Integrate 2026-09-14 geometric-balance structural and directional consequences

AGENTS.md

@@ -1,26 +1,38 @@
 # Working on Matching One
 
-Read `docs/RESEARCH-FRONTIER.md` and `docs/ROADMAP.md`, then the relevant live
-Issue and its latest comments. `docs/STATUS.md` distinguishes current scope
-from the verbatim historical ledger. Old acquisition instructions, opening
-Issue bodies and publication-portfolio snapshots are not a current run queue.
+Read `docs/WORK-NOW.md`, live Issue #650 and the relevant issue's latest
+comments before scheduling new work. Issue #801 maps the owner's seven running
+machines to actual jobs; do not infer a runtime inventory from issue titles.
+`docs/RESEARCH-FRONTIER.md` and `docs/ROADMAP.md` retain dated research history.
+Their older publication/acceptance focus and automatic width ladders are not
+the current execution queue. The previous AGENTS version remains in Git.
 
-Owner-delegated focus dated 2026-09-13, reconciled with the latest #650:
-- One active acceptance package: consolidate and independently audit #735's
-  arbitrary-period root theorem, with #613/#736's sharp axial full-law boundary,
-  as one probability manuscript. Return the package to #735.
-- Uniform oblique winding corridors are a possible strengthening within this
-  programme, not a new mandatory parallel project or duplicate census.
-- #636 is a visible representation reserve, paused for new extension this round.
-  Reuse #708/#710/#733/#737 rather than re-commissioning their finite results.
-- #275: original-U candidate maps before more sampling; theory-blocked P1,
-  with its original source/normalizer/moving-root contract retained.
+Owner-delegated allocation, 2026-09-14:
+- P0 question A: #768 identifies the first non-common sector insertion; #802
+  predicts and computes a physical joint root-tangent / shape-normal response.
+  An intrinsic curve can erase a thermal-tangent correction that moves the root.
+- P0 question B: #780 measures/proves the shared-label lineage merger bound
+  needed to transport the dilute cut model to a fixed-subcritical thermal window.
+  More exact moments of the limiting model are not a substitute for that bridge.
+- P1 support: #613, #740, #760, #761, #769, #775, #776, #778. Support is bounded,
+  not permission to run all tasks in parallel. #769/#775 share raw rank tables;
+  finish the current smallest useful artifact, not an automatic L5--8 ladder.
+- P2 topics remain legitimate mathematical interests but have no default new
+  shared-machine allocation. #787 -> #740, #788 -> #778, #784 -> #783 are merged
+  issue entrypoints; their original research text and results remain available.
+- #275 keeps its original source, normalizer and moving-root contract. New rank
+  observers do not replace original U, and no frozen adjudication is changed.
+
+For running work, preserve checkpoints, completed shards and seeds before an
+operator pauses at a safe batch boundary. Do not kill unknown processes, delete
+raw data, change credentials, purchase resources or assume a priority label has
+already stopped a machine. Unused capacity is preferable to duplicate production.
 
 Choose work by the mathematical or physical distinction it can settle, not by
-how many PRs, scripts, new widths or compatibility scores it generates. A useful
-new idea may replace this allocation, but state the new question and why its
-answer would change the research. Do the small calculation now rather than
-opening an issue asking someone else to repeat an already available result.
+how many PRs, scripts, new widths or compatibility scores it generates. Pure
+curiosity needs no publication rationale, but does not automatically expand the
+shared compute queue. Do the small calculation directly instead of assigning
+someone to repeat an already available result.
 
 Preserve existing data and frozen target history. Count one random block once.
 Name site versus bond, occupied graph versus matching complement, rank versus
@@ -29,11 +41,10 @@ of sites, not the linear size. Distinguish actual operator Jordan structure
 from a derivative-jet lift and from an observed polynomial length factor.
 
 Open/closed, merged/unmerged and correct/incorrect are separate. Do not silently
-merge another research PR, alter a source contract, or change a result's claim
-level merely to tidy navigation. Use a narrow branch and a clear diff. Run
-mathematical checks proportional to the change; report exactly what ran.
-Do not claim parent CI for a child commit or full CI from local tests.
+merge another research PR, alter a source contract, or promote a result merely
+to tidy navigation. Use a narrow diff. Run mathematical checks proportional to
+the change and report what actually ran; local checks are not full-repository CI.
 
