Add fail-closed real P formula data contract

MANIFEST.json

@@ -1,11 +1,11 @@
 {
-    "schema":  "aiflow-hf-research-snapshot-v7",
-    "generated_at":  "2026-07-23T19:59:31.9187849Z",
+    "schema":  "aiflow-hf-research-snapshot-v8",
+    "generated_at":  "2026-07-23T20:04:13.5124140Z",
     "track":  "R_noncommercial_plus_rejected_P_proxy",
     "product_validation":  false,
     "public_release":  true,
     "contains_raw_dataset":  false,
-    "tests":  "278 passed",
+    "tests":  "282 passed",
     "retracted_paths":  [
                             "models/auxiliary/boundary_auxiliary_head.pt",
                             "models/auxiliary/seed17/boundary_joint_delta.pt",
@@ -28,6 +28,16 @@
                       "bytes":  6803,
                       "sha256":  "4f842852093ca46b1942c942fd5e475ca6c19f044ba9e27b6d372f1aed56056e"
                   },
+                  {
+                      "path":  "reports/RESEARCH_REPORT.md",
+                      "bytes":  33159,
+                      "sha256":  "19c06349b4316cb538a48fbe1cf5fccaaa386ca215615ae6ca53bfaefc0995df"
+                  },
+                  {
+                      "path":  "scripts/evaluate_math_ink_06_p_boundary_device_stress.py",
+                      "bytes":  10444,
+                      "sha256":  "bdd75047c4887a6e53720f1c84d224545844cdbd9b0239826a605d578b3c92a6"
+                  },
                   {
                       "path":  "scripts/evaluate_crohme_tray_joint_selector.py",
                       "bytes":  11671,
@@ -38,16 +48,6 @@
                       "bytes":  11900,
                       "sha256":  "f32a18c8e7d3a0ea36379293e6be88bfb509b7df99846c38149fb8458e6cc994"
                   },
-                  {
-                      "path":  "reports/RESEARCH_REPORT.md",
-                      "bytes":  31962,
-                      "sha256":  "704e9d2af5fc5ef36136a80b0f6d66cd0984c21a254ab937cd9d1cdd5603ce47"
-                  },
-                  {
-                      "path":  "reports/p_boundary_joint_seed17.json",
-                      "bytes":  6920,
-                      "sha256":  "7af3bb995041e5ea621d3c9535f3552e264860f12a7e6145637849f5cd0220a8"
-                  },
                   {
                       "path":  "reports/online_casecontext_seed31.json",
                       "bytes":  33576,
@@ -63,6 +63,16 @@
                       "bytes":  15740,
                       "sha256":  "27b31da71b9f39f7ded38aa1ce3694911af140d22854543d4ae2b5f9e709b479"
                   },
+                  {
+                      "path":  "reports/online_casecontext_seed47.json",
+                      "bytes":  33727,
+                      "sha256":  "c3dfd328d9ff0a55eed2cb74657ad87e5e164968fddd7fae8c8fd92e137a4557"
+                  },
+                  {
+                      "path":  "reports/p_boundary_joint_seed17.json",
+                      "bytes":  6920,
+                      "sha256":  "7af3bb995041e5ea621d3c9535f3552e264860f12a7e6145637849f5cd0220a8"
+                  },
                   {
                       "path":  "reports/p_boundary_device_stress_sharedfix_3seed.json",
                       "bytes":  10867,
@@ -73,11 +83,6 @@
                       "bytes":  16685,
                       "sha256":  "9d250e5c75d4f104971551c07a702810bf94fb5b6e5e587035a624933766356e"
                   },
-                  {
-                      "path":  "reports/online_casecontext_seed47.json",
-                      "bytes":  33727,
-                      "sha256":  "c3dfd328d9ff0a55eed2cb74657ad87e5e164968fddd7fae8c8fd92e137a4557"
-                  },
                   {
                       "path":  "src/math_ink_06.py",
                       "bytes":  54708,
@@ -93,6 +98,11 @@
                       "bytes":  18055,
                       "sha256":  "6fa378ccb7d08f605d4976b6ae08247d0b1fa3f2cb7ce00ba5d35b79c6dfbb47"
                   },
+                  {
+                      "path":  "src/p_formula_gate06.py",
+                      "bytes":  7910,
+                      "sha256":  "00c8cb3fd5b53f2d118886d7333fe75d62f2d7b7e7b161b662adbd43d1b14a7f"
+                  },
                   {
                       "path":  "src/tray_joint.py",
                       "bytes":  19404,
@@ -108,25 +118,30 @@
                       "bytes":  13772,
                       "sha256":  "8cc2dc1e13b56c21d53a76b9b863cdf5c8f8dd315da6eb18c1bd2b5b87c1a616"
