Platform/Trust Observatory/Methodology Directory
📐

Canonical Methodology & Provenance Directory

Tier 1 §14 Audited

Universal mathematical derivations, primary source attribution, and pre-registered falsification criteria for all 57 numerical indicators across UTP. Every metric in the user interface is typed and verified against this canonical registry by construction.

Tier 1 §2 • Single Source of Truth

No fact or formula exists in two places. Metric keys in UI code are derived directly from this registry at compile-time.

Tier 1 §6 • NULL Not Zero

Missing telemetry renders as an explicit uncalculated state. Defaulting unobserved values to 0 is strictly prohibited.

Tier 1 §14 • Strict Falsification

Every single metric carries a pre-registered falsification rubric defining the exact empirical evidence that invalidates the model.

Showing 57 of 57 metrics

Multi-Channel Momentum Velocity

momentum
metricKey: momentum_score
1. Mathematical Derivation

Composite velocity score calculated as normalized 30-day velocity across GitHub activity (35%), OpenAlex publications (25%), SEC Form D venture funding (25%), and USPTO patent filings (15%).

Formula: M = 0.35 G_{gh} + 0.25 G_{pub} + 0.25 G_{fund} + 0.15 G_{pat}

2-Year Commercial Arrival Probability

forecasting
metricKey: arrival_probability
1. Mathematical Derivation

Logistic regression classifier predicting probability that an innovation reaches at least one confirmed commercial deployment event within 24 months, conditioned on current TRL, momentum, and foundational science citations.

Formula: P(\text{arrival} \le 2\text{yr}) = \sigma(\mathbf{w}^T \mathbf{x} + b)

Economic Disruption Magnitude

disruption
metricKey: disruption_magnitude
1. Mathematical Derivation

Projected percentage disruption scale (0-100) combining total addressable market substitution potential, gross margin compression headroom, and unit cost arbitrage ratio relative to legacy incumbents.

Formula: D = \min\left(100, \, 100 \times \left[0.4 \frac{\text{TAM}_{sub}}{\text{TAM}_{total}} + 0.35 \left(1 - \frac{C_{new}}{C_{old}}\right) + 0.25 \Delta_{\text{margin}}\right]\right)

Unified Disruption Composite

disruption
metricKey: composite_score
1. Mathematical Derivation

Harmonic mean of capability benchmark (40%), commercial evidence count (35%), and academic/patent velocity (25%), bounded between 0% and 100%.

Formula: S_{\text{composite}} = \left( \frac{0.40}{S_{\text{cap}}} + \frac{0.35}{S_{\text{ev}}} + \frac{0.25}{S_{\text{vel}}} \right)^{-1}

Technical Capability Benchmark Score

opportunity
metricKey: capability_score
1. Mathematical Derivation

Normalized benchmark score (0-100) calibrated against empirical domain-specific leaderboards: LMSYS Arena for LLMs, MLPerf for accelerators, and IEEE/IEDM for physical semiconductor device density.

Formula: C = \frac{\text{Performance} - \text{Baseline}}{\text{Frontier} - \text{Baseline}} \times 100

Addressable Economic Need (Annual USD)

opportunity
metricKey: economic_need_usd
1. Mathematical Derivation

Quantified annual economic expenditure or labor cost currently spent on tasks directly addressed by this technology across relevant NAICS sector codes: sum(employment * mean_annual_wage * task_exposure).

Formula: N = \sum_{j \in \text{NAICS}} L_j \cdot w_j \cdot \omega_j

Annual Labor Spend at Risk (USD)

labor
metricKey: labor_spend_at_risk
1. Mathematical Derivation

Aggregate annual payroll exposure in occupational codes where task automation potential exceeds 50%: W_exposed = sum(employment_j * wage_j * task_overlap_j).

Formula: W_{\text{exposed}} = \sum_j L_j \cdot w_j \cdot \omega_j

Stranded Physical Capital Assets at Risk

disruption
metricKey: stranded_capital_assets_usd
1. Mathematical Derivation

Cumulative undepreciated asset base rendered economically obsolete by emerging paradigm substitution: S(t) = Net PP&E * Disruption Rate.

Formula: S(t) = \text{PPE}_{\text{net}} \cdot D(t)

Exposed Labor Headcount

labor
metricKey: exposed_labor_headcount
1. Mathematical Derivation

Headcount in occupational codes where task-level exposure exceeds displacement threshold: H(t) = sum(employment_i * task_overlap_i).

