{"schema_version":1,"research_id":"eoa_inverse_innovation_exp03_external48_20260801","source_assessment_id":"eoa_inverse_innovation_exp03_opportunity320_20260801","cell_id":"invariant_mode_decomposition_design__innovation_entrepreneurship","selection_stratum":"DEPLOYABLE_PRIORITY","search_queries":["startup metrics pivot decision making multiple metrics runway empirical research","startup performance measurement systems empirical study KPI early stage ventures","site:sciencedirect.com startup pivot empirical study metrics decision making","official startup failure cash flow data small business government","dynamic mode decomposition with control paper data-driven system identification","\"dynamic mode decomposition\" business metrics","\"dynamic mode decomposition\" entrepreneurship startup","Koopman \"business metrics\" control","patent dynamic mode decomposition business performance","PyDMD official documentation DMDc dynamic mode decomposition control","site:bls.gov Occupational Outlook Handbook data scientists median pay 2024","site:bls.gov employer costs employee compensation private industry 2025 benefits percent"],"sources":[{"source_id":"S1","title":"The evolution of performance measurement systems in SaaS startups: a contingency-based approach across the investment cycle","publisher":"Journal of Entrepreneurship in Emerging Economies / Emerald Publishing","url":"https://doi.org/10.1108/JEEE-06-2025-0319","source_class":"PRIMARY_RESEARCH","publication_date":"2026-06-19","accessed_at":"2026-08-02","claims_supported":["Nine interviews with SaaS startup founders and CEOs found that performance-measurement systems changed dynamically and reactively with market expansion, product development, and fundraising.","Startup performance measurement is contingent on stage and business model rather than standardized.","Founders and CEOs are credible participants in startup metric-system decisions."]},{"source_id":"S2","title":"Determinants of Early-Stage Startup Performance: Survey Results","publisher":"Harvard Business School","url":"https://www.hbs.edu/ris/Publication%20Files/21-057_0c4f5410-3dcb-4c2f-8c4e-6fcbc358b92f.pdf","source_class":"PRIMARY_RESEARCH","publication_date":"2020-10-27","accessed_at":"2026-08-02","claims_supported":["The study surveyed CEOs of 470 early-stage startups across product, marketing, operations, finance, funding, team, and founder factors.","Its multivariate analysis associated lean-startup practices, particularly an optimal pivoting rate, with stronger seed-equity valuation growth.","The study is associative and does not test coupled-mode analysis or metric-thrashing causation."]},{"source_id":"S3","title":"Dynamic Mode Decomposition with Control","publisher":"SIAM Journal on Applied Dynamical Systems","url":"https://doi.org/10.1137/15M1013857","source_class":"PRIMARY_RESEARCH","publication_date":"2016-01-26","accessed_at":"2026-08-02","claims_supported":["DMD with control extracts low-order input-output models from time snapshots of observables and actuation data.","The method separates estimated underlying dynamics from effects of external actuation.","The published demonstrations concern high-dimensional dynamical systems rather than startup operating metrics."]},{"source_id":"S4","title":"Challenges in dynamic mode decomposition","publisher":"Journal of the Royal Society Interface / The Royal Society","url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC8692036/","source_class":"PRIMARY_RESEARCH","publication_date":"2021-12-22","accessed_at":"2026-08-02","claims_supported":["DMD is sensitive to noise and failures of closure when modeling nonlinear systems.","Controlled numerical experiments found that DMD can fail to recover the spectrum and can have poor predictive ability even under mildly nonlinear conditions.","Conditioning, geometry, spectrum, observable choice, and measurement noise materially affect reliability."]},{"source_id":"S5","title":"DMD with control — PyDMD documentation","publisher":"PyDMD project","url":"https://pydmd.github.io/PyDMD/dmdc.html","source_class":"OFFICIAL_PRODUCT_DOCUMENTATION","publication_date":"n.d.","accessed_at":"2026-08-02","claims_supported":["PyDMD provides an implemented DMDc class.","The implementation exposes singular-value and total-least-squares rank controls.","The documented implementation reduces algorithm-construction burden but does not supply startup-specific validation or governance."]},{"source_id":"S6","title":"Data Scientists: Occupational Outlook Handbook","publisher":"U.S. Bureau of Labor Statistics","url":"https://www.bls.gov/ooh/math/data-scientists.htm","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"2025","accessed_at":"2026-08-02","claims_supported":["The May 2024 median annual wage for U.S. data scientists was $112,590.","Data scientists develop statistical models, analyze data, and communicate business recommendations.","The wage provides an official labor-cost anchor rather than a project quote."]},{"source_id":"S7","title":"Compensation Percentiles: A tool for assessing employee compensation","publisher":"U.S. Bureau of Labor Statistics","url":"https://www.bls.gov/ecec/factsheets/compensation-percentile-estimates.htm","source_class":"GOVERNMENT_OR_REGULATOR","publication_date":"2026-06-12","accessed_at":"2026-08-02","claims_supported":["In March 2026, wages represented 69.9% and benefits 30.1% of private-industry employer compensation.","Benefit-inclusive labor costs are materially higher than wages alone.","The figures support loaded-labor assumptions but not startup-specific software, compliance, or coordination costs."]