The Verification Gap in Networked Physical AI: A Post-Semantic Communication Framework

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The Verification Gap in Networked Physical AI: A Post-Semantic Communication Framework

arXiv:2608.19593v1 [cs.RO] 20 Aug 2026

Shunsuke Saruwatari The University of Osaka, Japan

Abstract—A task-effective proposal is not yet a justified physical action. In networked Physical AI, a proposal may be understood while valid, timely, proposal-bound evidence or the authority required to finalize an action remains unavailable. We call this mismatch the verification gap and introduce a Post-Semantic Communication Framework for the systems interface between proposal formation and physical execution. The framework begins with application-declared evidence requirements, represents qualifying observations as evidence records, validates supporting and conflicting records through one path, and separates evidence sufficiency from authorized finalization and a downstream runtime gate. It further distinguishes evidence transfer, which can enlarge the record set reachable by a finalizer, from evidence coordination, which can suppress transmission around records already held at the finalization endpoint. Finitestate framework checks verify that the evaluator implements the declared distinctions consistently. Under the declared model, the controlled communication study exposes a finalizer-dependent asymmetry: sender-finalized Feedback uses evidence transfer to expand evidence reachability throughout the feasible plotted region, whereas receiver-finalized Feedback uses coordination to suppress redundant payload until loss, latency, freshness, and deadline costs shift selection to One-way. Finally, an episodelevel reporting schema defines common denominators for future measured Physical-AI studies. Index Terms—Post-semantic communication, verification gap, Networked Physical AI, evidence contracts, evidence records, receiver feedback, authorized finalization.

I. I NTRODUCTION “The aisle appears clear. Proposal: Proceed.” A cameraequipped warehouse robot sends this proposal to another robot approaching an occluded aisle. The bits arrive, the meaning is decoded, and the proposal may be useful. The receiving system Physical Perception

Semantic Proposal

nevertheless cannot justify motion if the application requires a fresh Visual-clearance record and a Radio-no-motion record bound to this proposal, but only one is available. A nearby agent may hold the missing record; it may instead hold an admissible conflict that should stop the action. A task-effective proposal is not yet a justified physical action. The same distinction arises when a cooperative vehicle receives a trajectory, a manipulator receives a grasp proposal, or an inspection drone receives a route. Networked Physical AI inherits long-standing cyber–physical and cloudrobotics concerns: sensing, computation, communication, and actuation are distributed across components and time [1], [2]. This distribution can also separate evidence location from finalization authority. We define the verification gap as the mismatch between a task-effective proposal and the valid, timely, proposal-bound evidence and authorization required at the permitted finalizer before action. Figure 1 places this gap inside a Networked Physical-AI loop [3], [4]. Post-semantic communication names the systems interface after semantic or task-level proposal formation and before physical execution. At this interface, agents expose evidence holdings, transfer validated evidence records, reevaluate application-declared requirements, and make a sufficient record set available to the authorized finalizer. The interface does not prescribe a transport, topology, learned representation, or number of agents. It identifies a responsibility boundary that is easily hidden inside a generic “receiver decision.” The downstream runtime gate remains independent: it may stop an action even after evidence verification and authorized finalization.

Verification Gap

Post-Semantic Interface

Runtime Gate & Physical Action

Coordinate and exchange evidence across agents

Runtime check ACT or STOP

Aisle appears clear. Proposal: Proceed.

Action not yet justified

Observe physical world via wireless signals and sensors

Semantic understanding & action proposal

Missing, invalid, or stale evidence—or unavailable finalization authority

Fig. 1. The verification gap and post-semantic interface within a networked Physical-AI loop. Figure 1 locates the interface between semantic proposal formation and runtime action; Figure 2 defines its internal framework.

