Joint Spatial-Temporal Graph

Mechanism

The joint spatial-temporal graph composes the mesh-derived coordinate primitive of Chapter 16 with the mesh-derived time primitive of Chapter 17. Each agent maintains both coordinate bearings and time bearings within a single governance-chain-preserving structure. The spatial side resolves agent positions through cooperative localization from admitted range observations and anchor positions; the temporal side resolves agent time-offsets through a cooperative time-estimation engine that combines synchronization observations and temporal anchor contributions. Where direct-anchor synchronization is insufficient, a transitive time-propagation extender produces agent time-offsets through neighbor references.

The composition is driven by a joint admission interface that admits combined range-and-synchronization observations, wherein the ranging exchanges produce jointly-optimized spatial and temporal estimates rather than feeding two separately maintained solvers. Because the same governance-credentialed inter-agent exchange carries both the ranging measurement and the timing measurement, the spatial and temporal estimates for the participating agents are produced together rather than in sequence.

A joint uncertainty propagator produces per-agent spacetime uncertainty across the graph. A four-dimensional observation emitter produces observations carrying (x, y, z, t) together with joint uncertainty, and a joint-lineage recorder links spatial and temporal lineage into a single spacetime derivation record. Downstream consumers therefore read a unified spacetime reference, with its uncertainty, rather than reading separately maintained position and time.

Operating Parameters

The temporal side of the graph is maintained continuously. A drift-compensation mechanism continuously compensates local-clock drift through fresh synchronization exchanges, and a clock-model learning mechanism refines per-agent drift characterizations through governance-credentialed training per Chapter 12. Each participating agent maintains a local clock with governance-policy-characterized drift properties, so the admissibility and weighting applied to its contributions follow governance policy rather than a fixed rule.

The graph admits heterogeneous observation sources. The time side combines synchronization observations between participating mesh agents and governance-credentialed temporal anchor contributions, and an evidential-fusion mechanism combines mesh-derived time with externally-sourced time, including satellite time, network time, and atomic reference, through the composite admissibility evaluator of Chapter 4. When no anchor observations are available, an anchor-less temporal bootstrap mechanism produces a relative-only temporal frame, and a time-frame federation mechanism aligns independently-maintained temporal frames where multiple frames are present.

Alternative Embodiments

The mesh-derived time primitive operates through cooperative consensus without a master clock and self-organizes through the participating mesh agents. It does not depend on a central time authority, a stratum-1 server, or a designated grandmaster clock. Time-offsets are determined by the cooperative time-estimation engine from synchronization observations and anchor contributions, and where direct-anchor synchronization is insufficient the transitive time-propagation extender produces agent time-offsets through neighbor references.

The time-synchronization mechanism produces time-synchronization observations between participating mesh agents through at least one of a plurality of synchronization modalities. The joint admission interface admits combined range-and-synchronization observations, so a single governance-credentialed ranging exchange can serve both the spatial and the temporal estimate. Where relativistic effects are significant, a relativistic-consistency evaluator is applied, and the four-dimensional observation emitter carries the resulting joint estimate as (x, y, z, t) with joint uncertainty.

Lineage support is integral to the architecture. A time-lineage recorder records each synchronization exchange, anchor admission, time-estimation event, frame alignment, rejection event, federation event, and timestamp attestation in the governance-chain lineage field, and the joint-lineage recorder links spatial and temporal lineage into a single spacetime derivation record. Downstream audit reconstructs the timestamp's lineage, the synchronization chain producing the attesting agent's time, the composite admissibility evidence, and the authority-credential chain from the governance lineage, supporting regulatory, legal, forensic, and governance-enforcement audit.

Composition With Mesh Operation

The joint spatial-temporal graph composes with the broader mesh through a governance-credentialed timestamp attestation interface. The interface produces timestamp observations carrying the attesting agent's authority credential, mesh-derived time value, estimated time uncertainty, and cryptographic signature, and it admits a plurality of attestation patterns, including single-attester attestation, multi-attester consensus attestation producing a timestamp signed by a governance-policy-defined quorum of independent attesters for high-assurance applications, authority-hierarchy attestation, content-bound attestation, event-bound attestation, transaction-bound attestation per Chapter 20, and continuity-bound attestation per Chapter 10. The time value carried by a timestamp is accompanied by its estimated time uncertainty, so consumers evaluate timing-sensitive operations against the mesh-derived time and its uncertainty rather than against any single agent's local clock.

