{ "title": "Engineering Capacity OS Formula Registry", "version": "1.1", "schema_version": "1.0.0", "status": "public_research_registry", "purpose": "Map published TeamStation Engineering Doctrine formulas and algorithmic concepts to Engineering Capacity OS research questions, private MCP evidence, answer cards, and workflow reports.", "privacy_boundary": "The public registry defines formulas, evidence requirements, and interpretation rules. Customer source code, secrets, raw logs, customer records, payroll data, legal records, and employee-level performance records stay inside the organization.", "how_to_use": [ "Select the operating problem and matching research question.", "Find the related formula or algorithmic concept in this registry.", "Retrieve only aggregate or redacted evidence from approved internal systems.", "Apply the interpretation rules to create answer cards with observed state, confidence, missing evidence, risk flags, and next safe action.", "Do not treat a formula as a private scoring engine unless the required evidence is present and source-cited." ], "formula_registry": [ { "id": "engineering_performance_function", "label": "Engineering Performance Function", "formula_type": "system_function", "doctrine_source": { "route": "/research/engineering-operating-system/", "file": "data/research/engineering-os.json", "title": "Engineering Capacity Operating System" }, "formula": "P(t)=f(C,T,K,D,O,A,L,G) -> {Speed, Quality, Cost, Risk, Value}", "plain_language": "Engineering performance at time t is a system output, not a headcount output. It depends on capacity, topology, knowledge, execution, telemetry, agentic action, adaptive learning, and governance.", "diagnostic_use": "Use this as the top-level dependency map for every Engineering Capacity OS report.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "knowledge_architecture_memory", "execution_harness", "decision_grade_telemetry", "governed_agentic_sdlc", "governed_adaptive_control_loops", "governance_security_failure_modes" ], "related_question_ids": [ "capacity-001", "topology-003", "knowledge-001", "execution-001", "telemetry-001", "agent-001", "adaptive-001", "gov-006" ], "required_signals": [ "committed work", "completed work", "review queue age", "cycle time", "deployment success", "incident interruption load", "ownership map", "approval path", "rollback evidence" ], "mcp_source_categories": [ "work tracker", "source control", "pull request system", "CI/CD system", "incident system", "architecture catalog", "telemetry platform", "policy system" ], "interpretation_rules": [ "If speed improves while quality, cost, risk, or value degrade, the system did not improve.", "If one variable is unknown, mark the answer as partial rather than forcing a recommendation.", "If governance evidence is missing, do not recommend capacity expansion or autonomous workflow changes." ], "answer_card_fields": [ "observed_state", "evidence_summary", "confidence", "missing_evidence", "risk_flags", "next_safe_action" ], "report_sections": [ "Executive Summary", "System Function Map", "Risk Boundary", "Next Safe Action" ], "maturity": "research_hypothesis", "validation_status": "conceptual_dependency_map_not_calibrated", "assumptions": [ "Each input is defined independently before use.", "Outputs are evaluated together rather than optimized in isolation." ], "units": "No common unit. Inputs and outputs require separate operational measures.", "limitations": [ "This function states dependency, not magnitude or causality.", "It cannot predict performance until variables, interactions, and calibration data are specified." ] }, { "id": "sequential_probability_network", "label": "Sequential Probability Network", "formula_type": "probability_model", "doctrine_source": { "route": "/teams/", "file": "data/teams/overview.ts", "title": "Pillar I: On Teams" }, "formula": "P = product(p_i) for i=1..n", "plain_language": "In a sequential engineering chain, the probability of system success is multiplied across nodes. One weak upstream node can cap the entire downstream system.", "diagnostic_use": "Use this to test whether adding capacity will improve throughput or only add more weak links to a fragile chain.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "knowledge_architecture_memory", "execution_harness" ], "related_question_ids": [ "capacity-002", "capacity-005", "topology-001", "topology-006", "knowledge-003", "execution-010" ], "required_signals": [ "workstream sequence", "handoff count", "blocked work", "dependency wait", "review queue age", "rework by upstream source", "deployment dependency map" ], "mcp_source_categories": [ "work tracker", "pull request system", "architecture catalog", "service registry", "CI/CD system" ], "interpretation_rules": [ "If success depends on a long chain of handoffs, capacity should be modeled as chain reliability, not seat count.", "If downstream teams are waiting on ambiguous upstream output, adding downstream contributors will not repair the constraint.", "If one service or role caps the sequence, report it as the probability ceiling." ], "answer_card_fields": [ "chain_map", "constraint_node", "dependency_wait", "confidence", "missing_evidence" ], "report_sections": [ "Capacity Constraint Map", "Topology Readiness", "Execution Failure Modes" ], "maturity": "derived_model", "validation_status": "valid_under_explicit_probability_chain_assumptions", "assumptions": [ "Node probabilities are independent, or are explicitly defined as conditional probabilities in sequence.", "Success requires every modeled node to succeed." ], "units": "Dimensionless probability from 0 to 1.", "limitations": [ "A simple product is invalid for correlated unconditional probabilities.", "Parallel paths, retries, and partial success require a richer reliability model." ] }, { "id": "strict_complementarity", "label": "Strict Complementarity", "formula_type": "economic_constraint", "doctrine_source": { "route": "/teams/sequential-probability-networks/", "file": "data/teams/sequential.ts", "title": "The Sequential Pipeline Reality" }, "formula": "p_{k+2} - p_{k+1} > p_{k+1} - p_k", "plain_language": "Improving one node creates more value when the rest of the chain is already strong. Strong people at the wrong point in a broken chain can be wasted.", "diagnostic_use": "Use this to decide whether the system needs stronger upstream architecture, better review capacity, or fewer handoffs before adding contributors.