Formula: H(t) = \sum_i E_i \cdot O_i

Active Critical Bottleneck Gates

supply_chain
metricKey: active_critical_bottlenecks
1. Mathematical Derivation

Count of unresolved gating dependencies in the critical path across science, supply chain, and regulatory regimes.

Formula: B(t) = \sum_j \mathbb{I}(\text{gate}_j = \text{blocked})

Financial Speculative Multiple F(t)

s_curve
metricKey: perez_financial_multiple
1. Mathematical Derivation

Speculative financial multiple modeled via Carlota Perez Frenzy dynamics: captures enterprise valuation expansion, venture multiple inflation, and public equity market capitalization relative to installed baseline.

Formula: F(t) = P(t) + \Delta_{\text{bubble}} \cdot e^{-\frac{(t - t_{\text{frenzy}})^2}{2\sigma^2}}

Production Deployment Capital P(t)

s_curve
metricKey: perez_production_capital
1. Mathematical Derivation

Real installed economic deployment modeled via logistic diffusion: P(t) = L / (1 + e^{-k(t - t_0)}), calibrated against physical adoption statistics (fabs, gigawatt capacity, units shipped).

Formula: P(t) = \frac{L}{1 + e^{-k(t - t_0)}}

Installed Infrastructure Capacity I(t)

s_curve
metricKey: perez_infrastructure
1. Mathematical Derivation

Cumulative physical infrastructure capacity installed to support deployment (e.g. gigawatts of energized datacenter power, extreme ultraviolet lithography wafer capacity, transmission lines).

Formula: I(t) = \int_0^t \text{CapEx}_{\text{infra}}(\tau) \cdot \eta(\tau) \, d\tau

Perez Speculative Decoupling Delta

disruption
metricKey: perez_decoupling_delta
1. Mathematical Derivation

Dual-trajectory divergence: Delta(t) = F(t) - P(t), measuring speculative financial capital acceleration relative to installed production deployment.

Formula: \Delta(t) = F(t) - P(t)

Infrastructure Utilization Overhang (I - P)

s_curve
metricKey: perez_util_overhang
1. Mathematical Derivation

Capacity spread between installed physical infrastructure and current productive utilization: Overhang(t) = I(t) - P(t). Identifies stranded capacity and timing risk.

Formula: \text{Overhang}(t) = I(t) - P(t)

Corporate Debt Structure (D/E & ICR)

finance
metricKey: corporate_debt_ratios
1. Mathematical Derivation

Debt-to-Equity ratio (D/E = Total Debt / Book Equity) and Interest Coverage Ratio (ICR = EBIT / Interest Expense) for companies funding physical infrastructure buildout.

Formula: \text{D/E} = \frac{\text{Total Debt}}{\text{Total Equity}}, \quad \text{ICR} = \frac{\text{EBIT}}{\text{Interest Expense}}

Perez Techno-Economic Phase

s_curve
metricKey: perez_phase
1. Mathematical Derivation

Algorithmic classification into Irruption, Frenzy, Synergy, or Maturity based on key factor cost deflation, speculative decoupling delta, and infrastructure buildout.

Formula: \text{Phase} = \arg\max_{\phi} P(\phi \mid \Delta(t), I(t), P(t), \text{Cost}(t))

Wright's Law Cost Parity Crossover

cost_parity
metricKey: wrights_law_crossover
1. Mathematical Derivation

Predicted calendar year at which entrant learning-curve cost intersects incumbent cost threshold: C_entrant(Y) <= C_incumbent.

Formula: t_{\text{crossover}} = t \text{ s.t. } C_1 \cdot Y(t)^{-w} \le C_{\text{incumbent}}

Wright's Law Progress Ratio / Learning Rate

cost_parity
metricKey: wrights_law_learning_rate
1. Mathematical Derivation

Empirical percentage cost reduction achieved for each doubling of cumulative manufacturing production volume: Learning Rate = 1 - 2^{-w}.

Formula: \text{LR} = 1 - 2^{-w}, \quad \text{where } C(Y) = C_1 \cdot Y^{-w}

Verified Commercial Adoption Events

commercial
metricKey: commercial_evidence_count
1. Mathematical Derivation

Discrete count of independently verified commercial adoption events meeting Rubric C criteria (dated, cited, deployed at scale in real production environments).

