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:

current snapshot/read validity;
global invariant preservation;
shared resource feasibility;
all required affected-domain certificates;
authority;
non-quarantine status;
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:

proposal transforms commute: $$ F_{P_i} \circ F_{P_j}
F_{P_j} \circ F_{P_i}; $$
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:

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:

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:

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:

$\mathcal P_F(x)$ is finite and nonempty;
feasible proposals are ranked by a total preorder;
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:

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:

is not produced/authorized by $i$ ;
has no required dependency path from $i$ ;
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:

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:

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:

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

proposal_id
runtime_id
local_champion
snapshot
read_set
write_set
preconditions
effect
resource_delta
local_certificates
semantic_adapter_versions
priority

87. Runtime registry

runtime_id
organization
trust_state
capabilities
rtc_scopes
safety_scopes
schema_version
dependencies
quarantine_status

88. Quarantine packet

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<P_2<P_1.

$\square$

98. Atomic composite transaction

Some cyclicly coupled local operations can be compiled into one atomic global operation:

\boxed{ P_{12}. }

It must have its own:

global invariant proof/check;
authority;
compensation/recovery semantics.

99. Multi-domain current literature

Current 2026 digital-twin work increasingly treats multi-domain/federated twins as:

heterogeneous;
coordinated;
distributed across edge/cloud;
orchestrated for joint decisions;
connected through shared state and control consequences.

VWDC-09's contribution is not federation itself.

It is the explicit boundary between federation-level reasoning and shared-state commit correctness.

100. Federation world graph

The full state has at least:

\boxed{ G_{\mathrm{fed}} = ( G_{\mathrm{runtime}}, G_{\mathrm{dependency}}, G_{\mathrm{transaction}}, G_{\mathrm{certificate}}, G_{\mathrm{evidence}}, G_{\mathrm{provenance}} ). }

One untyped federation graph is insufficient.

101. Runtime graph

Which runtimes exist and communicate?

102. Dependency graph

Which runtime/service/certificate is required by another?

103. Transaction graph

Which proposals conflict/read/write shared objects?

104. Certificate graph

Which local RTC/safety scopes are required for which global action?

105. Evidence graph

Which claims depend on which models/evaluators/data?

106. Provenance graph

Which events/versions/commits produced the current system state?

107. VWDC09-N11 — One untyped federation graph cannot preserve all operational semantics

Parentage, data dependence, transaction conflict, certificate requirement, and communication are distinct relations.

Collapsing them into one generic edge loses information required for:

quarantine;
commit ordering;
evidence aggregation;
rollback;
authorization.

Therefore:

\boxed{ \text{one generic federation edge relation} \not\Rightarrow \text{complete federation semantics}. }

108. Commit boundary hierarchy

Suggested:

\boxed{ \text{Local World/Agent} \to \text{Local Governor} \to \text{Federation Prepare} \to \text{Global Commit Authority} \to \text{Reality}. }

109. Proposal concurrency

Local worlds can generate proposals asynchronously.

No global lock is required for proposal generation.

Strong coordination is concentrated at the shared mutation boundary.

110. Read-only federation

Read-only/analysis operations can have weaker coordination requirements if they do not mutate hard shared invariants.

111. Advisory federation

Some runtimes may have:

PROPOSE_ONLY

with no direct authority.

This improves cognitive diversity without increasing write authority.

112. Authority matrix

\boxed{ A_{ij} \in \{ \text{none}, \text{read}, \text{propose}, \text{certify}, \text{commit} \} }

for runtime $i$ and domain/resource $j$ .

113. Least authority

A runtime should not hold global commit power merely because it is allowed to model/observe a domain.

114. Separation of duties

Possible independent roles:

proposer;
validator;
resource-reserver;
committer;
auditor.

This can reduce one-component failure blast radius.

115. Single-point commit authority boundary

A logically single commit order need not mean one physical server.

It can be implemented by:

consensus;
replicated state machine;
transactional database;
domain-specific atomic controller.

VWDC specifies semantics, not implementation.