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This paper makes four contributions. First, it defines the verification gap as a communication-relevant state between proposal understanding and physical action. Second, it proposes the Post-Semantic Communication Framework, which connects evidence requirements, evidence records, verification, authorized finalization, and a downstream runtime boundary. Third, it implements the framework in a finite-state evaluator and checks consistency with the declared structural distinctions, including conflict-first verification and the separation between evidence transfer and evidence coordination. Fourth, a controlled communication study demonstrates a requirementpreserving comparison and supplies reporting guidelines and an episode-level reporting schema for reuse. The checks stop at authorized finalization; measured sensing, credential operation, runtime control, and physical safety remain future work. II. R ELATED W ORK AND M OTIVATION Semantic and task-oriented communication move the objective beyond symbol fidelity toward meaning and task effectiveness [5], [6]. Our question begins after a meaningful proposal already exists. In Weaver’s broad effectiveness sense, the framework isolates the post-proposal transition from task effectiveness to evidence-backed, authorized action toward Level C [7]; it does not redefine communication theory. Receiver side information and interactive coding explain why a sender need not retransmit what a receiver already has [8], [9], while learned multi-agent communication asks when agents should exchange information [10]. These lines motivate efficient delivery, but do not by themselves declare which evidence must be verified before a particular physical action is finalized. Active perception and information-directed sensing ask what observation to acquire next [11], [12]; distributed sensor fusion asks how heterogeneous observations should be combined [13]. Distributed detection, distributed hypothesis testing, and team decision theory show how observations and decisions can be distributed [14], [15]. Work on information structures in distributed control similarly shows that who knows what, and when, constrains achievable decisions. The present framework fixes the required evidence and authorized finalizer before comparing how already available records reach that endpoint. Physical evidence location is therefore not silently credited as authority over an action. Embodied multimodal models ground sensors in language, while closed-loop LLM planners use scene descriptions, success signals, and human feedback to replan [16], [17]. Uncertainty-aware planners can ask supervisors for help under ambiguity, while interactive multimodal systems can choose epistemic actions to gather visual, acoustic, haptic, or proprioceptive observations [18], [19]. They motivate AI-assisted diagnosis and information seeking, but do not themselves define which observation qualifies as action-specific evidence, how it is bound to a proposal, or who may authorize finalization. The proposed framework supplies that verification and authority boundary. Selective prediction supplies Accept, Reject, and Abstain outcomes [20]. Provenance and verifiable-sensing work motivate checkable records [21]–[23]; safety and assurance cases

motivate explicit claim–evidence structure [24]; runtime assurance protects execution after a decision [25]; and zero-trust and capability-based mechanisms inform delegated command authorization [26], [27]. These mechanisms address different layers. A valid record does not grant action authority, and authorized finalization does not replace current-state runtime enforcement. Contract-based design and assume–guarantee reasoning associate components with environmental assumptions and behavioral guarantees, supporting compositional design, refinement, and verification [28]. Such contracts support compositional verification of modular robots and ROS nodes [29]. Our evidence contract instead declares action-specific claims and validity conditions for proposal-bound records at the permitted finalizer after proposal formation; it does not specify component behavior under environmental assumptions. They are complementary: component contracts constrain behavior; an evidence contract governs what information may justify an action. Our contribution is to make the post-proposal state an explicit communication framework. It binds application-declared evidence requirements to proposal-specific records, separates verification from authorized finalization and runtime enforcement, and exposes evidence transfer and evidence coordination as distinct communication functions. Related fields contain individual elements of this design; the framework integrates them around the verification gap and a common episode boundary. Table I is a representational counterexample, not an impossibility theorem: a richer proposal could carry these fields. The point is to preserve them as explicit, independently reportable framework objects. III. P OST-S EMANTIC C OMMUNICATION F RAMEWORK Section II identified episode distinctions that a proposalonly representation can hide. We now define the proposed framework that makes those distinctions explicit and communicable; this is the paper’s main contribution. The framework answers four questions: what evidence is required; how records are validated and combined; who may finalize and what remains for runtime control; and how communication can transfer evidence or coordinate delivery. Figure 2 summarizes the resulting architecture. A. Evidence Requirements and Records An evidence contract is the application-declared set of evidence requirements and validity rules that must be satisfied before an action can be finalized. It specifies the required claims, acceptable record modalities and sources, support and conflict semantics, freshness and uncertainty limits, provenance checks, proposal binding, and evidence deadline. We use evidence requirements for the individual conditions and evidence contract for the formal collection of those conditions. A communication policy may change delivery but must not silently relax this contract. An evidence record identifies its claim, relation to that claim, modality, source, measurement time, freshness limit,

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TABLE I S AME P ROPOSAL , D IFFERENT ACTION O UTCOMES .

