{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp05_complete_proposal_portfolio20_20260803","cell_id":"invariant_mode_decomposition_design__information_theory","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"cand05_trapping_mode_relay_routing","proposal_index":5,"version":0,"title":"Trapping-Mode Routing Repair for Intermittent Relay Networks","problem":"An intermittently connected store-and-forward network routes each undelivered packet among relay nodes until it reaches a destination gateway. Operators assess individual links, node queues, and nominal paths, but those coordinates do not reveal how the routing policy moves packet-location probability across the network as a whole. A combination of relay nodes can form a slowly decaying or oscillatory mode in the transient routing operator: packets circulate within that joint pattern even though no single link appears defective. Repairing the worst link or adding retries can leave the trapping mode intact and consume transmission opportunities without moving information toward the gateway.","actors":["Network architect who defines the routing and custody-transfer policy","Operations controller who approves routing-table and gateway-contact changes","Relay-node operators responsible for local availability and duty-cycle limits","Information producers whose packets enter the relay network","Destination service that receives and acknowledges delivered packets"],"observable_state":"After comparable packet injections, the distribution of undelivered packet locations repeatedly aligns with a similar cross-node pattern and leaves that pattern slowly over successive routing epochs. The corresponding transient routing operator has a nontrivial mode with gain near the persistence boundary or an oscillatory mode, while constituent links individually satisfy their ordinary success-rate checks.","consequence":"Packets can miss delivery deadlines and occupy relay storage, contact time, or energy while cycling through a structurally persistent node combination that coordinate-level routing metrics do not identify.","affected_objective":"Move information to the destination within declared deadline and transmission-resource constraints while maintaining node duty-cycle, coverage, and service-priority requirements.","intervention":"For one fixed topology, contact regime, and custody-routing policy, define a transient operator Q mapping the distribution of undelivered packet locations across relay nodes from one routing epoch to the next; delivery to the gateway is represented as mass leaving Q. Decompose Q, exclude any destination state, and classify nontrivial relay modes by decay rate and oscillation. Read node loadings in the slowest consequential modes as a trapping-participation map, then use a modal sensitivity sweep to perturb feasible forwarding probabilities, recirculating edges, and scheduled gateway contacts. Select a bounded set of routing changes that most strongly lowers the persistence of the trapping mode while holding transmission opportunities and duty-cycle ceilings fixed: reduce transfers that recirculate packet mass inside the mode and redirect those opportunities toward edges or custody windows that leak mass toward the gateway. Validate the modified policy on held-out contact sequences, retain residual visibility, and withdraw the policy when topology or modal drift invalidates the fitted operator.","structural_mapping":[{"archetype_element":"Transformation Scope","domain_realization":"The one-epoch transient routing operator over non-destination relay nodes for a frozen topology, contact regime, and custody-transfer policy."},{"archetype_element":"State-Vector Definition","domain_realization":"A vector giving the probability or normalized expected mass of undelivered packets located at each relay node at an epoch boundary."},{"archetype_element":"Invariant Mode Basis","domain_realization":"Cross-node packet-location patterns whose direction is approximately preserved as the routing policy advances another epoch."},{"archetype_element":"Modal Gain Spectrum","domain_realization":"Each eigenvalue describes the rate and, where applicable, oscillation with which an undelivered-location mode decays under repeated routing."},{"archetype_element":"Dominant Mode Selection Rule","domain_realization":"After excluding destination behavior, a slow mode becomes actionable when its persistence, deadline consequence, conditioning, and stability across held-out contact sequences meet declared criteria."},{"archetype_element":"Stable/Unstable Mode Partition","domain_realization":"Modes are classified as rapidly escaping, slowly escaping, marginally trapped, or oscillatory within the specified routing regime."},{"archetype_element":"Modal Intervention Map","domain_realization":"Changes to forwarding probabilities, recirculation edges, and gateway-contact opportunities are mapped to changes in modal persistence, delivery behavior, and node resource use."},{"archetype_element":"Mode-Coupling Register","domain_realization":"The analysis records routing changes that damp one trap while strengthening another, shifting load to another node group, or coupling nearly degenerate modes."},{"archetype_element":"Reconstruction Residual Check","domain_realization":"Observed held-out packet-location trajectories are reconstructed from retained modes, and unexplained residuals are checked for deadline-relevant spatial or temporal structure."