{"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":"cand03_weak_mode_parity_archive","proposal_index":3,"version":0,"title":"Weak-Mode Parity Design for Failure-Domain Archives","problem":"A distributed archive stores quantized scientific arrays as linear projection shards across several storage failure domains. Redundancy dashboards count available shards, replicas, or racks, but those coordinates do not show how the surviving shard operator represents combinations of source coefficients. Under a correlated outage, the survivor operator can retain many shards while weakly transmitting one joint source direction. Reconstruction then amplifies quantization and read noise along that direction, or loses it if the direction enters the operator's null space. Adding generic redundancy or repairing the most visibly depleted rack may leave the weak direction unchanged.","actors":["Data-preservation engineer who defines the linear projection code","Storage operator who controls shard placement, migration, and repair","Reliability reviewer who approves bounded failure scenarios and recovery criteria","Scientific data owner who specifies fidelity requirements for reconstructed arrays"],"observable_state":"For bounded rack, zone, or controller-unavailability scenarios, the surviving-shard matrix has an isolated small singular value or a repeatable weak right-singular subspace. Recovery residuals align with that source-space direction even when total surviving shard count remains above the operational threshold.","consequence":"Archived arrays can satisfy coordinate-level redundancy checks yet reconstruct a particular combination of coefficients unreliably, producing structured scientific-data error or preventing recovery under an otherwise tolerated failure configuration.","affected_objective":"Preserve declared reconstruction fidelity across approved correlated failure scenarios under fixed storage overhead, repair bandwidth, and failure-domain constraints.","intervention":"Represent the archive's actual real-valued projection encoder as an explicit matrix E from standardized source-block coefficients to stored shard values. For each approved failure scenario, remove unavailable rows to form a survivor operator and apply singular value decomposition to identify source directions with the lowest transmission gains. Group only weak directions that remain stable across scenario and data partitions. Use a modal sensitivity sweep to test which feasible parity-row coefficients and placements raise recovery fidelity for those directions without violating storage, repair, or precision budgets. During a reversible migration, replace a bounded set of generic parity shards with versioned parity projections aligned to the highest-consequence weak subspace and place them in failure domains that survive the scenarios producing that weakness. Retain old shards until dual decoding passes held-out recovery tests. Monitor the selected subspace, its separation from the remaining spectrum, and structured reconstruction residuals after topology or encoder changes.","structural_mapping":[{"archetype_element":"Transformation Scope","domain_realization":"The rectangular linear mapping from source-block coefficients to the subset of projection shards available under a specified bounded failure scenario."},{"archetype_element":"State-Vector Definition","domain_realization":"A fixed, standardized vector of quantized scientific-array coefficients whose reconstruction fidelity is governed by the data owner's declared error measure."},{"archetype_element":"Invariant or Paired Mode Basis","domain_realization":"Right singular vectors identify source-coefficient combinations transmitted by the surviving shards; paired left singular vectors identify their observable shard patterns."},{"archetype_element":"Modal Gain Spectrum","domain_realization":"Singular values measure how strongly each source direction remains represented after the scenario removes shards."},{"archetype_element":"Dominant Mode Selection Rule","domain_realization":"Here decision relevance is assigned to the weakest reproducible modes when their gain, reconstruction consequence, and scenario relevance cross declared thresholds."},{"archetype_element":"Modal Intervention Map","domain_realization":"Candidate parity coefficients and placements are mapped to the weak source modes they strengthen and to their storage, repair, and precision costs."},{"archetype_element":"Reconstruction Residual Check","domain_realization":"Held-out source arrays are decoded from surviving shards, and residuals are examined for both total error and alignment with omitted or supposedly repaired modes."},{"archetype_element":"Mode-Coupling Register","domain_realization":"The design records parity changes that strengthen one direction while weakening another, plus near-degenerate weak subspaces that cannot be governed as separate modes."