Canonical definitions for terms used across the IPS essays, economics notes, and Aion software. When two phrases appear in different folders for the same quantity, this page picks one primary name and lists aliases.
Document index: README.md · DOCUMENTS.md
Formal derivation: information_persisting_systems.md
Related theories: ips_and_related_theories.md
\(\Phi\) / \(\Psi\) / redundancy: substrate_shelter_and_redundancy.md
Cross-layer bridge: fractal_layers.md
Software map: fractal_layers.md
Alias table: glossary_table.csv (machine-readable; status = canonical | domain_alias | legacy | …)
Use these primary names in all new writing under docs/, papers/, to_publish/, and aion-core/docs/. Domain essays may substitute once per section (e.g. “budget/revenue” for \(P_{\mathrm{in}}\) in sociology), then revert to symbols.
| Term | Symbol | One-line meaning |
|---|---|---|
| Information-persisting system | \(\Sigma\) / IPS | Bounded subsystem with blanket, drive, internal model, and identity over \(\tau \gg \tau_{\mathrm{relax}}\) |
| Fractal Persistence Equation | FPE | Master accounting identity; persistence requires \(\mathcal{R} \ge 1\) |
| Persistence ratio | \(\mathcal{R}\) | Usable power income over required dissipation, modulated by \(\Psi\) and \(\Phi\) |
| Delusion divergence | \(\mathcal{D}_{\mathrm{KL}}\) | KL gap between internal model and resolved reality |
| Structural fatigue | \(\Gamma\) | Backlog of unresolved damage and obligations |
| Substrate integrity | \(\Phi\) | Health of level-\((L-1)\) sub-nodes in the composition graph |
| Shelter coefficient | \(\Psi\) | Attenuation of enclosing noise by level-\((L+1)\) IPS |
| Power income | \(P_{\mathrm{in}}\) | Environmental free energy imported before efficiency losses |
| Coupling efficiency | \(\eta\) | Fraction of \(P_{\mathrm{in}}\) converted to boundary-maintaining work |
| Complexity | \(\omega\) | Structural constraint tax on the blanket |
| Internal noise floor | \(\mathcal{E}_\Sigma\) | Irreducible fluctuation power at information-carrying modes |
| Internal model | \(\mu\) / \(q_\mu\) | Running probability structure over external causes |
Writing rules: See CONTRIBUTING.md. Do not introduce new synonyms without a glossary entry. Prefer trustworthiness (\(T\)) or millitrust (mT) over bare “trust” in technical prose.
| Field | Meaning |
|---|---|
| Symbol | Mathematical notation (when applicable) |
| Primary name | Preferred term in new writing |
| Also called | Accepted aliases — do not treat as different concepts |
| Definition | One-sentence meaning |
| Not | Common confusions to avoid |
Alias lifecycle (legacy, domain_alias, …) is tracked in glossary_table.csv. New terms: CONTRIBUTING.md.
Level index \(L\) orders nodes from fine (\(L-1\) = components) to coarse (\(L+1\) = enclosing shelter). The same equation applies at every level; only the substitutions change.
Also called: persistence equation, Fractal Persistence Law (domain aliases); Universal Persistence Equation (UPE) (legacy — do not use in new docs).
Definition: The dimensionless accounting identity
that governs whether a pattern at level \(L\) persists over timescales much longer than its relaxation time.
Condition: Persistence requires \(\mathcal{R}^{(L)} \ge 1\).
Not: A forecast of GDP, a moral score, or a single scalar you can measure directly without domain-specific substitutions.
Symbol: \(\Sigma^{(L)}\)
Definition: A bounded, far-from-equilibrium subsystem with (i) a Markov blanket, (ii) non-zero drive, (iii) an internal generative model, and (iv) identity preserved over interval \(\tau \gg \tau_{\mathrm{relax}}\).
Examples: Cell, firm, household, equity market, nation-state, prediction-market service.
Not: Any stable object. A rock in equilibrium is not an IPS; a company with delusion and no error correction failing slowly is one until \(\mathcal{R} < 1\).
Symbol: \(\mathcal{R}\) (or \(\mathcal{R}^{(L)}\) at a level)
Also called: sustainability ratio (legacy — use persistence ratio).
