# RUN-019 — Round 16: every pilot number rebuilds, but its frontier profile measures its 40-direction sampling; APR can never fire on this root, and 19 HARD cells hold configurations below 0.835

**Arm:** 懸衡 (Xuán Héng) / AMRAL Research Lab
**Date:** 2026-09-25
**Subject:** `AMRAL_Lebesgue_Finite_Closure_Round_16_Global_Pilot_v0.1.md` (AMRAL-LUC-FC-R16, dated 2026-09-19) and its package, read from the archive:

- `GLOBAL_PILOT_SUMMARY.json`, `depth18_raw.json`, `LONG_RUN_SPEC.json`, `VALIDATION.json`, `State_Crystal`;
- `global_pilot.py`, read only after this tree's reconstruction, and never run.

**Tools:** [`run019_round16_global_pilot.py`](../code/run019_round16_global_pilot.py) — the root and both split rules from the text; nine trees (exact common cores, the pilot's sampling, the other tie-break); B7 lifts; Mishra's seed from Round 07's repository record; RUN-012's core pieces and RUN-009's exact hull
**Logs:** [`run019-round16-global-pilot.json`](../data/gate-logs/run019-round16-global-pilot.json)

**Verdict: PASS for the pilot's computations and its three decisions; PARTIAL for the near-frontier profile and its proxy; §7's reading of APR is wrong.**

- **Every number rebuilds, under two choices only the code makes.**
  - From the text's root and split rules, three trees: official to depth 18, exact-τ and
    the immediate 0.835 root to depth 16.
  - The scheduler table, the root comparison and the depth-18 counts agree in every
    entry. The depth-18 quantiles agree to 3×10⁻¹⁶. The near-frontier counts, cycle
    tails, tiers and top eight cells agree exactly, and so do both B7 probes' counts
    (their least slack to 3×10⁻¹⁶).
  - The two choices:
    - the sampling. The text says "40 finite boundary inner points"; the code takes
      contact points in the 40 directions 2πk/40, the disc's included.
    - the ties of both split rules. The code breaks them toward the earlier axis. Broken
      the other way, the counts move: exact-τ at depth 16 has 29,571 nodes and 5,688 HARD
      leaves, not 28,771 and 5,252.
- **The three decisions survive both choices.**
  - With exact common cores (this tree's reconstruction from the text), official still
    uses 17.27% fewer nodes and 21.68% fewer HARD leaves than exact-τ at depth 16.
  - The master root still costs less than the immediate root: 21,971 nodes against 22,759.
  - The exact depth-18 frontier, 9,234 HARD cells, lies inside the pilot's 10,448.
  - The B7 probes still leave most leaves open (2,251 nodes, 549 closed, 577 open).
  - With the ties broken the other way, every comparison keeps its direction too.
- **The frontier profile measures the sampling.**
  - The 40-direction hull puts every HARD cell's centre 1.6×10⁻³ to 5.6×10⁻³ below its
    true hull area (median 3.5×10⁻³).
  - With exact centres the lowest is 0.8385552, not 0.8356828.
  - No cell is within +0.002 of the target (8 claimed), and 12 are within +0.005 (70
    claimed).
  - None needs 7 cycles (8 claimed), and 92 need at least 5 (142 claimed).
  - Round 16's qualitative point, that the raw frontier is far larger than the
    near-minimizer frontier, only gets stronger.
- **APR can never fire on this root.**
  - `f(d)` is the area of the hull of the disc and one point. It exceeds π/4 only for
    `d > ½`.
  - Every body centre in the root lies within `√2·t_n ≤ 0.287` of the origin. So APR is
    `π/4 ≈ 0.785` everywhere, at every depth: not "not yet close enough to 0.835" (§7).
  - The square corners of §1 are closed by CORE. The pilot implements no a-priori corner
    rule, and in these trees it would never have fired.
- **Nineteen HARD cells hold configurations below 0.835.**
  - The base area is exactly invariant under a mirror and a 2π/3 turn, so Mishra's seed
    `q†` (0.834780946) has images.
  - The two lowest pilot cells hold its turns `Rq†` and `R²q†`. `q†` itself lies on
    three cell faces (`y₃ = −3.7×10⁻⁸`, `y₅ = −3.9×10⁻⁶`, `φ₅ = 2.4×10⁻⁵`), in cells
    outside the top eight.
  - Among the 900 cells within one step of an image, 19 hold a configuration below 0.835
    (witness areas 0.834781 to 0.834971). Every one is HARD in both trees, as it must be.
  - §12 calls its cycle proxy conservative. It gives these 19 cells 3 to 8 cycles, and no
    base refinement closes them.
  - Still, the tiers route all 19 to the tail (14 to Tail-A, 5 to Tail-B, none to Bulk),
    and on 80 random cells with 1–2 predicted cycles the prediction holds 80 times. A
    good heuristic, not a conservative one.
- **The symmetry signal is exact.**
  - The base area is invariant under the mirror `(y₃, φ₅, y₅) → (−y₃, −φ₅, −y₅)` and
    under the 2π/3 turn, to 8×10⁻¹⁶.
  - The mirror maps the pilot's grid onto itself. Every closed and HARD cell, in both
    trees, has its mirrored twin, and the two lowest cells are twins.
  - The turn does not map the grid: it shifts `φ₅` by 10⅔ cells.
- **The shipped code did not write the shipped summary.**
  - The summary, raw file, spec, crystal and text agree, and VALIDATION's digests are the
    archive's.
  - But `global_pilot.py` runs depths 16 and 18 only, never 10, 12 or 14. It writes none
    of the summary's keys `scheduler_table`, `cycle_tail_ge`, `b7_probes`, `cap`,
    `top8`, `near_counts` and `priority_tiers`.
  - It also times one run where the summary records two (13.77 s and 13.51 s).
  - Every number the summary holds rebuilds all the same.

