{"taskid":"6c1f9106465fbc29f72b58e082470d816c1bbbda9a04d2877e5455a19ba238dei0","node":"hunt","result":{"target_statement":"W-semi-flat（spec 采纳版 V1 的可证伪弱化链上的半平坦加严版）：极化极大退化族中，X_t 上体积占比 >= 1-eps 的开子集带光滑拉格朗日 T^n 纤维化，且该纤维化由全纯椭圆纤维化（semi-flat 模型）给出；n=2 时计数满足 sum e(F_i) = chi(K3) = 24。注：V4（去校准弱化版）由上游 spec 显式保留给本节点作可证伪目标；本条在其上追加 semi-flat 假设，是为了让它落到格论与算术上可判。","artifact":{"bundle":"metafile://273447dbab3e6446c8b957adf852270504e97cfe30f9039e51c163f3c6c80a87i0","bundle_sha256":"3d803cb9134802dcfaf27e5c5b9cc71a5a310c4bf0885fc928ed922af189b6d2","contains":["README.md（对象、可证伪表述、复跑步骤、范围声明）","syz_hunt_v1.mjs（可运行脚本，node 标准库，无网络）","out/hunt_result.json（确定性输出）","out/run.log（命令、退出码、sha256）"]},"reproduction":{"command":"node syz_hunt_v1.mjs","runtime":"node v24.11.1 / Windows x64","dependencies":"无第三方依赖（node:crypto / node:fs / node:path）","network":false,"exit_code":0,"deterministic_reruns":4,"rerun_note":"四次运行 out/hunt_result.json 字节一致；结果无时间戳、键序固定","result_sha256":"47da4a926336697282aadda2df8239328d917d58e2b35101b34ef4435ccb502d","script_sha256":"bb2e39f51975086712b341a4d7a42abd022d00b035b1c3969fb01839a33a95be"},"search_space":{"P1_misotropic_box":"|m|,|n| <= 64，gcd(m,n)=1，共 16640 个格点（对照组）","P2_polarization_degrees":"2d = 2,4,...,128（d=1..64，逐档）","P2_k_box":"|k| <= 4096，每档 8192 个 k，合计 524288 次判定","P2b_lattice_family":"Q(m,n)=a m^2+2b mn+c n^2，a in ±1..±6，b,c in -6..6，det=ac-b^2 != 0，共 1984 个格","P3_euler_partitions":"sum e(F_i)=24，每个 e 取自 Kodaira 表 {1..12}（I_n, I_n*, II..IV*），做无顺序多重集穷举","P4_grid_and_tolerance":"9x9=81 个底空间采样点；容差 1e-12；负对照 6 档 delta in {0,1e-6,1e-4,1e-3,1e-2,1e-1}","stop_rule":"搜索止于上述边界：极化次数 <= 128、|k| <= 4096、|a|,|b|,|c| <= 6、欧拉数和恰为 24、网格 81 点。脚本不搜索度量层（PDE）的 SLAG 存在性。"},"results":{"P1_positive_and_negative_control":{"rows":4,"all_matched":true,"detail":[{"gram":[0,1,0],"form":"2mn","expected":true,"found":true,"witness":[-1,0],"note":"Q=2mn=0 iff mn=0，故本原迷向向量恰为 (±1,0),(0,±1)，无两坐标皆非零的解"},{"gram":[1,1,1],"form":"(m+n)^2","expected":true,"found":true,"witness":[-1,1]},{"gram":[-2,1,-2],"form":"-2(m^2-mn+n^2)","expected":false,"found":false},{"gram":[2,0,2],"form":"2(m^2+n^2)","expected":false,"found":false}],"meaning":"检测器既能命中也能拒绝，P2 的『找不到』不是搜索器失灵"},"P2_rho1_polarization_scan":{"degrees":64,"k_checked":524288,"degrees_with_isotropic_class":0,"analytic_reason":"(kH)^2 = 2d*k^2 >= 2d > 0 对所有 k != 0；秩 1 的 NS 里不存在原根迷向类","enumeration_table":"逐档表见 artifact 内 out/hunt_result.json 的 parts.P2_rho1_lattice_scan.rows（64 行，每行 degree_2d / k_box / checked_k / isotropic_found=false）"},"P2b_classifier_calibration":{"lattices_tested":1984,"criterion_predicts_isotropic":312,"enumerator_found_isotropic":312,"agreements":1984,"mismatches":0,"criterion":"Q 有原根迷向向量 iff D = b^2-ac > 0 且 D 为完全平方（a != 0, det != 0）","meaning":"在 1984 个格上与精确判据逐格对表，零漏判零误判；标定了 P2 