Formula: E_{\text{count}} = \sum_{i \in \text{events}} \mathbb{I}(\text{Rubric C verified})

Distinct Adopting Entities

commercial
metricKey: distinct_adopters
1. Mathematical Derivation

Count of unique, non-affiliated corporate, government, or academic entities with confirmed production deployments of the specified technology.

Formula: A_{\text{distinct}} = |\{ \text{Entity}_k : \exists \text{ deployment event} \}|

Tracked Supply Chain Companies

commercial
metricKey: tracked_companies
1. Mathematical Derivation

Census count of distinct commercial organizations tracked across the 6-stage AI revolution supply chain architecture (EDA/Foundry, GPUs, ASICs, Cooling/Power, Hyperscalers, Frontier Labs).

Formula: C_{\text{tracked}} = \sum_{s=1}^6 |\{ \text{Company}_{i,s} \}|

Tracked Applied Technologies

coverage
metricKey: technologies_tracked
1. Mathematical Derivation

Census count of active applied technologies and innovations with verified commercialization paths, patent signals, or adoption evidence in the platform graph.

Formula: T_{\text{tracked}} = |\{ \text{Innovation}_k \in \text{Active Graph} \}|

Market Capitalization (USD)

market_valuation
metricKey: market_cap_usd
1. Mathematical Derivation

Total public equity market value calculated as the latest closing share price multiplied by diluted common shares outstanding as disclosed in the most recent SEC Form 10-Q/K.

Formula: \text{Market Cap} = P_{\text{close}} \times S_{\text{diluted}}

Trailing 12-Month Price-to-Earnings (P/E)

market_valuation
metricKey: trailing_pe
1. Mathematical Derivation

Ratio of current market share price to GAAP diluted earnings per share (EPS) over the trailing four fiscal quarters.

Formula: \text{P/E} = \frac{P_{\text{current}}}{\sum_{q=1}^4 \text{EPS}_q}

Trailing 12-Month Price-to-Sales (P/S)

market_valuation
metricKey: price_to_sales_ttm
1. Mathematical Derivation

Ratio of enterprise market capitalization to total GAAP net revenue generated over the trailing four fiscal quarters.

Formula: \text{P/S} = \frac{\text{Market Cap}}{\sum_{q=1}^4 \text{Revenue}_q}

Enterprise Value (EV)

market_valuation
metricKey: enterprise_value_usd
1. Mathematical Derivation

Theoretical takeover price of a company: Market Capitalization plus Total Short- and Long-Term Debt, minus Cash and Cash Equivalents.

Formula: \text{EV} = \text{Market Cap} + \text{Total Debt} - \text{Cash}

Translation Latency (Gestation Horizon)

basic_science
metricKey: translation_latency_years
1. Mathematical Derivation

Duration in calendar years between the publication date of foundational basic science discovery (t_basic) and the first verified commercial deployment at scale (t_commercial).

Formula: \Delta t_{\text{translation}} = t_{\text{commercial}} - t_{\text{basic\_pub}}

AI Science Translation Speedup Multiplier

basic_science
metricKey: ai_speedup_multiplier
1. Mathematical Derivation

Ratio comparing the historical mean translation latency of physical science / biotechnology (~13.0 years) against computer science / modern AI foundation models (~2.2 years).

Formula: \text{Speedup} = \frac{\overline{\Delta t}_{\text{Hardware/Bio}}}{\overline{\Delta t}_{\text{AI/Software}}} = \frac{13.0\text{y}}{2.2\text{y}} \approx 5.8\times

Historical Citations (Web of Science / OpenAlex)

basic_science
metricKey: historical_citations_wos
1. Mathematical Derivation

Cumulative global peer-reviewed citation count indexed across Web of Science Core Collection and OpenAlex academic corpora for landmark foundational research papers.

Formula: C_{\text{historical}} = \sum_{w \in \text{corpus}} \mathbb{I}(w \text{ cites paper})

Annual Paper Velocity (Normalized)

basic_science
metricKey: paper_velocity
1. Mathematical Derivation

Annual rate of peer-reviewed publications and co-citations referencing a foundational discovery node, normalized against the discipline baseline mean over a rolling 3-year window.

