# RUN-038 — Round 35: cell 68's certificate is this tree's own, leaf for leaf — every density and hull count agrees, and every one of its 2,126,336 vertices checks out here; cells 75 and 76 certify here too; the lost frontier is noted, not guessed **Arm:** 懸衡 (Xuán Héng) / AMRAL Research Lab **Date:** 2026-09-27 **Subject:** `AMRAL_Lebesgue_Finite_Closure_Round_35_RHCERT_Mass_Production_Durable_Frontiers_v0.1.md` (AMRAL-LUC-FC-R35, dated 2026-09-20) and its package, read from the archive: - `PUBLICATION_CANDIDATE_SHARD_68.json`, `CELL75_STATUS.json`, `CELL76_STATUS.json`, `COVERAGE_DASHBOARD.json`, `DFRONT_SPEC.json`, `GEOMETRY_RECOVERY_LEDGER.json`, `VALIDATION.json`, `State_Crystal`; - cell 68's certificate package — `cell68.rhcert` (35,940,305 bytes), its index, manifest and replay record, each also shipped as a copy — the three dominance audits, markers 75 and 76's replay, and cells 75 and 76's ledgers; Round 33's trees and Round 29's markers again. The round ships no script. **Tools:** [`run038_round35_rhcert_production.py`](../code/run038_round35_rhcert_production.py) — RUN-037's decoder and replay on cell 68's bytes; RUN-031's certificates on cells 75 and 76; RUN-032's and RUN-034's outer polygons for markers 75 and 76; RUN-036's state count **Logs:** [`run038-round35-rhcert-production.json`](../data/gate-logs/run038-round35-rhcert-production.json) **Verdict: PASS for cell 68's certificate and its promotion, cells 75 and 76's lower bounds, markers 75 and 76's independent upper replays, the audits' state counts, the stage counts and the decision to claim no geometry; PARTIAL for the two marker judgments that pair the independent replay with the MPFR one, whose record is not shipped and whose arithmetic is not here.** - **Cell 68's certificate.** - Decoded here: its header, the leaves using up the file, and the index of L + 1 offsets. - On every one of the 9,255 leaves, its density and hull count are those of this tree's own certificate of cell 68 under the emitter's start bands (RUN-037). The bytes are the polygons this tree builds, up to their 10⁻¹⁸ grid: the margins agree to 2.6×10⁻¹⁶. - Every stored vertex is in its tagged core under this tree's integer arithmetic. Every polygon is strictly convex, and every area is above 167/200. - The least margin, 2.232921067369829×10⁻⁸ at `00111011001001010000010`, and each of the four chunks' least margins are the replay record's, bit for bit. - **Cells 75 and 76.** - The ledgers' paths are this tree's lifts (RUN-036). Every leaf passes on its intended box at the ledger's density, with the ledger's hull count and its margin to 2.6×10⁻¹⁶. - Every density is the first that passes from the start band. - The least margins are 6.2518×10⁻⁸ and 2.0477×10⁻⁸, on the leaves whose slack RUN-036 found least. - **Markers 75 and 76.** - The replay rows are Round 29's files. - The full polygons under the package's normals and ceiling have the replays' 1,312 and 2,593 active constraints and their areas, and the float-reduced ones are Round 29's. - This tree's certificates need 128 normals each; the exact margins are 1.38×10⁻⁴ and 7.87×10⁻⁵. - The MPFR replays' records are not shipped. - **The audits.** 1,565, 1,690 and 1,688 unique witness-core states on this tree's lifts of cells 68, 75 and 76, as the audits say. Their MPFR results are recorded here, not recomputed. - **The stages and the geometry.** - Candidates {47, 48, 68, 69, 70}, 5/77; closed or better {47, 48, 68, 69, 70, 75, 76}, 7/77; 59 = 66 − 7 below. - The recovery ledger's eleven residual records are Round 27's, and no closure is claimed. - §6 is right that a count and a volume do not give back the boxes, and DFRONT's codes are sound as specified — a dyadic sub-interval per axis, independent of split order. - This tree's own frontier at depth 40 is kept in RUN-030's cache as box paths, and rebuilt by rerunning. It is the kind of thing DFRONT keeps, in another encoding; RUN-035 continues three cells from it. Drill: 15 / 15 plants caught by exactly the named checks, 4 / 4 controls undisturbed, 173 / 173 must-stay-green assertions held. Each of the ten checks was blinded in turn, and each was reported blind in exactly as many cases as plants name it. --- ## What Round 35 claims 1. **Cell 68** (§0, §2). 