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "knowledge_architecture_memory" ], "related_question_ids": [ "capacity-004", "capacity-007", "topology-002", "topology-005", "knowledge-004", "knowledge-008" ], "required_signals": [ "senior review dependency", "architecture decision age", "rework by reviewer", "handoff failure", "critical knowledge ownership" ], "mcp_source_categories": [ "pull request system", "architecture decision records", "work tracker", "engineering review records" ], "interpretation_rules": [ "If senior review is the scarce multiplier, adding contributors increases queues unless review capacity changes.", "If architecture decisions are stale or missing, downstream delivery probability is capped.", "If high-skill nodes are placed after weak upstream inputs, report wasted capacity risk." ], "answer_card_fields": [ "pivotal_node", "upstream_quality_signal", "downstream_blockage", "risk_flags" ], "report_sections": [ "Capacity Constraint Map", "Knowledge and Ownership Risk" ], "maturity": "research_hypothesis", "validation_status": "testable_inequality_not_empirically_calibrated", "assumptions": [ "The ordered probability terms measure comparable outcomes under comparable conditions.", "The node index represents a meaningful sequence." ], "units": "Difference between dimensionless probabilities.", "limitations": [ "The inequality is a proposed diagnostic condition, not a universal law.", "Observed complementarity can be confounded by role, work type, or measurement window." ] }, { "id": "shirking_margin_zeta", "label": "Shirking Margin", "formula_type": "incentive_model", "doctrine_source": { "route": "/teams/ai-incentive-structure/", "file": "data/teams/incentives.ts", "title": "The Incentive Structure" }, "formula": "zeta_i^x = P(project succeeds | e_i=0, policy x)", "plain_language": "Zeta measures how safe a contributor feels when they do not apply full effort. If the system hides weak effort behind downstream rescue, incentive quality degrades.", "diagnostic_use": "Use this to test whether AI, QA, senior rescue, or vendor buffering is hiding low-quality upstream work.", "related_domains": [ "capacity_intelligence", "governed_agentic_sdlc", "governance_security_failure_modes" ], "related_question_ids": [ "capacity-006", "agent-004", "agent-005", "agent-006", "gov-001", "gov-006" ], "required_signals": [ "review correction rate", "reopened work", "QA rescue count", "senior rescue count", "agent-generated rework", "approval override history" ], "mcp_source_categories": [ "pull request system", "test system", "incident system", "work tracker", "agent audit logs" ], "interpretation_rules": [ "If downstream rescue repeatedly masks upstream defects, do not treat delivered work as healthy capacity.", "If agent output lowers effort discipline, require stronger validation and ownership boundaries.", "If responsibility is unclear, classify the risk as governance failure before capacity failure." ], "answer_card_fields": [ "rescue_pattern", "quality_escape", "owner_boundary", "confidence" ], "report_sections": [ "Agentic Workflow Control Report", "Governance and Risk Boundary" ], "maturity": "derived_model", "validation_status": "principal_agent_model_requires_local_estimation", "assumptions": [ "Effort state and project success are defined for the same policy and time window.", "The probability can be estimated without exposing individual private records." ], "units": "Dimensionless probability from 0 to 1.", "limitations": [ "The construct is not directly observable and requires a defensible proxy.", "Do not infer individual intent from aggregate delivery outcomes." ] }, { "id": "incentive_compatibility_constraint", "label": "Incentive Compatibility Constraint", "formula_type": "incentive_model", "doctrine_source": { "route": "/teams/ai-incentive-structure/", "file": "data/teams/incentives.ts", "title": "The Incentive Structure" }, "formula": "p_n * w_i - c >= zeta_i^x * w_i", "plain_language": "A contributor exerts effort when the expected value of working is greater than the expected value of shirking.", "diagnostic_use": "Use this as a qualitative operating model for effort, friction, unclear ownership, time-zone delay, and downstream safety nets.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "governance_security_failure_modes" ], "related_question_ids": [ "capacity-003", "topology-004", "topology-009", "gov-001", "gov-006" ], "required_signals": [ "decision latency", "blocked time", "handoff delay", "context switching", "work ownership", "review accountability" ], "mcp_source_categories": [ "work tracker", "calendar metadata if approved and aggregated", "pull request system", "decision records" ], "interpretation_rules": [ "If coordination cost is high, effort drops even when people are busy.", "If ownership is unclear, activity signals are not evidence of productive effort.", "If downstream teams constantly catch upstream issues, the incentive model is distorted." ], "answer_card_fields": [ "effort_friction", "blocked_time", "ownership_gap", "next_safe_action" ], "report_sections": [ "Capacity Constraint Map", "Topology Readiness" ], "maturity": "derived_model", "validation_status": "algebraically_defined_under_principal_agent_assumptions", "assumptions": [ "The wage is outcome contingent.", "Effort cost and success probabilities are expressed on compatible expected-value terms.", "The decision maker is modeled as risk neutral for this simplified constraint." ], "units": "Expected currency on both sides of the inequality.", "limitations": [ "Risk aversion, multi-period incentives, and non-monetary utility are omitted.", "The model must not be used as an individual compensation decision without additional evidence." ] }, { "id": "wage_equation", "label": "Wage Equation", "formula_type": "economic_model", "doctrine_source": { "route": "/teams/ai-incentive-structure/", "file": "data/teams/incentives.ts", "title": "The Incentive Structure" }, "formula": "w_i^x = c / (p_n - zeta_i^x)", "plain_language": "As the incentive margin shrinks, the cost required to sustain high effort rises.", "diagnostic_use": "Use this to explain why cheap capacity can become expensive when coordination friction, review drag, and rescue work rise.