 0.83563803 is 1.5×10⁻⁵ above the true 0.8356226, and its bracket 5.5×10⁻⁵ above. - H17 and H19 at high resolution are 3.6×10⁻⁶ below and 1.4×10⁻⁶ above the true 0.8350819 and 0.8350482. Both stay above T, by 8.2×10⁻⁵ and 4.8×10⁻⁵. - **The lift pilot rebuilds node for node.** - B7's depth-20 tree is RUN-023's: 7,037 nodes, 1,015 open. Its root volume is (2π/7)(2t₇)², with t₇ = 0.2014734. - The harmonic trees rebuild exactly under one convention, stated nowhere: - δ = |Δt| + 2(½ + |a|) sin(Δφ/2), the largest boundary-point motion; - the core h − δ at the pilot's 40 directions, with the bound π/4 while δ > σ; - the root [0, 2π/k) × [−0.21, 0.21]², and RUN-023's split. - Nodes and open boxes: H11 9,623/1,929; H13 9,211/1,755; H17 7,399/1,533, and at depth 22 15,581/4,252; H19 7,221/1,504 and 14,973/4,102. Every volume follows, to 10⁻¹². - §18's tail rates hold in the pilot's own terms. From depth 20 to 22 the open volume falls ×0.258 for B7, ×0.69 for H17 and ×0.68 for H19. - **With dense cores, the proof-cost ranking inverts.** - The pilot's 40-direction hull loses about 1.2×10⁻³ of area (RUN-022, RUN-024). With exact cores, B7 closes the cell at lift depth 21 with 2,509 nodes. - With cores at 4,096 directions — still a lower bound — H11 closes at depth 27 with 21,029 nodes, and H13 at depth 30 with 43,111: 8 and 17 times B7. - The pilot's δ is the loose part. The support of ½ + a cos kθ moves by only 2|a| sin(kΔφ/2), about a tenth of the boundary motion. With that δ, H11 closes at depth 24 with 1,581 nodes and H13 at depth 26 with 3,257. - H17 and H19 cannot close this cell at any depth, with any core. With the cell's erosion cores in place of the base bodies, their hull falls to 0.8346707 and 0.8346480 at a placement, below T by its upper bound. Their pilot volume at depth 20 is a floor, not a cost. - B7, H11 and H13 reach 0.8367313, 0.8354118 and 0.8352942 there, above T. - At the cell's centre with the whole base bodies, H17 and H19 stay above T, by 9.9×10⁻⁵ and 8.3×10⁻⁵. The cell's cores cost them 4.3×10⁻⁴. Only a finer base cell could let them close. - **What the package ships.** `repro.py` is 18 lines. It holds the budget sum and the pure-harmonic arithmetic, and prints H11's and H19's a, σ, period and ratio. Nothing ships the searches, the mixture, the multi-mode candidate or the lift pilot. Drill: 22 / 22 plants caught by exactly the named checks, 4 / 4 controls undisturbed, 288 / 288 must-stay-green assertions held. Each of the twelve checks was blinded in turn, and each was reported blind in exactly as many cases as plants name it. --- ## What Round 22 claims 1. **A symmetry-breaking family** (§1–4). - h = (1 − λ)h_{B₇} + λ/2 + Σ_{k ∈ {3,5,7,9,11}} (a_k cos kθ + b_k sin kθ). - Odd modes keep the width at 1. - Σ(k² − 1)√(a_k² + b_k²) ≤ λ/2 is a sufficient convexity condition. - The symmetry order is d = gcd(7, S), so any mode not a multiple of 7 costs a full 2π orientation domain: seven times B7's. 2. **The full-orientation oracle** (§5–6). - K = 0.92 B7 + 0.08 B3 shows an optimistic basin at 0.83742146, but a full-circle, multi-seed search finds 0.83583910. - The oracle's levels: TRAINING-SCORE, OPTIMISTIC-CANDIDATE, ROBUST-SEARCH-CANDIDATE, COMPILED-CANDIDATE, LIFT-VERIFIED. 3. **The multi-mode candidate** (§7–8). Training 0.83770073 and a single fresh seed 0.83733308, but four-cell minima 0.83683248, 0.83677292, 0.83674967, 0.83668617 — against B7's worst, 0.83692628. Re-training does not change the picture. 