アーキテクチャ

数学的基盤

形式仕様、再帰的自己改善、マルチユニバース状態管理 — MARIA OSの背後にある数理理論。

PLANNER × ARCHITECT — DUAL CORE

デュアルコアアーキテクチャ時間軸 + 空間軸 = システム整合性

2つの中心的な役割が分散型マルチエージェントの崩壊を防ぐ。Plannerは時間的フローを設計する。Architectは構造的フレームを守る。両者の緊張が暴走を防ぐ。

Planner

Time Axis Designer

Decomposes missions into deterministic phases
Designs Decision Graph DG = (V, E)
Builds Execution Graph with dependencies
Assigns Human / Agent ratios per node
Defines Gate entry / exit conditions
Prevents scope drift with immutable specs

Architect

Space Axis Guardian

Universe→Galaxy→Planet→Zone→Agent integrity
Responsibility boundaries fixed at Zone level
Parallel conflict avoidance rules (Slice model)
DB-native audit trace enforcement
Skill registry governance and boundaries
Structural drift detection and rejection

Planner(time) × Architect(space) = Integrity(system)

フロー作成者 vs. フレーム守護者。その緊張がアーキテクチャである。

デュアルコアなし — 4つの失敗モード

1Goal mutation

Purpose changes mid-execution

2Responsibility dissolution

Ownership becomes ambiguous

3Parallel collision

Concurrent writes corrupt quality

4Manual-only improvement

Optimization cannot scale

劣化なき分散。 崩壊なき加速。

PLANNER — DECISION GRAPH ALGORITHM

Decision Graphの構築DG = (V, E) — 6ステップ決定論的アルゴリズム

すべてのミッションはDecision Nodeの有向非巡回グラフに分解される。ヒューリスティックなジャンプなし。すべてのタスクが監査可能なノードにマッピングされる。

Algorithm Steps

1
Phase DecompositionSplit mission M by deliverable type and responsibility stage
M → {P₁, P₂, …, Pₙ}
2
Node GenerationExtract decision points per phase as typed nodes
∀Pᵢ : extract Vᵢ = {v | v requires judgment}
3
Edge ConstructionLink outputs to dependent inputs; separate concurrent writes
E = {(u,v) | outputs(u) ∩ inputs(v) ≠ ∅}
4
Gate AssignmentMap risk level to gate templates for entry and exit
risk(v) → (gate_entry(v), gate_exit(v))
5
Completion VerificationEnsure all leaf nodes have acceptance tests, all paths have gates
∀ path(root→leaf) : ∃ gate_exit on path
6
Scope Drift GuardNew requirements create new nodes, never mutate existing specs
Δreq → new V′ + diff Gate + propagate(E′)

Decision Node Schema

node_idUnique identifier
phaseLifecycle stage
owner_roleResponsible role
inputsRequired artifacts
outputsProduced artifacts
risk_levelRisk classification
gate_entryEntry conditions
gate_exitExit conditions
testsAcceptance criteria
allocationHuman/Agent ratio

Execution Flow

MissionPhasesNodesEdgesGatesDG

決定論的分解。 すべてのノードで監査可能。

ARCHITECT — PARALLEL CONFLICT AVOIDANCE

衝突のない並列数学的コンフリクト回避モデル

Conflict Definition

Artifact Slice Model
Conflict(i, j, t) = 1 iff WriteSeti(t) ∩ WriteSetj(t) ≠ ∅
Goal: ∀t, ∀i≠j : Conflict(i, j, t) = 0

Artifact S is split into minimal Slices. Conflict is zero when no two agents write the same slice simultaneously.

A

Slice Partition

Strongest

Divide artifact into disjoint slices. Each agent owns exactly one partition.

S = ⊔ Sᵢ , Agent i writes only Sᵢ

WriteSet_i ∩ WriteSet_j = ∅ by construction

B

Propose-Merge

Collaborative

Multiple agents propose changes. A single Merger integrates. Only Merger writes.

Agents → propose only , Merger → write

WriteSet limited to Merger ⇒ Conflict = 0

C

Lease Lock

Dynamic

Time-bounded exclusive write access per slice. Lease expires at Gate boundary.

write(i, s, t) = 1 iff holder(L(s), t) = i

Lease renewal forbidden across Gate boundaries

D

Fail-Closed

Fallback

When no concurrency pattern can guarantee safety, insert human arbitration.

¬(A ∨ B ∨ C) → Human Gate insertion

Responsibility never dissolves — it escalates

Automatic Selection Rule

Partition>Propose-Merge>Lease Lock>Fail-Closed

Strongest guarantee first. Human inserted only when no structural pattern suffices.