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "decision_grade_telemetry" ], "related_question_ids": [ "capacity-008", "topology-003", "telemetry-002", "telemetry-006" ], "required_signals": [ "cycle time", "review drag", "rework rate", "defect escape", "incident load", "coordination delay", "topology cost" ], "mcp_source_categories": [ "work tracker", "pull request system", "incident system", "finance or planning summaries if approved" ], "interpretation_rules": [ "If low-cost capacity creates high review drag, the system cost is not low.", "If the evidence does not include rework and delay, do not make a cost claim.", "If capacity topology changes reduce friction, treat the gain as operating leverage." ], "answer_card_fields": [ "cost_driver", "delay_driver", "rework_driver", "evidence_gap" ], "report_sections": [ "Cost, Value, and Risk Economics", "Topology Readiness" ], "maturity": "derived_model", "validation_status": "algebraic_solution_requires_positive_probability_margin", "assumptions": [ "p_n is greater than zeta_i^x.", "The incentive compatibility assumptions hold.", "Cost and wage use the same currency and period." ], "units": "Currency per modeled outcome period.", "limitations": [ "The equation is undefined when p_n equals zeta_i^x and unstable when the margin is close to zero.", "It is a theoretical boundary, not a market wage recommendation." ] }, { "id": "replacement_kinetics_derivative", "label": "Replacement Kinetics Derivative", "formula_type": "agentic_automation_model", "doctrine_source": { "route": "/teams/replacement-kinetics/", "file": "data/teams/kinetics.ts", "title": "Replacement Kinetics" }, "formula": "partial C / partial x_i = Direct Savings - Incentive Distortion", "plain_language": "Replacing or automating a position creates direct savings only if it does not distort incentives and coordination around the rest of the chain.", "diagnostic_use": "Use this to decide whether AI should automate a workflow, augment it, or stay outside the approval path.", "related_domains": [ "governed_agentic_sdlc", "governed_adaptive_control_loops", "governance_security_failure_modes" ], "related_question_ids": [ "agent-001", "agent-002", "agent-006", "adaptive-002", "gov-002", "gov-006" ], "required_signals": [ "workflow step position", "blast radius", "human approval path", "agent error rate", "review correction rate", "rollback evidence" ], "mcp_source_categories": [ "agent audit logs", "pull request system", "CI/CD system", "policy system", "incident system" ], "interpretation_rules": [ "End-of-chain validation tasks are more automation tolerant than middle-of-chain architecture decisions.", "If automation removes a human signal needed by other contributors, classify it as protected or human-gated.", "If rollback is missing, do not mark the workflow as safe for adaptive change." ], "answer_card_fields": [ "workflow_position", "automation_class", "blast_radius", "rollback_path" ], "report_sections": [ "Agentic Workflow Control Report", "Governed Adaptive Control Loop Report" ], "maturity": "research_hypothesis", "validation_status": "directional_decomposition_not_calibrated", "assumptions": [ "Direct savings and incentive distortion are measured in the same currency and period.", "Cross-effects on quality, queues, knowledge, and risk are included in incentive distortion." ], "units": "Currency change per unit change in replacement exposure.", "limitations": [ "Omitted cross-effects can reverse the sign.", "The expression does not prove that replacement creates savings." ] }, { "id": "kingman_wait_time", "label": "Kingman Wait Time Approximation", "formula_type": "queueing_model", "doctrine_source": { "route": "/work/", "file": "data/work/overview.ts", "title": "Pillar II: On Work" }, "formula": "E[W_q] approx (rho / (1-rho)) * ((C_a^2 + C_s^2) / 2) * tau", "plain_language": "As utilization approaches 100 percent, wait time explodes. Variance makes the queue worse.", "diagnostic_use": "Use this to test whether a team is actually capacity constrained or queue constrained.", "related_domains": [ "capacity_intelligence", "execution_harness", "decision_grade_telemetry" ], "related_question_ids": [ "capacity-001", "capacity-003", "capacity-005", "execution-010", "telemetry-004", "telemetry-006" ], "required_signals": [ "utilization proxy", "active WIP", "queue age", "cycle time", "arrival variability", "service-time variability", "blocked work" ], "mcp_source_categories": [ "work tracker", "pull request system", "CI/CD system", "incident system" ], "interpretation_rules": [ "If utilization is high and queue age is rising, adding more work will worsen delivery.", "If task-size variance is high, normalize work before scaling capacity.", "If queue data is missing, mark telemetry as insufficient for capacity decisions." ], "answer_card_fields": [ "queue_age", "wip_level", "cycle_time_variance", "capacity_risk" ], "report_sections": [ "Capacity Constraint Map", "Telemetry Trust Report" ], "maturity": "established_model", "validation_status": "established_queueing_approximation", "assumptions": [ "Single-server GI/G/1 approximation.", "Arrival and service processes are stable and utilization is below 1.", "Mean and variability estimates use a representative window." ], "units": "Time in the same unit as mean service time tau.", "limitations": [ "Delay grows nonlinearly as utilization approaches 1; no universal 80 percent infinity threshold exists.", "Multi-server, priority, batching, and network queues require other models." ] }, { "id": "little_law", "label": "Little's Law", "formula_type": "flow_model", "doctrine_source": { "route": "/work/code-inventory-axioms/", "file": "data/work/axioms.ts", "title": "Inventory Liability, Little's Law, and The Kingman Invariant" }, "formula": "L = lambda * W", "plain_language": "Average work in progress equals throughput multiplied by time in system.", "diagnostic_use": "Use this to show why more active work can increase lead time even when people look busy.", "related_domains": [ "capacity_intelligence", "execution_harness", "decision_grade_telemetry" ], "related_question_ids": [ "capacity-003", "execution-008", "telemetry-002", "telemetry-004" ], "required_signals": [ "active WIP", "throughput", "lead time", "cycle time", "work item aging" ], "mcp_source_categories": [ "work tracker", "pull request system" ], "interpretation_rules": [ "If WIP rises faster than throughput, lead time must rise.", "If throughput is flat and work starts increase, the system is manufacturing delay.", "If WIP is not measured, do not claim the team has usable spare capacity." ], "answer_card_fields": [ "wip_level", "throughput", "lead_time", "queue_risk" ], "report_sections": [ "Capacity Constraint Map", "Execution Control Report" ], "maturity": "established_model", "validation_status": "established_flow_conservation_identity", "assumptions": [ "The observed system is stable over the measurement window.", "WIP, throughput, and time share the same boundary and population." ], "units": "Items = items per unit time multiplied by time.", "limitations": [ "Little's Law does not identify the cause of delay.", "Mixed work classes require segmentation before interpretation." ] }, { "id": "wip_rule_of_two", "label": "Rule of Two WIP Constraint", "formula_type": "operating_constraint", "doctrine_source": { "route": "/work/wip-regulation/", "file": "data/work/regulation.ts", "title": "Regulation: Enforceable Constraints" }, "formula": "WIP_person <= 2", "plain_language": "A contributor should not carry unlimited active work. Too much WIP hides blocked flow and destroys feedback.", "diagnostic_use": "Use this to identify false capacity created by multitasking and fragmented ownership.", "related_domains": [ "capacity_intelligence", "execution_harness" ], "related_question_ids": [ "capacity-003", "capacity-005", "execution-003", "execution-007" ], "required_signals": [ "active items per contributor", "work state aging", "blocked items", "handoff count", "review waiting time" ], "mcp_source_categories": [ "work tracker", "pull request system" ], "interpretation_rules": [ "If contributors carry more active work than the operating limit, treat capacity as fragmented.", "If blocked work causes new work starts, the system is optimizing busyness over delivery.", "If the tracker cannot show WIP by contributor or workstream, mark telemetry incomplete." ], "answer_card_fields": [ "active_wip", "fragmentation_risk", "blocked_work", "next_safe_action" ], "report_sections": [ "Capacity Constraint Map", "Execution Control Report" ], "maturity": "operating_heuristic", "validation_status": "policy_threshold_requires_local_experiment", "assumptions": [ "Active work is defined consistently.", "Expedite and incident work are accounted for separately." ], "units": "Active work items per person.", "limitations": [ "Two is a proposed control limit, not a mathematical law.", "The useful threshold varies by work type, role, and queue design." ] }, { "id": "cost_of_delay", "label": "Cost of Delay", "formula_type": "economic_model", "doctrine_source": { "route": "/work/cost-of-delay-economics/", "file": "data/work/economics.ts", "title": "Economics of Work" }, "formula": "CoD = dV_lost / dt = -dV_remaining / dt", "plain_language": "Cost of delay is the rate at which waiting destroys remaining value or accumulates lost value. The sign convention must be stated before comparing work.", "diagnostic_use": "Use this to prioritize work by time-sensitive value rather than loudness, politics, or activity volume.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "decision_grade_telemetry" ], "related_question_ids": [ "capacity-008", "topology-003", "telemetry-002", "telemetry-008" ], "required_signals": [ "business milestone", "work age", "expected value", "cycle time", "blocked dependency", "release date movement" ], "mcp_source_categories": [ "product roadmap", "work tracker", "release management", "finance or planning summaries if approved" ], "interpretation_rules": [ "If business value is time-sensitive, queue age becomes economic loss.", "If work priority lacks value and time basis, do not treat priority labels as evidence.", "If telemetry cannot connect work to outcome, report missing value instrumentation." ], "answer_card_fields": [ "value_at_risk", "time_sensitivity", "blocked_dependency", "confidence" ], "report_sections": [ "Cost, Value, and Risk Economics", "Executive Summary" ], "maturity": "derived_model", "validation_status": "economic_rate_definition_requires_value_model", "assumptions": [ "Value loss is estimated over a defined decision horizon.", "The value model includes relevant revenue, risk, cost, or mission impact." ], "units": "Currency or value units per unit time.", "limitations": [ "The derivative is only as credible as the value model.", "Use scenarios or intervals when value is uncertain." ] }, { "id": "dependency_density", "label": "Dependency Density", "formula_type": "graph_model", "doctrine_source": { "route": "/integration/dependency-density/", "file": "data/integration/dependency.ts", "title": "Dependency Density and Gall's Law" }, "formula": "E_max = N(N-1)/2; D = E/E_max", "plain_language": "A system with N nodes can contain at most N(N-1)/2 undirected pairwise dependencies. Actual dependency density is the observed edge count divided by that bound.", "diagnostic_use": "Use this to test whether team, service, or vendor topology is creating integration cost faster than delivery value.", "related_domains": [ "distributed_capacity_topology", "knowledge_architecture_memory", "governance_security_failure_modes" ], "related_question_ids": [ "topology-003", "topology-006", "knowledge-003", "knowledge-006", "gov-006" ], "required_signals": [ "service count", "team count", "interface count", "cross-service changes", "owner map", "dependency incidents" ], "mcp_source_categories": [ "service registry", "architecture catalog", "source control", "incident system", "work tracker" ], "interpretation_rules": [ "If dependency count grows without ownership clarity, integration risk rises.", "If service boundaries exist only on diagrams and not in code or deployment independence, classify as distributed monolith risk.", "If dependency evidence is missing, do not recommend distributed ownership." ], "answer_card_fields": [ "dependency_map", "owner_map", "integration_risk", "missing_evidence" ], "report_sections": [ "Topology Readiness", "Failure Mode Register" ], "maturity": "established_model", "validation_status": "established_complete_graph_bound_with_derived_density", "assumptions": [ "Dependencies are represented as undirected pairwise edges for the bound.", "N counts comparable system nodes and E counts observed edges within the same boundary." ], "units": "Edge count for E_max; dimensionless ratio for D.", "limitations": [ "N(N-1)/2 is the maximum possible edge count, not actual complexity.", "Directed, weighted, higher-order, and dynamic dependencies need richer graph measures." ] }, { "id": "synchronization_penalty", "label": "Synchronization Penalty", "formula_type": "distributed_work_model", "doctrine_source": { "route": "/integration/asynchronous-amplifier/", "file": "data/integration/async.ts", "title": "The Asynchronous Amplifier" }, "formula": "S_p = sum(T_wait + T_context_switch)", "plain_language": "Distributed work pays a