9,255/9,255 bytes-only replay, 2,126,336 vertices, 35,940,305 bytes, 0 failures, least margin 2.2329×10⁻⁸, MPFR dominance over 1,565 states: PUBLICATION-CANDIDATE-SHARD. 2. **Cells 75 and 76** (§0, §3–4). - 10,948/10,948 and 10,932/10,932 lower, with their density counts. - Least margins 6.2518×10⁻⁸ and 2.0477×10⁻⁸; marker outers 0.8349344874879304 and 0.8349600023952688. - Dominance over 1,690 and 1,688 states. Only the bytes remain. 3. **Stages** (§1, §5). Candidates 5/77, closed or better 7/77, geometry 66/77. 4. **The durability gap** (§6–7). The pending boxes were kept only in runtime checkpoints, now gone; counts and volumes do not reconstruct them, so no closure is claimed. DFRONT-v0.1 keeps each pending box as dyadic codes (k, m) per axis, independent of split order. ## A — sources **A0.** 27 anchors. Round 35 has no reference list. ## W — rebuilt | check | Round 35 | rebuilt | result | | --- | --- | --- | --- | | W1 | §0, §2 | cell 68's bytes decoded; each leaf's density and hull count against this tree's certificates | PASS, 9,255 of 9,255 | | W2 | §0, §2 | every vertex in this tree's arithmetic; convexity; exact areas | PASS, 0 refused | | W3 | §3–4 | cells 75 and 76 certified here at the ledgers' densities | PASS; the start bands on every leaf | | W4 | §3–4 | markers 75 and 76 | PASS; the MPFR replays' records not shipped | | W5 | §0 | the audits' state counts on this tree's lifts | PASS | | W6 | §1, §5–7 | the stages; the residual records; DFRONT | PASS | ## P — the package **P1.** - Cell 68's manifest has its file's digests and sizes. The replay record's chunks tile the leaves, and its least margin is the manifest's. - The shard file carries the manifest's figures and the package's size and digest. Both shipped copies are identical. - The status files of cells 75 and 76 match their ledgers (counts, least margin and path, digest, density counts), their manifests and their audits. - The dashboard's cells, and the crystal's candidates, cell 68's figures, its 1,565 states and DFRONT. **P2.** `VALIDATION.json` describes the document and the crystal correctly. Its seven digests are the archive's and the package's, and its twelve checks follow from the data. ## Round 35, read | Round 35 | statement | verdict | note | | --- | --- | --- | --- | | §0, §2 | cell 68's bytes replay 9,255/9,255, 0 failures; promotion | PASS | this tree's arithmetic; this tree's own polygons (W1, W2) | | §0, §3–4 | 10,948/10,948; 10,932/10,932; the density counts; the least margins | PASS | W3 | | §0, §3–4 | markers: independent + MPFR upper | PARTIAL | the independent polygons rebuilt; the MPFR not (W4) | | §0 | dominance states 1,565 / 1,690 / 1,688 | PASS | the counts (W5); the MPFR results not recomputed | | §1, §5 | stage counts | PASS | W6 | | §6–7 | no reconstruction from counts; DFRONT | PASS | reading; the residual records Round 27's (W6) | ## The status registry Round 35's 7 judgments are reviewed. It uses no phrase for the first time, and census v5 adds none. | verdict | judgments | | --- | ---: | | PASS | 5 | | PARTIAL | 2 | ## The drill | kind | cases | named checks | | --- | ---: | --- | | the document's 1,688 | 1 | A0 | | an index offset | 1 | W1 | | a vertex refused; a record's chunk minimum | 2 | W2 | | a ledger margin | 1 | W3 | | a ledger density | 1 | W3 (also P1) | | a marker's active count | 1 | W4 | | an audit's state count | 1 | W5 (also P1) | | the dashboard's count; a residual record | 2 | W6 | | the shard's package size; the crystal's 1,565 | 2 | P1 | | a VALIDATION digest; a VALIDATION check | 2 | P2 | | a review dropped | 1 | R1 | Four controls: - the unmodified inputs; - the document with CRLF line endings; - the dashboard with its keys sorted; - the shard file with its keys sorted. **15 / 15 plants, 4 / 4 controls, 173 / 173 must-stay-green assertions; no check without a plant.** | check blinded | cases reported blind | plants naming it | | --- | ---: | ---: | | A0 | 1 | 1 | | W1 | 1 | 1 | | W2 | 2 | 2 | | W3 | 2 | 2 | | W4 | 1 | 1 | | W5 | 1 | 1 | | W6 | 2 | 2 | | P1 | 4 | 4 | | P2 | 2 | 2 | | R1 | 1 | 1 | ## What this round does not establish - **The MPFR replays and audits**, as before. - **Cells 75 and 76's certificate bytes.** They come in Round 36.