並列は衝突ではない。 並列 = ガバナンスされた拡張。

HUMAN / AGENT ALLOCATION OPTIMIZATION

定量化された自律性意思決定ノードごとのリスクスコアに基づくHuman/Agent比率

Allocation Equation

H(v) = clamp( αR + βU + γI + δA − εC , 0, 1 )
G(v) = 1 − H(v)

H(v) = human ratio, G(v) = agent ratio. Risk scores drive allocation, not intuition.

Factor Weights

R(v)0.35Risk — Probability of failure
U(v)0.25Uncertainty — Information incompleteness
I(v)0.25Impact — Blast radius on failure
A(v)0.20Audit — Compliance criticality
C(v)-0.20Reversibility — Undo-ability (reduces H)

Graduated Autonomy via Gate Evidence

Hk(v) = H0(v) × exp(−λ · EQk(v))

k = iteration count through Gate

EQ = Evidence Quality score [0..1]

λ = learning coefficient (e.g. 1.0)

More evidence accumulated → human ratio decreases. But never to zero where Architect fixes responsibility.

Industry Allocation Profiles

FinanceRegulation and audit weight high
Start
70/30
Stable
40/60
GovernmentPublic accountability required
Start
60/40
Stable
35/65
ManufacturingSafety-gated, high automation ceiling
Start
50/50
Stable
20/80
EducationData privacy and pedagogical judgment
Start
65/35
Stable
45/55

リスクスコアに基づく自動化。 直感ではない — 方程式である。

META RECURSIVE ENGINE

自己改善するOS

PlannerとArchitectの品質はメタレイヤーエージェントによって測定・改善される。すべての改善はエビデンスに裏付けられ、書き換えではなく差分を生成する。

Quality Metrics (per run)

CR
Completion Rate↑ maximize
completed_nodes / total_nodes
RR
Rework Rate↓ minimize
rework_tasks / total_tasks
SD
Scope Drift↓ minimize
scope_change_events / total_nodes
AD
Audit Deficit↓ minimize
missing_audit_fields / total_records
CC
Conflict Count↓ minimize
conflicts_detected / parallel_windows

Improvement Update Rule

ΔP = w1·∇CR − w2·∇RR − w3·∇SD − w4·∇AD − w5·∇CC

Rule-based diff patches grounded in Evidence. Not gradient descent — structured improvement proposals.

Meta Agents

Meta Planner

Evaluates plan completability, drift resistance, gate appropriateness, and evidence sufficiency. Outputs quality reports and plan patches.

Meta Architect

Detects boundary violations, write conflicts, audit trace gaps, and uncontrolled skill growth. Outputs structural patches and enforcement rules.

Diff Patch Patterns

1
Tighten Gates— Add evidence requirements to high-risk node entry/exit
2
Split Nodes— Decompose failing nodes to clarify responsibility boundaries
3
Introduce Merge— Convert conflict zones to propose-merge pattern
4
Insert Human— Restore human approval at high-uncertainty nodes
5
Freeze Skills— Lock successful skill combinations as reusable presets
ExecutePlanner + ArchitectEvidenceImmutable logsMeasureCR, RR, SD, AD, CCProposeDiff patchesApproveHuman gateApplyNext iterationLoop

エビデンス駆動の改善。 書き換えではなく差分。人間が承認する進化。

FORMAL SPECIFICATION

The Governing EquationState Transition as Operator Composition

MARIA OS can be expressed as a single equation governing all state transitions.

Xt+1 = Et ∘ Gt ∘ Jt ( Xt )

World state at time t+1 equals the composition of Execution, Gate, and Judgment operators applied to current state

J_t

Judgment Operator

Parallel agents generate proposals and hypotheses

G_t

Gate Operator

Responsibility phase determines routing: permit, reject, approve

E_t

Execution Operator

ops@ or i@ acts on external world, leaves evidence

Xt
Current State
Jt
Judgment
Gt
Gate
Et
Execution
Xt+1
Next State

One equation. Three phases. Complete governance.

STATE TENSOR

Multi-Dimensional StateThe World as a 5-Axis Tensor

Every state in MARIA OS is addressed by five coordinates simultaneously.

Xt[p, s, a, k, r]

A non-zero entry means: this phase, this scope, this actor, this knowledge, this risk level — is active now

pPhase
judgmentresponsibilityexecution
sScope
galaxyuniverseplanetzone
aActor
agent_iops@i@
kKnowledge
skill_idpolicy_id
rRisk Tier
R1R2R3R4R5

Transition as Sparse Matrix Composition

Xt+1
=
( Et · Gt · Jt )
×
Xt

Each operator acts as a sparse linear or rule-based operator on the tensor

Five dimensions. Complete addressability.

