§ 01Abstract
The Black Hole Index (BHI) measures structural lock-in for digital platforms — the degree to which a user, organisation, or counterparty cannot leave a system without proportional cost. We define a single dimensionless quantity B as the ratio of total capture surface to total escape surface, computed from eleven independently-scored parameters across capture, escape, and extended dimensions. This document specifies the scoring rubric, the V3.1 aggregation function, and the validation regime against external migration-cost data.
§ 02Axiom & framing
The instrument rests on a single axiom: structural lock-in is asymmetric capture relative to substitution. A platform with high capture surface but high substitution availability is not locked-in; a platform with modest capture and zero substitution is. The B-index makes this ratio explicit and bounded, so that platforms across radically different sectors (a stablecoin, an IDE assistant, a national grid operator) can be placed on the same scale.
BHI is intentionally not a quality, ethics, or pricing measure. A platform can clear B = 3 because its lock-in is structural, useful, and welcome — or because it is exploitative. The instrument reports the structural fact; interpretation belongs to the reader.
§ 03Eleven parameters
Each parameter is scored on a 0-to-10 ordinal rubric with anchored definitions at 0, 5, and 10. The rubric is published in full in the appendix to the paper.
| # | Parameter | Group | Anchor at 10 |
|---|---|---|---|
| 01 | Data | Capture | All user-generated state lives inside the platform with no equivalent export. |
| 02 | Memory | Capture | Persistent, system-side context that compounds with use and cannot be reconstructed elsewhere. |
| 03 | Action | Capture | Platform executes consequential actions on behalf of the user across multiple external surfaces. |
| 04 | Process | Capture | Operating procedures of the user/org are written around the platform's primitives. |
| 05 | Network | Capture | Direct two-sided network effects with no portable identity layer. |
| 06 | Closeness | Capture | Daily, intimate, multi-modal use; the platform has surface area against habit. |
| 07 | Portability | Escape | Full one-click export of all state to a competing system, including history and configuration. |
| 08 | Substitutability | Escape | Multiple commodity-grade alternatives exist at parity feature, parity price. |
| 09 | Human Fallback | Escape | The work the platform performs can be done by a human in reasonable time at reasonable cost. |
| 10 | Org Depth | Extended | Platform is embedded across >10 functions of the user organisation; removal requires structural change. |
| 11 | Momentum | Extended | Lock-in is increasing year-over-year; the gradient ∂B/∂t is positive and material. |
§ 04Aggregation function (V3.1)
Let K = (D, M, A, P, N, C) denote the capture vector and O = (Po, Sb, Hf) the escape vector, each on [0, 10]. Let Ω = (Od, Mo) be the extended pair.
The capture core is a simple mean lifted by a memory-action synergy term and modulated by the extended pair:
§ 05Zone thresholds
The continuous B is bucketed into five interpretive zones. Thresholds were calibrated against external migration-cost data on a 36-platform reference set; see the validation report for residuals and ICC.
- Useful Tool · 0 ≤ B < 0.5 — substitutable in days; no structural friction.
- Growing Gravity · 0.5 ≤ B < 1.0 — friction is real but reversible at modest cost.
- Transition Zone · 1.0 ≤ B < 1.5 — migration is a project, not a decision.
- Event Horizon · 1.5 ≤ B < 2.5 — leaving requires re-platforming the user or org.
- Black Hole · B ≥ 2.5 — exit cost approaches the value of the dependent activity itself.
§ 06Universe construction
The Q1 2026 universe is the top 100 platforms by economic relevance, drawn from twelve sectors. Inclusion criteria, in order: (i) market cap or comparable economic footprint, (ii) user/transaction volume, (iii) sector representativeness, (iv) data availability for all eleven parameters. Borderline cases are noted in the appendix.
The list is not a ranking of importance — it is a fixed evaluation universe, kept stable across releases so that quarter-on-quarter trajectories are comparable.
Twelve sectors · 100 platforms
§ 07Scoring protocol
Each platform is scored independently by two analysts using the published rubric. The protocol enforces:
- Anchored evidence. Every parameter score must be backed by a citation — a public filing, an API/export specification, a published migration case, or an admin-console screenshot.
- Blind first pass. Analysts score without seeing each other's notes.
- Adjudication. Scores diverging by more than 1.0 on any axis are reconciled by a third analyst with documented reasoning.
- Inter-rater coefficient. Cohort-level ICC(3,k) is reported per release. The Q1 2026 release reports ICC = 0.84.
§ 08Release cadence
Quarterly. Major version bumps (V1 → V2 → V3) revise the aggregation function; minor bumps (V3.0 → V3.1) revise rubric anchors or universe composition. Every numerical change is documented in the changelog, and historical scores are reissued under each new function so trajectories are not retroactively warped.
§ 09Limitations
BHI is a structural measure, not a behavioural one. It does not capture: (i) willingness to pay the migration cost, (ii) sector-specific regulatory dynamics, (iii) macro-cyclical effects on substitutability. The instrument is most useful when read alongside, not instead of, sector domain knowledge.
§ 10Changelog
- V3.1 · Q1 2026 — Org-depth multiplier introduced; momentum normalised; ε-floor formalised.
- V3.0 · Q3 2025 — Eleven-parameter rubric; capture/escape/extended split.
- V2.x · 2024 — Eight-parameter rubric; first public release.
- V1.x · 2023 — Six-parameter pilot; internal use only.