                   },
-                  {
-                      "path":  "scripts/train_math_ink_06_p_boundary_auxiliary.py",
-                      "bytes":  20688,
-                      "sha256":  "70ca8a05dcbd48e79d812cd7ff44ee3d8479055f898143daa6d6ea7580b2973e"
-                  },
                   {
                       "path":  "scripts/summarize_math_ink_06_p_boundary_joint.py",
                       "bytes":  4580,
                       "sha256":  "c6ce78f521232bdb7e967b0c358232a72dd3f79747f9e32eb240d9bb10c6a422"
                   },
+                  {
+                      "path":  "scripts/preflight_math_ink_06_p_formula.py",
+                      "bytes":  1664,
+                      "sha256":  "36aeeab2f2474ce874ef932b24eb062dfc3b9e6cf3c0d59410a052a9c9835a07"
+                  },
                   {
                       "path":  "scripts/export_math_ink_06_litert.py",
                       "bytes":  8637,
                       "sha256":  "e96b30ded57d33d4505b065c1ac69c5ac7db43618c0eb7f3b7fb787b6fcaf1f6"
                   },
                   {
-                      "path":  "scripts/evaluate_math_ink_06_p_boundary_device_stress.py",
-                      "bytes":  10444,
-                      "sha256":  "bdd75047c4887a6e53720f1c84d224545844cdbd9b0239826a605d578b3c92a6"
+                      "path":  "scripts/sweep_math_ink_06_component_competition_guard.py",
+                      "bytes":  9084,
+                      "sha256":  "e2dee616e2c6ebdc32281624889017685648b7076515242e04a1452d98d1c7da"
+                  },
+                  {
+                      "path":  "scripts/train_math_ink_06_p_boundary_auxiliary.py",
+                      "bytes":  20688,
+                      "sha256":  "70ca8a05dcbd48e79d812cd7ff44ee3d8479055f898143daa6d6ea7580b2973e"
                   },
                   {
                       "path":  "scripts/train_math_ink_06_boundary_behavior_guard.py",
@@ -138,21 +153,6 @@
                       "bytes":  9063,
                       "sha256":  "28cfc7b9b695256cfa9199d912d1d938d402292b88e9411d42fddb3508446d3b"
                   },
-                  {
-                      "path":  "scripts/sweep_math_ink_06_component_competition_guard.py",
-                      "bytes":  9084,
-                      "sha256":  "e2dee616e2c6ebdc32281624889017685648b7076515242e04a1452d98d1c7da"
-                  },
-                  {
-                      "path":  "reports/local_baseline_overmerge_audit.json",
-                      "bytes":  1237409,
-                      "sha256":  "33a9ccafebd559ca8b173f011e9a0a6f495d37b8fdb2693673663479d3457071"
-                  },
-                  {
-                      "path":  "exports/seed17/raster.pt2",
-                      "bytes":  9465689,
-                      "sha256":  "419301d67bbfe7b807e1ea676a33827c749f632300392d54eaf48c701ca07512"
-                  },
                   {
                       "path":  "exports/seed17/online.pt2",
                       "bytes":  9192090,
@@ -163,6 +163,16 @@
                       "bytes":  1030,
                       "sha256":  "48a224d03fb2e8f1c4fcb6ca3f61456521f4437b4cfc845572111cd84cb93833"
                   },
+                  {
+                      "path":  "contracts/aiflow_p_formula_v1.schema.json",
+                      "bytes":  1903,
+                      "sha256":  "c78c8a612d2f24a5c09fe1aa158b365481102869c3f84b3a5510a895b416c424"
+                  },
+                  {
+                      "path":  "exports/seed17/raster.pt2",
+                      "bytes":  9465689,
+                      "sha256":  "419301d67bbfe7b807e1ea676a33827c749f632300392d54eaf48c701ca07512"
+                  },
                   {
                       "path":  "models/seed17/online_adapter.pt",
                       "bytes":  2875654,
@@ -178,11 +188,6 @@
                       "bytes":  8638290,
                       "sha256":  "f3b0e53b50e41cf57d4881c501371b35648cf049d603984a0edf6148c2b62bd7"
                   },
-                  {
-                      "path":  "assets/stroke_encoding.svg",
-                      "bytes":  3882,
-                      "sha256":  "66bf7659c2e86fd53e6583e7c5deb8d371432469c07d4e4ca0dd165b4a81f4ed"
-                  },
                   {
                       "path":  "pyproject.snapshot.toml",