Changed condition

Proposal-only view

Evidence-aware view

Required response

Proposal binding

“Proceed” is unchanged.

The record hash refers to an earlier proposal.

Freshness / expiry

“Proceed” is unchanged.

Admissible conflict

“Proceed” is unchanged.

Finalization authority

“Proceed” is unchanged.

A required record expires before finalization. A validated record conflicts with a required claim. The endpoint holding sufficient records is not authorized to finalize.

Abstain: the record cannot satisfy the current requirements. Abstain: evidence is no longer timely. Reject before testing support completeness. Make the required evidence available to the authorized finalizer, or abstain.

Semantic Proposal Evidence Contract Available Evidence Records

Receiver transfers required record

Reject

Verifier

Accept

Authorized Finalization

Runtime Gate

evidence record

Finalizer re-evaluates the evidence set

b) Transfer: expands evidence reachability

Abstain Evidence Gap

Authorization Policy

acquire | transfer | coordinate a) Post-semantic framework

Receiver-held record IDs

evidence status

Sender forwards only missing records

selected records c) Coordination: suppresses redundant payload

Fig. 2. The Post-Semantic Communication Framework. (a) A semantic proposal, an application-declared evidence contract, and available evidence records enter a common verifier. An admissible conflict yields Reject; complete support with no admissible conflict yields Accept, which can be finalized only under the separate authorization policy; missing, invalid, stale, or incomplete evidence yields Abstain and an evidence gap. The gap may trigger acquisition, transfer, or coordination followed by re-verification, while the runtime gate remains downstream of authorized finalization and outside the present evaluation. (b) Evidence transfer moves a required record to the finalizer, expanding evidence reachability. (c) Evidence coordination exchanges record-status information so that the sender forwards only missing records, suppressing redundant payload; status is not evidence. Acquisition is a future extension, whereas Section IV evaluates transfer and coordination.

provenance, uncertainty, proposal binding, and payload or content hash. These fields state which contract item the record can satisfy and allow a verifier to check the record mechanically. They do not define a new data type: an image, radio observation, signed state estimate, or reference can be an evidence record when it carries the required attributes. In the warehouse example, one record addresses corridor clearance and another addresses the absence of a moving obstacle. Proposal binding prevents a record for an earlier route or control cycle from satisfying the current requirements. Decision-time freshness prevents a record that was valid when transmission began from being accepted after expiry. Provenance, source, calibration, and uncertainty rules determine whether the application admits the record. A delivery policy may change packetization, routing, references, or interaction without changing any of these tests.

B. Evidence Verification Supporting and conflicting records traverse the same validation pipeline. Expired, untrusted, calibration-revoked, excessively uncertain, or binding-mismatched records are inadmissible: they can neither satisfy an evidence requirement nor

trigger Reject. This common path prevents an invalid negative observation from bypassing the checks applied to support. The verifier follows the principle Conflict First, Then Sufficiency. Among admissible records, any conflict produces Reject; a complete supporting set with no conflict produces Accept; and every remaining case produces Abstain. Reject reports a contradiction. Abstain reports that the declared evidence requirements were not completed. A conditional record error can still create incorrect support, so verification establishes compliance with the declared contract rather than physical truth. An unresolved verification gap takes one of two forms: an evidence gap, when required admissible records are missing, invalid, stale, incomplete, or unavailable at the permitted finalizer; or an authority gap, when evidence is sufficient but authorized finalization is unavailable. An admissible conflict is not a gap: it is a resolved negative outcome that produces Reject. An inadmissible conflict does not enter the verifier’s admissible set and therefore cannot trigger Reject. C. Finalization and Runtime Safety Evidence sufficiency, authorized finalization, and runtime safety are three separate responsibilities. Evidence sufficiency