4. **Pure harmonics** (§9–15). - h = ½ + a cos kθ is legal exactly when |a| ≤ 1/(2(k² − 1)), with reserve σ = ½ − (k² − 1)|a|; h − δ is a legal core while δ ≤ σ. - At 90% of the bound σ = 0.05. H11 (a = 0.00375) reaches 0.83574698, and its bracket [0.83578614, 0.83581539]. H13 reaches 0.83563803, and [0.83567775, 0.83569731]. H17 and H19 reach 0.83507834 and 0.83504963 at high resolution. 5. **A generic support-core lift pilot** (§16–18). On the depth-50 cell, the open volume at depth 20 is B7 1.4107×10⁻⁴, H11 1.8536×10⁻⁴, H13 1.4270×10⁻⁴, H17 9.5317×10⁻⁵ and H19 8.3671×10⁻⁵. B7's tail contracts faster. 6. **The Pareto map** (§19–28). - Π(K) = (m_force, P_φ, σ, N_d, V_d, ρ_tail). - Roles: B7 the primary robust closer; H11/H13 balanced auxiliaries; H17/H19 cheap, razor-thin auxiliaries. The full symmetry-breaking candidate is not promoted. - A PURE-HARMONIC-CW compiler path, and Round 23: portfolio closure and batch cover. ## A — sources **A0.** 55 anchors. Round 22 has no reference list. ## W — rebuilt | check | Round 22 | rebuilt | result | | --- | --- | --- | --- | | W1 | §2–4, §9–12 | width, the budget and its sharpness, the recorded budget; the harmonic bound and reserve; symmetry | PASS | | W2 | §7 | B7 on the four cells, exact area | the worst cell right; cell-01 in the other channel | | W3 | §5 | the mixture as exact arcs, on Round 21's q† image | PASS | | W4 | §7 | the recorded candidate under four facings of B7 | PASS, with a vertex of B7 at θ = π | | W5 | §13–15 | H7–H19 on the four cells, bracketed | off in both directions | | W6 | §16–18 | the pilot's trees, roots and volumes | PASS, under an unstated δ | | W7 | — | the same cell with dense cores, both δ; the bounds' limits | the ranking inverts; H17/H19 cannot close | | W8 | — | what is shipped | the legality arithmetic only | **W1 — legality.** - The recorded candidate: budget 0.033950744437483665 of λ/2 = 0.036936283277021795, exactly the summary's, and fraction 0.9191706. Its width is 1 to 2×10⁻¹⁶. Its radius of curvature, (1 − λ)ρ_{B₇} + λ/2 + Σ(1 − k²)(a_k cos kθ + b_k sin kθ), has least value 0.00516 against the floor λ/2 − budget = 0.00299. - On 48 random draws of λ and of the active modes, scaled to spend exactly the budget, the least radius is 8.8×10⁻¹¹ ≥ 0. With one mode at 1.02 times its own budget, placed so its trough falls on a vertex's normals (where B7's radius is 0), the radius goes negative for each of k = 3, 5, 7, 9, 11. The bound is sufficient and, for a single mode, sharp. - Pure harmonics, k = 7 … 19: ρ = ½ − (k² − 1)a cos kθ is 0 at the bound and negative 0.1% past it. σ = 0.05 and 0.0025 at 90% and 99.5%, to 10⁻¹⁵. Each has symmetry order k and width 1. - The package's amplitudes (0.00375, 0.0026785714…, 0.0015625, 0.00125), reserves and ratios 7/k are these, as are the coarse scan's. - B7 plus small modes S has symmetry order gcd(7, S), measured on five sets. **W2 — B7 on the four cells.** - 28 exact-area Nelder–Mead starts per cell, φ over [0, 2π/7). Both of B7's channels are reached on every cell: | cell | package | channel A | channel B | least | package above | | --- | ---: | ---: | ---: | ---: | ---: | | 00 | 0.8370810228 | 0.8370777154 | 0.8370961319 | 0.8370777154 | 3.3×10⁻⁶ | | 01 | 0.8371419744 | 0.8371415885 | 0.8370210981 | 0.8370210981 | 1.21×10⁻⁴ | | 02 | 0.8369848645 | 0.8369847609 | 0.8369979155 | 0.8369847609 | 1.0×10⁻⁷ | | 03 | 0.8369262850 | 0.8370802310 | 0.8369262831 | 0.8369262831 | 1.9×10⁻⁹ | - Cell-01's value is channel A's local minimum, 3.9×10⁻⁷ above it. The worst cell, 03, gives §7's 0.83692628. **W3 — the mixture.