Drill: 20 / 20 plants caught by exactly the named checks, 4 / 4 controls undisturbed,
264 / 264 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 16 claims

1. **The master root** (§0–1). The whole five-dimensional base root `D + B₃ + B₅`:
   - sized at the phase master `T_M = 0.8365` (`t₃`, `t₅`, `t₇` to 17 digits);
   - with `φ₅` over `[0, 2π/5)`;
   - profiled toward `T = 0.835`.
2. **Four modes** (§2), all one-sided, under the pilot policy `N_sample = 40`,
   `e_pilot = 10⁻⁹`:
   - `APR`: `f(d)`, the disc with a body's centre;
   - `REP`: the centre's inner hull minus `4Tτ + πτ²`;
   - `CORE`: the inner hull of the common erosion cores;
   - `HARD`: none of them closes.
3. **Schedulers** (§3–5).
   - Mishra's first-order weights against Round 09's exact-τ rule, tabulated at depths
     10–16.
   - Official uses 18.48% fewer nodes and 21.71% fewer HARD leaves at depth 16.
   - One-step τ-optimality is not tree-cost optimality: `R09-STRENGTHENING-EMPIRICAL-001`.
4. **The master root costs no more** (§6): 23,455 nodes at depth 16 against 24,691 for
   the immediate 0.835 root.
5. **The depth-18 frontier** (§7–14).
   - 45,651 nodes, 12,378 CORE, 10,448 HARD, and APR and REP both zero.
   - No HARD centre below the target; the least is 0.8356828349502634.
   - Near-frontier counts and quantiles.
   - A cycle proxy from `τ⋆(m, T)`, with its tails.
   - The two lowest cells, with a core loss of 3.66×10⁻².
6. **B7 later** (§15–16). Shallow B7 lifts on the two lowest cells leave 634 of 1,202
   leaves open, so: base refinement first, B7 later.
7. **Policy** (§17–26).
   - Official stays the production baseline; a prune-gain scheduler is the target.
   - A symmetry signal.
   - The master root is kept.
   - Tiers of 142, 2,044 and 8,262 seeds.
   - The long-run architecture, the status ledger and Round 17's topic.

