# VWDC-09 — Federated World Governance, Multi-Champion Arbitration, and Shared Reality Commit Protocols ## 聯邦世界治理、多冠軍仲裁與共享現實提交協議：全域不變量、交易提交、證書相容、隔離與聯邦故障邊界 **Bridge Series:** Visual–World Domain Computation (VWDC) — Paper 09 **Depends on:** VWDC-01–08, GVSS-01–10, WDC-01–08, WDC Runtime Whitepaper, frozen RRT-20 **Author:** Neo.K / EveMissLab **Version:** v0.1 **Date:** 2026-08-18 **Status:** Formal federated-governance paper. Local/global validity separation, factorized/disjoint safe composition, global-slack composition, conflict-serializable schedule safety under state revalidation, version-stamped stale proposal rejection, atomic reservation safety, idempotent logical commit, certificate-scope intersection, semantic-compatibility no-go, quorum non-equivocation under Byzantine bounds, quarantine closure, compensation-versus-history-rollback separation, append-only federation lineage, and deterministic multi-runtime arbitration are proved under explicit hypotheses. Federated digital-twin ecosystems, linearizability, serializability, distributed transactions, Byzantine quorum ideas, fault-tolerant federation, and multi-agent coordination are established neighboring research and are not claimed as VWDC inventions. No strong novelty claim is made. **Keywords:** federated digital twin, distributed world model, shared reality, atomic commit, serializability, linearizability, quorum, quarantine, fault containment, multi-agent governance, digital twin ecosystem, WDC --- # Abstract VWDC-08 established: $$ \boxed{ \text{many proposing worlds} \to \text{one governed reality commit boundary}. } $$ VWDC-09 generalizes this architecture. Instead of one WDC runtime containing many world branches, suppose there are: $$ \boxed{ \mathcal F = \{ \mathcal R_1, \ldots, \mathcal R_N \} } $$ independent or semi-independent WDC runtimes. Each runtime can have its own: - world models; - Reality Transport Contracts; - policies; - safety contracts; - authority domain; - data; - organization; - deployment champion; - version history. Yet several runtimes may affect the same physical reality or shared resource substrate. Examples include: - several domain digital twins controlling one infrastructure; - multiple organizational twins sharing one logistics system; - edge/local twins coordinated by a global twin; - several AI agents operating shared actuators/resources; - multiple world-model services proposing changes to one live system. The central federated warning is: $$ \boxed{ \text{locally certified} \not\Rightarrow \text{globally composable}. } $$ The federation therefore distinguishes: $$ \boxed{ \text{proposal authority} \neq \text{shared-reality commit authority}. } $$ Every proposal becomes a transaction-like object: $$ \boxed{ P = ( ID, RuntimeID, Snapshot, ReadSet, WriteSet, Precondition, Effect, ResourceDelta, CertificateSet, EvidenceSet, AuthorityScope, Priority, Prov ). } $$ The shared reality layer maintains: $$ \boxed{ X^R } $$ and global invariants: $$ \boxed{ \mathcal I_G = \{ I_1,\ldots,I_m \}. } $$ A federated commit protocol must ensure that the committed sequence of effects remains compatible with: - current global state; - shared resource capacities; - affected RTC/safety scopes; - transaction conflicts; - authority; - provenance; - fault/quarantine status. This makes federation more than message exchange. It makes federation a **shared-state governance problem**. --- # 1. Federation runtime ## Definition VWDC09-D1 A federated runtime is: $$ \boxed{ \mathfrak F = ( \mathcal R, X^R, \mathcal I_G, \mathsf{Ledger}, \mathsf{CommitAuthority}, \mathsf{TrustState}, \mathsf{Prov} ). } $$ where: - $\mathcal R$ is the runtime set; - $X^R$ is shared reality/resource state; - $\mathcal I_G$ is the global invariant family; - $\mathsf{Ledger}$ records committed events/reservations; - $\mathsf{CommitAuthority}$ serializes or otherwise safely coordinates shared side effects; - $\mathsf{TrustState}$ records current runtime/certificate/quarantine status. --- # 2. Local runtime Each runtime: $$ \mathcal R_i $$ maintains: $$ \boxed{ C_i = ( M_i, RTC_i, \pi_i, Safety_i, Authority_i, Prov_i ). } $$ A local champion is meaningful inside its own