116. Commit liveness

Strong safety can reduce availability under:

partitions;
failed validators;
unavailable authorities.

VWDC-09 prioritizes the correctness boundary and does not solve the full CAP/BFT liveness trade space.

117. Fail closed versus degraded federation

If global commit cannot be certified:

continue read-only simulation;
continue local nonshared actions;
enter degraded mode;
stop shared mutation.

118. Local autonomy under partition

A runtime can continue actions that provably:

do not touch shared state;
remain inside local authority;
preserve local invariants;
do not depend on stale shared certificates.

119. VWDC09-T13 — Partition-safe local autonomy under disjoint authority

Theorem VWDC09-T13

Suppose runtime $i$ is disconnected from federation commit service.

If action $a$ :

modifies only state/resource coordinates exclusively owned by $i$ ;
has no cross-runtime dependencies;
preserves all local hard invariants;
cannot affect any shared/global invariant by contract;

then executing $a$ does not violate a global invariant solely because the federation link is unavailable.

Proof

By assumption, the action has no shared/global effect and preserves its isolated local invariant factors.

$\square$

This is a very strong contract condition.

120. Network partition no-go

If action can affect shared state/resources, partitioned local certification is insufficient.

121. VWDC09-N12 — Network partition does not justify shared-state local commit

Two partitioned runtimes can each believe they own the same shared resource.

Without coordination/ownership lease/certificate, both can commit conflicting actions.

Therefore:

\boxed{ \text{partition} + \text{local confidence} \not\Rightarrow \text{shared-state authority}. }

122. Lease boundary

Time-bounded exclusive leases can grant temporary commit authority to one runtime/domain.

Lease safety depends on:

clock/timing assumptions;
renewal;
fencing tokens;
failure handling.

VWDC-09 does not formalize lease protocols.

123. Fencing token

A monotonically increasing fencing/epoch number can help actuators reject commands from an expired former authority.

This is established distributed-systems engineering.

124. Reality acknowledgement

COMMITTED in the ledger should distinguish:

LOGICALLY_COMMITTED
PHYSICALLY_ACKNOWLEDGED
PHYSICAL_STATUS_UNKNOWN
FAILED_COMPENSATION_REQUIRED

Distributed commit and physical execution are not identical.

125. VWDC09-N13 — Logical distributed commit does not prove physical side-effect completion

A transaction can be durably recorded while an actuator command:

fails;
is delayed;
is duplicated;
produces partial effect.

Therefore:

\boxed{ \text{ledger commit} \not\Rightarrow \text{physical completion}. }

Physical acknowledgement/effect evidence is a separate contract.

126. Commit evidence

A physical side effect should produce evidence:

\boxed{ E_{\mathrm{commit}} = ( CID, Command, Actuator, Ack, ObservedEffect, Time, Prov ). }

127. Post-commit validation

After irreversible/high-impact commit:

observe actual reality;
update shared state;
compare expected effect;
trigger compensation/incident if mismatch.

128. Federated reality feedback

Reality feedback should be routed back to all affected runtimes.

They may update:

local world models;
RTCs;
evidence;
policy.

The shared commit ID provides causal/provenance anchor.

129. Delayed feedback

Later outcomes remain attached to:

CID

and originating coordinated plan.

Do not credit the currently active runtime automatically.

130. Cross-runtime learning

Runtimes can learn from shared commit outcomes without sharing all private local state.

Federated learning/analytics can be one implementation family.

VWDC does not equate model federation with commit federation.

131. VWDC09-N14 — Federated learning convergence does not imply federated control safety

A set of runtimes can successfully learn a shared model while their live actions still conflict over shared resources.

Therefore:

\boxed{ \text{federated model learning} \not\Rightarrow \text{safe shared reality mutation}. }

132. Byzantine learning versus Byzantine commit

Robust gradient aggregation protects one learning channel.

Shared reality commit requires separate:

authorization;
state consistency;
resource;
safety;
transaction;

mechanisms.