## A — sources

**A0.** 76 anchors. Round 16 has no reference list. One of the anchors keeps a typo: the
official weight rule closes with `\right\\}`, which does not typeset.

## W — rebuilt

| check | Round 16 | rebuilt | result |
| --- | --- | --- | --- |
| W1 | §1–2 | `t₃, t₅, t₇` at 0.8365; `f(d)` against the exact hull of the disc and a point | PASS |
| W2 | §2, §7 | how far APR and REP reach | APR never fires on this root; REP cannot at depth 18 |
| W3 | §3 | both split sequences; the top cells' paths | PASS |
| W4 | §4, §6–7 | nine trees | PASS, under the code's sampling and ties |
| W5 | §8–14, §21 | the depth-18 profile, sampled and exact | PASS as computed; the profile measures the sampling |
| W6 | §9, §12, §14 | `q†` and its images; cells below 0.835; the proxy | the proxy is not conservative |
| W7 | §15 | the B7 probes, sampled and exact | PASS |
| W8 | §19 | the base area's symmetries on the grid | PASS, and exact |

**W1 — the root.**

- `t₃, t₅, t₇ = 0.20102352900741138, 0.20261828623043537, 0.20147344578628762` at
  0.8365. They match the text's 17 digits to 1.6×10⁻¹⁶.
- `f(d)` equals the exact hull of the disc and one point at `d = 0.55, 0.7, 1, 1.5`. It is
  Round 07's `Φ_{1/2}`.

**W2 — how far the cheap routes reach.**

- **APR.** `f(d)` exceeds `π/4` only when the point leaves the disc, at `d > ½`. The
  farthest body centres in the root lie at `√2·t₃ = 0.2843` and `√2·t₅ = 0.2865`;
  `√2·t₇ = 0.2849` bounds the lift probe's centre too. So APR is `π/4 ≈ 0.785` in every
  cell, at every depth.
  - §7's "APR contained-center bound仍不夠接近 0.835" reads as though depth would help.
    It cannot.
  - The corners of the square root (§1: "still excludable by analytic a-priori rules")
    need the corner rule behind `t_n`: a corner of `B_n` lies beyond `d⋆`. The pilot
    does not implement it. Nothing is lost here: its corner cells close by CORE while
    their boxes still meet the disc `|t| ≤ t_n(0.835)`. No closed or HARD cell of the
    official tree, and no HARD cell of the other two, lies wholly outside it.
- **REP.** At depth 18, `τ = 0.03855318146790454`, the text's value. It comes from the
  half-widths `(t₃/8, t₃/8, π/80, t₅/16, t₅/16)` to 10⁻¹⁵. REP then needs a centre of
  at least `T + 4Tτ + πτ² = 0.96844`, and the highest HARD centre is 0.92641, so REP
  cannot fire there. That is the text's own reason.
- No tree here closes a cell by APR or REP.

**W3 — the schedulers.**

- The official rule splits `(φ₅, x₅, y₅, x₃, y₃)` in turn. That gives depth-18 cells of
  half-widths `(t₃/8, t₃/8, π/80, t₅/16, t₅/16)`.
- The exact-τ rule splits `φ₅, φ₅, x₅, φ₅, x₃, y₅, y₃, x₅, φ₅, x₃, y₅, y₃, x₅, φ₅,
  x₃, y₅`.
- Both are RUN-012's implementations of Round 09's rules.
- Decoded with the lower child as 0, the eight top cells' 18-bit paths give their
  recorded centres and half-widths.
- Ties are frequent in both rules, and neither rule's statement settles them:
  - the official weights of `x` and `y` tie at every level;
  - exact-τ ties whenever the other body dominates `τ`. At its fourth split, halving
    `φ₅` and halving `y₅` both leave `τ = √2·t₃`.