The architecture also resists adversarial timing. An adversarial-time rejection mechanism rejects spoofed, injected, or inadmissible time-synchronization observations, and a time-uncertainty propagator propagates synchronization uncertainty through the temporal graph to produce per-agent time-uncertainty estimates. Each rejection event is recorded in the governance-chain lineage by the time-lineage recorder, providing an audit trail of admission and rejection decisions.

Implementation Details

The temporal estimate is held current through two cooperating mechanisms. A drift-compensation mechanism continuously compensates local-clock drift through fresh synchronization exchanges, and a clock-model learning mechanism refines per-agent drift characterizations through governance-credentialed training per Chapter 12. Each agent maintains a local clock with governance-policy-characterized drift properties, and a time-uncertainty propagator propagates synchronization uncertainty through the temporal graph to produce per-agent time-uncertainty estimates.

Time admission combines internal and external sources. The cooperative time-estimation engine determines agent time-offsets through combination of synchronization observations and temporal anchor contributions, and an evidential-fusion mechanism combines mesh-derived time with externally-sourced time, including satellite time, network time, and atomic reference, through the composite admissibility evaluator of Chapter 4. Where direct-anchor synchronization is insufficient, the transitive time-propagation extender produces agent time-offsets through neighbor references. Where no anchor observations are available, the anchor-less temporal bootstrap mechanism produces a relative-only temporal frame, and the time-frame federation mechanism aligns independently-maintained temporal frames.

Lineage is persisted to the governance chain. The time-lineage recorder records each synchronization exchange, anchor admission, time-estimation event, frame alignment, rejection event, federation event, and timestamp attestation, and the joint-lineage recorder links spatial and temporal lineage into a single spacetime derivation record. This record supports deterministic reconstruction of each timestamp's derivation chain.

Distinction Over Prior Art

The mesh-derived time primitive is structurally distinguished from prior time-distribution architectures in several respects. Prior satellite-derived time services operate through broadcast signals from centrally-operated constellations whose acquisition is required for timing and whose denial precludes timing, whereas the present primitive produces time bearings from cooperating mesh agents without dependence on satellite availability. Prior network-time-protocol systems are client-server hierarchical and depend on centralized stratum-1 time servers, whereas the present primitive operates through cooperative consensus without a master clock. Prior precision-time-protocol systems require hierarchical master-slave configuration with dedicated grandmaster clocks, whereas the present primitive is master-less and self-organizes through mesh agents. Prior blockchain timestamp protocols timestamp at block-commit granularity, producing coarse timestamps with minute-scale precision, whereas the present primitive produces continuous governance-credentialed timestamps at observation granularity. Prior trusted-timestamp-authority systems centralize timestamp issuance at a single authority, whereas the present primitive produces multi-authority timestamps admissible through composite admissibility. Prior chip-scale atomic clocks provide high-precision time-of-day without distributed consensus, whereas the present primitive combines precision clock sources with distributed mesh consensus.

Disclosure Scope

The joint spatial-temporal graph mechanism is disclosed as a feature of the mesh-derived time primitive within U.S. Provisional Application No. 64/049,409. The joint spatial-temporal graph composing coordinate and time bearings in a single governance-chain-preserving structure, the joint admission interface for combined range-and-synchronization observations, the joint uncertainty propagator producing per-agent spacetime uncertainty, the four-dimensional observation emitter carrying (x, y, z, t) with joint uncertainty, the relativistic-consistency evaluator, and the joint-lineage recorder are each disclosed within the specification.

The unified spacetime reference enables applications requiring joint spatial and temporal consistency, including retrospective reconstruction of mesh state at any prior time with the known spatial configuration at that time, causality analysis for incident forensics determining the ordering and spatial propagation of events, cross-jurisdictional temporal consistency where observations span time zones or international date lines, multi-agent coordination requiring both spatial and temporal precision, scientific applications requiring relativistic corrections to both space and time, predictive modeling wherein spatial and temporal projections are jointly forecast per Chapter 5, and any governance-policy-defined spacetime-dependent application.