** - On each interval where both owners are fixed, (1 − λ)B7 + λB3 is one arc: centre and radius the combinations of theirs. With both bodies facing the same way, that is 18 arcs. The support agrees with (1 − λ)h₇ + λh₃ to 2×10⁻¹⁶. - The base is Round 21's image of q†, whose least over the whole circle matches the package's full-orientation value. §5 does not say which base it used. | search | least | φ | package | | --- | ---: | ---: | ---: | | 28 exact polishes, spread over the circle | 0.8358390980 | −0.0769 | 0.8358391023 | | from B7's own placement (0.34722, −0.01081, 0.00663) | 0.8374213467 | 0.2911 | 0.8374214584 | | held to [0, 2π/7), 14 starts | 0.8368710231 | 0 (edge) | — | **W4 — the multi-mode candidate.** - Searched on each cell from 42 starts: B7's two channel minima turned by j·2π/7 (j = 0 … 6), and 28 random ones over the circle. Polished at 24,000 directions, bracketed at 64,000 to 2×10⁻⁹. | facing of B7 | cell 00 | cell 01 | cell 02 | cell 03 | worst gap | | --- | ---: | ---: | ---: | ---: | ---: | | package | 0.8368324777 | 0.8367729236 | 0.8367496726 | 0.8366861665 | | | vertex at θ = π | 0.8368301985 | 0.8367753081 | 0.8367532965 | 0.8366861861 | 3.6×10⁻⁶ | | vertex at θ = 0 | 0.8368490074 | 0.8368121127 | 0.8367535759 | 0.8367201607 | 3.9×10⁻⁵ | | vertex at π, mirrored | 0.8368272950 | 0.8367849274 | 0.8367428044 | 0.8366961183 | 1.2×10⁻⁵ | | vertex at 0, mirrored | 0.8368600371 | 0.8367896699 | 0.8367667813 | 0.8366988508 | 2.8×10⁻⁵ | - Only one facing reproduces the package. Its residuals — +2.3, −2.4, −3.6 and −0.02 ×10⁻⁶ — are of the size RUN-024 found in the package's area. - B7's least exceeds the candidate's by 2.48, 2.46, 2.31 and 2.40 ×10⁻⁴. **W5 — the harmonics.** - h = ½ + a cos k(θ − φ) + ⟨t, u⟩ at 90% of the bound. Per cell: 28 random starts over [0, 2π/k) at 6,000 directions, the best four polished at 24,000, bracketed at 64,000. | k | least over the cells (lower bracket) | cell | margin | package coarse | package refined | | ---: | ---: | ---: | ---: | ---: | ---: | | 7 | 0.8367395219 | 03 | 1.74×10⁻³ | +1.21×10⁻⁵ | | | 9 | 0.8354915864 | 02 | 4.92×10⁻⁴ | −3.55×10⁻⁵ | | | 11 | 0.8357638060 | 01 | 7.64×10⁻⁴ | −3.88×10⁻⁵ | −1.68×10⁻⁵ | | 13 | 0.8356225717 | 03 | 6.23×10⁻⁴ | +2.54×10⁻⁵ | +1.55×10⁻⁵ | | 15 | 0.8352261924 | 00 | 2.26×10⁻⁴ | −4.93×10⁻⁵ | | | 17 | 0.8350819469 | 01 | 8.19×10⁻⁵ | −4.56×10⁻⁵ | −3.61×10⁻⁶ | | 19 | 0.8350481986 | 00 | 4.82×10⁻⁵ | −4.99×10⁻⁵ | +1.43×10⁻⁶ | The package columns are its value minus the true least. The coarse k = 19 value (0.83499834) is below T; the true least is not. - The package's "dense brackets at the found worst placement" lie above the true least: by 2.23×10⁻⁵ for H11 and 5.52×10⁻⁵ for H13. Its searched values sit about 4×10⁻⁵ below its own brackets — a coarse area, it seems — and its placements are not the minimisers. **W6 — the pilot.** - B7: RUN-023's sampled lift on the tracked depth-50 cell (τ = 3.82517×10⁻⁴), read at depth 20: 7,037 nodes, 1,015 open. The fraction is 1015/2²⁰ and the root volume (2π/7)(2 · 0.2014734)², both exactly the summary's. - The harmonics: the box's lower bound is the pilot's hull of 40 points each on the disc, the two base cores and the core h − δ, less the 10⁻⁹ pad. Every count rebuilds: | witness | depth | nodes | open | volume | | --- | ---: | ---: | ---: | ---: | | H11 | 20 | 9,623 | 1,929 | 1.8536×10⁻⁴ | | H13 | 20 | 9,211 | 