                       "bytes":  669,
@@ -198,6 +203,16 @@
                       "bytes":  2406,
                       "sha256":  "2419245ba889772d562d524999e9d14f801e70d87ce75e38231722eb5aecd697"
                   },
+                  {
+                      "path":  "README.md",
+                      "bytes":  11248,
+                      "sha256":  "d102514283972dbddc061848a1fb33a5d4f581dea0b43dc9eb3f4f8de46d5885"
+                  },
+                  {
+                      "path":  "assets/stroke_encoding.svg",
+                      "bytes":  3882,
+                      "sha256":  "66bf7659c2e86fd53e6583e7c5deb8d371432469c07d4e4ca0dd165b4a81f4ed"
+                  },
                   {
                       "path":  "assets/architecture.svg",
                       "bytes":  5695,
@@ -208,11 +223,6 @@
                       "bytes":  824191,
                       "sha256":  "18aff472c1bdb25a519b1553364229c9869aed1f36a9d663cf88a1bc808fab8f"
                   },
-                  {
-                      "path":  "README.md",
-                      "bytes":  11132,
-                      "sha256":  "5d08c5e2735e52acb557ef6b7792f5573508508297ca8054ca5ecad2e7311d8d"
-                  },
                   {
                       "path":  "reports/behavior_role_seed47.json",
                       "bytes":  30091,
@@ -228,6 +238,16 @@
                       "bytes":  29047,
                       "sha256":  "e2072fec1b1065777f0e9218c48d27f096b22f5545e7cc8d9962939282719561"
                   },
+                  {
+                      "path":  "reports/boundary_behavior_guard_report.json",
+                      "bytes":  72053,
+                      "sha256":  "f55a230a9f0892b9676c71db46e9e527862b3d8da776dc43db767ce7a0f6a5c7"
+                  },
+                  {
+                      "path":  "reports/local_baseline_overmerge_audit.json",
+                      "bytes":  1237409,
+                      "sha256":  "33a9ccafebd559ca8b173f011e9a0a6f495d37b8fdb2693673663479d3457071"
+                  },
                   {
                       "path":  "reports/local_baseline_guard_report.json",
                       "bytes":  24052,
@@ -238,16 +258,6 @@
                       "bytes":  22284,
                       "sha256":  "4d3db5f71e5008381dd072f2c10aafb22e08f96e23f2a32f82a3a46abd9c70b9"
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-                  {
-                      "path":  "reports/boundary_behavior_guard_report.json",
-                      "bytes":  72053,
-                      "sha256":  "f55a230a9f0892b9676c71db46e9e527862b3d8da776dc43db767ce7a0f6a5c7"
-                  },
-                  {
-                      "path":  "reports/behavior_role_3seed_summary.json",
-                      "bytes":  3567,
-                      "sha256":  "b16049218d2d006d952f59f55642fa9f3fbfbc3cc3a730fbd7b075f507c3b251"
-                  },
                   {
                       "path":  "models/seed31/online_adapter.pt",
                       "bytes":  2875654,
@@ -263,6 +273,16 @@
                       "bytes":  8638290,
                       "sha256":  "e3c57bc8cbbd4542cacf7ab9200a9031dcdc5ee63ffbd6ad6c9f7ef4f0a64f37"
                   },
+                  {
+                      "path":  "models/seed47/base_378.pt",
+                      "bytes":  8638290,
+                      "sha256":  "4131b21f6b00471c1c5a82aee4a2da45e599e42dc742fc1dd0dd8afb970f8939"
+                  },
+                  {
+                      "path":  "reports/behavior_role_3seed_summary.json",
+                      "bytes":  3567,
+                      "sha256":  "b16049218d2d006d952f59f55642fa9f3fbfbc3cc3a730fbd7b075f507c3b251"
+                  },
                   {
                       "path":  "models/seed47/online_adapter.pt",
                       "bytes":  2876038,
@@ -272,11 +292,6 @@
                       "path":  "models/seed47/behavior_role_head.pt",
                       "bytes":  75794,
                       "sha256":  "f28fad4e0289e3bc9400829f41aba9bbd75c43d445b7462a84aadbdbe635c10b"
-                  },
-                  {
-                      "path":  "models/seed47/base_378.pt",
-                      "bytes":  8638290,
-                      "sha256":  "4131b21f6b00471c1c5a82aee4a2da45e599e42dc742fc1dd0dd8afb970f8939"
                   }
               ]
 }

