# RUN-022 — Round 19: every tree, bracket and probe rebuilds; lazy evaluation changes nothing but cost; the depth-20 recheck is complete; the B7 floor is mostly the pilot's sampling **Arm:** 懸衡 (Xuán Héng) / AMRAL Research Lab **Date:** 2026-09-25 **Subject:** `AMRAL_Lebesgue_Finite_Closure_Round_19_Necessity_Lazy_Lift_v0.1.md` (AMRAL-LUC-FC-R19, dated 2026-09-19) and its package, read from the archive: - `BENCHMARK_SUMMARY.json`, `ACTIVATION_POLICY.json`, `VALIDATION.json`, `State_Crystal`; - the reference files: the tracked branch (`official_seed_branch_track.json`), the segmentation's brackets and exact profile, the Tail-Window continuation's summaries at depth 18 and 20, and the depth-20 profile; - `continuation_probe.py` and `official_exact_kernel_minimal.py`, read only after this tree's reconstruction, and never run. **Tools:** [`run022_round19_necessity_lift.py`](../code/run022_round19_necessity_lift.py) — the three bounds with the pilot's sampling and the lazy cascade; the continuation from Round 18's decoded Tail-Window checkpoint (RUN-021's decoder); this tree's exact hull (RUN-009) and a 20,000-direction bracket; the tracked branch from RUN-020's D3 root; RUN-019's B7 probe, with the pilot's cores and with exact ones **Logs:** [`run022-round19-necessity-lift.json`](../data/gate-logs/run022-round19-necessity-lift.json) **Verdict: PASS for the cascade, the continuation, the depth-20 correction, the tracked branch, the necessity semantics and the segmentation, and for the switch curve as computed; PARTIAL for the τ ≈ 10⁻³ scheduler parameter, whose value belongs to the pilot's sampled lift bound.** - **Lazy evaluation changes nothing but cost.** - Theorem 2.1 is right: APR, then CORE, then REP only if both fail, accepts exactly what the eager maximum accepts. On all 152,875 evaluations of the three trees here the lazy and the eager classifier agree. - The fixed-tree A/B from Round 18's 2,048 pending roots rebuilds exactly: 13,206 nodes, 4,944 pending, REP computed 12,659 times eagerly and 10,523 times lazily (−16.87%). - Every accepted leaf closes by CORE — all 2,136 in the A/B, all 2,228 and 5,398 in the continuations. §4's "almost all" is all. APR never fires here, as RUN-019 found for the whole root. - On the Tail-Window tree, lazy values could in principle change an override, since its key uses the children's best values. They never do: eager values pick the same axis at every override. - **The continuation and κ rebuild.** - Tail-Window 16 → 18: 12,634 nodes, 514 SYM, 2,228 CORE, 4,599 pending, 287 overrides. 18 → 20: 26,455, 15, 5,398, 10,114, 884. Both match the package's summaries count for count. - The shipped probe's evaluation counts, 41,375 and 98,841, are rebuilt exactly. They include 3,845 and 8,062 re-evaluations of a parent at the target, done whenever the official children certify nothing (9.3% and 8.2%). The rebuild needs none of them. - The arithmetic holds: 22.7531 + 55.3844 = 78.1375 CPU-s, 38.15 ms per root, against Round 18's break-even of 14.41 ms (2.65 times). - The timings are single runs, taken as recorded. They include the parent re-evaluations, and Round 18's break-even is itself inflated by its emitter's (RUN-021). So the conclusion — the Tail-Window checkpoint pays for itself — holds with room. - **The depth-20 correction is right, and complete.