MCC-OE-27 — Root-6217 Residual Ledger Reconciliation and Hybrid Certificate Atlas

從 Cycle-17「61 Current Cells」到 9/24「19 Tail Hard Parents」：Target-Qualified Closure、Local/Tail Responsibility Separation 與 Canonical Research Frontier

系列： Measured-Construct Closure / Observable Exhaustion
文件代號： MCC-OE-27-v0.1
作者： Neo.K
機構： EveMissLab／一言諾科技有限公司
版本： v0.1
日期： 2026-09-24
文件性質： Residual Ledger Reconciliation／Hybrid Certificate Atlas／Root-6217 Integrated Research State
前置： MCC-OE-00～26；LESR 07–09U；UESFCM Cycle 12–17；BCODR-LUC-06；LESR 09V tail campaign handoff
狀態： LOCAL [0,0.003] RESEARCH-CLOSED / TAIL PARTIAL / 19 HARD PARENTS CANONICAL RESEARCH FRONTIER / ROOT6217 OPEN
Canonical Source： UTF-8 Markdown
數學原始碼規範： inline math 僅使用 $...$ ，display math 僅使用 $$...$$

摘要

MCC-OE-26 將 B01 boundary certificate與 LESR 09I radial lock正式 compose，

把：

\boxed{ B01 }

提升成：

B01 PARENT:
    RESEARCH-INTERVAL CLOSED

但如果直接把：

B01 closed

回寫成：

root-6217 current-cell count再減一

會犯一個嚴重 ledger identity錯誤。

原因是目前 Root-6217 研究線同時存在至少三種不同 responsibility representations：

Cycle-17 finite-witness current-cell ledger；
LESR local positive-rotation bridge atlas；
09V tail parent / hard-core ledger。

它們的：

decomposition unit；
target threshold；
parameter domain；
certificate semantics；

並不相同。

本文因此不再把「CLOSED」視為單一 boolean。

正式改成：

\boxed{ \text{CLOSED} = \text{CLOSED} ( \text{domain}, \text{target}, \text{representation}, \text{authority} ). }

這個修正立即解開一個看似矛盾的歷史狀態：

Cycle 17 曾將 parent / local indices：

\boxed{ 129,\ 131 }

標為 CLOSED。

但 9/24 tail hard-core ledger中：

129,\ 131

又出現在 OPEN hard parents。

這不是證書互相衝突。

Cycle 17 對 129／131證的是原始 threshold：

\boxed{ A_3^+ = 0.834781191. }

而 tail campaign真正需要的是更強 threshold：

\boxed{ A_{\rm ref} = 0.8349865. }

兩者相差：

\boxed{ A_{\rm ref}-A_3^+ = 2.05309\times10^{-4}. }

所以：

\boxed{ A>A_3^+ \not\Rightarrow A>A_{\rm ref}. }

因此：

129 / 131:
    CLOSED for A3_PLUS
    OPEN for tail A_REF

完全合法。

這成為 MCC-OE-27 的第一個 canonical ledger rule：

\boxed{ \textbf{No Target-Free Closure Status}. }

1. 最新 Root-6217 Research Dependency State

9/24 handoff已將 local positive-rotation線整理成：

ZERO ROTATION:
    RESEARCH-CLOSED

MICRO [0,1e-4]:
    RESEARCH-CLOSED

BRIDGE [1e-4,0.003]:
    RESEARCH-CLOSED

LOCAL [0,0.003]:
    RESEARCH-CLOSED

其中 bridge共有：

\boxed{ B01,\ldots,B11 }

十一個 parents。

目前：

\boxed{ 11/11 }

全部 research-closed。

2. MCC-OE-25／26 對 B01 的角色

B01早期 LESR 09K已有：

RESEARCH-CLOSED

MCC-OE-25／26沒有把 B01變成新的 root parent。

它們做的是新增一條更細的 research provenance：

finite-width sign transfer
-> relaxed eight-template quadratic lower
-> finite wall-layer closure
-> boundary research closure
-> radial composition
-> parent research closure