133. Fault containment layers

Suggested:

MODEL_UPDATE_QUARANTINE
EVIDENCE_QUARANTINE
PROPOSAL_QUARANTINE
CERTIFICATE_QUARANTINE
COMMIT_QUARANTINE
NETWORK_ISOLATION

Use the smallest sufficient layer.

134. Quarantine monotonicity

Revoking more capabilities reduces what a runtime can directly change.

It can also reduce federation availability.

This is a safety/availability tradeoff.

135. Revalidation after quarantine

Dependent proposal/certificate descendants enter:

STALE
REVALIDATION_REQUIRED

not automatically permanently invalid.

136. Faulty runtime history

Historical valid outputs from a later-faulty runtime need not all be invalid.

Invalidate according to:

fault onset;
dependency;
evidence scope;
provenance.

137. Global incident

A shared incident can implicate several runtimes through one commit plan.

Dependency/transaction lineage identifies blast radius.

138. Incident compensation plan

A federated compensation can require coordinated actions across several domains.

Treat it as a new globally certified plan.

139. Federation recovery point

A valid recovery point is:

\boxed{ RCP = ( SharedSnapshot, CommitLedgerPosition, Reservations, RuntimeVersionSet, RTCSet, SafetySet, PhysicalAckState ). }

140. Recovery point completeness

Missing in-flight transaction/physical acknowledgement state can make recovery ambiguous.

141. Federation version lineage

Every:

runtime version;
proposal;
certificate;
commit;
quarantine;
compensation;
recovery;

is append-only.

142. VWDC09-T14 — Append-only federation governance DAG

Theorem VWDC09-T14

If every federation artifact/event is created with a strictly increasing logical creation index and all derivation/commit/provenance edges point from earlier to later indices, then the federation provenance graph is acyclic.

Proof

Strict index increase along edges forbids a directed cycle.

$\square$

143. Federal governance debt

Define:

\boxed{ \mathbf D_F = ( D_{\mathrm{conflict}}, D_{\mathrm{resource}}, D_{\mathrm{certificate}}, D_{\mathrm{semantic}}, D_{\mathrm{trust}}, D_{\mathrm{evidence}}, D_{\mathrm{availability}}, D_{\mathrm{recovery}}, D_{\mathrm{provenance}} ). }

144. Hard federation gates

Examples:

no resource overcommit;
no unauthorized write;
no stale exclusive-owner command;
no invalid mandatory safety certificate;
no commit from quarantined authority.

145. Soft federation goals

Examples:

throughput;
latency;
fairness;
energy cost;
model diversity.

Hard violations cannot be averaged away by soft gains.

146. Federation Pareto frontier

Among globally feasible plans, compare:

utility;
latency;
commit coordination cost;
resilience;
evidence quality;
rollback/compensation debt.

147. VWDC09-T15 — Federated plan Pareto necessity

Theorem VWDC09-T15

Every optimum of a scalar federation objective that is strictly monotone in the declared benefit/cost coordinates lies on the nondominated feasible federation frontier.

Proof

Standard dominance argument.

$\square$

148. Benchmark A — local/global resource conflict

Two local twins each request $0.6$ under shared cap $1$ .

149. Benchmark B — disjoint factorized composition

Two runtimes update independent coordinates.

Verify commutativity and invariant preservation.

150. Benchmark C — atomic reservation

Launch many requests.

Verify total granted reservation never exceeds capacity.

151. Benchmark D — version-stamped stale proposal

Prepare proposal on version 3.

Mutate read object to version 4.

Verify commit rejected.

152. Benchmark E — conflict graph

Build acyclic and cyclic schedules.

Verify topological serial order exists only for acyclic graph.

153. Benchmark F — duplicate delivery

Send same $CID$ many times.

Verify one logical effect.

154. Benchmark G — empty certificate intersection

Two nonempty incompatible RTC scopes.

Verify federation rejects joint action.

155. Benchmark H — semantic adapter

Use Celsius/Fahrenheit mismatch.

Verify syntactic API success but semantic validation failure.