README.md

@@ -247,4 +247,5 @@ PyTorch checkpoint와 joblib/pickle은 신뢰할 수 없는 출처에서 로드
 - P boundary 정정 3-seed: [`reports/p_boundary_joint_sharedfix_3seed_summary.json`](reports/p_boundary_joint_sharedfix_3seed_summary.json)
 - 정정 main device stress: [`reports/p_boundary_device_stress_sharedfix_3seed.json`](reports/p_boundary_device_stress_sharedfix_3seed.json)
 - Seed-17 composite export: [`exports/seed17/export_manifest.json`](exports/seed17/export_manifest.json)
+- 실제 P formula schema: [`contracts/aiflow_p_formula_v1.schema.json`](contracts/aiflow_p_formula_v1.schema.json)
 - 파일 checksum: [`MANIFEST.json`](MANIFEST.json)

contracts/aiflow_p_formula_v1.schema.json

@@ -0,0 +1,63 @@
+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "$id": "https://aiflow.local/schemas/p-formula-v1.json",
+  "title": "AIFlow Math Ink 0.6 P Formula Record",
+  "type": "object",
+  "required": [
+    "formula_id",
+    "origin_id",
+    "writer_id",
+    "device_id",
+    "source_id",
+    "split",
+    "canvas_width",
+    "canvas_height",
+    "rights_track",
+    "commercial_training_allowed",
+    "symbols"
+  ],
+  "properties": {
+    "formula_id": {"type": "string", "minLength": 1},
+    "origin_id": {"type": "string", "minLength": 1},
+    "writer_id": {"type": "string", "minLength": 1},
+    "device_id": {"type": "string", "minLength": 1},
+    "source_id": {"type": "string", "minLength": 1},
+    "split": {"enum": ["training", "validation", "test"]},
+    "canvas_width": {"type": "number", "exclusiveMinimum": 0},
+    "canvas_height": {"type": "number", "exclusiveMinimum": 0},
+    "rights_track": {"const": "P"},
+    "commercial_training_allowed": {"const": true},
+    "symbols": {
+      "type": "array",
+      "minItems": 1,
+      "items": {
+        "type": "object",
+        "required": ["token", "strokes"],
+        "properties": {
+          "token": {"type": "string", "minLength": 1},
+          "strokes": {
+            "type": "array",
+            "minItems": 1,
+            "items": {
+              "type": "array",
+              "minItems": 1,
+              "items": {
+                "type": "object",
+                "required": ["x", "y"],
+                "properties": {
+                  "x": {"type": "number"},
+                  "y": {"type": "number"},
+                  "t": {"type": ["number", "null"]},
+                  "pressure": {"type": ["number", "null"]}
+                },
+                "additionalProperties": true
+              }
+            }
+          }
+        },
+        "additionalProperties": true
+      }
+    }
+  },
+  "additionalProperties": true
+}

reports/RESEARCH_REPORT.md

@@ -409,6 +409,19 @@ Joint delta 없이 정정된 main과 새 auxiliary head만 대상으로 device s
 
 Seed 17·31·47 모두 online/raster 각각 대표 입력 76개에서 eager 대비 top-1 100% 일치, 최대 logit 절대오차 0.0으로 strict `torch.export` gate를 통과했다. Seed당 두 graph 합계는 18,657,779 bytes로 25MB 예산 안이다. 다만 `.pt2`는 Android LiteRT artifact가 아니다. 공식 LiteRT Torch 0.9.1은 Linux 환경을 요구하며 WSL 변환 환경 설치 중 WSL filesystem I/O 오류가 발생해 `.tflite` 변환과 runtime parity는 아직 미완료다.
 