},{"source_id":"S8","title":"Pivot decisions in startups: a systematic literature review","publisher":"International Journal of Entrepreneurial Behavior & Research / Emerald Publishing","url":"https://doi.org/10.1108/IJEBR-12-2019-0699","source_class":"AUTHORITATIVE_SECONDARY","publication_date":"2021-02-26","accessed_at":"2026-08-02","claims_supported":["A systematic review of 86 peer-reviewed papers characterized pivots as strategic decisions involving changes in course, resource reconfiguration, and possible modification of business-model elements.","The review organized pivoting into recognition, option generation, seizing and testing, and reconfiguration.","The review reported that entrepreneurs' pivot decisions remained poorly understood and did not establish isolated-KPI thrashing as a prevalent causal problem."]}],"problem_evidence":{"support":"WEAK","rationale":"Primary research confirms that startup performance systems are multidimensional, contingent, and sometimes reactively changed, while survey and review evidence link pivoting and resource reconfiguration to venture decision-making. None of the opened sources measures the candidate's exact problem: recurring budget or product reversals caused by isolated KPI review, their prevalence, or associated runway loss. The problem is plausible but not independently verified as stated.","source_ids":["S1","S2","S8"]},"stakeholder_evidence":{"support":"WEAK","rationale":"Founders and CEOs demonstrably participate in performance-measurement and pivot decisions, making them credible prospective adopters or authorizers. The bounded search found no evidence that ventures are requesting modal decomposition, will provide sufficiently consistent weekly data, or prefer it to simpler multivariate analytics.","source_ids":["S1","S2","S8"]},"prior_art":{"proximity":"ADJACENT_PRIOR_ART","closest_analogues":[{"name":"Dynamic Mode Decomposition with Control (DMDc)","similarity":"DMDc already estimates low-order modes and input-output dynamics from time snapshots of multivariate observables plus control inputs. This substantially overlaps the candidate's decomposition and intervention-sensitivity mechanism.","remaining_difference":"The published work does not apply DMDc to a declared startup product-segment-pricing-channel regime, compare it with isolated-KPI and regularized nonmodal venture models, or combine resampling, residual, spectral-gap, drift, authority, and reversible-budget gates.","source_ids":["S3"]},{"name":"PyDMD DMDc implementation","similarity":"An official open-source implementation already supplies rank-controlled DMDc estimation, reducing the algorithmic novelty and implementation burden.","remaining_difference":"It provides neither venture-specific state definitions nor evidence that 26–52 weekly startup observations yield stable, decision-useful modes; it also lacks the candidate's governance and comparative evaluation protocol.","source_ids":["S5"]},{"name":"Contingent performance-measurement systems in SaaS startups","similarity":"This domain-specific analogue treats startup performance measurement as multidimensional, stage-dependent, and dynamically adjusted by founders and CEOs.","remaining_difference":"It is a qualitative account of measurement-system evolution, not modal system identification, out-of-sample transition prediction, sensitivity-guided allocation, or a controlled comparison against simpler models.","source_ids":["S1"]}],"distinctive_claim_remaining":"The remaining testable claim is narrow: within one preregistered and demonstrably stable venture regime, a gated DMDc-style decomposition of weekly operating metrics and recorded interventions will add out-of-sample objective prediction or recommendation value beyond isolated-KPI review and a regularized nonmodal multivariate transition model, while surviving resampling, conditioning, residual, gap, direction-stability, and drift tests. This is an unverified application-and-evaluation claim, not a claim that modal decomposition or data-driven control is new.","confidence":"MODERATE"},"implementation_evidence":{"support":"MODERATE","rationale":"The core estimator is published and available in maintained software, so a retrospective prototype is technically feasible. However, primary research documents serious DMD failures under noise, nonlinear observables, unfavorable geometry, and ill-conditioning. A venture history of only 26–52 weekly observations, with endogenous management actions and changing definitions, may be too short to produce stable modes. Implementability is therefore credible only as a gated feasibility study, not as a reliable decision system.","source_ids":["S3","S4","S5"]},"scores":{"meaningful_impact":{"score":3,"rationale":"Pivoting and cross-functional venture choices can affect resource configuration, and one CEO survey associated appropriate pivoting with stronger valuation growth. The exact frequency, runway cost, customer consequences, and causal role of isolated KPI review remain unmeasured.","source_ids":["S2","S8"]},"stakeholder_pull":{"score":2,"rationale":"Founders and CEOs actively configure startup performance systems, but no direct