-`GOVERNANCE.md` keeps exploration lightweight. Do not add document-wording
-tests, digest ceremonies, a new audit framework or a speculative production
-scheduler. Keep proof, executable control, inference and novelty claims apart.
+`GOVERNANCE.md` keeps exploration lightweight. Do not add wording tests, digest
+ceremonies, another audit framework or an autonomous production scheduler.
+Keep proof, executable control, inference and conjecture separate.

docs/WORK-NOW.md

@@ -0,0 +1,76 @@
+# 当前研究与算力分配：两处缺口，不再按公式数扩张
+
+2026-09-14。所有者授权的优先级重排。本页与 #650 是当前分配入口，优先于旧 README、AGENTS、Issue 正文中的自动尺寸阶梯及发表/验收计划。数学兴趣不需要发表理由；共享算力需要一个尚缺的判断。
+
+## 现在主攻什么
+
+**问题 A：什么微观差异在拓扑消去之后仍然移动匹配根？**
+
+- **#768 / P0，深度理论与定向检索**：比较 scalar 8-arm、thermal-family spin ±4 及低阶竞争通道。区分旋转允许、匹配奇性、实际出现、差矩阵元非零。优先核对 c=0、h=5/8 的 level-2 奇异向量在实际模块里是否解耦，以及积分总导数、接触项和周期闭合。
+- **#802 / P0，分析后定向 CPU**：同一实际源下同时保留根位移和定 b 的形状变化。内禀 C_L(b) 会消掉纯热切向修正；不能仅凭它很小就排除一个根位移机制。先给两个不同预测，再计算一项现有表缺少的响应。
+
+**问题 B：稀疏极限的漂亮过程是否真的运送到固定亚临界热窗口？**
+
+- **#780 / P0，共同标签理论与计算**：新的[双见证证明](manuscripts/geometric-balance/thermal-window-no-merger-20260914.md)已给出固定严格亚临界 p0 附近收缩参数窗口内的无宏观并合界，并控制 B_w/nu_- 指数下降。它是有明确输入的作者推导，不是小尺寸外推。接下来先处理强度时钟的可实现性、一致误差和实际标签接口；已有两参数谱系作业可完成一个最小产物用于核对或反例，不需要直接模拟指数长窗口反复等待并合。静态边缘、Laguerre 层级和更多极限核的矩不能替代该接口。
+
+#650 是协调 P0；#801 是作业映射 P0。它们不是新增数学主线，也不是两项重计算。
+
+## 算力边界：七台机器的真实作业还未核实
+
+所有者报告七台机器在运行；本轮没有读取主机进程、当前资源使用或调度器。以下是给操作人员的指令，**不是已经停止/迁移作业的记录**。
+
+先在 #801 为每台回填：机器别名、Issue、代码与输入、进度、检查点、下一最小独立产物、剩余工作的估计依据、CPU/RAM瓶颈。不要贴地址、令牌、密钥。未知内容写未知。
+
+对无明确新问题的作业，在安全批次边界保存检查点、分片和种子，取消自动续跑。已经接近一个真正有用产物的，可以先完成该产物。不得杀未知进程或丢弃不可恢复工作。已经完成的结果照常提交，负结果也保留。空闲机器不是失败，不用一个新猜想填满每个槽位。
+
+### 七个逻辑槽位（不是已识别的七台硬件）
+
+|槽位|建议用途|什么时候不继续占用|
+|---|---|---|
+|1|#802 一项源响应主算|候选尚无不同预测时不启动大算|
+|2|同一响应的短交叉核对/必要分片|不是长期重复生产|
+|3|#780 同标签两参数接口、时钟与有限误差|不重跑渐近无并合，也不退回更多静态矩|
+|4|#761 独立质量区间|精度改善不能改变振幅/根判断时停|