},{"archetype_element":"Mode Drift Monitor","domain_realization":"The archive re-estimates weak subspaces and spectral separation after placement, topology, encoder, quantizer, or failure-model changes."},{"archetype_element":"Interpretation Scope Contract","domain_realization":"The analysis applies only to the declared real-valued linear projection code, numerical precision, and failure scenarios; it is not treated as a guarantee for unmodeled failures or finite-field codes."}],"mechanism_mapping":[{"mechanism_slug":"singular_value_decomposition","role":"Factor each rectangular survivor operator into paired source and shard directions with ordered non-negative transmission gains.","counterfactual_removal":"Without SVD, the archive can count surviving shards but cannot identify the joint source direction that those shards represent poorly."},{"mechanism_slug":"modal_sensitivity_sweep","role":"Perturb candidate parity rows and placements to rank their effect on weak-mode recovery, overall fidelity, repair cost, and cross-mode degradation.","counterfactual_removal":"Without the sweep, a parity row could align geometrically with a weak mode yet provide little benefit in the scenarios that matter or damage another recovery direction."},{"mechanism_slug":"residual_reconstruction_test","role":"Decode held-out arrays under held-out noise, quantization, and failure realizations to determine whether the retained modal account captures consequential recovery error.","counterfactual_removal":"Without residual testing, a better minimum singular value could be accepted while structured reconstruction error persists outside the modeled subspace."},{"mechanism_slug":"spectral_gap_monitor","role":"Track separation between the governed weak subspace and the rest of the spectrum, together with rotations caused by storage-layout changes.","counterfactual_removal":"Without monitoring, the archive could continue maintaining parity for an obsolete direction after the weak subspace rotates or becomes inseparable from adjacent modes."},{"mechanism_slug":"spectral_decomposition_report","role":"Record scenario scope, source and shard loadings, gains, conditioning, mode couplings, parity decisions, residuals, and interpretation limits for reliability approval.","counterfactual_removal":"Without the report, operators could mistake a scenario-bounded numerical analysis for a general durability guarantee or independently modify coupled parity rows."}],"causal_chain":["The encoder maps each source vector into multiple projection shards distributed across failure domains.","A correlated failure removes a structured subset of encoder rows, creating a survivor transformation that may damp some source combinations much more than others.","Shard-count and rack-count metrics conceal this directional loss because they describe coordinates rather than the survivor operator's modes.","SVD exposes the weak source directions and their scalar transmission gains under each approved scenario.","Sensitivity testing identifies parity projections and placements that strengthen consequential weak directions without merely increasing generic redundancy.","Versioned parity shards aligned with the selected weak subspace add observable information where the survivor operator previously transmitted little.","Dual-decoder reconstruction tests verify whether the added modal coverage reduces structured held-out residuals before old shards are retired.","Residual, gap, and subspace-drift checks determine whether the parity design remains authorized after the archive changes."],"baseline":"Maintain uniform replication or generic linear parity according to shard-count and failure-domain quotas, then repair missing shards reactively without decomposing the survivor operator or targeting source-space recovery directions.","nearest_rivals":["A standard maximum-distance-separable or erasure code configured for a declared number of missing shards","Rack-aware replication that distributes complete copies across independent failure domains","Direct worst-case optimization of encoder conditioning across enumerated failure scenarios without a retained modal interpretation","Random additional projection shards placed according to capacity and independence rules","Reactive repair prioritization based on the number, age, or location of missing shards"],"remaining_contrastive_claim":"The proposal's testable distinction is that fixed redundancy is reoriented toward reproducible, consequential weak directions of scenario-specific survivor transformations, rather than allocated by shard counts, generic parity, or failure location alone. Whether this directional allocation improves held-out recovery under matched storage and repair budgets remains an empirical question.","authority_safety":{"decision_authority":"The data-preservation engineer may design and simulate candidate parity rows. The storage operator and reliability reviewer must jointly