demand, willingness-to-pay, data-sharing commitment, or preference for modal analysis was found.","source_ids":["S1","S2"]},"incremental_advantage":{"score":2,"rationale":"Modes could offer interpretable coupled directions, but DMDc already provides the core input-output decomposition and no venture evidence shows better prediction or decisions than a regularized nonmodal model. Documented DMD fragility further limits expected advantage.","source_ids":["S3","S4"]},"distinctiveness_plausibility":{"score":2,"rationale":"The venture-specific regime declaration, diagnostics, comparisons, and reversible governance form a distinctive protocol, but its technical core closely follows established DMDc and its domain premise overlaps contingent startup performance measurement.","source_ids":["S1","S3","S5"]},"technical_implementability":{"score":3,"rationale":"Published methods and an official implementation make fitting possible. Short histories, endogenous controls, nonlinearities, noise, rank sensitivity, and regime changes may prevent any trustworthy mode from passing the proposed gates.","source_ids":["S3","S4","S5"]},"adoption_authority_feasibility":{"score":4,"rationale":"Founders and CEOs are evidenced participants in performance-system and pivot decisions, and the candidate retains accountable functional and experiment oversight. Actual consent, cross-functional coordination, and data authority remain to be secured.","source_ids":["S1","S2","S8"]},"evidence_readiness":{"score":3,"rationale":"The method can be implemented and compared retrospectively, but evidence readiness depends on one venture having consistently defined metrics, intervention records, decision logs, and enough stable observations. DMD's known failure modes make a null feasibility result likely enough to require preregistered rejection rules.","source_ids":["S4","S5"]},"safety_net_benefit":{"score":4,"rationale":"A shadow-only first study plus residual, conditioning, stability, drift, and authority gates directly addresses documented risks of poor DMD recovery and prediction. These safeguards do not independently resolve privacy, metric gaming, or causal overinterpretation.","source_ids":["S4"]},"scalability":{"score":2,"rationale":"Startup measurement systems vary by stage and business model and change reactively, while DMD reliability depends on dataset geometry and observables. Each new regime would require metric harmonization, re-estimation, validation, and governance rather than simple model transfer.","source_ids":["S1","S4"]}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"50K_TO_250K","scope":"One venture, no live decisions: metric and intervention definition; permission and privacy review; cleaning 26–52 weekly vectors and decision logs; implementation of isolated-KPI, regularized nonmodal, and gated DMDc analyses; preregistration; rolling-origin evaluation; four shadow weeks; and a written go/no-go assessment. Includes data-science labor, fractional product/growth/finance/legal participation, software and compute, coordination, and evaluation.","confidence":"LOW","assumptions":["Existing analytics systems contain usable historical data and intervention timestamps; no warehouse rebuild is required.","Roughly three to six months of fractional specialist and cross-functional effort is needed.","PyDMD or comparable open-source software is usable, so license expense is minor relative to labor.","The U.S. data-scientist wage and 2026 benefit share are labor anchors, not contractor quotes or startup-specific observed costs."],"source_ids":["S5","S6","S7"]},"initial_deployment_startup":{"band_2026_usd":"50K_TO_250K","scope":"Only after retrospective and shadow gates pass: establish repeatable regime-specific pipelines, versioned metric definitions, access controls, monitoring, permissions, decision records, human-review procedures, guardrails, and rollback drills for one venture and one regime. Includes engineering, data science, privacy/compliance review, stakeholder coordination, software, and validation.","confidence":"LOW","assumptions":["Existing analytics and experiment infrastructure can be adapted.","One product-segment-pricing-channel regime is covered.","No automated allocation, customer-wide policy change, or major data-platform replacement is included.","Specialized labor dominates equipment and software expense."],"source_ids":["S5","S6","S7"]},"operational_launch":{"band_2026_usd":"50K_TO_250K","scope":"A possible later, separately authorized launch: prepare, monitor, and evaluate one reversible two-week reallocation capped at 5% of an existing experiment budget, with a preregistered holdout, nonmodal rival recommendation, customer and cash guardrails, human approval, incident response, and rollback. This cost band does not authorize or imply live deployment.","confidence":"LOW","assumptions":["All retrospective, shadow, authority, privacy, and technical gates have already passed.","The test reallocates an existing experiment budget and does not create a new product program.","No protected-group, employment, compensation, fundraising, eligibility, or automated decision is involved.","The band includes evaluation and coordination labor but excludes the underlying experiment budget already committed."],"source_ids":["S6","S7"]},"annual_recurring":{"band_2026_usd":"50K_TO_250K","scope":"For one venture and a small number of declared regimes: maintain