** - 12 of the 10,114 depth-20 centres have a sampled area below 0.835, the least 0.8339513918. With this tree's exact hull none is below: the least is 0.8358650284, and so are all of their outer brackets. - The recheck of 12 is enough. Everywhere at depth 20 the pilot's 40-direction value lies at least 1.23×10⁻³ below the exact one, so every exact sublevel centre would have been a candidate. Over all 10,114 the exact minimum is that same 0.8358650284. - The profile file — quantiles, near-target counts, the top eight — rebuilds exactly. - **The tracked branch rebuilds row by row, and depth 31 is the first certified centre.** - q† goes to the canonical wedge as `s∘r(q†)` (the package's "refrot1"), with `arg t₃ = π/3 − 3.05×10⁻⁶` and the same area, 0.8347809459115. - All 51 rows of the track agree to 1.2×10⁻¹⁵, once two unstated conventions are known. Every "sample" field in the package is the pilot's hull less its 10⁻⁹ pad. The "seed-to-centre distance" is taken in x₃, y₃, x₅, y₅ only, without the phase. - Depth 30: exact centre 0.8352534195, outer bracket 0.8352704487 > T. Depth 31: 0.8349033738 and 0.8349184947 < T. So the depth-31 centre is below 0.835 with a margin of 8.2×10⁻⁵, in the pilot's floating arithmetic, as §12 says. - This tree's first bracket lost 7.5×10⁻¹⁰ to the rounding of `cos d` in its edge formula. Written with `1 − cos d = 2 sin²(d/2)`, it agrees with the package's vertex formula to 3×10⁻¹⁴. The package's value is the accurate one. - **The necessity theorem is right, and the segmentation rebuilds.** - Theorem 13.1 is one line: a sound base-only lower bound cannot exceed the infimum over the cell, which a point with area below T already bounds. - The depth-31 cell refined to depth 40: 561 nodes, 256 pending (the same at T and at T_search). 85 exact centres below 0.835, the least 0.8348018420; 77 of them with the 20k outer bracket below too. - All 85 brackets in the package rebuild to 1.2×10⁻¹³, and the exact profile — count, quantiles, the lowest 20 with their paths — exactly. - **The B7 switch curve and floor rebuild exactly — and with exact cores they are much lower.** - With the pilot's sampled cores, all ten depth-12 probes along the branch give the benchmark's nodes, closed and open leaves (483 at depth 20 down to 125 at depth 50). The base-zero floor at q† is 108 at depth 12 and 412 at depth 18. The excess over the floor falls as τ^0.704 over the ten points, τ^0.696 over the text's nine. - With exact cores, every probe leaves fewer leaves open: 456 down to 83. The floor is 76 at depth 12 (1.86%, not 2.64%). At depth 18 it is **7 leaves**, not 412. The excess falls as τ^0.91. - So §22's "witness-only floor" and §23–24's τ ≈ 10⁻³ regime describe the pilot's 40-direction lift bound more than the lift. §22 says so of the floor; §23–26 and the policy file do not say it of the scheduler parameter. - §27 stands — B7 is not closed at depth 18 even at the exact base point — but in exact arithmetic it misses by 7 leaves of its 2¹⁸-resolution grid. - **The package.** - `VALIDATION.json` is right: digests, bytes, `$$` counts, and its seven key checks from the data. - The activation policy departs from the text in two places. Its states drop §25's `NECESSITY-SEGMENTED` and add `BASE-CERTIFIED`. Its marker payload drops §14's target. - The shipped probe loads Round 18's emitter, verifier and checkpoint from an absolute path outside the package, and writes its output outside too. Its own B7 probe runs to depth 10 on four cells, a result reported nowhere. - It did not write the depth-20 profile in the package: the profile has quantile levels and near-target margins the probe does not compute. - Nothing shipped tracks the branch, segments it, brackets it, or runs the depth-12 curve and floor. - The exact kernel is independent and sound: pairwise tangent angles, caps, and the bracket by the vertex formula. - **Three small slips in the text.