1,755 | 1.4270×10⁻⁴ | | H17 | 20 / 22 | 7,399 / 15,581 | 1,533 / 4,252 | 9.5317×10⁻⁵ / 6.6094×10⁻⁵ | | H19 | 20 / 22 | 7,221 / 14,973 | 1,504 / 4,102 | 8.3671×10⁻⁵ / 5.7051×10⁻⁵ | - δ = |Δt| + 2R sin(Δφ/2), with R = ½ + |a| the witness's radius, is the analogue of B7's vertex motion. The support's own motion, |Δt| + 2|a| sin(kΔφ/2), would give 2,893/772, 2,737/749, 6,225/2,111 and 5,689/2,010 at the same depths. - H19's depth-22 volume differs from fraction × root in its 13th digit, as a sum of the open boxes' volumes would. **W7 — the same cell with dense cores.** - A tree can close only if its bound can exceed T in the limit, where the core is the placed witness itself. With the cell's erosion cores for the base (the cores alone: 0.8343637): | witness | least hull, cores + witness | at the centre, whole base | | --- | --- | --- | | B7 | 0.8367313336 (exact) | | | H11 | [0.8354118255, 0.8354118266] | [0.8357992106, 0.8357995407] | | H13 | [0.8352941791, 0.8352941804] | [0.8357061482, 0.8357064787] | | H17 | [0.8346707431, 0.8346707443] | [0.8350991908, 0.8350995209] | | H19 | [0.8346480422, 0.8346480434] | [0.8350827261, 0.8350830564] | H17's and H19's placements lie inside their lift roots. Any box containing one has a bound no higher than that hull's upper end, which is below T. So neither tree can close this cell, at any depth. - The trees, each to where it closes (H17/H19 stopped at 22): | witness | δ | closes at | nodes | open at depth 20 | open volume at 20 | | --- | --- | ---: | ---: | ---: | ---: | | B7 (exact cores) | vertex motion | 21 | 2,509 | 35 | 4.9×10⁻⁶ | | H11 | boundary motion | 27 | 21,029 | 736 | 7.1×10⁻⁵ | | H11 | support motion | 24 | 1,581 | 109 | 1.0×10⁻⁵ | | H13 | boundary motion | 30 | 43,111 | 642 | 5.2×10⁻⁵ | | H13 | support motion | 26 | 3,257 | 140 | 1.1×10⁻⁵ | | H17 | boundary / support | never | — | 615 / 160 | 3.8 / 1.0×10⁻⁵ | | H19 | boundary / support | never | — | 596 / 157 | 3.3 / 0.9×10⁻⁵ | At depth 22, H17 still has 1,330 and 357 open, H19 1,192 and 348. **W8 — the code.** `AMRAL_LUC_FC_Round_22_repro.py` is 18 lines. It defines `legality_budget` (never called) and `pure_harmonic`, and prints the latter for k = 11 and 19: a = frac/(2(k² − 1)), σ, 2π/k and 7/k. It has no search, no hull, no lift and no absolute path. ## P — the package **P1.** - The text's seventeen search values are the summary's, rounded to eight digits. §17's nodes and volumes are the summary's lifts, to five digits. - Each harmonic's recorded margin is its worst value minus T. §20's "6–7×10⁻⁴" margins are 0.00075 and 0.00064. - The spec's modes are 3–11, its harmonic period 2π/k, its core rule "motion_delta ≤ sigma". The summary's status is "PROOF-COST-PARETO-PILOT-NOT-THEOREM". - The crystal carries the same numbers. **P2.** - `VALIDATION.json` describes the document and the crystal correctly: SHA-256, bytes, `$$` 190 and 30, both flags. - Its digests of the spec, the summary and the script are the archive's. - Its six checks follow from the summary. "H19's depth-20 unresolved volume smaller than B7's" is true of the pilot's numbers — W7 is what it means. ## Round 22, read | Round 22 | statement | verdict | note | | --- | --- | --- | --- | | §0 | summary; boxed verdicts | PARTIAL | the legality and oracle rules hold (W1, W3); the Pareto map does not (W7) | | §1–4 | family; width; budget; symmetry | PASS | W1 | | §5–6 | full-orientation oracle; levels | PASS | W3; the optimistic value is B7's own basin | | §7–8 | the