Formula: V_{\text{paper}}(t) = \frac{\text{Citations}(t) - \mu_{\text{discipline}}(t)}{\sigma_{\text{discipline}}(t)}

Rubric C Claim Evidence Score (0–5)

epistemic_audit
metricKey: claim_evidence_score
1. Mathematical Derivation

Expert-audited score (0 to 5) evaluating empirical support across 8 independent pre-registered dimensions: primary source rigor, falsifiability, replication, analog match, code availability, data freshness, boundary bounds, and conflict disclosure.

Formula: S_d \in \{0, 1, 2, 3, 4, 5\}, \quad d \in [1..8]

Scientific Disciplines Represented

coverage
metricKey: disciplines_represented
1. Mathematical Derivation

Count of unique OECD/NSF academic scientific disciplines represented among foundational basic discovery nodes (Computer Science, Condensed Matter Physics, Molecular Biology, Mathematics, Materials Science, Electrical Engineering).

Formula: D_{\text{count}} = |\{ \text{Discipline}(n) : n \in \text{Basic Nodes} \}|

Kaplan-Meier Non-Parametric Survival Estimate

statistics
metricKey: kaplan_meier_survival
1. Mathematical Derivation

Non-parametric survival probability function S(t) correcting for right-censoring in pending, uncompleted technology gestation horizons: S(t) = prod_{t_i <= t} (1 - d_i / n_i).

Formula: S(t) = \prod_{t_i \le t} \left(1 - \frac{d_i}{n_i}\right)

Point-in-Time Brier Calibration Loss

forecasting
metricKey: brier_score
1. Mathematical Derivation

Strictly proper scoring rule evaluating probability calibration. Mean squared error between predicted probabilistic forecast P(breakout) and binary empirical ground truth outcome Y ∈ {0, 1} across historical test cases: BS = (1/N) ∑ (p_i - y_i)².

Formula: \text{BS} = \frac{1}{N} \sum_{i=1}^N (p_i - y_i)^2

Directional Prediction Hit Rate

forecasting
metricKey: hit_rate_pct
1. Mathematical Derivation

Percentage of historical test cases where the model's binary decision threshold (p ≥ 0.50) correctly matched empirical ground truth breakout or flop status across blinded historical epochs.

Formula: \text{Hit Rate} = \frac{\text{TP} + \text{TN}}{\text{Total Cases}} \times 100

Key Factor Unit Cost Deflation

cost_parity
metricKey: key_factor_deflation
1. Mathematical Derivation

Empirical unit cost of the techno-economic paradigm's core key factor (e.g. inference intelligence per token, energy per kWh, transistor per mm²), tracking cumulative experience curve deflation according to Wright's Law C(Y) = C_1 · Y^{-w} relative to emergence base year.

Formula: C(Y) = C_1 \cdot Y^{-w}, \quad \Delta_{\text{deflation}} = \frac{C_{\text{current}} - C_{\text{base}}}{C_{\text{base}}} \times 100

Hyper-Decoupling Paper vs. Real Capital Multiple

macro_bubble
metricKey: hyper_decoupling_multiple
1. Mathematical Derivation

Perez frenzy phase multiple comparing total financialized enterprise value (EV) of paradigm leaders against the cumulative tangible capital stock (CapEx) and physical R&D deployed into real production capacity: M = ∑ EV_i / ∑ (CapEx_i + R&D_i).

Formula: M_{\text{decoupling}} = \frac{\sum_{i} \text{Enterprise Value}_i}{\sum_{i} (\text{Capital Stock}_i + \text{Cumulative R\&D}_i)}

Socio-Institutional Mismatch Delta Δ_inst(t)

perez_framework
metricKey: institutional_mismatch_delta
1. Mathematical Derivation

Carlota Perez structural friction metric calculating the spread between technological deployment velocity P_tech(t) and statutory/regulatory institutional absorption capacity A_inst(t): Δ_inst(t) = P_tech(t) - A_inst(t).

Formula: \Delta_{\text{inst}}(t) = P_{\text{tech}}(t) - A_{\text{inst}}(t)

Non-Core NAICS Cross-Sector Diffusion

diffusion
metricKey: cross_sector_penetration
1. Mathematical Derivation

Proportion of traditional, non-tech NAICS super-sectors (e.g. Agriculture, Discrete Manufacturing, Freight Logistics, Healthcare, Retail) that have deployed the general-purpose technology into active revenue production beyond pilot stage.