Definition: Usable power income divided by required dissipation, modulated by shelter \(\Psi\) and substrate integrity \(\Phi\). \(\mathcal{R} \ge 1\) is necessary for long-horizon persistence.
Software note: Treat \(\mathcal{R}\) as a regulated setpoint with fluctuations, not a one-shot live/die flag. R_below_1 in aion-core is a trip/watchdog signal (out of band), not instantaneous dissolution.
Not: “Resilience” in the vague sense, ROI, or stock-market return.
Symbol: \(\partial\Sigma\)
Also called: boundary, perimeter, interface.
Definition: The states separating internal subsystem from environment such that internals and externals are conditionally independent given the blanket (Pearl/Friston factorisation).
Examples: Cell membrane, corporate legal entity + firewall, exchange rules + order book, personal boundary (“no”).
Not: A geographic border alone (unless it actually implements conditional separation).
Symbol: \(\mu\); generative density \(q_\mu\)
Also called: ISM (internal self-model, at agent scale), world-model, collective \(Q\), consensus measure \(p_t\) or \(p_m\) (in markets).
Definition: The subsystem’s running probability structure over external causes — what it believes will happen, encoded in states inside the blanket.
Not: Public narrative only. The working shadow model and ceremonial model are both internal models; their gap is \(\mathcal{D}_{\mathrm{KL}}\) exported as anomie when the ceremonial layer controls currency.
Symbol: \(P_{\mathrm{in}}\)
Also called: drive, usable free-energy import, budget/revenue (social), capital inflow (markets), primary energy throughput (states).
Definition: Rate at which environmental free energy is harvested and converted to information-bearing work before efficiency losses.
Not: Gross turnover, trading volume, or nominal GDP without quality adjustment. Churn is not \(P_{\mathrm{in}}\).
Symbol: \(\eta_I(\mathcal{D}_{\mathrm{KL}})\); often shortened to \(\eta\)
Definition: Fraction of imported power converted to useful boundary-maintaining work. Carnot-like bound decreases with delusion: a maximally wrong model extracts less structure from the environment.
Also called: algorithmic efficiency, coordination efficiency, TFP-like institutional quality.
Not: Moral virtue. High \(\eta\) is competence at converting energy into maintained identity, not niceness.
Symbol: \(\omega\)
Definition: Effective number of constraints or bits required to specify the blanket and internal state — structural complexity tax multiplier.
Also called: bureaucratic depth, ritual load, org-chart weight.
Not: Intelligence or sophistication. Extra \(\omega\) without \(\eta\) return is pure denominator drag.
Symbol: \(\mathcal{E}_\Sigma\)
Definition: Summed fundamental fluctuation power (thermal, quantum, environmental) at the scale of information-carrying modes.
Also called: environmental volatility, background noise, aleatoric uncertainty (finance).
Not: Epistemic disagreement alone. \(\mathcal{E}_\Sigma\) is irreducible stochasticity; epistemic volatility lives in belief dispersion (see Volatility).
Symbol: \(\mathcal{D}_{\mathrm{KL}}\) or \(\mathcal{D}_{\mathrm{KL}}^{(\Sigma)}\)
Also called: delusion, delusion tax, model divergence, KL gap, cross-entropy surplus.
Definition: Kullback–Leibler divergence between the internal model \(q_\mu\) and the true posterior over external causes given blanket states. Non-negative; zero iff the model is calibrated.
Operational forms:
- Agent: gap between stated beliefs and resolved outcomes.
- Market: gap between priced distribution and realised fundamentals.
- State: gap between official forecasts and base-rate reality.
- Software (aion-core): in control-theory terms, \(\mathcal{D}_{\mathrm{KL}}\) is also readable as setpoint tracking error between the internal model (prediction-market belief, rec-engine fusion) and resolved task outcomes — see papers/aion_core_control_theory.md.
Not: Ordinary uncertainty before outcomes resolve (that is epistemic volatility). Not “lying” alone — honest wrong models still pay \(\mathcal{D}_{\mathrm{KL}}\).
Symbol: \(\Gamma\)
Also called: friction, senescence, unresolved friction set, ossification, friction ledger.
Definition: Irreversible or deferred damage and unresolved obligations — micro-defects, grudges, rolled debt, institutional scar tissue — that raise maintenance cost without being fully priced as \(\mathcal{D}_{\mathrm{KL}}\) yet.