penalty whenever waiting time and context switching replace direct feedback.", "diagnostic_use": "Use this to measure whether time-zone overlap, unclear ownership, or missing self-serve context is slowing the SDLC.", "related_domains": [ "distributed_capacity_topology", "capacity_intelligence", "decision_grade_telemetry" ], "related_question_ids": [ "topology-004", "topology-009", "capacity-003", "telemetry-003", "telemetry-004" ], "required_signals": [ "wait time", "handoff delay", "blocked comments", "review latency", "time-zone overlap", "context switch count" ], "mcp_source_categories": [ "work tracker", "pull request system", "calendar metadata if approved and aggregated", "engineering chat summaries if approved and redacted" ], "interpretation_rules": [ "If wait time is caused by missing context, add documentation or ownership before adding people.", "If time-zone overlap materially affects cycle time, topology choice must include overlap as a constraint.", "If context switching is unmeasured, report capacity as partially unknown." ], "answer_card_fields": [ "wait_time", "context_switching", "topology_constraint", "confidence" ], "report_sections": [ "Topology Readiness", "Capacity Constraint Map" ], "maturity": "operating_heuristic", "validation_status": "measurement_definition_requires_local_baseline", "assumptions": [ "Wait time and context-switch time are measured in the same time unit.", "Only avoidable synchronization costs are included." ], "units": "Person-hours or another declared time unit.", "limitations": [ "The sum does not capture quality loss or delayed learning unless those effects are measured separately.", "Attribution requires a defined workflow boundary." ] }, { "id": "availability_mttr", "label": "Availability and MTTR", "formula_type": "reliability_model", "doctrine_source": { "route": "/failure/recovery-metrics/", "file": "data/failure/metrics.ts", "title": "Recovery Metrics" }, "formula": "A = MTBF / (MTBF + MTTR)", "plain_language": "Availability improves when recovery time drops. Modern software systems should optimize fast recovery, not frozen change.", "diagnostic_use": "Use this to test whether engineering governance improves recovery or only slows delivery.", "related_domains": [ "execution_harness", "decision_grade_telemetry", "governance_security_failure_modes" ], "related_question_ids": [ "execution-004", "execution-005", "telemetry-005", "gov-002", "gov-006" ], "required_signals": [ "deployment frequency", "change failure rate", "MTTR", "rollback duration", "incident detection time", "incident diagnosis time" ], "mcp_source_categories": [ "CI/CD system", "incident system", "observability platform", "change management" ], "interpretation_rules": [ "If rollback is slow, execution governance is not production-grade.", "If MTTR improves while deployment frequency improves, governance is enabling flow.", "If incident data is missing, do not make reliability claims." ], "answer_card_fields": [ "mttr", "rollback_time", "change_failure_rate", "governance_gap" ], "report_sections": [ "Execution Control Report", "Governance and Failure Mode Register" ], "maturity": "established_model", "validation_status": "established_steady_state_availability_model", "assumptions": [ "Failure and repair cycles are represented by stable mean times.", "The service boundary and failure definition are consistent." ], "units": "Dimensionless ratio from 0 to 1.", "limitations": [ "Mean values hide tail risk and correlated failures.", "User-perceived availability can differ from component availability." ] }, { "id": "mttr_limit_behavior", "label": "MTTR Limit Behavior", "formula_type": "reliability_model", "doctrine_source": { "route": "/failure/recovery-metrics/", "file": "data/failure/metrics.ts", "title": "Recovery Metrics" }, "formula": "lim_{MTTR -> 0} MTBF / (MTBF + MTTR) = 1", "plain_language": "As recovery time approaches zero, availability approaches one even when failures still happen.", "diagnostic_use": "Use this to evaluate rollback, feature flags, observability, and authority delegation.", "related_domains": [ "execution_harness", "decision_grade_telemetry", "governance_security_failure_modes" ], "related_question_ids": [ "execution-003", "execution-004", "telemetry-003", "telemetry-005", "gov-002" ], "required_signals": [ "rollback path", "feature flag coverage", "incident time to mitigation", "approval latency", "audit record" ], "mcp_source_categories": [ "CI/CD system", "feature flag system", "incident system", "policy system" ], "interpretation_rules": [ "If mitigation requires manual escalation, MTTR is governed by authority latency, not tooling.", "If deployment and release are not separated, rollback risk is higher.", "If feature flags lack ownership and audit, they are not sufficient governance." ], "answer_card_fields": [ "mitigation_time", "approval_latency", "rollback_authority", "auditability" ], "report_sections": [ "Execution Control Report", "Governance and Risk Boundary" ], "maturity": "derived_model", "validation_status": "algebraic_limit_of_availability_model", "assumptions": [ "MTBF remains positive and finite as MTTR approaches zero." ], "units": "Dimensionless ratio.", "limitations": [ "The limit does not imply zero operational recovery cost.", "Detection, rollback, and data repair can remain material even when service restoration is fast." ] }, { "id": "mutation_score", "label": "Mutation Score", "formula_type": "quality_model", "doctrine_source": { "route": "/quality/blameless-quality-protocols/", "file": "data/quality/regulation.ts", "title": "Regulation: Blameless Science" }, "formula": "MS = K / (T - E)", "plain_language": "Test quality is measured by whether tests kill injected faults, not whether lines were merely executed.", "diagnostic_use": "Use this to test whether quality telemetry is meaningful enough to trust AI-generated or distributed engineering output.", "related_domains": [ "decision_grade_telemetry", "governed_agentic_sdlc", "execution_harness" ], "related_question_ids": [ "telemetry-005", "agent-002", "agent-004", "execution-009" ], "required_signals": [ "test coverage", "mutation score if available", "failed tests", "escaped defects", "review correction rate", "reverts" ], "mcp_source_categories": [ "test system", "CI/CD system", "pull request system", "incident system" ], "interpretation_rules": [ "If tests do not catch injected or known defect classes, do not trust automation output.", "If quality telemetry is limited to coverage percentage, mark