},{"archetype_element":"Mode Drift Monitor","domain_realization":"The mode directions, gains, ordering, and separation are re-estimated after contact, topology, gateway, routing-table, or node-availability changes."},{"archetype_element":"Interpretation Scope Contract","domain_realization":"A mode describes packet motion under a bounded routing regime; it is not evidence that a node is defective or a guarantee for unmodeled disruptions and traffic interactions."}],"mechanism_mapping":[{"mechanism_slug":"eigendecomposition_workflow","role":"Factor the explicit transient routing operator into a complete set of cross-node modes and their epoch-to-epoch gains.","counterfactual_removal":"Without the decomposition, investigation remains focused on individual links and paths and cannot expose a packet-location pattern preserved by the whole routing policy."},{"mechanism_slug":"modal_stability_analysis","role":"Classify relay modes by how rapidly undelivered packet mass escapes, persists, or oscillates under repeated application of the policy.","counterfactual_removal":"Without stability analysis, a currently small trapping pattern cannot be distinguished from a large but rapidly clearing queue distribution."},{"mechanism_slug":"network_spectral_centrality_analysis","role":"Read entries of the selected slow-mode eigenvector as bounded node-level participation scores for locating where routing intervention can affect the trap.","counterfactual_removal":"Without the node loading map, the slow mode is mathematically visible but cannot be traced to concrete relay nodes, edges, or gateway-contact opportunities."},{"mechanism_slug":"modal_sensitivity_sweep","role":"Perturb feasible routing controls and rank their effects on modal persistence, deadline delivery, transmissions, and cross-mode load shifts.","counterfactual_removal":"Without the sweep, operators might act on the highest-loading node even when its available controls have little leverage or merely move the trap elsewhere."},{"mechanism_slug":"residual_reconstruction_test","role":"Test whether retained modes reproduce held-out packet-location trajectories and whether omitted residuals retain consequential trapping structure.","counterfactual_removal":"Without residual testing, an apparently damped leading mode could conceal a lower-energy route cycle that still causes deadline misses."},{"mechanism_slug":"spectral_gap_monitor","role":"Track the separation and directional stability of governed trapping modes as contacts and routing conditions evolve.","counterfactual_removal":"Without monitoring, a fixed routing repair could continue after the slow subspace rotates, mode ordering changes, or no distinct target remains."},{"mechanism_slug":"spectral_decomposition_report","role":"Record operator scope, node loadings, gains, conditioning, control sensitivities, couplings, residuals, and prohibited interpretations for operations review.","counterfactual_removal":"Without a bounded report, operators could mistake modal participation for node fault or apply a regime-specific routing change across incompatible conditions."}],"causal_chain":["The custody-routing policy moves an undelivered packet among relay nodes at each routing epoch while gateway delivery removes it from the transient state.","Repeated application of that policy acts on combinations of node occupancies, not on links independently.","A cross-node direction with gain near the persistence boundary retains packet mass inside a relay pattern even when its constituent links appear individually usable.","Eigendecomposition and stability classification expose that trapping direction and its rate of escape or oscillation.","Node loadings trace the mode back to participating relays, while outcome sensitivity identifies which feasible routing or gateway-contact controls can actually reduce its persistence.","A bounded routing-table change redirects fixed transmission opportunities away from internal recirculation and toward exits from the trapping subspace.","Held-out trajectory and residual tests determine whether the changed policy releases packet mass toward the gateway without creating another consequential mode or violating node constraints.","Spectral and topology monitoring withdraw the modified policy when the operator no longer supports its modal rationale."],"baseline":"Route by shortest nominal path, per-link delivery estimate, local queue pressure, or static forwarding preference, and troubleshoot deadline failures by adjusting the worst visible link or increasing retries without decomposing the transient network update.","nearest_rivals":["Backpressure routing based on local queue differentials","Shortest-path or expected-transmission-count routing using per-edge estimates","Epidemic or bounded-copy forwarding that trades additional transmissions for delivery opportunity","Direct optimization of expected gateway hitting time without retaining a modal interpretation","Scheduled gateway-contact expansion based on node traffic volume","End-to-end reinforcement or simulation-based routing optimization under the same resource constraints"],"remaining_contrastive_claim":"The candidate's testable distinction is that routing controls are chosen to damp consequential invariant patterns of undelivered packet location, rather than to improve individual links, shorten nominal paths, or respond only to local queues. Whether that criterion improves held-out delivery behavior under matched