** - §5–6 call 12,634 and 26,455 "new" nodes. They include the 2,048 and 4,599 roots. - §21 lists nine of the ten switch-curve depths, omitting 43. The fit barely moves. - §4's "almost all by CORE" is all. - **Reading Round 19 led to census v5.** Its boxed global verdict put the claim in math and the status alone in `\text`, a third missed form. So the whole corpus was swept once for every missed form of a position already read: 229 judgments, reviewed where their rounds are already read. See [RUN-003](./RUN-003-ROUND00-GOVERNANCE.md#correction--census-v5-2026-09-25-while-reading-round-19). Drill: 21 / 21 plants caught by exactly the named checks, 4 / 4 controls undisturbed, 251 / 251 must-stay-green assertions held. Each of the eleven checks was blinded in turn, and each was reported blind in exactly as many cases as plants name it. --- ## What Round 19 claims 1. **The lazy cascade** (§1–4). The three one-sided bounds are evaluated APR → CORE → REP, REP only on a CORE failure. Theorem 2.1: on a fixed cell the lazy and eager classifications agree. From Round 18's 2,048 pending roots, official split to depth 18: 13,206 nodes and 4,944 pending both ways; REP calls 12,659 → 10,523 (−16.87%); time 7.2903 → 6.8687 s (−5.78%). REP is kept, since nothing proves it never beats CORE. 2. **Continuation cost** (§5–7). The Tail-Window continuation 16 → 18: 12,634 nodes, 4,599 pending, 22.7531 s (11.11 ms a root). 18 → 20: 26,455 nodes, 10,114 pending, 55.3844 CPU-s. Cumulative 78.1375 CPU-s, 38.15 ms per original root — 2.65 times Round 18's break-even of 14.41 ms, so the Tail-Window checkpoint has paid for itself. 3. **The sampled-centre correction** (§8–9). 12 depth-20 centres have a sampled area below 0.835 (least 0.83395139); the exact kernel finds 0 / 12 (least 0.83586503). `CORRECTION-R19-001`: a sampled value below T is a search signal only; only an exact or rigorous upper bound may trigger necessity. 4. **The tracked branch** (§10–12). q† in the canonical wedge, area 0.8347809459115. The official split's branch holding it: depth 30, exact 0.8352534195 and outer 0.8352704487 > T; depth 31, 0.8349033738 and 0.8349184947 < T — `CENTER-SUBLEVEL-CERTIFIED-PILOT`. 5. **Necessity** (§13–20). Theorem 13.1: a cell holding a point with area below T has no base-only certificate, nor does any descendant holding it. A marker stores the point and its bound; only the child holding the point inherits it. The depth-31 cell lifted whole leaves 227 of 4,096 B7 leaves open at depth 12 (5.54%). Refined first to depth 40: 561 nodes, 1.69 CPU-s, 256 pending, 85 exact centres below T, 77 with the outer bracket below. Two queues: `BASE-UNRESOLVED` and `NECESSITY-MARKED`. Logical necessity is not a reason to lift a whole ancestor now. 6. **The switch curve** (§21–26). B7 depth-12 open leaves along the branch, τ from 0.02448 to 0.000383: 483 … 125. At the exact base point 108 (2.64%) — the "witness-only floor" of this machinery. The excess over it falls roughly as τ^0.70; near τ ≈ 10⁻³ further base refinement stops paying (`LIFT-EFFICIENCY-REGIME-PILOT`). A state machine and an activation policy. 7. **Limits and the ledger** (§27–32). B7 is not closed at depth 18 even at the exact base point; no global claim. The status ledger; Round 20's topic. ## A — sources **A0.