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is the verifier’s result over admissible records. An authorization policy is a separate application declaration that identifies the endpoint or endpoint set permitted to turn an Accept result into an accountable action decision. Authorized finalization requires both verifier Accept and membership in that declared set; authority is not part of the evidence contract. Runtime safety is the later decision of an independent gate using current physical conditions. An agent can contribute a record without acquiring permission to act. An authorized finalizer can use remote records without claiming to have measured them locally. If sufficient records are assembled at an unauthorized endpoint, the records must become available to the declared finalizer or the system must abstain. A content-addressed manifest may preserve record-set identity across that handoff, but it creates neither authority nor freshness. The runtime gate receives a finalized action and may return ACT or STOP. It can account for conditions not represented in the evidence contract, including a new obstacle or degraded actuator. Section IV evaluates only through authorized finalization. It does not evaluate runtime-gate performance, sensorstatement correctness, operational credential enforcement, or physical safety. D. Evidence Transfer and Coordination Post-semantic communication can serve two functions. Evidence transfer carries an admissible record that the authorized finalizer does not yet hold. For sender finalization, successful feedback may return a receiver-held record and thereby enlarge the admissible set reachable before finalization. This distinction gives Feedback a less obvious role: even when the sender retains finalization authority, the reverse message may carry missing evidence back to the decision point rather than merely report receiver state. In contrast, evidence coordination reports which records are already held at the receiver so that the sender can avoid transmitting redundant payload. When the receiver finalizes, Feedback instead coordinates delivery around records already available at the decision point. The status message guides delivery but does not satisfy an evidence requirement. The controlled evaluator compares the formal policies Sender/One-way, Sender/Feedback, Receiver/One-way, and Receiver/Feedback. The first term fixes the authorized finalizer; the second changes interaction. A One-way policy sends all validated sender-held records. Feedback adds a reverse logical message. Under receiver finalization, loss of status triggers the declared One-way fallback, so coordination does not acquire an artificial reachability advantage. Both functions have costs. A reverse message can be lost, add fixed latency, age a record past its lifetime, or exhaust the decision deadline. Conversely, a short status exchange can suppress a large redundant record. These are communication effects; changes in the evidence contract, finalizer, or runtime gate must be evaluated separately. The framework therefore imposes four comparison invariants: evidence requirements remain fixed within a communication comparison; supporting and conflicting records share

one validation boundary; evidence location does not confer finalization authority; and runtime outcomes are not credited to pre-action verification. Section V-B carries these invariants into the reporting checklist. IV. F RAMEWORK C HECKS AND C OMMUNICATION S TUDY A. Questions and Setup This section checks the framework’s internal distinctions and implementation consistency, and then studies communication choices under controlled assumptions. It does not evaluate deployment effectiveness or runtime safety. The analysis asks three questions. RQ1: Can the framework distinguish sameproposal episodes that differ in proposal binding, freshness, conflict, or finalization authority? RQ2: Does the evaluator expose evidence transfer and evidence coordination as distinct observable effects? RQ3: Can One-way and Feedback be compared while evidence requirements, finalizer, and evidence quality are held fixed? The synthetic setup has two evidence items and two endpoints. Each endpoint observation is missing, invalid, supporting, or conflicting; forward and reverse delivery each succeed or fail. The same 4096 weighted states are enumerated once and reused across all four communication cases. Records follow the common validation path, freshness is rechecked at decision time, and the finalizer is fixed within each comparison. The episode begins after proposal formation and ends at authorized finalization. The common 10-ms processing time is included, and the baseline deadline is 33 ms. Section IV-B operationalizes the cases motivated by Table I. Unconditional coverage is the probability of timely Accept over all proposal episodes. Selective error is the ground-truthunsupported mass among timely accepts. Expected evidence payload counts transmitted evidence-record bytes over all proposal episodes, including episodes that later Reject or Abstain. These metrics describe the declared finite model; they are not measured robot, wireless, or safety results. Headers, acknowledgments, retransmissions, channel occupancy, airtime, and energy are not represented by the payload field. B. Framework Checks RQ1 – structural distinctions. The artifact executes 11 checks and passes all 11. Complete admissible support with no conflict returns Accept; an admissible conflict returns Reject even before support is complete; and incomplete support returns Abstain. Expired, untrusted, binding-mismatched, calibration-revoked, and excessively uncertain conflicts do not trigger Reject. Finally, complete evidence at an unauthorized endpoint does not produce authorized finalization. These checks operationalize the distinctions in Table I; they test declared framework logic, not the physical correctness of a sensor claim. RQ2 – transfer versus coordination. With timing and expiry removed for this structural check, sender-finalized Feedback uniquely reaches a complete admissible support set in 64 enumerated states. Under the declared synthetic state distribution, these states carry 8.3% probability mass. This is an evidence-transfer effect, not an estimate of real episode