data pipelines and access controls; reconcile metric definitions; monitor residuals, conditioning, gaps, direction stability, and drift; periodically refit and compare models; conduct human review; preserve audit records; and repeat privacy, compliance, and outcome evaluation after material changes.","confidence":"LOW","assumptions":["Coverage remains limited and every recommendation receives human review.","Open-source modeling software remains suitable.","Major strategy, pricing, product, channel, or data-system changes trigger separate revalidation.","Loaded analyst and cross-functional labor, rather than compute or equipment, remains the principal recurring resource."],"source_ids":["S5","S6","S7"]}},"verified_pipeline_gates":{"externally_supported_problem":{"status":"UNCERTAIN","reason":"External research supports reactive performance-system changes, pivot decisions, and resource reconfiguration, but does not establish recurring isolated-KPI thrashing or quantify resulting runway waste.","source_ids":["S1","S2","S8"]},"externally_credible_adopter_or_authorizer":{"status":"YES","reason":"Founders and CEOs are documented participants in startup performance measurement and pivot decisions. The proposed product, growth, finance, data, and experiment authorities are organizationally credible, although no specific partner has consented.","source_ids":["S1","S2","S8"]},"distinct_testable_incremental_claim":{"status":"YES","reason":"Because DMDc is established but startup-specific value is not, the candidate can make a distinct comparative claim: gated modal analysis must outperform isolated-KPI and regularized nonmodal models on preregistered out-of-sample prediction or recommendation criteria.","source_ids":["S3","S4","S5"]},"bounded_next_evidence_step":{"status":"YES","reason":"A single-venture retrospective analysis followed by four shadow weeks can test problem presence, regime stability, estimator reliability, and comparative prediction without changing allocations or customer treatment.","source_ids":["S3","S4","S5"]},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"The next step is retrospective and shadow-only, retains human authority, and can stop on data-permission, privacy, residual, conditioning, stability, drift, or predictive failures. Any later live test requires separate authorization.","source_ids":["S4"]},"credible_cost_scope_and_range":{"status":"YES","reason":"The four ranges are bounded by one venture, limited regimes, specified tasks, and explicit exclusions. Official wage and benefit data support labor magnitude, while low confidence appropriately reflects unknown data remediation, compliance, and coordination effort.","source_ids":["S5","S6","S7"]}},"next_evidence_step":"With one consenting venture, preregister a retrospective and shadow-only falsification study using 26–52 weeks from one unchanged product-segment-pricing-channel regime plus four subsequent shadow weeks. First audit decision logs for repeated cross-metric reversals and associated budget or runway consequences. Then compare gated DMDc with (a) isolated-KPI forecasts and (b) the preregistered regularized nonmodal multivariate transition model using rolling-origin out-of-sample transition error, objective prediction, calibration, and directional decision agreement. Reject progression if reversals are absent; metric or intervention definitions drift; no mode survives blocked resampling, conditioning, residual-structure, spectral-gap, and direction-stability gates; or DMDc fails to improve a preregistered decision-relevant endpoint beyond uncertainty. Do not alter budgets, product priorities, prices, eligibility, or customer treatment.","blocking_evidence":["Direct prevalence and consequence data for recurring isolated-KPI budget or priority reversals in early-stage ventures.","A consenting venture with 26–52 genuinely comparable weekly observations, stable metric definitions, intervention timestamps, and usable decision logs.","Resample-stable, well-conditioned modes with acceptable residuals, spectral separation, and four-week shadow persistence.","Out-of-sample advantage over both isolated-KPI review and the regularized nonmodal multivariate rival.","Evidence that a selected mode is controllable by a feasible small allocation rather than merely correlated with management actions.","Partner consent, data authority, privacy review, and demonstrated willingness to use shadow recommendations without causal overinterpretation.","Evidence that objective improvement can be measured without masking low-frequency customer or employee harms.","Broader patent, proprietary-product, unpublished-consulting, and non-English prior-art review if defensible novelty or intellectual-property claims are contemplated."],"research_disposition":"PARTNERED_RESEARCH_PROGRAM","world_novelty_boundary":"This bounded English-language search, completed 2026-08-02 across scholarly literature, official documentation, government cost data, and targeted business-metric and patent queries, found established DMDc technical prior art and adjacent startup performance-measurement research but no opened source reporting the complete venture-specific gated protocol. That absence only defines the present search boundary. It is not evidence of world novelty, freedom to operate, patentability, commercial uniqueness, or absence of proprietary and unpublished implementations."}