** 57 anchors. Round 19 has no reference list. ## W — rebuilt | check | Round 19 | rebuilt | result | | --- | --- | --- | --- | | W1 | §1–4 | Theorem 2.1 on every evaluation; the fixed-tree A/B | PASS; every accepted leaf by CORE | | W2 | §5–7 | both continuations; the probe's counts; κ | PASS; 8–9% of the probe's evaluations re-evaluate parents | | W3 | §8–9 | all 10,114 depth-20 centres, sampled and exact; the profile | PASS, and the 12-candidate recheck is complete | | W4 | §10–12 | q†'s image; the 51-row track; the brackets | PASS, with two unstated conventions | | W5 | §13–18 | Theorem 13.1; the segmentation; 85 brackets; the profile | PASS | | W6 | §16, §21–24, §27 | ten B7 probes and the floor, sampled and exact; the fits | PASS as computed; with exact cores the floor is 76 / 7, the exponent 0.91 | | W7 | §3–8, §12, §17–22 | the shipped probe and kernel, read | the probe reads outside the package; it did not produce the profile or anything after §8 | **W1 — the cascade.** - The three bounds are Round 16's, with the pilot's 40-direction sampling: - APR, the disc-and-point hull at the box's distance; - CORE, the sampled hull of the disc and the erosion cores; - REP, the centre's sampled hull less `4tτ + πτ²`. - As the shipped probe does, REP is built with the threshold it is compared against. Built with T instead of T_search it changes no classification anywhere. - Lazy against eager, on every evaluation of the A/B and both continuations — 12,659, 41,375 and 98,841 — never a disagreement. - The A/B, official split from the 2,048 roots to depth 18: | | nodes | SYM | accepted | by CORE | pending | REP eager | REP lazy | | --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | | the text | 13,206 | — | — | — | 4,944 | 12,659 | 10,523 | | rebuilt | 13,206 | 547 | 2,136 | 2,136 | 4,944 | 12,659 | 10,523 | 12,659 − 10,523 = 2,136: the lazy cascade skips REP exactly where CORE accepts. - Theorem 2.1 is scoped to one cell and a fixed tree, rightly. On the Tail-Window tree the override key uses the children's best values, and a lazy best stops at CORE when CORE accepts. So lazy and eager could order two axes differently if REP exceeded an accepting CORE. At every override here the eager values pick the same axis. **W2 — the continuation.** - Round 18's Tail-Window checkpoint is decoded by RUN-021's decoder, and its 2,048 PENDING leaves are the roots. - The Tail-Window rule is Round 18's: - try the other axes when the official children certify nothing, from depth 10, if the parent's best is at least T − 0.025; - keep the axis with the largest (certified, least best, summed best, −τ, −axis); - stop at an axis certifying both children. | | nodes | SYM | CORE | pending | overrides | probe's evaluations | of them parents | REP calls | | --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | | 16 → 18 | 12,634 | 514 | 2,228 | 4,599 | 287 | 41,375 | 3,845 | 38,933 | | 18 → 20 | 26,455 | 15 | 5,398 | 10,114 | 884 | 98,841 | 8,062 | 93,088 | - Every figure is the package summaries'. The probe evaluates a parent a second time, at T, whenever its official children certify nothing: 9.3% and 8.2% of its evaluations. The first time was as a child, at T_search. This tree reuses the child's bounds. The same redundancy, larger, was in Round 18's emitter (RUN-021). - §5 and §6 call the 12,634 and 26,455 "new" nodes. They count the roots: 10,586 and 21,856 are new. - κ: 22.7531 + 55.3844 = 78.1375; 78.1375 / 2,048 = 38.153 ms; 22.7531 / 2,048 = 11.110 ms. Round 18's break-even: (17.3205 − 6.9773) / 718 = 14.406 ms, from its cost policy. Ratio 2.648. **W3 — depth 20.