156. Benchmark I — Byzantine conflicting certificates

Set:

n=3f+1.

Try to construct two conflicting $2f+1$ quorums with honest non-equivocation.

Verify impossibility.

157. Benchmark J — quarantine blast radius

Create dependency DAG.

Quarantine one high-centrality runtime.

Compute descendants.

158. Benchmark K — local rollback no-go

Commit a shared shipment/resource transfer.

Rollback one local twin only.

Verify reality/other runtimes remain changed.

159. Benchmark L — consistent federation checkpoint

Create interleaved transfer and local checkpoints.

Verify arbitrary mixed checkpoints fail global consistency test.

160. Benchmark M — partition-safe local action

Disconnect one runtime.

Allow only exclusive-local coordinates.

Verify shared state unchanged.

161. Benchmark N — physical acknowledgement

Log logical commit but simulate failed actuator.

Verify status remains:

PHYSICAL_STATUS_UNKNOWN / FAILED

rather than complete.

162. Current literature boundary — federated digital twins

Federated/composite/trans-domain digital-twin ecosystems are active current research.

VWDC does not claim federation as new.

163. Current literature boundary — distributed transactions

Linearizability, serializability, atomic commit, version checks, idempotence, consensus, leases, and distributed snapshots are classical distributed-systems/database concepts.

VWDC imports them where shared reality mutation needs their semantics.

164. Current literature boundary — Byzantine robustness

Byzantine consensus/quorum and Byzantine-resilient federated learning/optimization are established fields.

VWDC09-T10 is only a simple quorum-intersection safety lemma.

165. Current literature boundary — fault-tolerant twins

Fault-tolerant/self-healing digital-twin processing and isolation are active current topics.

VWDC integrates fault containment with proposal/certificate/commit capabilities.

166. Candidate VWDC-specific synthesis

Subject to broader literature audit, candidate bridge-specific synthesis is:

explicit separation between federated cognition/proposal and federated shared-reality commit authority;
transaction packets that bind WDC proposal provenance, RTC/safety scopes, read/write sets, resource deltas, and physical acknowledgement;
factorized/disjoint safe concurrency plus global-slack/resource reservation certificates;
certificate-scope and semantic-adapter compatibility as transaction gates;
federation trust/quarantine defined at capability layers rather than binary membership only;
separation of commit authorization quorums from epistemic evidence independence;
compensation transactions rather than silent world-history rewind for shared reality rollback;
a multi-graph federation state separating runtime, dependency, transaction, certificate, evidence, and provenance relations;
support for partition-safe local autonomy only under explicit disjoint-authority contracts.

No strong novelty claim is made in v0.1.

167. What VWDC-09 proves

Under explicit hypotheses, VWDC-09 proves:

local proposal validity does not imply global composability;
disjoint factorized invariant-preserving transforms commute and safely compose;
aggregate bounded resource deltas preserve a shared capacity when they fit within current slack;
atomic serialized reservation never exceeds declared scalar capacity;
read-version checks reject proposals made stale by changes to their read sets;
an acyclic transaction conflict graph admits a serial order preserving all conflict constraints;
eventual state convergence does not prevent transient hard-invariant violation;
a commit-ID guard makes duplicate logical transaction delivery idempotent;
adding mandatory affected-domain certificate scopes can only shrink federation admissibility;
nonempty local certificate scopes can have empty global intersection;
syntactic interoperability does not imply semantic interoperability;
deterministic arbitration selects one winner from a finite nonempty feasible proposal set under a total preorder plus unique tie-break;
quarantine structurally preserves proposals with no dependency/authority/resource relation to the quarantined runtime;
quarantine can nevertheless have nonlocal blast radius through dependencies;
$2f+1$ quorums among $3f+1$ validators with at most $f$ Byzantine and honest non-equivocation cannot certify two conflicting commits for the same epoch/key;
averaging incompatible hard constraints does not produce a valid compromise contract;
commit quorum size does not determine evidence independence;
local history rollback does not undo an already committed shared reality side effect;
compensation recorded as a new event preserves append-only commit history;
arbitrary local checkpoints need not form a consistent global recovery point;
a finite acyclic proposal dependency graph admits an execution order respecting all precedence constraints;
cyclic strict precedence constraints have no serial realization;
under strong disjoint-authority assumptions, local action during federation partition preserves global invariants;
partitioned local confidence does not authorize shared-state mutation;
logical commit does not prove physical side-effect completion;
federated learning convergence does not imply safe shared reality control;
append-only federation event creation yields an acyclic governance provenance graph;
every strictly monotone scalar optimum lies on the nondominated feasible federation frontier.