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Sender finalization fixed Receiver finalization fixed Feedback effect: expands evidence reachability Feedback effect: suppresses redundant payload Decision deadline D (ms)

50

40

30

20

10 0

2

4

6

Fixed latency per logical message δ (ms) One-way

Feedback

8

0

2

4

6

8

Fixed latency per logical message δ (ms) Infeasible

baseline (0.5, 33)

Fig. 3. Controlled communication study under the declared synthetic model, with evidence requirements and evidence-quality assumptions fixed across cases and finalization authority fixed within each panel. Orange, blue, and gray denote Feedback selected, One-way selected, and infeasible, respectively. Every feasible sender-finalized cell is orange: reverse transfer can make receiver-held evidence available at the sender decision point, while One-way violates the selective-error requirement in those cells; tighter timing makes both alternatives infeasible. For receiver finalization, Feedback is selected at low latency, One-way when the extra reverse message makes Feedback miss the coverage requirement, and both eventually become infeasible. Feasibility requires at least 40% unconditional coverage and at most 0.75% selective error; the star marks the baseline.

frequency. Under receiver finalization and the declared Oneway fallback, the pre-timing reachability mismatch between One-way and Feedback is 0 states. Feedback instead reduces expected evidence payload by 6.49 KiB per proposal episode, an evidence-coordination effect without enlarging the reachable evidence set; its extra message can nevertheless change the timely result. At the ordinary timing baseline, the generated expected payloads are 9.80 KiB for One-way, 8.45 KiB for sender-finalized Feedback, and 3.31 KiB for receiver-finalized Feedback; the matched receiver-finalized One-way value is 9.80 KiB. These checks isolate the two mechanisms that Figure 3 later combines with timing: transfer changes the reachable evidence set at a sender finalizer, whereas coordination leaves pre-timing reachability unchanged under the declared fallback but reduces payload at a receiver finalizer. C. Communication Study RQ3 – requirement-preserving communication choice. RQ3 adds message latency, record ageing, and the decision deadline to the two structural effects isolated in RQ2. Figure 3 holds the two evidence requirements, authorized finalizer, evidencequality model, record sizes, link rate, processing time, initial ages, and lifetime fixed. It varies only fixed latency per logical message and the decision deadline. A candidate is feasible only if unconditional coverage is at least 40% and selective error is at most 0.75%. Among feasible candidates, the declared rule minimizes expected evidence payload, then logical-message count, with an exact tie assigned to One-way. The resulting map contrasts the two communication benefits with their timing costs.