+|5|#769 或 #775 当前最小有用产物|两者共享原始 rank 表，不重复生成|
+|6|#778 既有档案及便宜后处理|短作业按需用，不常驻大机器|
+|7|预留|不为满载而开新梯度/宽度扫描|
+
+操作人员按实际内存与作业依赖重排。#801 回报之前，不对任何具体机器作“浪费/该杀”的断言。本页不启动付费资源、GPU、自动任务或远程凭据操作。
+
+## 已经落地的优先级
+
+P0：#768、#802、#780；协调 #650、作业映射 #801。
+
+P1，有限支持而非全部并行：#613（已有几何论证的具体缺口）、#740（实际周期缝合，先比较界）、#760（质量局部性）、#761（独立质量区间）、#769（当前 L5 原始联合表封口）、#775（当前最小系数产物后停）、#776（复用自匹配控制，不开新阶梯）、#778（已有 paired 档案）。
+
+P2，不默认分配新增共享大算力：#593、#758、#762、#767、#772、#774、#777、#779、#781、#783、#786、#789、#790。具体数学障碍或真正有区分力的反例可重新提升；这不禁止参与者自愿做理论探索。
+
+已合并入口并关闭 duplicate：#787 → #740（周期留数）；#788 → #778（二次变差后处理）；#784 → #783（Fourier 有限接口）。原文与已有结果保留；关闭不等于证明。
+
+#275 原始 U 保留其原源、正规化和 moving-root 合同。没有用新 rank 观察量完成旧候选识别，也没有修改冻结实验判决。未列入本轮主队列的历史标题不是七机自动运行指令。
+
+## 当前重计算怎样瘦身
+
+#775 不再要求首轮 L=5,6,7,8 全部完成。先复用 #769 可能已给出的 L5 rank-by-occupancy 表，计算原始 C[L,j,k] 与一个必要的根/形状对比。Fisher 曲率、面积、Bayes 距离、TP2、KK、源零点和高阶累积量都可以是后处理，但不能各自变成第二份原始枚举。
+
+#769 保留 paired-flip 语义、位移原始表和代表见证，不再因新增一个描述符延长全部枚举。jump-two 的匹配偶性与 odd-sector 幅度是不同问题。
+
+#593 的旧 width9/10/11 阶梯不再是当前授权。#774、#776 不因缺几行表就自动补齐宽度。相关在运行产物先交 #801 安全评估。
+
+## 三项前序理论推进及本次跟进
+
+前序推导见 [root-response-and-bridge-targets-20260914.md](root-response-and-bridge-targets-20260914.md)。
+
+1. **切向盲点**：消去热坐标同时可能消去根位移机制。用根的切向响应 T 与形状法向响应 N 做联合比较。
+2. **条件模块筛选**：若 c=0、h=5/8 的 level-2 null 真正解耦，模去 L_-1 导数后 level 1..4 的维数为 0,0,1,1。C4 从这一热模块允许的首个非导数手征修正出现在 level4；这仍不证明它在实际扇区中非零，也不排除其他模块。
+3. **并合界本次已推进**：最终簇中的两个不交 essential 见证给 BK 平方界；统一体积尾处理大簇。固定 p0 下，宏观并合概率和 B_w/nu_- 的宽度对数上率均不超过 -kappa(p0)。连续正强度比 Lambda 的统一收敛仍是标记 Poisson 结论的明示条件；仿射热坐标、近临界统一性和所有路径/高阶矩不自动成立。
+
+有限 p0 的 fixed-location 应使用固定纵向行的 essential 跨度覆盖/最近屏障。固定微观点可能为黑色或属于有限白簇，不能照搬 p→0 对照中异常概率趋零的取样约定。
+
+这些结果决定下一步问什么；不是又一批为了精确而精确的宽度任务。
+
+## 返回方式
+
+理论返回一个被证明/反驳的具体箭头，或明确的最小缺口。计算返回原始新对象、成本、误差及它排除了什么；不能排除也如实记录。新文献只需要服务于实际模型、模块和扇区接口，不再按标题数量堆综述。
+
+不修改 STATUS 的科学判决，不删除数据，不自动合并 PR。局部测试、数学正确性和作者猜想分别记录，但不用一套新的“灯”代替思考。