  The code takes the earlier axis. W4 prices the other choice.

**W4 — the trees.** Each is emitted level by level from the text's root with the
text's order of routes (APR, REP, CORE):

- **the pilot's sampling:** contact points of the disc and of each core in the 40
  directions `2πk/40`, hull minus `10⁻⁹`, both cores required. It was read from the
  code after the exact reconstruction, as a contact-point rule like Round 10's.
- **exact cores:** the exact hull of the disc and the cores `∩ B(V_j, 1 − δ)` (empty
  once `1 − δ ≤ R_n`), minus the same pad.
- **the other ties:** the pilot's sampling, with ties to the later axis.

| depth | rule | pilot `N / CORE / HARD` | sampling rebuilt | exact cores | ties to the later axis |
| ---: | --- | --- | --- | --- | --- |
| 10 | official | 2,047 / 370 / 654 | same | 2,039 / 368 / 652 | 2,043 / 368 / 654 |
| 10 | exact-τ | 2,047 / 0 / 1,024 | same | 2,047 / 0 / 1,024 | 2,039 / 68 / 952 |
| 12 | official | 4,919 / 1,126 / 1,334 | same | 4,739 / 1,124 / 1,246 | 4,915 / 1,140 / 1,318 |
| 12 | exact-τ | 6,519 / 1,936 / 1,324 | same | 6,347 / 1,866 / 1,308 | 6,487 / 1,850 / 1,394 |
| 14 | official | 11,639 / 3,218 / 2,602 | same | 11,083 / 3,062 / 2,480 | 11,603 / 3,238 / 2,564 |
| 14 | exact-τ | 13,319 / 3,146 / 3,514 | same | 12,743 / 3,194 / 3,178 | 13,327 / 3,060 / 3,604 |
| 16 | official | 23,455 / 7,616 / 4,112 | same | 21,971 / 7,280 / 3,706 | 23,343 / 7,560 / 4,112 |
| 16 | exact-τ | 28,771 / 9,134 / 5,252 | same | 26,559 / 8,548 / 4,732 | 29,571 / 9,098 / 5,688 |
| 16 | immediate root | 24,691 / 8,004 / 4,342 | same | 22,759 / 7,542 / 3,838 | 24,263 / 7,790 / 4,342 |
| 18 | official | 45,651 / 12,378 / 10,448 | same | 41,899 / 11,716 / 9,234 | 45,503 / 12,304 / 10,448 |

- APR and REP are zero everywhere.
- The package's fractions 0.18476938583990823 and 0.21706016755521707 are the table's.
- The exact HARD sets lie inside the sampled ones in all three trees, as they must when
  one bound dominates the other.
- At depth 16, official against exact-τ saves:
  - 18.48% of nodes and 21.71% of HARD leaves with the pilot's sampling and ties;
  - 17.27% and 21.68% with exact cores;
  - 21.06% and 27.71% with the other ties.

  The master root beats the immediate root under all three. Round 16's decisions
  stand; its exact numbers are functions of two unstated choices.

**W5 — the frontier.**

- From the sampled tree's 10,448 HARD cells:
  - the centre, lower-bound and cycle quantiles agree to 3.3×10⁻¹⁶;
  - the near-frontier counts, the cycle tails `≥ 1 … ≥ 8`, and no centre below target
    agree exactly;
  - the same eight lowest cells, each with the recorded centre, bound and cycles;
  - the tiers 8 / 142 / 2,044 / 8,262.
- The top cell's core loss is `0.8356828 − 0.7990730 = 3.66×10⁻²`, as §14 says.
- §13 says about 90% of HARD cells are within 3 cycles. The share is 95.9%; 90% is the
  quantile's level.