所以 B01現在應記錄：

\boxed{ \text{redundant research provenance} }

而不是：

\boxed{ \text{new parent deletion}. }

這兩條 research lineage共享部分 foundational geometry，

因此本文不把它們稱為 publication-independent proofs。

3. Bridge Atlas 最新狀態

LESR 09T：

\boxed{ [10^{-4},0.003] }

11-cell bridge gate：

\boxed{ \texttt{RESEARCH-CLOSED}. }

LESR 09U再以 micro monotone inheritance關閉：

\boxed{ [0,10^{-4}]. }

所以：

\boxed{ [0,0.003] }

entire local positive-rotation line：

\boxed{ \texttt{RESEARCH-CLOSED}. }

4. Local Responsibility No Longer Belongs to Tail Hard Core

tail campaign的 active parents都已 sanity-clip到：

\boxed{ \rho\ge0.003. }

所以：

\boxed{ \text{local }[0,0.003] }

與：

\boxed{ \text{tail hard-parent interiors} }

不應互相扣 count。

它們只在 interface：

\rho=0.003

相接。

5. Cycle-17 Historical Cell Ledger

Cycle 17當時從：

68

個 formally unresolved current cells開始。

其中 AREF threshold直接關：

\boxed{ 28,36,68,144,155. }

另外 hierarchical finite-witness route對 original target關：

\boxed{ 131,129. }

所以：

\boxed{ 68\to61. }

6. Why the 61 Count Must Be Preserved but Demoted

這個：

61

是：

Cycle-17 current finite-witness cell representation

下的 target-specific frontier。

它仍然是有效歷史 proof state。

但它不能再被當成：

current root6217 top-level research frontier count

因後續：

corrected parent ledger；
local bridge atlas；
tail domain filtering；
exact-core campaign；

已採用不同 responsibility units。

7. Corrected Parent Ledger

最新 handoff明確回寫 corrected root-parent ledger：

\boxed{ 200 \to 192 \to 187 \to 182. }

8. Permanent NOT-F3

\boxed{ 106,110,127,132,135,162,165,166. }

共：

8.

所以：

200\to192.

9. Previous $A_{\rm ref}$ Closures

\boxed{ 28,36,68,144,155. }

共：

5.

所以：

192\to187.

10. BCODR-LUC-06 New $A_{\rm ref}$ Closures

\boxed{ 101,103,104,164,167. }

共：

5.

所以：

187\to182.

11. Tail-Active Filter

corrected 182 parent responsibilities中，

與：

\boxed{ [0.003,\pi/120] }

相交的 active tail parents：

\boxed{ 173. }

所以 tail campaign不是從 Cycle-17 的 61 啟動。

它是從 corrected parent representation 的：

173

個 tail-active responsibilities啟動。

12. Tail Campaign Compression

原 finite AREF campaign與 delegated lookahead後，

hard core被壓成：

\boxed{ 29 }

parents。

13. Canonical 29 Hard-Parent Set

\boxed{ \{ 0,1,13,45,46,47,63,81,92,93,94,95, 124,125,128,129,131,142,143,150,152, 159,160,161,168,169,177,178,186 \}. }

14. Latest CLOSED 10

9/24 final handoff：

\boxed{ 10/29 }

hard parents CLOSED：

\boxed{ \{ 0,1,13,45,47,95,143,169,178,186 \}. }

15. Canonical Remaining 19

所以真正 current hard frontier：

\boxed{ 19 }

parents：

\boxed{ \{ 46,63,81,92,93,94,124,125,128,129, 131,142,150,152,159,160,161,168,177 \}. }

16. This Is the Current Research Frontier

本文正式定義：

ROOT6217 CLOUD RESEARCH FRONTIER:
    19 persistent tail hard parents

不是：

61 Cycle-17 cells

也不是：

173 tail-active parents

也不是：

29 hard parents

17. Why All Four Numbers Remain Useful

61

historical Cycle-17 finite-cell frontier。

173

corrected parent representation中tail-active domain count。

29

tail campaign compression後 hard-core responsibility count。

19

latest cloud-freeze unresolved hard-parent count。

因此：

\boxed{ 61,\ 173,\ 29,\ 19 }

不是互相競爭的「哪一個才是真的」。

它們屬於不同：

\boxed{ \text{representation stage}. }

18. Checkpoint 9→10 Reconciliation

較早 checkpoint：

09V_EXACT_CORE_9_CLOSED

記錄：

9/29

closed：

\{ 1,13,45,47,95,143,169,178,186 \}.