+### 실제 P 연속식 데이터 계약
+
+실제 데이터가 도착하기 전에 `AIFlow P Formula v1` JSON Schema와 fail-closed preflight를 추가했다. 각 formula는 다음 근거를 모두 가져야 한다.
+
+- 고유 `formula_id`, 원본 추적용 `origin_id`
+- 비어 있지 않은 `writer_id`, `device_id`, `source_id`
+- `training|validation|test` split
+- `rights_track=P`, `commercial_training_allowed=true`
+- 양수 canvas 크기
+- token과 원본 raw stroke가 포함된 정답 symbol group
+
+Origin·writer·device·source가 둘 이상의 split에 나타나면 제품 평가를 거부한다. Timestamp와 pressure가 없는 symbol은 삭제하거나 관측값으로 위장하지 않고 missing slice로 센다. 검증된 formula의 실제 symbol group은 boundary 음성, 인접한 두 symbol group 결합은 boundary 양성으로 만든다. 이 계약은 실제 성능값을 만들지는 않지만, 향후 P 입력이 CROHME 정답 group이나 합성 고립기호 proxy와 섞이는 것을 방지한다. 전체 회귀는 282개가 통과했다.
+
 ## 산출물
 
 - `src/math_grid_drawer/research/behavior_context06.py`
@@ -432,9 +445,12 @@ Seed 17·31·47 모두 online/raster 각각 대표 입력 76개에서 eager 대
 - `scripts/summarize_math_ink_06_p_boundary_joint.py`
 - `scripts/evaluate_math_ink_06_p_boundary_device_stress.py`
 - `scripts/export_math_ink_06_litert.py`
+- `scripts/preflight_math_ink_06_p_formula.py`
 - `scripts/analyze_crohme_lattice_failures.py`
 - `tests/test_behavior_context06.py`
 - `tests/test_behavior_role_head06.py`
+- `tests/test_p_formula_gate06.py`
+- `research/contracts/aiflow_p_formula_v1.schema.json`
 - `research/AIFlow-MATH-INK-0.6-BEHAVIOR-CONTEXT-REPORT-20260724.md`
 - `research/runs/math_ink_06_behavior_role_3seed_20260724/run_summary.json`
 - `research/runs/math_ink_06_behavior_grouping_audit_20260724/report.json`

scripts/preflight_math_ink_06_p_formula.py

@@ -0,0 +1,44 @@
+"""실제 P 연속 수식 JSONL을 학습·평가 전에 fail-closed로 감사한다."""
+
+from __future__ import annotations
+
+import argparse
+from datetime import datetime, timezone
+import json
+from pathlib import Path
+import sys
+
+PROJECT_ROOT = Path(__file__).parents[1]
+SOURCE_ROOT = PROJECT_ROOT / "src"
+if str(SOURCE_ROOT) not in sys.path:
+    sys.path.insert(0, str(SOURCE_ROOT))
+
+from math_grid_drawer.research.external_corpus import read_jsonl
+from math_grid_drawer.research.p_formula_gate06 import audit_p_formula_records06
+
+
+def main() -> None:
+    """필요 변수: UTF-8 JSONL·최소 source 수·출력. 작동 원리: 실제 P gate 적격 여부와 모든 누수 원인을 JSON으로 남긴다."""
+
+    parser = argparse.ArgumentParser(description="Preflight real P continuous formula data")
+    parser.add_argument("--data", type=Path, required=True)
+    parser.add_argument("--minimum-independent-sources", type=int, default=2)
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    records = list(read_jsonl(args.data))
+    report = audit_p_formula_records06(
+        records, minimum_independent_sources=args.minimum_independent_sources,
+    )
+    report["generated_at"] = datetime.now(timezone.utc).isoformat()
+    report["data"] = str(args.data)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(
+        json.dumps(report, ensure_ascii=False, indent=2) + "\n", encoding="utf-8",
+    )
+    print(json.dumps(report, ensure_ascii=False, indent=2))
+    if not report["eligible_for_product_evaluation"]:
+        raise SystemExit(2)
+
+
+if __name__ == "__main__":
+    main()