domain. It is not automatically a global champion. --- # 3. Federated digital-twin literature boundary Current federated digital-twin research explicitly targets: - heterogeneous twin interoperability; - federation node managers; - controlled capability exposure; - protocol/schema adaptation; - distributed state/event exchange; - edge/cloud distribution; - system-level coordination; - multi-domain orchestration. VWDC-09 does not claim federated digital twins as new. Its focus is the **shared reality commit semantics** after federation becomes operational. --- # 4. Shared reality proposal ## Definition VWDC09-D2 Proposal $P$ contains: $$ \boxed{ R(P) } $$ the shared-state read set and: $$ \boxed{ W(P) } $$ the shared-state write set. It also has: $$ \boxed{ F_P: D_P \subseteq X^R \to X^R } $$ as its intended state transition. --- # 5. Local validity Runtime $i$ can certify: $$ \boxed{ \mathsf{LocalValid}_i(P)=1. } $$ This means $P$ satisfies the local runtime's current assumptions/contracts. --- # 6. Global validity ## Definition VWDC09-D3 At current shared state $x$: $$ \boxed{ \mathsf{GlobalValid}(P,x)=1 } $$ requires at least: 1. current snapshot/read validity; 2. global invariant preservation; 3. shared resource feasibility; 4. all required affected-domain certificates; 5. authority; 6. non-quarantine status; 7. provenance/transaction validity. --- # 7. VWDC09-N1 — Local validity does not imply global validity ## Counterexample Two independent runtimes control one power budget: $$ B=1. $$ Each observes current allocation: $$ 0. $$ Runtime A proposes: $$ +0.6. $$ Runtime B proposes: $$ +0.6. $$ Each is locally valid: $$ 0.6\le1. $$ Together: $$ 1.2>1. $$ Therefore: $$ \boxed{ \bigwedge_i \mathsf{LocalValid}_i(P_i) \not\Rightarrow \mathsf{GlobalValid}( \{P_i\} ). } $$ $\square$ --- # 8. Factorized state Suppose shared reality state factorizes: $$ \boxed{ X^R = X_1 \times \cdots \times X_m. } $$ Global invariant also factorizes: $$ \boxed{ \mathcal S = S_1 \times \cdots \times S_m. } $$ --- # 9. Disjoint proposal support Proposal $P$ has coordinate support: $$ \boxed{ \operatorname{supp}(P) \subseteq \{1,\ldots,m\}. } $$ --- # 10. VWDC09-T1 — Disjoint factorized safe composition ## Theorem VWDC09-T1 Let proposals: $$ P_1,\ldots,P_k $$ have pairwise disjoint coordinate supports. Assume each proposal: - modifies only its support coordinates; - preserves the corresponding local invariant factors. Then: 1. proposal transforms commute: $$ F_{P_i} \circ F_{P_j} = F_{P_j} \circ F_{P_i}; $$ 2. their joint composition preserves: $$ \mathcal S. $$ ### Proof Disjoint maps act on independent coordinates, so order does not affect any coordinate. Each changed coordinate remains in its invariant factor. Unchanged coordinates remain valid. Therefore the product state remains in: $$ S_1\times\cdots\times S_m. $$ $\square$ --- # 11. Interpretation Federation does not require global serialization for every operation. Operations that are: - genuinely disjoint; - semantically independent; - invariant-factorized; can safely execute concurrently. The difficulty is proving those conditions. --- # 12. Shared capacity invariant Let a shared scalar resource have current usage: $$ u $$ and capacity: $$ C. $$ Slack: $$ \boxed{ S=C-u. } $$ Proposal $i$ can increase usage by at most: $$ \Delta_i\ge0. $$ --- # 13. VWDC09-T2 — Global slack composition certificate ## Theorem VWDC09-T2 If: $$ \boxed{ \sum_{i=1}^k \Delta_i \le S, } $$ then committing all $k$ proposals preserves: $$ u_{\mathrm{new}} \le C. $$ ### Proof $$ u_{\mathrm{new}} \le u+\sum_i\Delta_i \le u+S = C. $$ $\square$ --- # 14. Individual feasibility is weaker Each: $$ \Delta_i\le S $$ does not imply: $$ \sum_i\Delta_i\le S. $$ Thus local resource certificates cannot replace global reservation. --- # 15. Reservation ledger Before a shared-resource commit, the federation can atomically reserve: $$ r(P). $$ Ledger state: $$ \boxed{ L = ( \text{available}, \text{reservations}, \text{commit IDs} ). } $$ --- # 16. VWDC09-T3 — Atomic reservation preserves scalar capacity ## Theorem VWDC09-T3 Suppose reservation requests are serialized/atomically compared against current remaining capacity. A