transmission and duty-cycle budgets remains to be tested.","authority_safety":{"decision_authority":"The network architect may fit and simulate candidate operators. The operations controller and affected relay-node operators must approve any routing-table or contact-schedule change under the existing service and duty-cycle rules.","authorized_first_step":"Replay one frozen routing policy against a bounded set of archived or simulated contact sequences, estimate its transient modes, and compare candidate routing changes offline without sending or rerouting live packets.","excluded_actions":["Changing live routing tables, custody rules, gateway schedules, or node duty cycles during the first evidence step","Reducing delivery priority, acknowledgement requirements, or resource reservations for protected traffic classes","Increasing transmissions or energy use beyond the matched evaluation budget","Treating a high node loading as evidence of operator fault, negligence, or physical node failure","Deploying a policy when the routing operator is materially nonstationary, eigenvectors are ill-conditioned, or residual trapping remains structured","Applying the model to flooding or multi-copy dynamics unless the state and operator are redefined and independently validated"],"halt_rollback":"Restore the signed baseline routing table if the candidate breaches a delivery, coverage, priority, storage, energy, or duty-cycle limit; creates a new persistent mode; produces consequential structured residuals; disconnects an authorized route; or encounters topology and contact conditions outside its scope. Preserve the prior table and configuration metadata throughout any canary evaluation."},"negative_tests":{"strongest_counterevidence":"Under identical traffic, transmission, and duty-cycle constraints, backpressure, expected-hitting-time optimization, or another direct routing rival meets every declared held-out delivery criterion at least as well, while the fitted slow modes fail to persist across admissible contact sequences.","problem_falsifier":"Deadline misses are explained by source injection timing, destination unavailability, or a single capacity bottleneck, and a coupled transient routing operator reveals no reproducible nontrivial packet-location mode beyond those coordinate-level causes.","intervention_falsifier":"A stable and consequential trapping mode is identified, but routing changes selected for leverage over it do not improve the predeclared held-out delivery and resource criteria relative to the strongest budget-matched rival.","risks":["Intermittent contacts may change too quickly for a stationary transient operator to have a useful interpretation window.","A non-normal or nearly defective routing operator may produce fragile eigenvectors and misleading node loadings.","Reducing recirculation may remove a path that provides resilience under an unmodeled outage.","Damping one mode may transfer congestion or packet residence time to another node group.","A single-packet linear model may omit queue interactions, priority scheduling, acknowledgements, or correlated traffic bursts.","Contact traces used for fitting may omit rare but authorized operating regimes.","Node-level modal scores could be misused as performance rankings rather than bounded structural participation measures."]},"next_evidence_step":"Freeze one topology, destination gateway, custody rule, routing table, traffic class, epoch definition, transmission budget, duty-cycle limits, and bounded contact-sequence set. Divide contact sequences and packet injections into fitting and held-out partitions. Estimate Q only on the fitting partition, compute its complete spectrum and eigenvector conditioning, identify a slow subspace using declared persistence, consequence, and separation criteria, and choose one bounded routing modification through the sensitivity sweep. On held-out sequences, compare deadline delivery, gateway hitting time, transmissions, node residence, duty-cycle compliance, residual structure, and mode stability against the unchanged policy, backpressure, expected-transmission-count routing, bounded-copy forwarding, and direct expected-hitting-time optimization. The result may authorize only a reversible shadow or isolated test-network canary.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 addressed numerical reconstruction-error propagation inside a predictive telemetry codec and transmitted mode-aligned refresh coefficients. Proposal 2 addressed protected-information disclosure through correlated analytics outputs and filtered or noised high-gain disclosure modes. Proposal 3 addressed scientific-array recoverability after storage-domain failures and changed parity projections and shard placement. Proposal 4 addressed semantic substitutions in a spoken-command alphabet and redesigned command tokens and confirmation checks. This proposal addresses packet-location persistence across an intermittent relay topology and changes routing probabilities, recirculating edges, and gateway-contact allocation to release trapping modes. Its state, transformation, actors, consequence, intervention, and adoption setting are distinct from each earlier proposal and require none of their codec, privacy-release, archival-storage, or command-vocabulary systems.","revision_record":{"parent_version":null,"progress_targets_addressed":[],"conceptual_changes":[],"operational_changes":[],"evidence_changes":[],"claim_changes":[]}}