src/p_formula_gate06.py

@@ -0,0 +1,186 @@
+"""실제 P 연속 수식의 권리·분할·symbol-group 계약을 fail-closed로 검사한다."""
+
+from __future__ import annotations
+
+from collections import defaultdict
+from collections.abc import Iterable, Sequence
+from typing import Any
+
+
+REQUIRED_SPLITS_06 = frozenset({"training", "validation", "test"})
+REQUIRED_RECORD_FIELDS_06 = (
+    "formula_id", "origin_id", "writer_id", "device_id", "source_id", "split",
+    "canvas_width", "canvas_height", "symbols", "rights_track",
+    "commercial_training_allowed",
+)
+
+
+def _identity_overlap06(records: Sequence[dict[str, Any]], field: str) -> dict[str, list[str]]:
+    """필요 변수: formula record·identity field. 작동 원리: 하나의 identity가 둘 이상의 split에 나타난 경우만 반환한다."""
+
+    split_by_identity: dict[str, set[str]] = defaultdict(set)
+    for record in records:
+        value = str(record.get(field) or "").strip()
+        if value:
+            split_by_identity[value].add(str(record.get("split") or ""))
+    return {
+        identity: sorted(splits)
+        for identity, splits in split_by_identity.items()
+        if len(splits) > 1
+    }
+
+
+def _valid_strokes06(strokes: Any) -> bool:
+    """필요 변수: symbol stroke payload. 작동 원리: 비어 있지 않은 획과 유한 좌표 필드를 구조적으로 검사한다."""
+
+    if not isinstance(strokes, list) or not strokes:
+        return False
+    for stroke in strokes:
+        if not isinstance(stroke, list) or not stroke:
+            return False
+        for point in stroke:
+            if not isinstance(point, dict) or "x" not in point or "y" not in point:
+                return False
+            try:
+                x, y = float(point["x"]), float(point["y"])
+            except (TypeError, ValueError):
+                return False
+            if not (-1e9 < x < 1e9 and -1e9 < y < 1e9):
+                return False
+    return True
+
+
+def audit_p_formula_records06(
+    records: Sequence[dict[str, Any]], *, minimum_independent_sources: int = 2,
+) -> dict[str, Any]:
+    """필요 변수: 실제 연속식 record. 작동 원리: P 권리·필수 metadata·identity 누수·group 정답을 한 번에 감사한다."""
+
+    issues: list[dict[str, Any]] = []
+    formula_ids: set[str] = set()
+    origin_splits: dict[str, set[str]] = defaultdict(set)
+    split_counts: dict[str, int] = defaultdict(int)
+    symbol_counts: dict[str, int] = defaultdict(int)
+    missing_timestamp_symbols = missing_pressure_symbols = total_symbols = 0
+
+    for index, record in enumerate(records):
+        missing = [
+            field for field in REQUIRED_RECORD_FIELDS_06
+            if field not in record or record[field] is None or record[field] == ""
+        ]
+        if missing:
+            issues.append({"type": "missing_fields", "record_index": index, "fields": missing})
+            continue
+        formula_id = str(record["formula_id"])
+        if formula_id in formula_ids:
+            issues.append({"type": "duplicate_formula_id", "formula_id": formula_id})
+        formula_ids.add(formula_id)
+        split = str(record["split"])
+        split_counts[split] += 1
+        if split not in REQUIRED_SPLITS_06:
+            issues.append({"type": "invalid_split", "formula_id": formula_id, "split": split})
+        origin_splits[str(record["origin_id"])].add(split)
+        if str(record["rights_track"]) != "P" or record["commercial_training_allowed"] is not True:
+            issues.append({"type": "rights_not_product_approved", "formula_id": formula_id})
+        try:
+            if float(record["canvas_width"]) <= 0 or float(record["canvas_height"]) <= 0:
+                raise ValueError
+        except (TypeError, ValueError):
+            issues.append({"type": "invalid_canvas", "formula_id": formula_id})
+
+        symbols = record["symbols"]
+        if not isinstance(symbols, list) or not symbols:
+            issues.append({"type": "empty_symbol_groups", "formula_id": formula_id})
+            continue