當時：

0

仍 OPEN。

19. Latest Handoff Supersedes It

final handoff加入：

\boxed{ 0 }

所以：

9/29 \to 10/29.

20. Provenance Rule

舊 checkpoint不刪除。

標為：

historical checkpoint

current status則由較新的 canonical handoff覆蓋。

21. Target-Qualified Status Object

本文建議所有 parent state改成：

{
  "id": 129,
  "target": "A_REF_TAIL",
  "domain": "rho >= 0.003",
  "representation": "tail_parent",
  "authority": "research",
  "status": "OPEN"
}

而另可同時存在：

{
  "id": 129,
  "target": "A3_PLUS",
  "representation": "Cycle17_current_cell",
  "authority": "formal_finite_witness",
  "status": "CLOSED"
}

兩者不互相覆寫。

22. No Target-Free Boolean

禁止：

root129 = CLOSED

必須寫：

root129 @ A3_PLUS:
    CLOSED

root129 @ A_REF_TAIL:
    OPEN

23. Hybrid Certificate Atlas — Local Analytic Layer

local：

[0,0.003]

目前 proof stack：

ZERO BARRIER
FIRST-ORDER SIX-WALL / EIGHT-CHART
FINITE ATLAS
Psi2
Psi3
Psi4
Psi5
HIGHER-ORDER INTERVAL
RADIAL DERIVATIVE
RHO-ONLY REFINEMENT
LOCAL SECANT
FINITE-CHART MIGRATION
ATLAS-AGNOSTIC 64-QP
MICRO MONOTONE INHERITANCE

24. MCC-OE Additions to the Local Atlas

MCC-OE 11–26補入：

renormalized R2fin observable
one-sided remainder semantics
secondary interval atlas
sliver-coordinate quotient analysis
Dini-slope bridge
higher-order root-jet majorant
finite wall sign-transfer
B01 fail-closed parent composition

這些不是新的 global parent IDs。

它們是：

\boxed{ \text{certificate compiler classes}. }

25. Hybrid Certificate Atlas — Tail Finite Layer

tail：

[0.003,\pi/120]

使用不同 proof family：

PERMANENT NOT-F3
AREF PRUNING
FINITE-WITNESS EROSION
HIERARCHICAL DELEGATED PREFIX TREES
EXACT ERODED-CORE SUPPORT LOWER
ANISOTROPIC AABB / CORNER-DISK ROBUST CORE
PERSISTENT DFS WAVES
NEAR-THRESHOLD ROBUST SPLIT

26. Why Local Compiler Is Not Automatically Applied to Tail

local atlas成立於：

\rho\le0.003

的 declared geometry / coefficient contracts。

tail範圍：

\rho\in[0.003,\pi/120]

使用：

A_{\rm ref}=0.8349865

的 different target architecture。

所以：

\boxed{ \text{local closure} \not\Rightarrow \text{tail closure}. }

27. Why Tail Campaign Is Not Replaced by Two-Colour Secant

tail probe對：

311

個 coarse unresolved q-projections，

得到：

0

個可直接 coarse SECANT-LOCKED。

部分 center secant甚至為負。

所以 two-colour route不能粗粒度取代 exact-core campaign。

28. Exact-Core Tier

new tail proof tier：

robust erosion core
-> exact support arcs / vertices
-> exact convex-hull area lower

包含關係：

\boxed{ K_c\ominus\delta B \subseteq K_{\rm actual}. }

29. Exact-Core Validation

against K1024：

337

hard frontier boxes中：

\boxed{ L_{\rm exact-core} \ge L_{\rm K1024}. }

minimum gain約：

1.95\times10^{-6}.