The orange region denotes cells in which Feedback is selected; it does not imply a single selection reason. The senderfinalized panel exposes the less obvious role of Feedback. Although the sender retains finalization authority, all 675 feasible plotted cells select Feedback under the declared model. In each, Feedback is the only feasible candidate because Oneway exceeds the selective-error ceiling. Feedback can transfer receiver-held evidence to the sender decision point, whereas One-way can use only sender-held evidence there. As latency rises or the deadline tightens, both alternatives fail the declared feasibility requirements in the other 1,998 cells; no senderfinalized cell selects One-way on the plotted grid. The receiver-finalized panel shows the complementary role. Feedback does not enlarge pre-timing evidence reachability under the declared fallback; it uses receiver-held record status to suppress redundant forward payload. Of the 836 Feedback-selected cells, both alternatives are feasible in 830 and Feedback minimizes expected payload; in the other 6, only Feedback is feasible. The 441 One-way-selected cells occur when the extra reverse message makes Feedback miss the coverage requirement. In the remaining 1,396 cells, both alternatives miss coverage and are infeasible. Where finalization occurs determines what Feedback is for: bringing missing evidence back to a sender finalizer or avoiding redundant evidence delivery to a receiver finalizer. This finalizer-dependent selection structure is specific to the declared synthetic model and plotted grid and does not establish a protocol ranking beyond those conditions.

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TABLE II M INIMUM R EPORTING C HECKLIST FOR P OST-S EMANTIC C OMPARISONS .

Layer

Report

Confounding avoided

Evidence

Requirements; support/conflict semantics; record source, modality, freshness, provenance, uncertainty, and proposal binding. One-way or Feedback; feedback function; success model; expected evidence payload per proposal episode; logical-message count; latency and deadline accounting. Authorized finalizer; evidence-assembly location; credential and handoff assumptions. Gate inputs, re-evaluation time, stop or backup action, and the execution-observation boundary.

A change in what counts as sufficient is not mislabeled as a delivery gain.

Delivery

Finalization Runtime

V. D ISCUSSION AND F UTURE D IRECTIONS A. Research Directions Evidence-gap detection separates deterministic checking from AI assistance. Contract checks identify missing, invalid, expired, or binding-mismatched records; authorization checks find an unavailable finalizer; admissible conflict yields Reject. Embodied multimodal models integrate language and sensor inputs [16]; uncertainty-aware planners seek help under ambiguity [18]. Within our framework, they could propose evidence needs or clarifications; checks still distinguish evidence gaps, authority gaps, and conflicts. Neither confidence nor diagnosis is an evidence record or replaces checks. Active acquisition and representation maps camera, LiDAR, contact, peer, human, or radio sensing to named requirements under freshness, uncertainty, and deadlines. Interactive agents select visual, acoustic, haptic, and proprioceptive informationgathering actions [19]; ISAC and perceptive mobile networks jointly support radio communication and environmental sensing [30], [31]. Within our framework, observations qualify as evidence only after requirement mapping and validation of proposal binding, provenance, freshness, uncertainty, and source. Semantic and task-oriented communication support task-relevant representation and delivery [5], [6]. The representation must additionally preserve the claim relation and those validation attributes. Closed-loop re-inference and runtime integration could build on embodied multimodal models, LLM planners, and world-model or digital-twin architectures that exemplify reasoning, replanning, and state-dependent revision [4], [16], [17]. Within our framework, such engines could use validated evidence records to revise a proposal. Revision creates a new binding, may select another application-approved template, and requires revalidation. The runtime gate remains downstream and unevaluated. AI agents may diagnose and plan, but the evidence contract, common validator, authorization policy, and runtime gate remain explicit decision boundaries. B. Reporting Guidelines Table II gives the minimum fields needed to preserve the separations in Section III when comparing communication designs.

Payload suppression is not confused with total onwire or energy reduction. Evidence location is not mistaken for action authority. Verifier Accept is not presented as a physical-safety result.

First, each field should be declared before comparison as fixed, varied, or unobserved. Evidence requirements, finalizer, freshness, and deadline are application inputs; the communication policy is the experimental factor. Second, an episode-level trace should link the proposal, admissible and rejected records, messages, verifier outcome, authorized finalizer, and any observed runtime result. Stable record identifiers and validation outcomes can preserve this structure without publishing sensitive payloads. Third, aggregate metrics should use explicit and common denominators. Unconditional coverage and expected payload use all proposal episodes; selective error uses timely Accept episodes; runtime rates use only episodes in which execution was observed. This accounting keeps the framework layers comparable without inventing unmeasured outcomes.