reservation is granted only when: $$ r(P) \le C-\sum_{Q\in\mathcal R_{\mathrm{active}}}r(Q). $$ Then total active reserved capacity never exceeds $C$. ### Proof Induction over reservation grants. Each new accepted reservation preserves the inequality. Release/abort only decreases total reservation. $\square$ --- # 17. Transaction states Suggested: ```text PROPOSED PREPARED RESERVED COMMITTED ABORTED EXPIRED COMPENSATED QUARANTINED ``` --- # 18. Prepare phase PREPARE validates: - current snapshot; - affected certificate scopes; - authority; - resource estimates; - compatibility; - global invariants. No shared side effect occurs yet. --- # 19. Commit phase COMMIT: - rechecks current required state/version; - atomically consumes reservation; - applies state transition; - records unique commit ID; - appends immutable provenance. --- # 20. Abort If any required gate fails: $$ \boxed{ \mathrm{ABORT} } $$ releases reservations and records reason. --- # 21. Snapshot version Each shared object/resource: $$ x_j $$ has version: $$ v_j. $$ Proposal records versions of its read set. --- # 22. VWDC09-T4 — Version-stamped stale-read rejection ## Theorem VWDC09-T4 Suppose a proposal $P$ is committed only if every object in: $$ R(P) $$ still has the same version observed during PREPARE. Then any proposal whose read-set object has changed since PREPARE is rejected before commit. ### Proof A changed object has a different version stamp. The equality check fails. $\square$ This is a stale-read safety mechanism, not a complete distributed transaction protocol. --- # 23. Conflict Two proposals conflict if: $$ \boxed{ W(P)\cap [ R(Q)\cup W(Q) ] \neq \varnothing } $$ or symmetrically. --- # 24. Precedence graph For one proposed schedule, construct conflict graph: $$ \boxed{ G_C } $$ with one node per transaction. Add directed edge: $$ P\to Q $$ when conflicting operations of $P$ precede those of $Q$. --- # 25. VWDC09-T5 — Acyclic conflict graph admits an equivalent serial order ## Theorem VWDC09-T5 If the precedence/conflict graph: $$ G_C $$ is acyclic, then any topological ordering of $G_C$ defines a serial transaction order preserving all conflict orderings. ### Proof Every edge: $$ P\to Q $$ appears in topological order with $P$ before $Q$. Thus all conflicting order constraints are preserved. Nonconflicting operations may be rearranged without changing conflict behavior. $\square$ This is the classical conflict-serializability theorem. VWDC does not claim it as new. --- # 26. Serial commit safety If every serial transaction: $$ P_t $$ is revalidated on current state and preserves the global invariant: $$ x_t\in\mathcal S_G \Rightarrow F_{P_t}(x_t)\in\mathcal S_G, $$ then an equivalent serializable schedule preserves: $$ \mathcal S_G. $$ This inherits VWDC-08 serialized invariant preservation. --- # 27. Linearizability boundary Linearizability is a classical correctness condition for concurrent objects requiring operations to appear as if they took effect atomically in a legal sequential order consistent with real-time precedence. VWDC's shared reality objects can use linearizable/serializable semantics where current-state correctness requires it. Not every federated information exchange needs linearizability. --- # 28. Eventual consistency boundary Eventual consistency can be acceptable for: - analytics; - advisory caches; - noncritical replicated metadata. It is insufficient by itself for operations such as: - exclusive actuator ownership; - strict resource caps; - one-time irreversible commands; when conflicting stale writes can violate hard invariants. --- # 29. VWDC09-N2 — Eventual convergence does not prevent transient invariant violation ## Counterexample Two replicas each see capacity 1 available. Each independently grants 1 unit. Before convergence, physical total allocation is 2. Later replicas converge to the same record. The hard capacity invariant was already violated. Therefore: $$ \boxed{ \text{eventual consistency} \not\Rightarrow \text{hard real-time invariant preservation}. } $$ $\square$ --- # 30. Commutative safe operation class Some operations can be implemented without strong global serialization if they are: - commutative; - idempotent; - monotone; - invariant-safe under concurrent composition. This is operation specific. --- # 31. Commit ID Every logical shared-reality transaction receives globally unique: $$ \boxed{ CID. } $$ Ledger records whether $CID$ has committed. --- # 32. Idempotent logical commit wrapper Define guarded commit: $$ \boxed{ \mathsf{Commit}(CID,P,x) = \begin{cases} (F_P(x),\mathrm{mark}(CID)), & CID\text{ unseen},\\ x, & CID\text{ already committed}. \end{cases} } $$ --- # 33. VWDC09-T6 — Duplicate-delivery logical idempotence ## Theorem VWDC09-T6 Under the guarded commit wrapper, repeated delivery of the same: $$ (CID,P) $$ after its first successful commit produces no additional logical state transition. ### Proof The first call marks: $$ CID. $$ Every later call selects the already-committed branch and leaves state unchanged. $\square$ This protects against duplicate message delivery at the logical transaction layer. --- # 34. Exactly-once caveat Idempotent logical commit does not guarantee exactly-once physical effect if external actuators cannot deduplicate/transactionally bind to $CID$. Physical side-effect design remains domain specific. --- # 35. Affected runtime set Proposal $P$ has affected runtime/domain set: $$ \boxed{ A(P) \subseteq \{1,\ldots,N\}. } $$ --- # 36. Local admissible state/action scope Runtime $i$ exposes: $$ \boxed{ \mathcal Z_i } $$ where its RTC/safety contracts are valid. --- # 37. Federation compatibility scope For proposal touching several domains: $$ \boxed{ \mathcal Z_F(P) = \bigcap_{ i\in A(P) } \mathcal Z_i^{\mathrm{translated}}. } $$ All scopes are first translated into compatible shared semantics. --- # 38. VWDC09-T7 — Contract-scope conjunction monotonicity ## Theorem VWDC09-T7 Adding another affected runtime/domain contract cannot enlarge the admissible federation scope: $$ \boxed{ A\subseteq B \Longrightarrow \bigcap_{i\in B}\mathcal Z_i \subseteq \bigcap_{i\in A}\mathcal Z_i. } $$ ### Proof Set intersection with additional sets cannot enlarge the result. $\square$ --- # 39. Empty intersection Each runtime can have a nonempty valid local scope: $$ \mathcal Z_i\neq\varnothing $$ while: $$ \boxed{ \bigcap_i\mathcal Z_i = \varnothing. } $$ Thus local validity may have no mutually compatible federation operating point. --- # 40. VWDC09-N3 — Nonempty local certificate scopes do not imply a nonempty federated scope ## Counterexample $$ \mathcal Z_1=[0,1], $$ $$ \mathcal Z_2=[2,3]. $$ Both are nonempty. Their intersection is empty. $\square$ --- # 41. Semantic adapter Different runtimes may use different: - units; - clocks; - coordinate systems; - entity IDs; - action semantics; - confidence levels. Define adapter: $$ \boxed{ T_{i\to F}. } $$ --- # 42. Adapter contract Every semantic translation records: - source ontology/schema; - target ontology/schema; - unit transform; - time transform; - uncertainty; - version; - provenance. --- # 43. VWDC09-N4 — Syntactic interoperability does not imply semantic interoperability ## Counterexample Runtime A reports: ```text temperature = 20 ``` in Celsius. Runtime B interprets the shared field as Fahrenheit. A perfectly successful schema/API exchange still produces the wrong physical meaning. Therefore: $$ \boxed{ \text{protocol/schema compatibility} \not\Rightarrow \text{semantic compatibility}. } $$ $\square$ --- # 44. Current federation-node precedent Current federated digital-twin ecosystem work explicitly uses controlled capability exposure, protocol/schema adaptation, and state/event exchange to integrate heterogeneous twins. VWDC's adapter contract adds the requirement that semantics and uncertainty also remain explicit before shared reality commit. --- # 45. Cross-domain orchestration precedent Current multi-domain/trans-domain digital-twin work connects heterogeneous state, errors, objectives, constraints, decisions, and controls through orchestration layers. VWDC-09's commit protocol is narrower: > after orchestration proposes a shared side effect, how is the effect globally certified and transactionally applied? --- # 46. Federation certificate packet Suggested: ```text proposal_id runtime_id snapshot_id read_set