** - For each of the 10,114 pending cells: - the probe's centre area — the pilot's sampled hull less its 10⁻⁹ pad; - this tree's exact hull of the disc, B₃ and B₅ at the centre (RUN-009's envelope). - 12 sampled values are below 0.835, the least 0.8339513917562; the package's min agrees to 10⁻¹⁶. None of the 12 is exact-sublevel, and neither are their 20k outer brackets. - Over all 10,114, sampled minus exact is at most −1.235×10⁻³: the sampling underestimates everywhere. So "sampled below T" is a complete filter for "exact below T", and the 12-cell recheck settles all 10,114. The exact minimum over all is the candidates' 0.8358650284. - The profile file rebuilds exactly, at its own quantile levels and margins: - the quantiles of the centres, the best bounds and τ; - the near-target counts (≤ T + m); - the top eight, with paths and boxes. **W4 — the branch.** - q† (Round 07's repository point) maps into the wedge by `s∘r`, turn then mirror (RUN-020's representative), the package's "refrot1". The image agrees with the package to 10⁻¹⁵ and with §10's printed digits. Its area equals q†'s, to 10⁻¹⁵. - The D3 root is split officially, keeping the child that holds the image, to depth 50. At every depth the track's path, box, containment, exact area, sampled area, τ, best bound and mode agree to 1.2×10⁻¹⁵. Two conventions come only from the data: - the sampled area is the pilot's hull less its pad; - the distance to the seed omits the phase coordinate. - The bracket, 20,000 support directions: - outer: the polygon of the support lines, which contains the hull; - inner: the polygon through the contact point of whichever body wins each direction, as the package draws it. | depth | exact | inner | outer | | ---: | ---: | ---: | ---: | | 29 | 0.8355069827 | 0.8355069554 | 0.8355250113 | | 30 | 0.8352534195 | 0.8352533932 | 0.8352704487 | | **31** | **0.8349033738** | 0.8349033542 | **0.8349184947** | | 32 | 0.8348801598 | 0.8348801423 | 0.8348959470 | The first outer bracket below 0.835 is at depth 31. Every exact value lies inside its bracket, at all 51 depths. - This tree's first version of the outer bracket used the plain edge formula `(h_{i±1} − h_i cos d) / sin d`. The rounding of `cos d` makes that 7.5×10⁻¹⁰ too small at 20,000 directions, and 3.7×10⁻⁹ at 40,000. The gate writes `1 − cos d = 2 sin²(d/2)` and sums with `fsum`. It then agrees with the package's vertex formula, summed either way, to 3×10⁻¹⁴. No conclusion was near that margin. **W5 — necessity and segmentation.** - Theorem 13.1: for `q⋆ ∈ C' ⊆ C`, `L(C') ≤ inf_{C'} A ≤ A(q⋆) < T`. It needs only that the base bound is sound, which Rounds 08–16 establish (RUN-011 to RUN-019). §15's propagation — only the child holding q⋆ inherits — is the same inequality. - The depth-31 cell is refined by the official split to depth 40, closing at T_search (the same at T): 561 nodes, 256 pending. | | exact below T | outer below T | least exact | | --- | ---: | ---: | ---: | | the text | 85 | 77 | — | | rebuilt | 85 | 77 | 0.8348018420 | 8 centres are below T but not certifiably so: their margin is smaller than the bracket's slack, about 1.5×10⁻⁵. - The package's 85 brackets are rebuilt by path — exact, inner and outer to 1.2×10⁻¹³, every flag. So is its exact profile: count, below-target count, minimum, quantiles, and the lowest 20 with their paths, τ and sampled areas. **W6 — the switch curve.** - RUN-019's B7 probe: - the phase-master B7 root over the base cell's erosion cores; - split by the least child δ₇; - a leaf closes at T, or stays open at depth 12. | base depth | τ | open, pilot's cores | open, exact cores | | ---: | ---: | ---: | ---: | | 20 | 0.02448 | 483 | 456 | | 24 | 0.01412 | 330 | 290 | | 28 | 0.00964 | 252 | 226 | | **31** | 0.00482 | **227** (of 1,051 nodes) | 210 | | 34 | 0.00353 | 198 | 160 | | 37 | 0.00241 | 183 | 136 | | 40 | 0.00153 | 161 | 117 | | 43 | 0.00120 | 144 | 100 | | 46 | 0.000602 | 135 | 91 | | 50 | 0.000383 | 125 | 83 | | q† exactly, depth 12 | 0 | **108** (2.64%) | **76** (1.86%) | | q† exactly, depth 