VI. C ONCLUSION A task-effective proposal is not yet a justified physical action. The verification gap is the mismatch between such a proposal and the valid, timely, proposal-bound evidence and authorization required at the permitted finalizer before action. Post-semantic communication makes explicit what must happen after a meaningful proposal is formed but before a physical action may proceed. The Post-Semantic Communication Framework makes the missing objects and responsibilities explicit through evidence requirements, proposalbound records, conflict-first verification, authorized finalization, and a downstream runtime boundary. Where finalization occurs determines what Feedback is for: evidence transfer brings missing evidence to a sender finalizer, whereas evidence coordination avoids redundant evidence delivery around records already held at a receiver finalizer. The finite-state checks verify implementation consistency with the declared operational distinctions, while the controlled communication study demonstrates one requirement-preserving comparison of One-way and Feedback. The reporting guidelines carry the same separations into future studies. Runtime effectiveness and physical safety remain subjects for measured systems; runtime control stays downstream of verification and authorized finalization.

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A PPENDIX A F ORMAL O BSERVATIONS AND S TRUCTURAL P ROPERTIES Observation 1 — Proposal-only representations can collapse distinct outcomes. Let π(w) be a reduced proposal representation and let a⋆ (w) be the required outcome. Suppose two physical or system states satisfy π(w1 ) = π(w2 ),

a⋆ (w1 ) ̸= a⋆ (w2 ).

(1)

If the outcome difference is caused by discarded proposal binding, decision-time freshness, admissible conflict, or finalization authority, no decision rule based only on π(w) can be correct in both states. Justification. For a proposal-only rule g, equality of the reduced representations gives g(π(w1 )) = g(π(w2 )).

(2)

The required outcomes differ, so the common value must disagree with at least one state. This is a statement about the reduced representation; a richer semantic representation could carry the omitted fields. □ Structural Property 1 — Conflict-first verifier consistency. Let Vq (e, d, t) be the common validation predicate for evidence record e, proposal d, decision time t, and contract q. Define the admissible set as Eq (d, t) = {e : Vq (e, d, t) = 1}.

(3)

The verifier   an admissible conflict exists, Reject, Γq (d, Eq ) = Accept, required support is complete, (4)   Abstain, otherwise satisfies three properties: inadmissible records neither contribute support nor trigger Reject; admissible conflict precedes support completeness; and complete admissible support without conflict is accepted. Argument. Validation first removes every record for which Vq = 0, establishing the first property. The first branch handles every remaining conflict before the support branch. If that branch is false and the required support is complete, the second branch applies; all residual cases enter the third branch. These exhaustive cases establish consistency with the declared verifier rule. They do not establish physical safety or deployment correctness. □ Authorized finalization is a separate predicate. For endpoint i and declared authorization policy A, an Accept result can authorize action only when Γq = Accept

and

i ∈ A.

(5)

A PPENDIX B C OMMUNICATION , F RESHNESS , AND AVAILABILITY M ODEL Fixed latency δ is charged once per logical message, evidence payload is serialized at rate R, and common pre-action

processing Tp covers validation, assembly, and finalization. The ready times are T1 (Bf ) = δ + 8Bf /R + Tp , TF (Br , Bf ) = 2δ + 8(Br + Bf )/R + Tp .

(6) (7)

For initial record age Ae , lifetime Le , and deadline D, a record used at finalization must satisfy Ae + Tx ≤ Le ,

Tx ≤ D.