approve any migration, and the scientific data owner must approve the reconstruction-fidelity criteria.","authorized_first_step":"Run an offline matrix and decoder evaluation using one frozen encoder configuration, approved synthetic or non-production array samples, and a bounded catalog of failure scenarios; do not alter stored production shards.","excluded_actions":["Deleting or overwriting an existing production shard during the first evidence step","Reducing the archive's current minimum replica, parity, or failure-domain requirements","Treating real-valued singular-value results as evidence about a finite-field code without a matching algebraic analysis","Optimizing only the selected weak modes while ignoring worst-case rank loss or data-owner fidelity constraints","Migrating parity without versioned metadata, dual decoding, integrity checks, and a recoverable old representation","Extending the result to unmodeled simultaneous failures, corruption mechanisms, or numerical-precision regimes"],"halt_rollback":"Stop the migration and continue reading from the old shard set if any candidate code loses rank in an approved scenario, breaches a fidelity or repair-cost limit, produces structured held-out residuals, has an unstable weak subspace, fails integrity checks, or cannot be decoded independently with both the old and new metadata. Retain or restore the old parity set until the candidate is re-evaluated."},"negative_tests":{"strongest_counterevidence":"Under matched storage and repair budgets, a standard erasure-code or rack-aware design meets every approved recovery criterion and is no worse on held-out reconstruction, while the identified weak directions fail to persist across scenario or data partitions.","problem_falsifier":"Recovery errors are explained by isolated corrupt shards, decoder defects, or insufficient shard count, and the survivor operators show no reproducible weak source direction or structured residual beyond those coordinate-level causes.","intervention_falsifier":"A stable and consequential weak subspace is identified, but parity rows aligned to it do not improve the predeclared held-out recovery criteria relative to generic parity or direct worst-case code optimization under identical resource constraints.","risks":["The approved failure catalog may omit the topology combinations that determine actual recovery risk.","Near-degenerate small singular values may cause the estimated weak basis to rotate across samples even when the subspace is stable.","Improving one weak direction may reduce gain or rank elsewhere in the source space.","Coefficient quantization and implementation precision may erase the benefit predicted by the ideal matrix.","New parity placement may share an unrecognized controller, power, or administrative failure domain.","A migration bug or metadata mismatch could make otherwise valid shards undecodable.","Scientific importance may not align with numerical residual energy, leaving a low-energy but consequential coefficient pattern underprotected."]},"next_evidence_step":"Freeze one non-production encoder matrix, numerical format, placement map, resource budget, fidelity measure, and bounded catalog of rack, zone, and controller failures. Divide approved synthetic or non-production arrays and failure realizations into design and held-out sets. On the design set, compute survivor-operator singular spectra, test weak-subspace stability, and use declared sensitivity and coupling criteria to select a small versioned parity replacement. On held-out arrays and failures, compare exact rank, reconstruction residual magnitude and structure, coefficient-specific fidelity, decoding conditioning, repair bandwidth, and placement independence against the unchanged baseline, a standard erasure-code configuration, rack-aware replication, random parity, and direct worst-case conditioning optimization. The result may authorize only a reversible non-production dual-decoder trial.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 addressed temporal reconstruction-error propagation inside a predictive telemetry codec and transmitted refresh coefficients to damp persistent error modes. Proposal 2 addressed protected-information transmission through correlated analytics outputs and attenuated or noised high-gain disclosure modes. This proposal instead addresses recoverability of scientific arrays after correlated storage-domain failures and redesigns persistent parity projections to strengthen low-gain source modes of survivor operators. It has a different asset, transformation, failure event, objective, intervention, authority structure, and causal path from both earlier proposals, and it can be adopted without predictive telemetry or an analytics-release privacy service.","revision_record":{"parent_version":null,"progress_targets_addressed":[],"conceptual_changes":[],"operational_changes":[],"evidence_changes":[],"claim_changes":[]}}