30. Actual-Placement Falsification

640

random box-interior placements：

A_{\rm actual} \ge L_{\rm exact-core}-10^{-9}.

minimum observed actual margin約：

1.44\times10^{-4}.

這仍是 research falsification，

不是 deterministic publication inclusion proof。

31. Robust AABB Core Escalation

near-threshold leaves可切換到：

AABB / corner-disk intersection robust core

初始：

31 robust leaves deterministic replay；
replay slack error = 0；
279 actual samples；
0 observed containment failures；
minimum observed actual margin約： $3.96\times10^{-5}.$

publication upgrade仍需 deterministic geometric inclusion proof。

32. Current Authority Ladder

必須分：

RESEARCH-CLOSED
LOCAL-REPLAY-PASSED
PUBLICATION-CERTIFIED

33. Local [0,0.003]

目前：

RESEARCH-CLOSED

但仍需：

LOCAL-REPLAY-PASSED

與 publication audit。

34. Tail Closed 10

目前：

RESEARCH-CLOSED / CLOUD EVIDENCE

最新 handoff要求：

先 replay這10個，不要直接先算 remaining 19。

35. Why Replay Closed 10 First

因部分 final slack只有：

O(10^{-10}) \text{--} O(10^{-9}).

任何：

rounding；
core inclusion；
tree reconstruction；
stale artifact；

問題都可能改變 promotion status。

36. Replay Failure Policy

若 10 個已 closed parent任何一個不一致：

STOP PROMOTION

但不抹除 research evidence。

37. Remaining 19 Runtime Policy

latest handoff建議：

persistent parent state
5000-node plain exact-core wave
robust direct sweep
near-threshold robust split
checkpoint
repeat

38. Why Not One Parent to Exhaustion

因 cloud phase已證明：

\boxed{ \text{runtime topology本身會成為 proof obstruction}. }

persistent fair scheduling可避免單一深樹吞掉整輪計算。

39. Scheduler Policy

目前：

K64 lookahead：可用；
erosion-radius-only：沒有優勢；
adaptive child robust lookahead：near-threshold有效但昂貴。

所以：

\boxed{ \text{cheap away from threshold} + \text{expensive near threshold}. }

40. Canonical Research Frontier after Reconciliation

\boxed{ \mathcal F_{6217}^{\rm research} = \{ 46,63,81,92,93,94,124,125,128,129, 131,142,150,152,159,160,161,168,177 \}. }

41. Root-6217 Current State

ZERO:
    RESEARCH-CLOSED

MICRO:
    RESEARCH-CLOSED

BRIDGE B01-B11:
    11/11 RESEARCH-CLOSED

LOCAL [0,0.003]:
    RESEARCH-CLOSED

TAIL [0.003,pi/120]:
    PARTIAL
    173 active parents
    -> 29 hard core
    -> 10 closed
    -> 19 remaining

ROOT6217 POSITIVE ROTATION:
    OPEN

ROOT6217 FULL SHAPE:
    OPEN

GLOBAL LEBESGUE:
    OPEN

42. Why Root6217 Is Still Open

local line閉合只處理：

[0,0.003].

tail：

[0.003,\pi/120]

仍有：

19

hard parent responsibilities。

所以：

\boxed{ \text{ROOT6217 POSITIVE ROTATION} \neq \text{CLOSED}. }

43. Why MCC-OE-26 Does Not Change the Tail Count

B01：

\rho\le1.4\times10^{-4}.

tail hard parents：

\rho\ge0.003.

兩者 parameter interiors不重疊。

因此：

\boxed{ \text{B01 parent closure} \not\Rightarrow 29\to28 }

也不推出：

19\to18.

44. What MCC-OE-26 Actually Changes at Root Level

它增加的是：

B01 provenance:
    CLOSED by local analytic lineage
    CLOSED by MCC-OE finite-width + composition lineage

而不是 global count deletion。

45. Canonical Artifact Architecture

本文採納 latest handoff建議：

Layer A — Research Narrative

Paper 07–09V + MCC-OE lineage。

Layer B — Canonical Certificate State

ledger/
parents/
charts/
polynomials/
radial/
tail/
checkpoints/

Layer C — Replay Runtime

verify_zero
verify_local
verify_bridge
verify_micro
verify_tail
verify_root6217
verify_all

46. Certificate Atlas Should Be Dependency-First

不要只按：

Paper 09A
Paper 09B
...