PROJECTION OPERATOR

Responsibility as ProjectionWhy Parallel AI Converges to Single Execution

The Gate is not a filter. It is a mathematical projection that preserves accountability.

Ct = Jt(Xt)

Judgment generates candidate set

At = Πt(Ct)

Gate projects to allowed set

Xt+1 = Et(Ut)

Execution updates world state

01

Boundary Enforcement

Π_t zeros out candidates crossing responsibility boundaries

No proposal can bypass its designated authority level

02

Consistency Constraint

Π_t(C) ∈ 𝒞

Output always satisfies the consistency constraint set 𝒞

03

Singular Execution

U_t = argmin ℓ(u; policy, evidence)

Final execution collapses to exactly one action

c1
c2
c3
c4
c5
Many Candidates Ct
Πt
Projection
Single Ut
ops@
i@

Parallel intelligence. Singular responsibility.

安定性証明

収束には 減少し続ける量 が必要

MARIA OS は『たまたま安定して見える』のではなく、系の不安定度を表す Lyapunov 関数を置き、その値をゲートで下げ続けることで収束を保証する。責任境界は説明責任だけでなく、動的安定性の条件でもある。

01

偏差を状態として定義

ξ_t = x_t - x*

望ましい平衡点からどれだけ逸れているかを、実行状態そのものとして観測する。

02

エネルギー関数を置く

V(ξ_t) = ξ_t^T Q ξ_t

ズレを一つの単調量に圧縮することで、系が落ち着いているかを横断的に比較できる。

03

ゲートで減少を強制

ΔV = V_{t+1} - V_t < 0

高リスク候補を止め、責任境界を守ることで、ループ全体のエネルギーを毎ステップ減衰させる。

系全体の減衰条件
ATQA - Q < 0

ローカル線形化したダイナミクスでもエネルギー差分が負なら、平衡点は漸近安定になる。

要するに、判断・ゲート・実行の各ステップが局所最適に見えても、全体エネルギーが減らなければ採用しない。これが MARIA OS における『止める能力』の数理的意味である。

エネルギーの単調減衰
t0
1.00
t1
0.74
t2
0.53
t3
0.36
t4
0.22

Gate が危険候補を遮断すると、ループの drift は増幅ではなく減衰系列に入る。

Fail-closed は安全装置ではなく減衰器

危険な提案を平均化せず停止することで、暴走を広げる前にエネルギーを落とす。

Industrial Loop の収束条件

Capital・Operation・Physical・External の各相で drift が蓄積しても、全体指標は単調減少へ戻される。

改善は発散でなく収束へ向く

自己改善は更新量が大きいことではなく、安定集合へ近づくことが成功条件になる。

Lyapunov 安定性は『改善している気がする』を拒否し、更新が本当に系を落ち着かせるかを判定する。次に必要なのは、複数エージェントの相互作用がなぜ固定点へ向かうのかというゲーム理論である。

数理基盤ゲーム理論へ
EXPERIMENTAL DEEP DIVE — MULTI-UNIVERSE

マルチユニバース状態アーキテクチャ

複数の現実、分離されたまま。

各Universeは独自の状態、観測、価値関数、リスク境界を持つ。世界は1つ — しかし各Universeは異なる射影を通して世界を見る。

s(t) = (s1(t), s2(t), …, sN(t))

Direct product state

oi(t) = hi(x(t), ηi(t))

Universe-specific projection

Lij : Si × Sj → ℝk

Inter-universe links

Company

Enterprise boundary

revenue
margin
headcount
sioiVi

Market

Competitive landscape

share
elasticity
growth
sioiVi

Regulatory

Legal constraints

compliance
risk_score
audit
sioiVi

Customer

Demand signals

NPS
churn
LTV
sioiVi

Talent

Human capital

attrition
engagement
skill_gap
sioiVi
Universe Links— coherence checks, not integration
company↔marketmetric_correlation
regulatory↔companyconstraint_bind
customer↔marketattribution
talent↔companypolicy_dependency

Observations auto. Policies proposal-only.

統合はシグナルを破壊する。 分離が真実を保つ。

EXPERIMENTAL DEEP DIVE — OBSERVATION TO BELIEF

Reality Signalレイヤー

自動的に観測する。 自動実行は決してしない。

外部シグナルはOSに流入するが、自動実行には使用されない。信念はベイズ推論で更新される。ポリシー変更には人間の承認が必要。

x(t) → oi(t) → beliefi(t)

Signal pipeline

bi(t+1) ∝ P(oi(t+1) | θi) · bi(t)

Bayesian belief update

External Signals
Revenue
+12.3%
Churn Rate
4.2%
Incident Rate
0.8/wk
NPS Score
72
Normalization Pipeline
Signalx(t)Normalizescale + lagAttributemap to nodeBeliefb_i(t+1)
Belief Panel — Hypotheses
H1