18 | 0 | **412** | **7** | - With the pilot's cores every node, closed and open count is the benchmark's. - The fractions are §23's: 227, 161, 135 and 108 of 4,096 are 5.54%, 3.93%, 3.30% and 2.64%. - A least-squares fit of `log(f − f₀)` on `log τ`: - pilot's cores: 0.704 over the ten points, 0.696 over the text's nine (§21 omits depth 43); - exact cores, against their own floor: 0.911. - §22 calls 108 "the witness-only floor of this B7 depth-12 lower machinery", and says plainly that it is not a mathematical floor. With exact cores it is 76, and at depth 18 the gap between machineries is 412 against 7. The switch policy (§23–26, and the activation policy's "tau around 1e-3") is calibrated on the sampled machinery. The text calls it a performance parameter, which it is. But its value would move with an exact or interval lift bound. - §27, "B7 not closed at depth 18 even at the exact base point", stands in both. **W7 — the shipped code, read after the rebuild.** - `continuation_probe.py`: - it imports Round 18's emitter and verifier and decodes Round 18's checkpoint, all from an absolute path outside this package, so it cannot run from the package; it writes its result outside too; - its lazy and eager evaluators, its Tail-Window rule and its counting are the ones rebuilt in W1–W2, including the parent re-evaluation at the target; - its own B7 probe runs to depth 10 on the four lowest depth-20 cells, a result the package does not report; - its profile uses quantile levels `0, .01, .1, .5, .9, .99, 1` and margins without `10⁻⁴`, while the package's profile has `0.001`, `0.05` and `10⁻⁴`, so that file came from other code. - `official_exact_kernel_minimal.py` is an independent exact hull: - candidate angles at every piece break and at every pairwise tangency `φ ± arccos(−Δr / |Δc|)`; - the winning piece on each interval, shoelace plus circular caps; - the 20k bracket by the vertex formula. Every exact value the package prints agrees with this tree's exact hull to 1.2×10⁻¹⁵. - Nothing shipped computes the canonical image, the track, the segmentation, the brackets of the 85, or the depth-12 curve and floor. Every one of those numbers was rebuilt here from the text. ## P — the package **P1.** - The benchmark's A/B, continuation cost, depth-20 block, branch block and segmentation block agree with the summaries, the profile, the track and the two segmentation files. - The switch curve's rows are the track's rows (exact area, τ), with fraction = open / 4,096. - The crystal carries the text's numbers, rounded as the text rounds them. - The activation policy's cascade order is the text's. It differs in two places: - its states are `BASE-UNRESOLVED, NECESSITY-MARKED, LIFT-ACTIVE, BASE-CERTIFIED, LIFT-CERTIFIED`, while §25 has `BASE-UNRESOLVED, NECESSITY-MARKED, NECESSITY-SEGMENTED, LIFT-ACTIVE, LIFT-CERTIFIED`; - its marker payload is `q, base_area_upper, geometry_hash, arithmetic_policy_hash`, while §14 adds the target. A marker without its target does not say which T it proves "below". **P2.** `VALIDATION.json` describes the document and the crystal correctly: - SHA-256, bytes, `$$` 252 and 22, both flags; - its digests of the benchmark and the activation policy are the archive's; - its seven key checks each follow from the benchmark, including the 77. ## Round 19, read | Round 19 | statement | verdict | note | | --- | --- | --- | --- | | §0 | summary and boxed verdicts | PASS | as below; the global claim stays deferred | | §1–2 | three one-sided bounds; Theorem 2.1 | PASS | W1 | | §3 | the fixed-tree A/B | PASS | W1; the timings are single runs | | §4 | REP kept; "almost all" by CORE | PASS | all by CORE, here (W1) | | §5–7 | continuation; κ; Tail-Window pays back | PASS | W2; "new" nodes include the roots | | §8–9 | 0 / 12; the correction | PASS | W3; the recheck is complete | | §10–12 | q†'s image; the track; depth 31 | PASS | W4 | | §13–15 | Theorem 13.1; markers; propagation | PASS | W5; the policy's marker omits the target (P1) | | §16–18 | whole-ancestor lift; segmentation | PASS | W5, W6 | | §19–20 | two frontiers; logical vs performance gate | PASS | a sound separation | | §21–24 | switch curve; floor; τ^0.70 model | PASS as computed / PARTIAL as a parameter | W6: the floor and exponent are the sampled machinery's | | §25–26 | state machine; activation policy | PASS | the policy file's states differ (P1) | | §27 | B7 not closed at depth 18 | PASS | 412 open with the pilot's cores, 7 with exact ones (W6) | | §28–32 | significance; stack; ledger; Round 20 | n/a | the ledger is reviewed in the registry | ## The status registry Round 19's 18 judgments are reviewed, and its 11 first-used phrases defined: - `PILOT-CALIBRATED`, `BASE-UNRESOLVED`, `NECESSITY-MARKED`, `CORRECTION-R19-001`, `CENTER-SUBLEVEL-CERTIFIED-PILOT`; - `PROVED + A/B PASS`, `MEASURED`, `VERIFIED-COMPUTATIONAL-PILOT`, `IMPLEMENTED / PILOT PASS`; - `NUMERICAL-EVIDENCE / SCHEDULER PARAMETER`, `LIFT-EFFICIENCY-REGIME-PILOT`. Two of the 18 are read from census v5 on: the boxed `a_{\mathrm{Leb}}\ge0.8350:\ \text{STILL COMPUTE-DEFERRED}` and the boxed `\texttt{CENTER-SUBLEVEL-CERTIFIED-PILOT}`. The one PARTIAL: "τ ∼ 10⁻³ lift-efficiency regime: NUMERICAL-EVIDENCE / SCHEDULER PARAMETER". It rebuilds for the pilot's sampled cores. With exact cores the floor and the exponent move. | verdict | judgments | | --- | ---: | | PASS | 11 | | PARTIAL | 1 | | n/a | 6 | ## The drill | kind | cases | named checks | | --- | ---: | --- | | the document's lazy REP count | 1 | A0 | | the A/B's REP count; "every accepted leaf by CORE" denied | 2 | W1 | | a summary's override count; the evaluation accounting denied; the "new" counts said to exclude the roots; Round 18's break-even | 4 | W2 | | a profile count; "sampled below exact" denied | 2 | W3 | | a track row's exact area; the first sublevel depth | 2 | W4 (the first also P1) | | a bracket's flag; the outer-below count | 2 | W5 (the first also P1) | | a switch-curve count; the exponent; the exact-core floor | 3 | W6 (the first also P1) | | the probe's lift depth | 1 | W7 | | the policy made to match the text | 1 | P1 | | the benchmark's recorded digest; a VALIDATION key check | 2 | P2 | | a review dropped | 1 | R1 | Four controls: - the unmodified inputs; - the document with CRLF line endings; - the track's rows in reverse order; - the brackets in reverse order. **21 / 21 plants, 4 / 4 controls, 251 / 251 must-stay-green assertions; no check without a plant.** | check blinded | cases reported blind | plants naming it | | --- | ---: | ---: | | A0 | 1 | 1 | | W1 | 2 | 2 | | W2 | 4 | 4 | | W3 | 2 | 2 | | W4 | 2 | 2 | | W5 | 2 | 2 | | W6 | 3 | 3 | | W7 | 1 | 1 | | P1 | 4 | 4 | | P2 | 2 | 2 | | R1 | 1 | 1 | ## What this round does not establish - **Any bound.** The 77 certified centres and the depth-31 marker are certified in the pilot's floating arithmetic, as §12 says, not in publication arithmetic. - **Timings.** The A/B's 5.78% and every CPU-second are single measurements. Only their arithmetic and the evaluation counts behind them are checked. - **The exact-core B7 figures as a certificate.** They come from this tree's exact hull in floating point, at one base point and along one branch. They show how much of the pilot's floor is sampling, and nothing more.