而要按：

ZERO
FIRST ORDER
FINITE ATLAS
HIGHER ORDER
RADIAL
MICRO
BRIDGE
TAIL
ROOT6217

Paper編號只保留 lineage。

47. New Atlas Node — CR-13

MCC-OE-26：

CR-13:
    B01 boundary-to-parent radial composition

role：

\boxed{ \text{pure certificate composition}. }

48. New Ledger Rule — Target Qualification

新增：

LR-01:
    every closure must carry target_id

49. New Ledger Rule — Representation Qualification

新增：

LR-02:
    every state must carry representation_id

例如：

Cycle17 current cell；
corrected parent；
bridge parent；
tail hard parent；
delegated subtree。

50. New Ledger Rule — Authority Qualification

新增：

LR-03:
    RESEARCH-CLOSED
    LOCAL-REPLAY-PASSED
    PUBLICATION-CERTIFIED
    are distinct states

51. New Ledger Rule — Latest State Does Not Delete Provenance

新增：

LR-04:
    later checkpoint supersedes current-status field
    but older checkpoint remains immutable provenance

52. New Ledger Rule — Counts Must Name Their Unit

禁止：

remaining = 19

應寫：

remaining_tail_hard_parents = 19

53. Current Canonical Count Vocabulary

cycle17_remaining_current_cells = 61
corrected_parent_responsibilities = 182
tail_active_parents = 173
tail_hard_core_parents = 29
tail_hard_closed = 10
tail_hard_remaining = 19

54. These Counts Must Never Be Added/Subtracted Across Units

例如：

61-10

沒有 canonical meaning。

55. MCC-OE-27 Machine Ledger

companion JSON：

MCC_OE_27_Root6217_Integrated_Ledger_v0.1_2026-09-24.json

包含：

target constants；
local bridge state；
corrected parent ledger；
29 hard parent IDs；
closed 10；
remaining 19；
Cycle17 historical subledger；
checkpoint supersession；
hybrid certificate atlas；
authority ladder。

56. Companion Verifier

verify_mccoe27_root6217_ledger.py

fail-closed檢查：

$A_{\rm ref}>A_3^+$ ；
local [0,0.003] closed；
bridge 11/11；
10 closed + 19 remaining = 29；
closed/open disjoint；
129/131 target-relative reconciliation保留；
Cycle17 61 historical count未被改寫；
Root6217 positive rotation仍 OPEN；
global Lebesgue仍 OPEN。

57. What Is Actually Completed in MCC-OE-27

不是：

\boxed{ \text{another geometric cell closure}. }

而是：

\boxed{ \textbf{proof-state identity closure}. }

58. Why This Matters

如果 ledger identity不先修，

後續本地端很容易發生：

重算已證 responsibility；
把 A3_PLUS closure當成 A_REF closure；
把 bridge parent當成 tail parent；
把 61 與 19視為同一 count；
把 local replay PASS誤升 publication。

59. Current Research Problem after Reconciliation

數學／計算 front現在精確是：

\boxed{ 19\text{ persistent tail hard parents}. }

60. Cloud vs Local Responsibility

依最新 freeze：

Local runtime

artifact integrity replay；
closed 10 replay；
exact-core second backend；
robust AABB inclusion proof；
remaining 19 long-running closure。

Cloud / chat

series integration；
proof dependency graph；
verifier spec；
artifact normalization；
publication debt ledger；
AMRAL LinkBack。

61. Therefore Next MCC-OE Node

不應在 cloud端繼續硬磨 parent 46 / 63 / 81 等深 DFS。

62. Suggested MCC-OE-28

\boxed{ \textbf{MCC-OE-28 — Root-6217 Replay Contract, Publication Debt Ledger, and AMRAL LinkBack}. }