write_set resource_delta affected_domains local_certificates translated_scopes global_invariant_checks authority_attestations trust_status commit_id ``` --- # 47. Multi-champion arbitration Each runtime can submit one or more current certified champions/proposals. Federation first removes: - infeasible; - incompatible; - stale; - quarantined; proposals. --- # 48. Feasible proposal set $$ \boxed{ \mathcal P_F(x) = \{ P: \mathsf{GlobalValid}(P,x)=1 \}. } $$ --- # 49. Federation objective A scalarized example: $$ \boxed{ J(P) = V(P) - C(P) - D(P). } $$ But federation can use multiobjective or lexicographic policy. --- # 50. VWDC09-T8 — Deterministic federation arbitration ## Theorem VWDC09-T8 If: 1. $\mathcal P_F(x)$ is finite and nonempty; 2. feasible proposals are ranked by a total preorder; 3. ties use a deterministic unique key; then the federation chooses exactly one winning proposal. ### Proof Same finite arbitration argument as VWDC-08. $\square$ For batch-compatible disjoint proposals, the federation can instead choose one admissible batch. --- # 51. Batch proposal $$ \boxed{ B = \{ P_1,\ldots,P_k \}. } $$ Batch validity requires: - resource feasibility; - certificate compatibility; - conflict/serializability safety; - global invariant preservation. --- # 52. Local champions are not votes A local champion is a certified local solution. It is not automatically one democratic vote in a federation. Weight/priority/authority can differ by domain. --- # 53. Evidence consensus is not commit authority Many runtimes can agree on a proposal. Commit still requires: - current global state; - resource validation; - certificates; - authority. This inherits VWDC-08. --- # 54. Trust domains Each runtime has trust state: ```text ACTIVE LIMITED PROBATION QUARANTINED REVOKED ``` --- # 55. Quarantine Quarantine removes runtime $i$ from: - proposal authority; - certificate authority; - shared writes; according to policy. It does not erase historical evidence/provenance. --- # 56. Dependency graph Let: $$ G_D $$ record required federation dependencies. If runtime $j$ requires live service/certificate from $i$, there is dependency: $$ i\to j. $$ --- # 57. Quarantine closure Define: $$ \boxed{ \operatorname{DepDesc}(i) } $$ as all runtimes/proposals whose currently required dependency chain includes $i$. --- # 58. VWDC09-T9 — Dependency-local quarantine preservation ## Theorem VWDC09-T9 Suppose runtime $i$ is quarantined. Any proposal $P$ that: 1. is not produced/authorized by $i$ ; 2. has no required dependency path from $i$ ; 3. does not require a resource/certificate currently held exclusively by $i$ ; remains **structurally unaffected by the quarantine itself**. ### Proof The quarantine removes only rights/dependencies involving $i$. By assumptions, $P$ has none. Other independent validity checks can still fail for unrelated reasons. $\square$ --- # 59. VWDC09-N5 — Quarantining one runtime can have nonlocal blast radius If runtime $i$ supplies a certificate/schema/service required by many others, then: $$ \operatorname{DepDesc}(i) $$ can be large. Therefore: $$ \boxed{ \text{runtime isolation} \not\Rightarrow \text{small federation impact}. } $$ Dependency topology determines blast radius. --- # 60. Current fault-tolerance precedent Current 2025–2026 work studies: - self-healing/fault-tolerant digital-twin processing; - Byzantine-resilient federated multi-agent optimization; - adaptive isolation under malicious/faulty participants. VWDC does not claim fault isolation or Byzantine robustness as new. --- # 61. Byzantine validator model Suppose federation has: $$ n=3f+1 $$ validators. At most: $$ f $$ are Byzantine. Honest validators never sign two conflicting commit certificates for the same transaction epoch/key. A commit certificate requires: $$ \boxed{ 2f+1 } $$ signatures. --- # 62. Quorum intersection Any two subsets: $$ Q_1,Q_2 $$ of size: $$ 2f+1 $$ inside a universe of size: $$ 3f+1 $$ satisfy: $$ \boxed{ |Q_1\cap Q_2| \ge f+1. } $$ --- # 63. VWDC09-T10 — Byzantine quorum non-equivocation certificate ## Theorem VWDC09-T10 Under the validator assumptions above, two conflicting commit certificates for the same epoch/key cannot