168. What VWDC-09 does not prove

It does not prove:

a universal distributed transaction implementation;
that every shared action requires global serialization;
that version stamps alone guarantee serializability;
that a $2f+1$ quorum solves Byzantine consensus/liveness;
that semantic adapters are always invertible or low-defect;
that runtime trust can be reduced to one score;
that quarantine is always locally contained;
that compensation can reverse every physical action;
that arbitrary federation checkpoints can be made consistent without coordination;
that network partitions always permit useful local autonomy;
that logical commit guarantees physical actuation;
that federated digital twins require blockchain;
that one global authority is the only implementation of commit semantics.

169. Proposed VWDC-10

The next paper should focus on hostile/faulty federation participants and cross-organization trust:

\boxed{ \textbf{ VWDC-10 — Byzantine-Resilient World Federation, Trust Domains, and Fault Containment } }

Chinese:

拜占庭韌性世界聯邦、信任域與故障遏制

Main questions:

How should federation trust be decomposed across proposal, evidence, certificate, and commit roles?
What can Byzantine runtimes corrupt if they cannot directly commit?
How should conflicting evidence and malicious certificates be isolated?
When should a runtime be partially quarantined versus fully revoked?
How should quorum assumptions interact with RTC/safety semantics?
How should federation remain available after trust-domain loss?
What evidence is needed for reentry from quarantine?
Can fault containment regions be formally bounded by dependency/capability graphs?

170. References

Christian Vergara-Marcillo et al., Integrating Heterogeneous Digital Twins in Federated Ecosystems, arXiv:2606.22791, 2026.
Alessandra Somma, Alessio Bucaioni, Toward Federated Cognitive Digital Twins over the Edge-to-Cloud Continuum, arXiv:2607.21357, 2026.
Mansoorali Amiri, Trans-Domain Digital Twin: Conceptual Foundations, Architecture, and Research Outlook, arXiv:2607.15908, 2026.
Berk Buzcu et al., Modular Multi-Domain Digital Twin Architecture: Sustainable Intent-Driven 6G Management, arXiv:2606.13069, 2026.
Francesco Maria Mancinelli et al., Multi-Agent Digital Twins for Strategic Decision-Making using Active Inference, arXiv:2604.12657, 2026.
Deepika Saxena, Ashutosh Kumar Singh, A Self-Healing and Fault-Tolerant Cloud-based Digital Twin Processing Management Model, arXiv:2505.01215, 2025.
Ali Peivand, Seyyed Mostafa Nosratabadi, Byzantine-Resilient Federated Multi-Agent Optimization Framework for Cyber-Secure Interconnected Microgrids, arXiv:2606.19080, 2026.
Flint Xiaofeng Fan et al., Fault-Tolerant Federated Reinforcement Learning with Theoretical Guarantee, arXiv:2110.14074.
Maurice P. Herlihy, Jeannette M. Wing, Linearizability: A Correctness Condition for Concurrent Objects, ACM TOPLAS 12(3), 1990.
VWDC-01–08, GVSS-01–10, WDC-01–08, WDC Runtime Whitepaper, and frozen RRT-20, internal series artifacts, 2026.

171. Conclusion

Federation allows multiple worlds, twins, models, and organizations to reason over one shared reality.

But reasoning federation and commit federation are different problems.