Pricing change drove revenue increase

0.78
H2

Support quality reduced churn

0.65
H3

Process change increased incidents

0.42
Gate

Human Approval Required

Belief update = automatic

Policy change = proposal only

belief update = automatic   |   policy change = proposal only

信念更新は自動。 ポリシー変更には承認が必要。

EXPERIMENTAL DEEP DIVE — GATE SCORE

フェイルクローズ型ゲートアーキテクチャ

最悪ケースゲート。 機械可読な理由。

ゲートはアクション候補をすべてのUniverseで同時に評価する。max（最悪ケース）を使用する — 平均は決して使わない。

GateScore(a) = maxi φi(ri, ci, qi, rev, time)
BLOCK: ∃i : ci(a|si) > 0 ∨ ri(a|si) > ρi
Action Candidate
actionvendor_switch
scopeG1.U2.*
cost$240k
reversiblefalse
Universe Evaluation (maxi)
Finance
r=0.42ρ=0.60
evidence0.88
uncertainty0.15
Regulatory
r=0.78ρ=0.50
evidence0.61
uncertainty0.44
Operations
r=0.31ρ=0.70
evidence0.92
uncertainty0.09
HR & Culture
r=0.55ρ=0.55
evidence0.73
uncertainty0.28
GateResult
decision
PAUSE
top_universeregulatory
reason_codes
RISK_OVER_BUDGETregulatory
EVIDENCE_INCOMPLETEregulatory
UNCERTAINTY_HIGHhr
BLOCK
PAUSE
ALLOW

maxは危険を保持する。 平均はそれを隠す。

EXPERIMENTAL DEEP DIVE — CONFLICT TENSOR

矛盾を統一するな。表面化させよ。

マルチユニバースコンフリクト検出

conflict_score0.78
01
K(a) = { sign(∂ui/∂a) }i

Contradiction tensor

Conflict(a) = Σi<j wij · max(0, −corr(Δui(a), Δuj(a)))

Weighted conflict score

Price Cut
score 0.72
Market Growth

price cut → growth +0.30

vs
Regulatory

price cut → compliance risk +0.20

Headcount Reduction
score 0.85
Finance

headcount reduction → margin +0.15

vs
Talent

headcount reduction → attrition +0.40

推奨アクション

SPLIT_SCOPERUN_SANDBOXREQUEST_HUMAN_APPROVALGATHER_MORE_EVIDENCE

矛盾はバグではない。 それは意思決定の真の構造である。

Experimental Deep Dive — Dual Loop

内側に高速ループ。外側に低速ループ。

デュアルループ改善アーキテクチャ

Fast Loop — Operational

Observe

s_i metrics

Evaluate

quality check

Adjust

local tweak

Deploy

auto apply

si → quality(si) → adjust(ai) → deploy   [auto]

Zone / agent level. Runs continuously. No human approval required.

Gate
Slow Loop — External Reality

Signal

x observed

Normalize

o_i mapped

Belief

belief_i

Propose

policy draft

Sandbox

isolated test

Approve

human gate

Update

commit

x → oi → beliefi → θi update → propose → sandbox → approve

Market / regulation / customer signals. Requires human approval gates before commit.

“Local improvement is automatic. Structural change requires verification.”

Local Improvement

Automatic

Structural Improvement

Verified

Principle Improvement

Governed

(order is fixed)

内側にスピード。外側に慎重さ。決して逆転しない。

EXPERIMENTAL DEEP DIVE — FINAL FORM

判断基盤 — 最終形態

より強いAIではない。 壊れないAIである。

X = (s1, …, sN) → Jt(φ) → Πt(maxi) → Conflict(a) → et → Learn(Π, φ, k, H) → Xt+1

Complete system: Multi-Universe state, worst-case gate, conflict detection, evidence-based learning

Responsibility Boundary
1

Multi-Universe Aware

Observes company, market, regulatory, customer, talent simultaneously without merging

2

Fail-Closed

Responsibility boundaries never dissolve, even at maximum autonomy

3

Contradiction Management

Does not resolve contradictions — manages them and surfaces to humans

4

Controlled Intelligence

Not omnipotent AI, but AI that cannot break

5

Judgment Infrastructure

From a tool that supports judgment to infrastructure that is judgment

Evolution Path

Tool

Assists decisions

Platform

Structures decisions

Infrastructure

Enables decisions

Judgment Layer

Is the decision layer

Multi-UniverseGate (max_i)ConflictDual LoopHuman Authority

最終形態はより強いAIではない。 壊れないAIである。

Multi-Universe Fail-Closed Judgment OS