用的检测器"},"P3_kodaira_euler_enumeration":{"target_euler_sum":24,"multiset_decomposition_count":1380,"decompositions_with_exactly_24_fibers":1,"only_24_fiber_solution":"24 x I_1","counter_to_naive_reading":[{"fibers":"12 x I_2","fiber_count":12,"euler_sum":24},{"fibers":"6 x IV","fiber_count":6,"euler_sum":24},{"fibers":"1 x I_24","fiber_count":1,"euler_sum":24}],"analytic_crosscheck":"1380 = p(24) - sum_{j=0}^{11} p(j) = 1575 - 195（由独立复算方给出）","scope":"仅算术约束层：每个 e 值至少对应一种 Kodaira 类型；具体配置的可实现性属 Persson 分类范围，本脚本不涉及"},"P4_semiflat_numeric_certificate":{"model":"乘积平坦环面 T^2 x T^2，Omega = dz1^dz2，纤维化 pi(z)=(Im z1, Im z2)","grid_points":81,"max_lagrangian_residual":"0.000e+0","max_phase_residual":"0.000e+0","distinct_phases_across_base":1,"max_fiber_volume_mismatch":"0.000e+0","passed_positive_control":true,"negative_control_detected":"5/5","negative_control_reading":"把纤维面扭出 Re 平面后 |omega| 精确等于 delta（1e-6..1e-1 全检出），而在 Re 平面内扭转时恒为 0；纤维体积始终为 1 —— 说明 Lagrange 性与体积归一是两个独立条件，测试不是恒真","scope_note":"常系数半平坦模型，验证的是校准代数与共同相位性质，不是一般 K3 上 SLAG 纤维化的存在性"}},"conclusions":[{"id":"C1_domain_restriction","type":"解析结论（可复算）","claim":"对任意 d，ρ=1 极化 K3 的 Néron–Severi 格为 Z·H，(kH)^2=2dk^2>=2d>0，不含原根迷向类；而 K3 的极大单值化退化要求 NS 中存在迷向类（等价于存在椭圆纤维化）。故 W 的『极化极大退化』前提在 ρ=1 族上不可满足。","consequence":"ρ=1 极化族不在 V1/V4 的定义域内，不能当作反例使用；这类族上的『失败』是域外事件。"},{"id":"C2_arithmetic_obstruction","type":"完全枚举","claim":"sum e(F_i)=24 的 1380 种欧拉数分解里，只有 24 x I_1 让『奇异纤维根数=24』成立；12 x I_2、1 x I_24 等根数远小于 24 而欧拉数和仍为 24。","consequence":"『24』只能按加权读法（sum e = 24）使用；朴素的根数计数是假的，任何下游论证若用根数读法即为表述错误。"},{"id":"C3_negative_result","type":"有限证据","claim":"在上述搜索区间内未找到 W 的反例。","consequence":"这不是『W 成立』的证明；它只说明在 n=2、semi-flat 层与算术层上，该加严版的破缺点不在本脚本可达范围内。"},{"id":"C4_where_to_go_next","type":"方向建议","claim":"要逼近 V1（保留校准与共同相位、去掉 semi-flat 要求），必须转入度量层：判别轨迹的局部模型 + (1-eps) 体积占比估计。","consequence":"属 PDE 层，本脚本不可达；hunt 与 pde 的分工应以此为界。"}],"independent_recheck":{"by":"本机 MetaBot『尺规』(metabot id 2)，未读取本脚本、仅按数学规格独立实现","result_file_sha256":"0ae0c4008b2cf2dbf03e93f220c1f82fb9770be188d5b6c9255492a74270832e","agreements":["P2 扫描 k 总数 524288","P2 迷向类 d 个数 0","P3 分解数 1380（DP / 递归枚举 / 生成函数三法互证，且 1575-195）","P3 恰 24 部分只有 [1 x 24]","P4 六个 delta 的相对误差精确为 0"],"discrepancy_found_and_fixed":"复算方指出：我在派单示例中把 (0,1,0) 的迷向向量写成 (1,1)，但 Q(1,1)=2≠0；本组本原迷向向量恰为 (±1,0),(0,±1)。存在性判定无误，示例错误。已据此修正脚本内注释（本提交的 script_sha256 为修正后版本），未改动任何计算与结果数字。"},"finite_evidence_declaration":"P1/P3/P4 为有限或完全枚举证据；P2 的盒搜索是对恒等式的数值复核，其结论另有解析理由 2dk^2>=2d>0 支撑；P2b 是 1984 个格上的全族对比。脚本不搜索度量层 SLAG 存在性，搜索止于 polarization degree <= 128、|k| <= 4096、|a|,|b|,|c| <= 6、sum e = 24、9x9 网格与容差 1e-12。『有限区间未找到』不等同于『不存在』，本提交不据此断言 W 成立或 V1 成立。","hash":"2e49a5b5f74941bbf717099f2b24cb4189ccab7d2850a5381c9e44baf1612e7e"},"hash":"72549dbab32aaca3dae72cc4a7eeb07b668a36011ee612c43f78e2c69988c766","contentType":"application/json;utf-8","attachment":null,"childids":[],"parentrefs":{"spec":"9a4460efb9f95df1806d0659d1dceee4a62011e17cc36c4ec9b8a056fc564776i0"}}