multi-mode candidate | PASS | W4, once B7 has a vertex at θ = π; §8's candidates not recorded | | §9–12 | pure harmonics; reserve | PASS | W1 | | §13–15 | H11, H13, H17, H19 | PARTIAL | the margins hold; the values are off both ways (W5) | | §16–17 | the lift pilot | PASS as computed | W6; the δ is unstated | | §18 | B7's faster tail | PASS | W6; with dense cores B7 closes first (W7) | | §19–23 | Pareto vector; roles; portfolio | FAIL for the volume axis | W7 | | §24–26 | search-only warning; compiler path | PASS | the warning applies to the package's own values (W2, W5) | | §27–28 | Round 23; handoff | n/a | | ## The status registry Round 22's 17 judgments are reviewed, and its 11 first-used phrases defined: the five oracle levels, `SEARCH ARCHIVE`, `PURE-HARMONIC-CW` and the four roles. Census v5 finds 6 of the 17: the boxed verdicts and roles set off on display lines. | verdict | judgments | | --- | ---: | | PASS | 6 | | PARTIAL | 3 | | FAIL | 2 | | n/a | 6 | The FAILs: - "PROOF-COST PARETO MAP: ESTABLISHED" — its volume axis is the pilot's sampled bound with a boundary-motion δ. With dense cores the order inverts. - "CHEAP / RAZOR-THIN AUXILIARY" — razor-thin, yes; cheap, no. H17 and H19 cannot close the cell. The PARTIALs: - "NEW SINGLE WITNESS DOMINATING B_7: NOT FOUND" — true of every recorded candidate; §8's are not recorded; - "SEARCH ARCHIVE" — one candidate is archived, rebuildable only once the unstated facing is found; - "BALANCED AUXILIARY" — the margins hold, but H11 and H13 cost 8 and 17 times B7's nodes with the pilot's δ. ## The drill | kind | cases | named checks | | --- | ---: | --- | | the document's ratio 7/19 | 1 | A0 | | the recorded budget; H13's amplitude | 2 | W1 | | cell-01's B7 value set to the true minimum; a B7 minimum | 2 | W2 | | the mixture's B7-basin value; the full minimum below the true one | 2 | W3 (the second also P1) | | the facing; one of the candidate's four minima | 2 | W4 (the second also P1) | | a harmonic minimum; the coarse scan's k = 9 value | 2 | W5 | | H17's depth-22 count; the support-motion counts; a tail rate | 3 | W6 | | H19 said closable; a dense tree's depth; a centre value | 3 | W7 | | the shipped script said to compute | 1 | W8 | | a crystal value | 1 | P1 | | the summary's recorded digest; a VALIDATION check | 2 | P2 | | a review dropped | 1 | R1 | Four controls: - the unmodified inputs; - the document with CRLF line endings; - the summary with its keys sorted; - the harmonic candidates in reverse order. **22 / 22 plants, 4 / 4 controls, 288 / 288 must-stay-green assertions; no check without a plant.** | check blinded | cases reported blind | plants naming it | | --- | ---: | ---: | | A0 | 1 | 1 | | W1 | 2 | 2 | | W2 | 2 | 2 | | W3 | 2 | 2 | | W4 | 2 | 2 | | W5 | 2 | 2 | | W6 | 3 | 3 | | W7 | 3 | 3 | | W8 | 1 | 1 | | P1 | 3 | 3 | | P2 | 2 | 2 | | R1 | 1 | 1 | ## What this round does not establish - **Any bound.** The closures and limits are floating-point values of this tree's own kernel, not certificates. - **The global minimum of any witness.** The searches find what they find. The minima quoted are the least found, and a 2×10⁻⁹ bracket holds only at the placement found. - **Which base §5 used, or which way the candidate's B7 faces.** Neither is stated. The answers here are the ones that reproduce the package's numbers, and no other tried does. - **What a finer base cell would cost H17 and H19.** Their centre values say one could let them close. How fine is not measured.