Formula: \text{Penetration} = \frac{\sum_{s \in \text{Traditional}} \mathbb{I}(\text{Adoption}_s \ge \theta)}{N_{\text{Traditional}}} \times 100

Prevailing Industry Gross Margin (%)

market_structure
metricKey: typical_gross_margin_pct
1. Mathematical Derivation

Prevailing gross profit margin percentage across incumbent and entrant firms in the defined market structure: (Revenue - Cost of Goods Sold) / Revenue * 100%.

Formula: \text{Gross Margin} = \frac{\text{Revenue} - \text{COGS}}{\text{Revenue}} \times 100\%

Lerner Pricing Power Index

market_structure
metricKey: pricing_power_index
1. Mathematical Derivation

Normalized Lerner Index measuring an industry's market power to price above marginal cost: L = (P - MC) / P, scaled from 0.0 (perfect Bertrand commodity competition at marginal cost) to 1.0 (unconstrained monopoly pricing umbrella).

Formula: L = \frac{P - \text{MC}}{P} \in [0.0, \, 1.0]

ASC 606 Statutory Valid Backlog (USD)

commercial_contracts
metricKey: statutory_backlog_usd
1. Mathematical Derivation

Audited commercial contract value meeting US GAAP ASC 606 standards: non-binding LOIs, memoranda of understanding, and uncommitted pipeline are assigned zero weight (0.0). Only binding take-or-pay purchase orders with fixed delivery schedules and termination fees qualify.

Formula: \text{Backlog}_{\text{ASC606}} = \sum_{i} V_i \cdot \mathbb{I}(\text{Binding Order}_i) \cdot (1 - \delta_i)

USGS Planetary Production Share (%)

physical_bounds
metricKey: planetary_production_share_pct
1. Mathematical Derivation

Physical mass conservation audit comparing the projected annual consumption of critical minerals/feedstocks at full technology scale against annual global primary mining extraction reported by the USGS.

Formula: S_{\text{planetary}} = \frac{\text{Annual Tech Consumption (metric tons)}}{\text{Global Annual Primary Extraction (metric tons)}} \times 100\%

Pareto Power Law Exponent (α)

power_law
metricKey: pareto_shape_parameter_alpha
1. Mathematical Derivation

Maximum likelihood estimate of the heavy-tailed power law shape parameter alpha governing economic value capture and citation concentration: P(X > x) = (x_min / x)^alpha.

Formula: P(X > x) = \left(\frac{x_{\min}}{x}\right)^\alpha, \quad \hat{\alpha} = 1 + n \left[\sum_{i=1}^n \ln\left(\frac{x_i}{x_{\min}}\right)\right]^{-1}

Net GDP Value-Added Delta (Chained 2024 USD)

disruption
metricKey: net_value_added_delta_usd
1. Mathematical Derivation

GDP contribution net of intermediate double-counting: (∑ created_frontier spend × VA_ratio) − (∑ destroyed_incumbent spend × VA_ratio), deflated to Chained 2024 USD via BEA GDP deflators. VA_ratio sourced from BEA Input-Output Use Tables by 4-digit NAICS code.

Formula: \Delta_{VA} = \sum_{c} S_c^{2024} \cdot \rho_c - \sum_{d} S_d^{2024} \cdot \rho_d

Net Upstream Supply Chain Ripple (Chained 2024 USD)

disruption
metricKey: net_upstream_ripple_usd
1. Mathematical Derivation

Symmetrical supply chain cascade: (∑ created_frontier × (B_k − 1)) − (∑ destroyed_incumbent × (B_k − 1)), where B_k is the Leontief backward multiplier for NAICS code k. Represents net change in orders placed on upstream supplier industries.

Formula: \Delta_{\text{upstream}} = \sum_c S_c^{2024}(B_c - 1) - \sum_d S_d^{2024}(B_d - 1)

Net Impaired Capital (Stranded Assets after Salvage, Chained 2024 USD)

disruption
metricKey: net_impaired_capital_usd
1. Mathematical Derivation

Physical capital rendered economically obsolete net of recoverable salvage value: ∑(stranded_capital_assets_usd × deflation_factor) − ∑(stranded_capital_assets_usd × salvage_recovery_rate × deflation_factor). Default salvage rate = 20% unless explicitly recorded.

Formula: K_{\text{impaired}} = \sum_d A_d^{2024} \cdot (1 - \sigma_d)

Total Consumer Surplus Gain (Harberger Triangle, Chained 2024 USD)

disruption
metricKey: total_consumer_surplus_gain_usd
1. Mathematical Derivation

Welfare gain to consumers from unit cost reduction via Harberger triangle approximation: CS = baseline_spend × (ΔP + 0.5 × |ε| × ΔP²), capped at 5× baseline_spend. Uses explicit consumer_surplus_gain_usd if recorded; otherwise computes from unit_cost_reduction_pct and price_elasticity (default ε = −1.5).