Then the centres were recomputed exactly:

| | sampled centre (the pilot) | exact centre |
| --- | ---: | ---: |
| least centre | 0.8356828 | 0.8385552 |
| within +0.002 | 8 | 0 |
| within +0.005 | 70 | 12 |
| within +0.01 | 196 | 128 |
| within +0.02 | 714 | 502 |
| cycles ≥ 5 | 142 | 92 |
| cycles ≥ 7 | 8 | 0 |

- The sampled centre is below the exact one in every cell, by 1.6×10⁻³ to 5.6×10⁻³
  (median 3.5×10⁻³). That is the price of 40 directions on a hull whose parts are arcs.
- The error exceeds §9's three smallest margins (0.00075 to 0.002) and matches the
  fourth (0.005). In that range the near-frontier table measures the sampling more than
  the geometry.
- The conclusion §9 draws, raw HARD ≫ the near-minimizer frontier, holds with room to
  spare.

**W6 — the minimizer's cells.**

- Round 07's repository gives Mishra's `q†` with area 0.834780945912. The exact hull
  here gives 0.834780945912 as well, below the target.
- The base area is exactly invariant under the mirror `M` and the 2π/3 turn `R` (W8), so
  `q†` has images. On the depth-18 grid:

  | image | cell | note |
  | --- | --- | --- |
  | `q†`, `Mq†` | `010000011100111001`, `111011001010010100` | `q†` lies on three faces: `y₃ = −3.7×10⁻⁸`, `y₅ = −3.9×10⁻⁶`, `φ₅ = 2.4×10⁻⁵` |
  | `Rq†`, `MR²q†` | `101100100111001010` | the pilot's lowest cell |
  | `R²q†`, `MRq†` | `000111110001100111` | the pilot's second-lowest cell |

- So the two lowest cells of §14 are the turns of Mishra's minimizer. The minimizer
  itself sits on cell faces, in cells whose sampled centres (0.838151) rank 21st and
  22nd.
- Across the 900 cells within one step of a cell holding an image, 19 hold a
  configuration below 0.835. Each has a witness point inside the cell:
  - the nearest image, clipped into the cell (10 cells);
  - or a bounded local search from there (9 cells).

  Witness areas run from 0.834781 to 0.834971.
- All 19 are HARD in the sampled tree and in the exact one. No sound base bound can
  close them at any depth.
- §12 calls its cycle proxy "保守" (conservative). It gives these 19 cells 3 to 8 cycles:

  | tier | cells |
  | --- | ---: |
  | Tail-A (≥ 5 cycles) | 14 |
  | Tail-B (3–4) | 5 |
  | Bulk (1–2) | 0 |

  The proxy reads a cell by its centre, and a cell's centre is not its minimum. The
  tiers do send all 19 to the tail, where §16's Phase C would lift them.
- As a forecast for the bulk, the proxy holds. Of 40 random HARD cells predicted to need
  1 cycle, all close within 1 full cycle (5 more official levels) of the pilot's own
  tree, and all 40 of those predicted 2 close within 2.
- The honest label is "a good heuristic". It is not conservative.

**W7 — the B7 probes.**

- The lift root is `φ₇ ∈ [0, 2π/7)`, `|x₇|, |y₇| ≤ t₇(0.8365)`. Round 10's was sized at
  `t₇(0.835)`, which RUN-018 found caps a proof at 0.835. Sized at the phase target,
  this root's exclusion supports every target up to 0.8365.
- Over each of the two lowest cells' cores, split by the least child `δ₇` (ties to
  `φ`, then `x`), to depth 12:

  | | nodes | closed | open | least slack |
  | --- | ---: | ---: | ---: | ---: |
  | the pilot (both cells) | 2,403 | 568 | 634 | 1.2487498×10⁻⁶ |
  | sampling rebuilt (both cells) | 2,403 | 568 | 634 | 1.2487498×10⁻⁶ (to 3×10⁻¹⁶) |
  | exact cores (both cells) | 2,251 | 549 | 577 | 1.6397113×10⁻⁶ |

- These base cells hold `Rq†` and `R²q†`, so no base refinement alone can close them.
  The lift is the only way.
- At this base resolution it cannot: the base cores have lost 3.7×10⁻², while B7 is worth
  about 1.7×10⁻³ at the four-body optimum. §15's verdict holds under exact cores.