both collect: $$ 2f+1 $$ valid signatures. ### Proof Two quorums of size $2f+1$ intersect in at least: $$ (2f+1)+(2f+1)-(3f+1) = f+1. $$ At most $f$ validators are Byzantine, so the intersection contains at least one honest validator. That honest validator would have to sign both conflicting certificates, contradicting honest non-equivocation. $\square$ --- # 64. Boundary of the theorem This is only a quorum-intersection safety statement. It does not prove: - liveness; - network synchrony; - full Byzantine consensus; - correct state-machine validation; - resistance to key compromise. VWDC does not rederive BFT consensus. --- # 65. Federation identity Every runtime has stable: $$ RuntimeID. $$ Every proposal has: $$ ProposalID. $$ Every shared commit has: $$ CID. $$ --- # 66. Capability exposure A runtime should expose only declared capabilities: ```text READ_STATE PROPOSE CERTIFY RESERVE COMMIT OBSERVE VALIDATE ADMIN ``` Least privilege applies. --- # 67. Capability revocation Quarantine can revoke a subset of capabilities rather than remove all federation visibility. Example: ```text PROPOSE = false READ_STATE = true AUDIT_HISTORY = true ``` --- # 68. Fault containment A runtime can remain useful as: - read-only observer; - historical evidence source; - simulation sandbox; while losing live commit authority. --- # 69. World-model disagreement Two runtimes can produce conflicting predictions: $$ q_i\neq q_j. $$ This is evidence/model disagreement. It does not automatically require quarantining either runtime. Use diagnostic/evidence comparison. --- # 70. Certificate disagreement If RTC scopes disagree: - restrict to intersection; - choose one authority by policy; - request revalidation; - abstain. Do not silently average incompatible hard certificates. --- # 71. VWDC09-N6 — Averaging incompatible hard constraints can authorize a forbidden state ## Counterexample Runtime A requires: $$ x\le0. $$ Runtime B requires: $$ x\ge2. $$ Averaging thresholds produces: $$ x=1, $$ which satisfies neither hard contract. Therefore: $$ \boxed{ \text{averaged certificate constraints} \not\Rightarrow \text{contract compatibility}. } $$ $\square$ --- # 72. Hard scope reconciliation For mandatory hard constraints, federation uses: - intersection; - lexicographic authority; - explicit exception/override contract. Never numeric averaging by default. --- # 73. Shared evidence dependence Different runtimes may share: - model family; - evaluator; - external data; - provider; - source twin. Thus federation consensus is not independent evidence count. This inherits VWDC-03. --- # 74. Evidence profile Proposal arbitration can carry: $$ \boxed{ \mathbf E(P) = ( LineageFamilies, ModelFamilies, EvaluatorFamilies, ExternalSources, Dependence ). } $$ --- # 75. Committee evidence versus quorum safety Distinguish: ### Commit quorum A distributed-systems authorization mechanism. ### Evidence committee An epistemic aggregation mechanism. A $2f+1$ signature quorum does not mean $2f+1$ independent scientific confirmations. --- # 76. VWDC09-N7 — Commit quorum size does not equal evidence effective sample size Validators can all rely on the same world model/evaluator/data. They can form a valid authorization quorum while having highly dependent evidence. Therefore: $$ \boxed{ \text{authorization diversity} \not\Rightarrow \text{epistemic independence}. } $$ --- # 77. Shared reality rollback After a federated commit: $$ x \to x', $$ one runtime may later decide it wants to "rollback." But shared reality has already changed. --- # 78. VWDC09-N8 — Local history rollback does not undo a shared reality commit ## Counterexample Runtime A commits physical shipment: $$ Warehouse\to Customer. $$ A later rewinds its local world/checkpoint. The shipment remains in reality and other runtimes' states/evidence reflect it. Therefore: $$ \boxed{ \text{local world rollback} \not\Rightarrow \text{shared reality rollback}. } $$ $\square$ --- # 79. Compensation Shared reality reversal should be represented as a new governed transaction: $$ \boxed{ P_{\mathrm{comp}} } $$ when a compensating physical action exists. Examples: - release reservation; - return resource; - reverse