telemetry as weak.", "If AI-generated code bypasses mutation or regression checks, require human gating." ], "answer_card_fields": [ "test_strength", "defect_signal", "ai_validation_boundary", "confidence" ], "report_sections": [ "Telemetry Trust Report", "Agentic Workflow Control Report" ], "maturity": "established_model", "validation_status": "established_software_testing_metric", "assumptions": [ "Equivalent mutants are excluded or estimated consistently.", "Killed and total mutants are generated under a documented operator set." ], "units": "Dimensionless ratio or percentage.", "limitations": [ "Mutation score measures test sensitivity to injected changes, not complete product quality.", "Operator quality and equivalent-mutant handling affect comparability." ] }, { "id": "cognitive_fidelity", "label": "Cognitive Fidelity", "formula_type": "cognitive_model", "doctrine_source": { "route": "/quality/", "file": "data/quality/overview.ts", "title": "Pillar IV: On Quality" }, "formula": "Quality ~ isomorphism(M_e, S_sys)", "plain_language": "Quality depends on how closely an engineer's mental model matches the actual system state.", "diagnostic_use": "Use this to evaluate whether ownership, documentation, and review systems keep human and agent contributors aligned with reality.", "related_domains": [ "knowledge_architecture_memory", "governed_agentic_sdlc", "decision_grade_telemetry" ], "related_question_ids": [ "knowledge-001", "knowledge-004", "knowledge-006", "agent-002", "agent-006", "telemetry-005" ], "required_signals": [ "architecture decision records", "documentation usage", "review comments", "rework caused by misunderstanding", "incident root cause", "agent correction rate" ], "mcp_source_categories": [ "architecture catalog", "documentation system", "pull request system", "incident system", "agent audit logs" ], "interpretation_rules": [ "If contributors act on stale or missing system knowledge, delivery failures are knowledge failures before people failures.", "If AI outputs are correct syntactically but wrong semantically, classify the workflow as human-gated.", "If incidents repeat because lessons are not stored, knowledge memory is broken." ], "answer_card_fields": [ "knowledge_gap", "mental_model_drift", "review_signal", "durable_memory_action" ], "report_sections": [ "Knowledge and Ownership Risk", "Agentic Workflow Control Report" ], "maturity": "research_hypothesis", "validation_status": "construct_requires_operational_definition_and_replication", "assumptions": [ "Mental-model and system-state representations can be defined and compared.", "The comparison does not use protected traits as quality proxies." ], "units": "Undefined until the isomorphism or similarity measure is operationalized.", "limitations": [ "The expression is conceptual and cannot be scored without a validated measurement instrument.", "Similarity does not by itself prove causal engineering judgment." ] }, { "id": "l2_adjusted_score", "label": "L2 Adjusted Communication Score", "formula_type": "fairness_model", "doctrine_source": { "route": "/quality/", "file": "data/quality/overview.ts", "title": "Pillar IV: On Quality" }, "formula": "s_adj = s_raw - beta * (f_error - E[f | P])", "plain_language": "Language form errors should not be allowed to erase correct technical reasoning.", "diagnostic_use": "Use this as a public doctrine mapping for fair evaluation of distributed contributors, not as a public scoring engine.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "governance_security_failure_modes" ], "related_question_ids": [ "capacity-007", "topology-008", "knowledge-008", "gov-004" ], "required_signals": [ "evaluation rubric", "technical reasoning evidence", "communication context", "review calibration", "bias control record" ], "mcp_source_categories": [ "approved evaluation records", "calibration records", "governance policy" ], "interpretation_rules": [ "Do not use accent or grammar as a proxy for engineering capability.", "Separate reasoning quality from language surface form.", "Do not expose individual evaluation records through the public research workflow." ], "answer_card_fields": [ "evaluation_boundary", "calibration_evidence", "bias_control", "confidence" ], "report_sections": [ "Governance and Risk Boundary", "Capacity Topology Readiness" ], "maturity": "derived_model", "validation_status": "statistical_adjustment_requires_calibration_and_fairness_audit", "assumptions": [ "Form error is measured separately from engineering content.", "Beta and the conditional expectation are estimated on representative data." ], "units": "Same standardized score unit as s_raw.", "limitations": [ "Adjustment can introduce bias when the conditioning model is misspecified.", "Report raw and adjusted scores with uncertainty and subgroup diagnostics." ] }, { "id": "frechet_semantic_distance", "label": "Frechet Semantic Distance", "formula_type": "semantic_fidelity_model", "doctrine_source": { "route": "/decisions/axiom-cortex-engine/", "file": "data/cortex.ts", "title": "Axiom Cortex" }, "formula": "FSD(y_q,b_q)=||mu_y-mu_b||_2^2 + Tr(Sigma_y + Sigma_b - 2(Sigma_y^(1/2) Sigma_b Sigma_y^(1/2))^(1/2))", "plain_language": "Semantic similarity should be measured by meaning, not surface phrasing.", "diagnostic_use": "Use this as a public doctrine reference for semantic matching and technical reasoning fidelity.", "related_domains": [ "knowledge_architecture_memory", "capacity_intelligence", "governance_security_failure_modes" ], "related_question_ids": [ "knowledge-005", "knowledge-008", "capacity-007", "gov-004" ], "required_signals": [ "approved rubric", "ideal answer blueprint", "semantic content evidence", "calibration record" ], "mcp_source_categories": [ "approved evaluation records", "knowledge base", "governance policy" ], "interpretation_rules": [ "Use semantic equivalence only inside approved evaluation or knowledge systems.", "Do not publish private transcript data or proprietary scoring parameters.", "If calibration evidence is missing, mark the semantic claim as unsupported." ], "answer_card_fields": [ "semantic_match_boundary", "calibration_status", "source_class", "missing_evidence" ], "report_sections": [ "Knowledge and Ownership Risk", "Governance and Risk Boundary" ], "maturity": "derived_model", "validation_status": "adapted_distribution_distance_requires_construct_validation", "assumptions": [ "Embedding distributions are adequately summarized by means and covariances.", "Compared samples use the same embedding model