(8)

For one evidence item, let endpoint holding indicators have marginal probabilities qS and qR and Pearson correlation ρ. The evaluator uses p Pr(HS = 1, HR = 1) = qS qR + ρ qS (1 − qS )qR (1 − qR ). (9) The joint probability must lie within the Fréchet bounds; the remaining three Bernoulli cells follow from the marginals. This correlation applies across endpoints for each item, not between the two independent claim truths. A PPENDIX C F EEDBACK F UNCTION S EPARATION AND R EQUIREMENT-BASED S ELECTION Structural Property 2 — Separation of feedback functions. Consider a fixed evidence contract and finalizer. For sender finalization, if a receiver holds a missing admissible record, the reverse transfer succeeds, and the record remains valid at decision time, Feedback can strictly enlarge the admissible evidence set reachable at the finalizer. For receiver finalization under a One-way fallback, coordination does not enlarge pretiming evidence reachability relative to One-way, but successful status delivery can weakly reduce forward evidence payload when the receiver already holds a required record. Added latency or expiry may still change the timely outcome. Argument. In the first case, let ES be the sender-held admissible set and eR a required record held only by the receiver. Successful transfer yields ES ⊂ ES ∪ {eR },

(10)

with strict inclusion; the added record may complete support. In the second case, One-way sends every sender-held admissible record. Delivered status lets the sender omit only records already available at the receiver; lost status invokes the same One-way set. The receiver’s pre-timing union is therefore unchanged, while transmitted payload is no larger and is smaller whenever a positive-size redundant record is omitted. Feedback has an extra logical message, so decisiontime freshness and deadline tests can reverse the timely outcome. □ For fixed finalization authority, let Cx , Ex , Bx , and Nx denote unconditional coverage, selective error, expected evidence payload per proposal episode, and logical-message count for interaction x. Feasibility requires Cx ≥ Cmin ,

Ex ≤ Emax .

(11)

Among feasible candidates, the controlled illustration minimizes (Bx , Nx , Ix ) (12)

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lexicographically, where Ix resolves an exact tie in favor of One-way. This is an application-declared ordering rather than a general utility. Sender-finalized Feedback can improve Cx through transfer; receiver-finalized Feedback can reduce Bx through coordination. In either case, an added message can reduce timely coverage through reverse loss, latency, record ageing, or expiry. A PPENDIX D S YNTHETIC S ETUP AND R EPRODUCTION B OUNDARY Table III records the fixed synthetic declarations. The perclaim truth prior and per-endpoint evidence availability happen to be 0.90 but are different quantities. The two truth bits are independent; availability for the same item is correlated across endpoints as defined in Appendix B. TABLE III S YNTHETIC BASELINE D ECLARATIONS . Parameter

Baseline

Required evidence Claim-truth prior ptruth Claim-truth dependence Evidence availability q Conditional validity Evidence-relation error Endpoint correlation ρ Delivery success (pf , pr ) Records (BV , BR ) Link rate R Per-message latency δ Processing time Tp Decision deadline D Initial ages (AV , AR ) Evidence TTL

Visual clearance + Radio no-motion 0.90 per claim Independent 0.90 per endpoint/item 0.99 0.10 0.25 (0.99, 0.99) (10, 1) KiB 100 Mbit/s 0.5 ms 10 ms 33 ms (20, 15) ms 35 ms

Exact enumeration weights two truth bits, four endpointrecord observations, and two delivery bits. Missing, invalid, supporting, and conflicting observations share the same weighted 4096-state population in all four communication cases. Communication selects validated records, charges their bytes, computes action-ready time, revalidates lifetime, and returns Accept, Reject, or Abstain; a separate authorization check determines whether Accept can be finalized. Enumeration removes Monte Carlo sampling noise only. The 11 generated RQ1 checks cover complete and incomplete support, an admissible Visual conflict, conflict before support completeness, six conflicts made inadmissible by provenance, binding, expiry, calibration, source, or uncertainty, and complete evidence at an unauthorized endpoint. They exercise Accept, Abstain, and conflict-first Reject, verify that inadmissible conflicts do not trigger Reject, and separate evidence sufficiency from the authorization policy. RQ2 uses the same weighted states without deadline or lifetime truncation. The sender-transfer metric measures states in which Feedback reaches complete support and One-way does not. The receiver metric checks One-way/Feedback reachability under the declared status-loss fallback, while an unconditional expectation measures evidence-record bytes suppressed by coordination. Timing is restored for the baseline values and Figure 3.

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