Formula: CS = S_{\text{base}} \cdot \left(\Delta P + \tfrac{1}{2}|\varepsilon| \Delta P^2\right)

Regularized Creative Destruction Ratio (CDR)

disruption
metricKey: creative_destruction_ratio
1. Mathematical Derivation

Laplace-smoothed ratio of gross created-frontier spend to gross destroyed-incumbent spend (Chained 2024 USD): CDR = (gross_created + $1B) / (gross_displaced + $1B). The $1B regularization constant prevents division-by-zero and ensures continuity near zero-displacement markets.

Formula: \text{CDR} = \frac{G_{\text{created}} + \$1\text{B}}{G_{\text{displaced}} + \$1\text{B}}

Ecosystem Public Market Capitalization (USD)

market_valuation
metricKey: ecosystem_market_cap_usd
1. Mathematical Derivation

Aggregate public equity market capitalization of all companies whose primary revenue derives from the tracked technology node, summed across SEC EDGAR-listed entities linked to the technology's market_metrics record. Computed by market_metrics_builder.py from company_market_signals.

Formula: \text{EcoMCap} = \sum_{i \in \text{ecosystem}} P_{i,\text{close}} \times S_{i,\text{diluted}}

Trailing 12-Month Private Capital Investment (USD)

market_valuation
metricKey: private_equity_investment_usd
1. Mathematical Derivation

Aggregate venture capital and growth equity financing volume raised by companies in the technology ecosystem over the trailing 12 months, sourced from SEC Form D filings and PitchBook/Crunchbase cross-referenced records.

Formula: \text{PE}_{\text{12m}} = \sum_{i, t \in [t-12, t]} \text{Raise}_i

Total Tracked Commercial Markets

coverage
metricKey: total_tracked_markets
1. Mathematical Derivation

Census count of all demand-side market arenas cataloged in the UTP market lifecycle registry, spanning active and extinct markets across 7 economic sectors and multiple Perez techno-economic surges.

Formula: M_{\text{total}} = |\{\text{Market}_k \in \text{Registry}\}|

Total Active Global TAM (USD)

market_valuation
metricKey: total_active_tam_usd
1. Mathematical Derivation

Sum of market_size_usd across all non-extinct markets in the UTP registry: ∑(market.market_size_usd) for markets where current_lifecycle_stage ≠ 'extinct_or_subsumed'. Sources: Gartner, IDC, WSTS, BloombergNEF, and UTP market sizing aggregation.

Formula: \text{TAM}_{\text{active}} = \sum_{m: \text{stage} \ne \text{extinct}} \text{TAM}_m

Average Active Market Gross Margin (%)

market_structure
metricKey: avg_active_gross_margin_pct
1. Mathematical Derivation

Unweighted arithmetic mean of typical_gross_margin_pct across all non-extinct tracked markets: ∑(market.typical_gross_margin_pct) / N_active. Each market's typical margin is sourced from SEC 10-K filings and CapitalIQ industry benchmarks.

Formula: \overline{GM} = \frac{1}{N} \sum_{m=1}^N GM_m

Industrial Organization Competitive Regimes Covered

market_structure
metricKey: io_regimes_covered
1. Mathematical Derivation

Count of distinct competitive structure archetypes classified in the UTP market taxonomy, based on Tirole (1988) Theory of Industrial Organization: Natural Monopoly, Cournot Oligopoly, Bertrand Price War, Monopolistic Competition, Bilateral Monopsony, Contestable Commodity.

Formula: R_{\text{IO}} = |\{\text{Regime}_k \in \text{UTP Taxonomy}\}|

Active & Historical Displacement Pairs

disruption
metricKey: displacement_pairs_count
1. Mathematical Derivation

Count of direct asymmetric entrant-vs-incumbent substitution pairs tracked in the UTP lifecycle graph where an entrant technology is displacing or has displaced a legacy incumbent, based on Christensen disruptive innovation framework and UTP cost-parity crossings.

Formula: D_{\text{pairs}} = |\{(\text{Entrant}_i, \text{Incumbent}_j) : \text{displacement\_active}\}|