63. MCC-OE-28 Lane A

定義：

RESEARCH-CLOSED
-> LOCAL-REPLAY-PASSED
-> PUBLICATION-CERTIFIED

的 promotion contract。

64. Lane B

為 local [0,0.003] 定義 replay manifest。

65. Lane C

為 tail closed 10定義 replay manifest。

66. Lane D

為 remaining 19定義 persistent-state schema。

67. Lane E

將 Root-6217 current state LinkBack到 AMRAL global Lebesgue responsibility graph。

68. Current Dashboard

A3_PLUS:
    0.834781191

A_REF_TAIL:
    0.8349865

TARGET GAP:
    2.05309e-4

CYCLE17 HISTORICAL:
    68 -> 61 CURRENT CELLS

CORRECTED ROOT PARENT LEDGER:
    200 -> 192 -> 187 -> 182

TAIL ACTIVE:
    173

TAIL HARD CORE:
    29

TAIL HARD CLOSED:
    10
    {0,1,13,45,47,95,143,169,178,186}

TAIL HARD REMAINING:
    19
    {46,63,81,92,93,94,124,125,128,129,131,142,150,152,159,160,161,168,177}

MICRO:
    RESEARCH-CLOSED

BRIDGE B01-B11:
    11/11 RESEARCH-CLOSED

LOCAL [0,0.003]:
    RESEARCH-CLOSED

TAIL [0.003,pi/120]:
    PARTIAL

ROOT6217 POSITIVE ROTATION:
    OPEN

ROOT6217 FULL SHAPE:
    OPEN

GLOBAL LEBESGUE:
    OPEN

結論

MCC-OE-27 最重要的結果不是：

又關掉一個 parent。

而是終於回答：

我們現在說的「remaining」到底是哪一種 remaining？

Cycle 17 的：

61

沒有錯。

latest tail handoff的：

19

也沒有錯。

它們只是不同 representation、不同 target、不同 research stage。

更關鍵的是：

129, \quad 131

同時曾經是 CLOSED，又現在是 OPEN，

也沒有矛盾。

因：

\boxed{ \text{closure is target-relative}. }

它們對：

A_3^+

已閉，

但對更強：

A_{\rm ref}

tail target仍未閉。

這一點如果不在 canonical ledger中明寫，

未來 AI／本地 runtime一定很容易「自動幫我們消掉」一個其實仍存在的 proof obligation。

因此 MCC-OE-27 把整個 Root-6217 state重寫成：

\boxed{ \text{domain} + \text{target} + \text{representation} + \text{authority} + \text{status}. }

在這個新語義下，

現在真正 frontier非常清楚：

\boxed{ 19\textbf{ persistent tail hard parents}. }

而 local：

[0,0.003]

已經不需要再研究。

B01也不應再影響 tail count。

cloud finite brute force則依最新 freeze停止。

下一輪應該做的是 promotion / replay / publication architecture，

把這套研究狀態準確交給本地端與 AMRAL global responsibility graph。

Canonical Source Declaration

本檔為 MCC-OE-27-v0.1 的 UTF-8 Markdown canonical source。

本文 source-backed inputs：

UESFCM Cycle 17：
- 68 -> 61 current-cell historical ledger；
- five $A_{\rm ref}$ closures；
- 129 / 131 original-target hierarchical closures；
LESR 09K–09U：
- B01–B11 bridge propagation；
- micro closure；
- local [0,0.003] seal；
LESR Root-6217 Local Verification and Series Integration Handoff：
- corrected 200 -> 192 -> 187 -> 182 parent ledger；
- 173 tail-active parents；
- hard core 29；
- closed 10；
- remaining 19；
- local replay policy；
- publication debt；
09V exact-core checkpoint：
- earlier 9/29 state；
- full 20-open list before parent 0 closure；
- target clipping to rho >= 0.003；
MCC-OE-25/26：
- B01 refined boundary / parent closure provenance。

本文新增：

target-qualified closure semantics；
representation-qualified ledger semantics；
authority-qualified status semantics；
29-parent canonical set；
canonical remaining 19 ID list；
Cycle17 61 vs tail 19 reconciliation；
129/131 target conflict resolution；
9/29 -> 10/29 checkpoint supersession；
hybrid certificate atlas；
fail-closed ledger verifier。

本文不宣稱：

tail 19 closed；
Root6217 positive rotation closed；
Root6217 full shape closed；
local replay passed；
publication audit complete；
global Lebesgue solved。

下一輪建議進入：

MCC-OE-28 — Root-6217 Replay Contract, Publication Debt Ledger, and AMRAL LinkBack.