routing command; - restore configuration. --- # 80. Compensation is not erasure A compensation creates: $$ x' \to x''. $$ History retains both commits. Even if: $$ x''=x $$ on selected state variables, time/provenance/event history differs. --- # 81. VWDC09-T11 — Compensation preserves append-only commit history ## Theorem VWDC09-T11 If compensation is recorded as a newly created commit event with parent/reference to the original commit, then commit/event lineage remains append-only and acyclic under strictly increasing creation indices. ### Proof Same creation-index DAG argument used throughout VWDC. $\square$ --- # 82. Distributed checkpoint A federation-wide recovery point requires a consistent snapshot of all shared objects/domains needed by the recovery contract. Independent local checkpoints taken at unrelated times need not form one valid global checkpoint. --- # 83. VWDC09-N9 — Arbitrary local checkpoints need not form a consistent global checkpoint ## Counterexample Runtime A checkpoint records: $$ x=0 $$ before transfer. Runtime B checkpoint records: $$ y=1 $$ after receiving the transferred unit. Combined snapshot has duplicated conservation total: $$ x+y=1 $$ when the intended jointly-timed snapshot semantics differ, or analogously can violate message/resource consistency. Therefore: $$ \boxed{ \text{local checkpoint set} \not\Rightarrow \text{consistent federation checkpoint}. } $$ $\square$ This is a distributed snapshot boundary. --- # 84. Global checkpoint contract Record: - snapshot epoch; - per-object versions; - in-flight transaction status; - reservations; - external side-effect status; - runtime versions; - RTC/safety versions. --- # 85. Federation commit ledger Suggested: ```text commit_id proposal_ids runtime_ids prepare_snapshot read_versions write_set resource_reservations affected_domains certificate_hashes quorum_or_authority commit_time physical_ack compensation_parent status ``` --- # 86. Proposal ledger ```text proposal_id runtime_id local_champion snapshot read_set write_set preconditions effect resource_delta local_certificates semantic_adapter_versions priority ``` --- # 87. Runtime registry ```text runtime_id organization trust_state capabilities rtc_scopes safety_scopes schema_version dependencies quarantine_status ``` --- # 88. Quarantine packet ```text runtime_id reason time revoked_capabilities dependency_descendants affected_pending_transactions historical_evidence_status reentry_requirements ``` --- # 89. Reentry A quarantined runtime can reenter only after: - fault remediation; - certificate refresh; - compatibility check; - trust policy; - possibly shadow/probation mode. --- # 90. Probation A recovered runtime may: - read; - simulate; - submit nonbinding proposals; before regaining commit/certification authority. --- # 91. Federated champion A federation-level champion can be: - one proposal; - a compatible batch; - one coordinated multi-runtime plan. It is not necessarily owned by one runtime. --- # 92. Coordinated plan $$ \boxed{ \Pi_F = ( P_1,\ldots,P_k, \text{order/constraints} ). } $$ --- # 93. Plan validity Requires: - certificate scope; - resource reservation; - order/transaction compatibility; - semantic alignment; - current state; - authority. --- # 94. Plan partial order If some proposals commute and others conflict, federation can use a partial order: $$ \boxed{ P_i\prec P_j } $$ only for necessary dependencies/conflicts. Independent proposals can execute concurrently. --- # 95. VWDC09-T12 — Acyclic dependency partial order admits an execution order ## Theorem VWDC09-T12 If the proposal dependency/conflict graph is finite and acyclic, a topological ordering exists. Executing proposals in that order respects every directed precedence constraint. ### Proof Classical DAG topological-order theorem. $\square$ --- # 96. Cyclic dependency If: $$ P_1 \prec P_2 \prec P_1, $$ there is no serial order satisfying both strict precedence constraints. The federation must: - reject; - redesign; - weaken dependency; - execute an atomic composite transaction. --- # 97. VWDC09-N10 — Cyclic strict precedence constraints have no serial realization Immediate from the contradiction: $$ P_1