+        for symbol_index, symbol in enumerate(symbols):
+            total_symbols += 1
+            token = str(symbol.get("token") or "").strip() if isinstance(symbol, dict) else ""
+            if not token or not isinstance(symbol, dict) or not _valid_strokes06(symbol.get("strokes")):
+                issues.append({
+                    "type": "invalid_symbol_group", "formula_id": formula_id,
+                    "symbol_index": symbol_index,
+                })
+                continue
+            symbol_counts[token] += 1
+            points = [point for stroke in symbol["strokes"] for point in stroke]
+            if not all(point.get("t") is not None for point in points):
+                missing_timestamp_symbols += 1
+            if not all(point.get("pressure") is not None for point in points):
+                missing_pressure_symbols += 1
+
+    for origin, splits in origin_splits.items():
+        if len(splits) > 1:
+            issues.append({"type": "origin_split_leakage", "origin_id": origin, "splits": sorted(splits)})
+    identity_overlap = {
+        field: _identity_overlap06(records, field)
+        for field in ("writer_id", "device_id", "source_id")
+    }
+    for field, overlaps in identity_overlap.items():
+        if overlaps:
+            issues.append({
+                "type": f"{field}_split_leakage",
+                "count": len(overlaps),
+                "examples": dict(list(overlaps.items())[:10]),
+            })
+    missing_splits = sorted(REQUIRED_SPLITS_06 - set(split_counts))
+    if missing_splits:
+        issues.append({"type": "missing_required_splits", "splits": missing_splits})
+    independent_sources = len({str(record.get("source_id") or "") for record in records if record.get("source_id")})
+    if independent_sources < minimum_independent_sources:
+        issues.append({
+            "type": "insufficient_independent_sources",
+            "observed": independent_sources, "required": minimum_independent_sources,
+        })
+
+    return {
+        "schema": "aiflow-p-formula-preflight-v1",
+        "records": len(records),
+        "symbols": total_symbols,
+        "split_counts": dict(sorted(split_counts.items())),
+        "label_count": len(symbol_counts),
+        "independent_sources": independent_sources,
+        "identity_overlap_counts": {
+            field: len(overlaps) for field, overlaps in identity_overlap.items()
+        },
+        "missing_metadata_slices": {
+            "timestamp_symbols": missing_timestamp_symbols,
+            "pressure_symbols": missing_pressure_symbols,
+        },
+        "issues": issues,
+        "eligible_for_product_evaluation": not issues,
+        "product_validation": False,
+    }
+
+
+def formula_boundary_candidates06(record: dict[str, Any]) -> list[dict[str, Any]]:
+    """필요 변수: 검증된 formula record. 작동 원리: 실제 단일 group과 인접 두 group 결합을 boundary 정답 후보로 만든다."""
+
+    symbols = record["symbols"]
+    candidates = [
+        {
+            "formula_id": str(record["formula_id"]),
+            "symbol_indices": [index],
+            "strokes": symbol["strokes"],
+            "boundary_target": 0,
+        }
+        for index, symbol in enumerate(symbols)
+    ]
+    for index in range(len(symbols) - 1):
+        candidates.append({
+            "formula_id": str(record["formula_id"]),
+            "symbol_indices": [index, index + 1],
+            "strokes": [*symbols[index]["strokes"], *symbols[index + 1]["strokes"]],
+            "boundary_target": 1,
+        })
+    return candidates
+
+
+def collect_formula_boundary_candidates06(
+    records: Iterable[dict[str, Any]],
+) -> list[dict[str, Any]]:
+    """필요 변수: 검증된 formula iterable. 작동 원리: formula별 실제 group 후보를 평가용 평탄 목록으로 만든다."""
+
+    return [
+        candidate
+        for record in records
+        for candidate in formula_boundary_candidates06(record)
+    ]