**W8 — the symmetry.**

- On random configurations, the base area is invariant under the mirror
  `(x₃, y₃, φ₅, x₅, y₅) → (x₃, −y₃, −φ₅, x₅, −y₅)` and the turns by `±2π/3`, to
  8×10⁻¹⁶. The disc, `B₃` in its gauge and `B₅` are all mirror-symmetric, and `B₃` is
  invariant under the turn.
- The mirror maps the pilot's grid onto itself: in the path it complements the `y₃`,
  `φ₅` and `y₅` bits.
- In both the sampled and the exact tree, every closed cell and every HARD cell has its
  mirrored twin in the same set, and the two lowest cells are twins. §19's "numerical
  symmetry signal" is an exact symmetry.
- The turn does not map the grid. It moves `φ₅` by `4π/15`, which is 10⅔ depth-18
  cells, and it rotates the translation boxes off the axes.
- None of the bodies is chiral, so no mirrored branch is missing from this root.

## P — the package

**P1.** The pieces agree with each other:

- `depth18_raw.json` is the summary's depth-18 block, value for value.
- The text carries every summary count, the rounded fractions, `t_n`, the near table,
  the rounded quantiles, the tails, the probes and the tiers.
- The long-run spec carries the summary's tiers and targets.
- The crystal carries the same numbers.

**P2.** `VALIDATION.json` describes the document and the crystal correctly: SHA-256,
bytes, `$$` count and parity (180 and 18), the two flags. Its digests of the summary,
the raw file and the code are the archive's.

**`global_pilot.py`, read after the reconstruction.**

- It computes what W4 rebuilds: 40 contact directions, both cores required, the pad
  subtracted, ties by `argmax` and `argmin`, and a depth-first order that visits the
  lower child first.
- It is not the program that wrote the summary.
  - It runs depths 16 and 18 only, so the table's rows at 10, 12 and 14 come from
    elsewhere.
  - It writes none of the summary's keys `scheduler_table`, `cycle_tail_ge`,
    `b7_probes`, `cap`, `top8`, `near_counts` and `priority_tiers`.
  - It reuses one depth-16 run for both the table and the root comparison, where the
    summary times two, 13.77 s and 13.51 s.
  - It writes a CSV of the HARD cells that the package does not ship.
- §23 lists "reproduction code" among the artifacts. The numbers do reproduce, here, by
  following it. The summary does not come from it.

## Round 16, read

| Round 16 | statement | verdict | note |
| --- | --- | --- | --- |
| §0–1 | the whole five-dimensional master root | PASS | W1, W4 |
| §2 | the four modes and the pilot policy | PASS | as defined; APR is `π/4` on this root (W2); the sampling is fixed only by the code |
| §3–5 | schedulers; official ahead; not a correction of Round 09 | PASS | W3, W4; the counts depend on ties the text leaves open, the direction does not |
| §6 | master against immediate root | PASS | W4, under every variant |
| §7 | the depth-18 counts | PASS | W4 |
| §7 | "APR/REP=0 does not mean they are never useful" | FAIL for APR | W2: APR cannot fire at any depth on this root; right for REP |
| §8 | no HARD centre below the target | PASS | W5, sampled and exact |
| §9–11 | near-frontier counts; centre and core quantiles | PARTIAL | they rebuild, but measure the 40-direction sampling (W5) |
| §12–13 | the cycle proxy, "conservative"; the tails; "about 90%" | PARTIAL | not conservative: 19 cells below 0.835 get 3–8 cycles (W6); the share within 3 cycles is 95.9% |
| §14 | the two lowest cells | PASS | W5; they hold the turns of `q†` (W6) |
| §15–16 | B7 probes; base first | PASS | W7, also with exact cores |
| §17–18 | production scheduler; prune-gain target | n/a | design |
| §19 | symmetry signal | PASS | exact (W8) |
| §20 | master root kept | PASS | W4 |
| §21 | tiers | PASS | W5; the 19 cells below 0.835 all fall in the tail tiers (W6) |
| §22–23 | architecture; the package's artifacts | PARTIAL | the shipped code did not write the shipped summary (P2) |
| §24 | status ledger | — | see the registry |
| §25–26 | Round 17; handoff | n/a | |