The central rule is:

\boxed{ \text{locally certified} \not\Rightarrow \text{globally composable}. }

Safe concurrency is possible when transforms are genuinely disjoint, factorized, or otherwise proven commutative/invariant preserving.

Shared resources require global slack/reservation semantics.

Conflicting shared writes require a serializable/linearizable or otherwise invariant-safe commit discipline.

Different RTCs must have compatible semantic scopes.

A quorum authorizes a commit under its trust assumptions; it does not create independent scientific evidence.

Quarantine should revoke the smallest necessary capabilities but dependency topology determines the true blast radius.

And once a shared reality transaction has happened, one runtime cannot erase it by rewinding its private world.

Rollback becomes compensation plus append-only history.

The canonical VWDC-09 principle is:

\boxed{ \textbf{ Federation may decentralize models, evidence, and proposals, but shared reality still requires a globally coherent mutation history. Local certificates must be translated, intersected, reserved, ordered, and revalidated at commit time; otherwise many individually intelligent worlds can jointly produce one invalid reality. } }

This establishes the shared-reality transaction layer for federated WDC runtimes.

Canonical-source policy

This file is the canonical UTF-8 source artifact.

Canonical inline mathematics uses $...$ .
Canonical display mathematics uses $$...$$.
No Unicode mathematical-symbol conversion is used as source normalization.
No unicode_escape round trip is used.
Backslashes and delimiters are preserved literally.
Validation is required before release.
This paper does not merge or rename GVSS, WDC, VWDC, or RRT.

VWDC-09 — Federated World Governance, Multi-Champion Arbitration, and Shared Reality Commit Protocols

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

Abstract

1. Federation runtime

Definition VWDC09-D1

2. Local runtime

3. Federated digital-twin literature boundary

4. Shared reality proposal

Definition VWDC09-D2

5. Local validity

6. Global validity

Definition VWDC09-D3

7. VWDC09-N1 — Local validity does not imply global validity

Counterexample

8. Factorized state

9. Disjoint proposal support

10. VWDC09-T1 — Disjoint factorized safe composition

Theorem VWDC09-T1

proposal transforms commute: $$ F_{P_i} \circ F_{P_j}

Proof

11. Interpretation

12. Shared capacity invariant

13. VWDC09-T2 — Global slack composition certificate

Theorem VWDC09-T2

Proof

14. Individual feasibility is weaker

15. Reservation ledger

16. VWDC09-T3 — Atomic reservation preserves scalar capacity

Theorem VWDC09-T3

Proof

17. Transaction states

18. Prepare phase

19. Commit phase

20. Abort

21. Snapshot version

22. VWDC09-T4 — Version-stamped stale-read rejection

Theorem VWDC09-T4

Proof

23. Conflict

24. Precedence graph

25. VWDC09-T5 — Acyclic conflict graph admits an equivalent serial order

Theorem VWDC09-T5

Proof

26. Serial commit safety

27. Linearizability boundary

28. Eventual consistency boundary

29. VWDC09-N2 — Eventual convergence does not prevent transient invariant violation

Counterexample

30. Commutative safe operation class

31. Commit ID

32. Idempotent logical commit wrapper

33. VWDC09-T6 — Duplicate-delivery logical idempotence

Theorem VWDC09-T6

Proof

34. Exactly-once caveat

35. Affected runtime set

36. Local admissible state/action scope

37. Federation compatibility scope

38. VWDC09-T7 — Contract-scope conjunction monotonicity

Theorem VWDC09-T7

Proof

39. Empty intersection

40. VWDC09-N3 — Nonempty local certificate scopes do not imply a nonempty federated scope

Counterexample

41. Semantic adapter

42. Adapter contract

43. VWDC09-N4 — Syntactic interoperability does not imply semantic interoperability

Counterexample

44. Current federation-node precedent

45. Cross-domain orchestration precedent

46. Federation certificate packet

47. Multi-champion arbitration

48. Feasible proposal set

49. Federation objective

50. VWDC09-T8 — Deterministic federation arbitration

Theorem VWDC09-T8

Proof

51. Batch proposal

52. Local champions are not votes