and preprocessing." ], "units": "Squared embedding-space distance.", "limitations": [ "The Gaussian approximation may be poor.", "Distance in embedding space is not direct proof of engineering quality or equivalence." ] }, { "id": "optimal_transport_code_switch", "label": "Optimal Transport With Code Switch Awareness", "formula_type": "semantic_fidelity_model", "doctrine_source": { "route": "/decisions/axiom-cortex-engine/", "file": "data/cortex.ts", "title": "Axiom Cortex" }, "formula": "s_q^OT = psi(W_2(P_q,Q_q; C o (1 - lambda M)))", "plain_language": "Code switching should not be treated as technical weakness when meaning is preserved.", "diagnostic_use": "Use this as public governance language for fair interpretation of multilingual technical reasoning.", "related_domains": [ "capacity_intelligence", "governance_security_failure_modes" ], "related_question_ids": [ "capacity-007", "knowledge-008", "gov-004" ], "required_signals": [ "language context", "semantic content", "evaluation calibration", "bias review" ], "mcp_source_categories": [ "approved evaluation records", "calibration records", "governance policy" ], "interpretation_rules": [ "Do not penalize multilingual phrasing when technical reasoning is preserved.", "Do not expose raw transcripts in public artifacts.", "Require governance review before using language-sensitive scoring." ], "answer_card_fields": [ "language_boundary", "semantic_evidence", "bias_review", "confidence" ], "report_sections": [ "Governance and Risk Boundary" ], "maturity": "research_hypothesis", "validation_status": "proposed_metric_requires_complete_cost_definition_and_replication", "assumptions": [ "P_q, Q_q, the cost matrix C, mask M, lambda, and transform psi are fully defined.", "The transport comparison preserves the engineering construct being measured." ], "units": "Defined by psi applied to the transport cost.", "limitations": [ "The current compact formula omits optimization constraints.", "A lower transport cost does not automatically imply better engineering reasoning." ] }, { "id": "integrity_l2", "label": "Composite L2 Integrity Score", "formula_type": "fairness_model", "doctrine_source": { "route": "/decisions/axiom-cortex-engine/", "file": "data/cortex.ts", "title": "Axiom Cortex" }, "formula": "Integrity_L2 = w1*ICC_band + w2*avg(s_OT) + w3*avg(c_q) + w4*R2_Phase2_to_Phase3 + w5*GC - w6*Delta_trans", "plain_language": "Integrity combines consistency, semantic fidelity, conceptual content, phase coherence, grounding, and translation drift.", "diagnostic_use": "Use this only as public schema context for evaluation governance. Do not expose proprietary weights or private evidence.", "related_domains": [ "capacity_intelligence", "governance_security_failure_modes" ], "related_question_ids": [ "capacity-007", "knowledge-008", "gov-004", "gov-005" ], "required_signals": [ "approved rubric", "calibration evidence", "grounding check", "translation drift check", "audit record" ], "mcp_source_categories": [ "approved evaluation records", "governance policy", "audit records" ], "interpretation_rules": [ "Never publish proprietary scoring weights or raw evaluation records.", "Use aggregate calibration and governance evidence only.", "If audit evidence is missing, classify the evaluation system as not decision-grade." ], "answer_card_fields": [ "calibration_status", "audit_status", "private_data_boundary", "missing_evidence" ], "report_sections": [ "Governance and Risk Boundary" ], "maturity": "research_hypothesis", "validation_status": "composite_index_requires_normalization_weighting_and_sensitivity_analysis", "assumptions": [ "Every component is normalized to a comparable scale.", "Weights are declared before evaluation and tested for sensitivity." ], "units": "Dimensionless composite score after normalization.", "limitations": [ "Weights can dominate the result and must not be hidden.", "A single composite score can conceal compensating failures across components." ] }, { "id": "counterfactual_esl_stability", "label": "Counterfactual ESL Stability", "formula_type": "fairness_constraint", "doctrine_source": { "route": "/decisions/zero-trust-scoring/", "file": "data/decisions/regulation.ts", "title": "Regulation: Zero Trust" }, "formula": "|c_q - c_q_prime| <= tau_trans", "plain_language": "A score should remain stable when the same technical meaning is expressed in standardized English.", "diagnostic_use": "Use this as an audit question for evaluation systems and AI-assisted talent decisions.", "related_domains": [ "governance_security_failure_modes", "capacity_intelligence" ], "related_question_ids": [ "capacity-007", "gov-004", "gov-005" ], "required_signals": [ "counterfactual test result", "score drift", "translation policy", "audit record" ], "mcp_source_categories": [ "approved evaluation records", "audit records", "governance policy" ], "interpretation_rules": [ "If meaning is stable but score changes materially, flag bias risk.", "If the evaluation system lacks counterfactual testing, mark governance incomplete.", "Do not expose raw candidate data through this public research system." ], "answer_card_fields": [ "score_stability", "bias_risk", "audit_record", "next_safe_action" ], "report_sections": [ "Governance and Risk Boundary" ], "maturity": "research_hypothesis", "validation_status": "counterfactual_test_requires_semantics_preserving_transformations", "assumptions": [ "The counterfactual changes language form without changing engineering meaning or difficulty.", "Tau_trans is set before evaluation." ], "units": "Same score unit as c_q.", "limitations": [ "Invalid counterfactuals can create false instability.", "Passing the threshold is evidence of local stability, not complete fairness." ] }, { "id": "adversarial_indistinguishability", "label": "Adversarial Indistinguishability", "formula_type": "fairness_constraint", "doctrine_source": { "route": "/decisions/zero-trust-scoring/", "file": "data/decisions/regulation.ts", "title": "Regulation: Zero Trust" }, "formula": "AUC_protected_prediction compared with the 0.5 random-classification baseline", "plain_language": "An adversary that performs near the random-classification baseline has not demonstrated useful prediction of the protected attribute. That result is one diagnostic, not proof of fairness or zero leakage.", "diagnostic_use": "Use this to audit whether evaluation telemetry is fair enough for capacity topology decisions.", "related_domains": [ "governance_security_failure_modes", "capacity_intelligence" ], "related_question_ids": [ "capacity-007", "gov-004", "gov-005" ], "required_signals": [ "adversarial test result", "AUC summary", "feature policy", "model audit record" ], "mcp_source_categories": [ "approved evaluation records", "model governance records", "audit records" ], "interpretation_rules": [ "If background prediction is materially better than random, classify the scoring system as biased or leaky.", "If model governance records are unavailable, do not treat the evaluation score as decision-grade.", "Use aggregate audit summaries only." ], "answer_card_fields": [ "auc_summary", "leakage_risk", "audit_status", "confidence" ], "report_sections": [ "Governance and Risk Boundary" ], "maturity": "operating_heuristic", "validation_status": "diagnostic_test_not_fairness_proof", "assumptions": [ "The adversary is appropriately powered and evaluated on held-out representative data.", "Protected or linguistic labels are valid for the stated audit purpose." ], "units": "Dimensionless AUC from 0 to 1.", "limitations": [ "AUC near 0.5 is necessary but not sufficient evidence that protected information is not recoverable.", "It does not prove fairness, absence of leakage, calibration, or equal outcomes." ] }, { "id": "agentic_intervention_load", "label": "Agentic Intervention Load", "formula_type": "agentic_system_model", "doctrine_source": { "route": "/integration/integration-topologies/", "file": "data/integration/topology.ts", "title": "Integration Topologies" }, "formula": "Intervention Load Hours = Agent Execution Volume * Error Rate * Mean Human Repair Time + Context Switching Hours", "plain_language": "Agent speed is not free. Convert agent errors and context switching into the same human-time unit before comparing agent execution volume with orchestration capacity.", "diagnostic_use": "Use this to decide whether an agentic workflow is increasing throughput or overloading human orchestrators.", "related_domains": [ "governed_agentic_sdlc", "governed_adaptive_control_loops", "decision_grade_telemetry" ], "related_question_ids": [ "agent-001", "agent-004", "agent-005", "agent-006", "adaptive-003", "telemetry-007" ], "required_signals": [ "agent execution volume", "agent error rate", "human review load", "correction rate", "context switching", "cycle-time impact", "rollback triggers" ], "mcp_source_categories": [ "agent audit logs", "pull request system", "work tracker", "CI/CD system", "incident system" ], "interpretation_rules": [ "If intervention load exceeds human orchestration capacity, throttle agent execution.", "If agent velocity increases review queues, do not classify the workflow as successful automation.", "If error rate is unknown, keep the workflow human-gated." ], "answer_card_fields": [ "agent_volume", "agent_error_rate", "human_review_load", "throttle_recommendation" ], "report_sections": [ "Agentic Workflow Control Report", "Governed Adaptive Control Loop Report" ], "maturity": "operating_heuristic", "validation_status": "operational_cost_model_requires_local_measurement", "assumptions": [ "Error rate is measured on comparable agent actions.", "Mean human repair time and context-switch time use the same time unit." ], "units": "Human time, normally person-hours per measurement window.", "limitations": [ "Error severity and review effort may be highly skewed, so averages need percentile reporting.", "The model excludes downstream incident cost unless added explicitly." ] }, { "id": "engineering_throughput_equation", "label": "Engineering Throughput Equation", "formula_type": "throughput_model", "doctrine_source": { "route": "/teams/agentic-development-workflows/", "file": "data/teams/agentic.ts", "title": "Agentic Engineering Workflows" }, "formula": "Throughput = f(Topology, Cognitive Load, Coordination Cost, AI Assistance)", "plain_language": "Throughput is shaped by team topology, cognitive load, coordination cost, and bounded AI assistance, not headcount alone.", "diagnostic_use": "Use this as the bridge between doctrine math and the Engineering Capacity OS capacity topology questions.", "related_domains": [ "capacity_intelligence", "distributed_capacity_topology", "governed_agentic_sdlc", "decision_grade_telemetry" ], "related_question_ids": [ "capacity-001", "capacity-003", "topology-003", "agent-001", "telemetry-006" ], "required_signals": [ "team topology", "active WIP", "context switching", "coordination delay", "agent usage", "cycle time", "quality signal" ], "mcp_source_categories": [ "work tracker", "pull request system", "agent audit logs", "telemetry platform" ], "interpretation_rules": [ "If throughput gains come with higher rework or risk, do not report a capacity improvement.", "If AI assistance lowers cognitive load and review drag, classify the workflow as promising but still governed.", "If topology and coordination cost are unknown, throughput claims are unsupported." ], "answer_card_fields": [ "throughput_signal", "topology_signal", "cognitive_load_signal", "agent_assistance_signal" ], "report_sections": [ "Capacity Topology Readiness", "Agentic Workflow Control Report" ], "maturity": "research_hypothesis", "validation_status": "dependency_map_not_predictive_equation", "assumptions": [ "Topology, load, coordination cost, and AI assistance are measured over the same workflow and time window.", "Quality and risk constraints are reported with throughput." ], "units": "Throughput uses completed value-bearing work per unit time; inputs retain their own units.", "limitations": [ "The function does not specify coefficients, interactions, or causal direction.", "Higher throughput is not system improvement when quality, risk, or value degrades." ] } ], "epistemic_policy": { "purpose": "Separate established mathematics from TeamStation-derived models, operating heuristics, and research hypotheses.", "classes": { "established_model": "A named or standard mathematical or engineering model used within its stated assumptions.", "derived_model": "An algebraic or statistical model derived from stated assumptions and requiring local parameter estimation.", "operating_heuristic": "A practical decision rule or diagnostic threshold that requires local testing and must not be presented as a universal law.", "research_hypothesis": "A proposed relationship or construct that is testable but not yet independently validated or calibrated." }, "decision_rule": "No formula may produce an automated recommendation when its assumptions, units, required signals, or validation boundary are unknown." } }