## The status registry

Round 16's 14 judgments are reviewed, and its 8 first-used phrases defined:

- the mode tags `APR`, `CORE` and `HARD`;
- `VERIFIED-COMPUTATIONAL / PILOT`;
- `EMPIRICAL-COMPUTE-POLICY`;
- `MASTER-ROOT-PERFORMANCE-NOT-A-THEOREM`;
- `NUMERICAL-SYMMETRY-SIGNAL`;
- `R09-STRENGTHENING-EMPIRICAL-001`.

The one PARTIAL is "Near-frontier compression signal: NUMERICAL-EVIDENCE". Its numbers
measure the sampling, and the proxy it leans on is not conservative. The APR tag's
review records W2.

| verdict | judgments |
| --- | ---: |
| PASS | 8 |
| PARTIAL | 1 |
| n/a | 5 |

## The drill

| kind | cases | named checks |
| --- | ---: | --- |
| the document's depth-18 node count | 1 | A0, P1 |
| `t₃` off in the fourteenth decimal | 1 | W1 |
| APR assumed able to fire; the corner rule assumed needed | 2 | W2 |
| the official rule's ties broken to the later axis | 1 | W3 |
| a table count in the summary | 1 | W4, P1 |
| the comparisons assumed to lose their direction; the ties assumed immaterial | 2 | W4 |
| a near-frontier count in the raw file | 1 | W5, P1 |
| the pilot's near count claimed for exact centres | 1 | W5 |
| a turn's cell misplaced; the proxy called conservative; a cell below 0.835 put in Bulk | 3 | W6 |
| a probe count in the raw file | 1 | W7, P1 |
| the exact probe claimed closed | 1 | W7 |
| a mirror that flips `x₃` instead | 1 | W8 |
| a tier in the long-run spec | 1 | P1 |
| the code's recorded digest; the code claimed to write the summary | 2 | P2 |
| a review dropped | 1 | R1 |

Four controls:

- the unmodified inputs;
- the document with CRLF line endings;
- the mirror written as a complement of cell indices;
- the exact-τ rule taken from RUN-012's implementation.

**20 / 20 plants, 4 / 4 controls, 264 / 264 must-stay-green assertions; no check
without a plant.**

The first drill caught 19 of 20. The plant on `t₃` moved it by 10⁻¹⁶, below W1's
tolerance of 10⁻¹⁵; the rebuilt value itself differs from the text's by 1.6×10⁻¹⁶. The
plant now moves the fourteenth decimal.

| check blinded | cases reported blind | plants naming it |
| --- | ---: | ---: |
| A0 | 1 | 1 |
| W1 | 1 | 1 |
| W2 | 2 | 2 |
| W3 | 1 | 1 |
| W4 | 3 | 3 |
| W5 | 2 | 2 |
| W6 | 3 | 3 |
| W7 | 2 | 2 |
| W8 | 1 | 1 |
| P1 | 5 | 5 |
| P2 | 2 | 2 |
| R1 | 1 | 1 |

## What this round does not establish

- **That these 19 cells are all the base-unclosable cells at depth 18.** The search
  looked only within one cell of an image of `q†`. It exhibits 19 cells; it does not
  rule out others.
- **Any bound.** The exact trees use floating-point hulls with the pilot's pad. They are
  measurements, as the pilot's are.
- **The proxy on all bulk cells.** The forecast holds on 80 random cells, not on all of
  them.
- **A quotient.** The mirror is an exact symmetry of the area and of this grid. Whether a
  certificate may keep one twin of each pair is Round 17's question.