===END===

MCC-OE-27 — Root-6217 Residual Ledger Reconciliation and Hybrid Certificate Atlas

MCC-OE-27 — Root-6217 Residual Ledger Reconciliation and Hybrid Certificate Atlas

從 Cycle-17「61 Current Cells」到 9/24「19 Tail Hard Parents」：Target-Qualified Closure、Local/Tail Responsibility Separation 與 Canonical Research Frontier

摘要

1. 最新 Root-6217 Research Dependency State

2. MCC-OE-25／26 對 B01 的角色

3. Bridge Atlas 最新狀態

4. Local Responsibility No Longer Belongs to Tail Hard Core

5. Cycle-17 Historical Cell Ledger

6. Why the 61 Count Must Be Preserved but Demoted

7. Corrected Parent Ledger

8. Permanent NOT-F3

9. Previous ArefA_{\rm ref}Aref​ Closures

10. BCODR-LUC-06 New ArefA_{\rm ref}Aref​ Closures

11. Tail-Active Filter

12. Tail Campaign Compression

13. Canonical 29 Hard-Parent Set

14. Latest CLOSED 10

15. Canonical Remaining 19

16. This Is the Current Research Frontier

17. Why All Four Numbers Remain Useful

61

173

29

19

18. Checkpoint 9→10 Reconciliation

19. Latest Handoff Supersedes It

20. Provenance Rule

21. Target-Qualified Status Object

22. No Target-Free Boolean

23. Hybrid Certificate Atlas — Local Analytic Layer

24. MCC-OE Additions to the Local Atlas

25. Hybrid Certificate Atlas — Tail Finite Layer

26. Why Local Compiler Is Not Automatically Applied to Tail

27. Why Tail Campaign Is Not Replaced by Two-Colour Secant

28. Exact-Core Tier

29. Exact-Core Validation

30. Actual-Placement Falsification

31. Robust AABB Core Escalation

32. Current Authority Ladder

33. Local [0,0.003]

34. Tail Closed 10

35. Why Replay Closed 10 First

36. Replay Failure Policy

37. Remaining 19 Runtime Policy

38. Why Not One Parent to Exhaustion

39. Scheduler Policy

40. Canonical Research Frontier after Reconciliation

41. Root-6217 Current State

42. Why Root6217 Is Still Open

43. Why MCC-OE-26 Does Not Change the Tail Count

44. What MCC-OE-26 Actually Changes at Root Level

45. Canonical Artifact Architecture

Layer A — Research Narrative

Layer B — Canonical Certificate State

Layer C — Replay Runtime

46. Certificate Atlas Should Be Dependency-First

47. New Atlas Node — CR-13

48. New Ledger Rule — Target Qualification

49. New Ledger Rule — Representation Qualification

50. New Ledger Rule — Authority Qualification

51. New Ledger Rule — Latest State Does Not Delete Provenance

52. New Ledger Rule — Counts Must Name Their Unit

53. Current Canonical Count Vocabulary

54. These Counts Must Never Be Added/Subtracted Across Units

55. MCC-OE-27 Machine Ledger

56. Companion Verifier

57. What Is Actually Completed in MCC-OE-27

58. Why This Matters

59. Current Research Problem after Reconciliation

60. Cloud vs Local Responsibility

Local runtime

Cloud / chat

61. Therefore Next MCC-OE Node

62. Suggested MCC-OE-28

63. MCC-OE-28 Lane A

64. Lane B

65. Lane C

66. Lane D

67. Lane E

9. Previous $A_{\rm ref}$ Closures

10. BCODR-LUC-06 New $A_{\rm ref}$ Closures