Not: A single argument. \(\Gamma\) is the backlog of unfinished repair. Operation 2 in all frameworks: lower \(\Gamma\) by resolve, renegotiate, or exit.
Symbol: \(\Phi\)
Also called: substrate, substrate health, fractal integrity (postfactor), \(\Phi\) of constituents.
Definition: Health of the level-\((L-1)\) substrate graph, expressed as a composition operator on child \(\mathcal{R}_i\) — not a fixed average. Critical constituents in series enter via \(\Phi \approx \min_{i \in \mathcal{C}} \mathcal{R}_i\) (Theorem 5.3); redundant (parallel) pools enter via softer aggregates. See substrate_shelter_and_redundancy.md.
Examples: Organ health (person), member skills and trust (firm), listed issuers and liquidity providers (market), population and grid (state).
Not: Headline index level, employee count, or the mean of country \(\mathcal{R}\) for humanity. A market can print ATH while \(\Phi\) rots in the issuer subgraph.
Symbol: \(\Psi\); overlapping enclosures → \(\Psi_{\mathrm{eff}}\)
Also called: shelter, enclosure, imported stability, supernode buffering.
Definition: Fraction of level-\((L+1)\) environmental noise transmitted to \(\Sigma^{(L)}\) after enclosing buffers (smaller \(\Psi\) = better shelter). Independent channels combine as \(\Psi_{\mathrm{eff}} = \prod_j \Psi_j\); overlapping buffers on the same noise obey \(\Psi_{\mathrm{eff}} \le \min_j \Psi_j\). Mere membership without buffering contributes \(\Psi_j = 1\). See substrate_shelter_and_redundancy.md.
Examples: Parental secure base, NATO umbrella, SEC enforcement, reserve-currency rails.
Not: Unconditional protection. \(\Psi\) is not a permanent property of printed money; it is not substrate (\(\Phi\)).
Symbol: \(i \in \mathcal{C}\)
Definition: A level-\((L-1)\) sub-IPS whose failure breaks Markov-blanket conditional independence at level \(L\), so \(\Phi \to 0\) regardless of other children or shelter. Enters \(\Phi\) through the minimum, not the mean.
Examples: Heart in a body, electrical grid in an industrial economy, zooxanthellae in a coral polyp, single-source fab on a chip cut-set.
Not: Every labelled part. Nominal departments, symbolic votes, or idle experts do not enter \(\mathcal{C}\) without operational blanket role.
Definition: Parallel capacity in the substrate graph — duplicate suppliers, stockpiles, substitutable organs — that raises \(\Phi\) when one link fails, priced in higher \(\omega\), \(\Gamma\), and foregone efficiency. Opposite pole: series substrate (lean chains, single source) optimises calm-environment \(\mathcal{R}\) but concentrates tail risk on \(\min_i \mathcal{R}_i\).
Examples: Dual power feeds, domestic grain reserve plus imports, friend-shoring after supply-shock repricing.
Not: Shelter (\(\Psi\)). Redundancy in alliances is shelter-channel overlap, not substrate health.
Definition: IPS at level \(L\) decomposes into sub-IPS \(\{\Sigma_i^{(L-1)}\}\) nested inside its blanket; persistence at \(L\) depends explicitly on \(\mathcal{R}_i^{(L-1)}\) via \(\Phi\) and on enclosing buffers via \(\Psi\) (Theorem 5.3). The aggregate rule is graph-indexed (series, parallel, mixed).
Also called: substrate graph, fractal graph, level recursion.
Definition: The pair of repairs that appear at every scale under different names:
Not: Separate theories per domain. Therapy, post-mortems, truth commissions, and bankruptcy are implementations.
At every scale an entity simultaneously:
| Role | Meaning |
|---|---|
| Substrate | Someone else’s \(\Phi\) |
| Node | Own \(\mathcal{R}^{(L)}\) at this level |
| Shelter | Someone else’s \(\Psi\) |
Pathology: Collapsing levels (identity fusion, enmeshment, treating nation as self).
Definition: The activity (not a separate quantity) of lowering \(\mathcal{D}_{\mathrm{KL}}\) by exposing an internal model to a resolution authority and erasing the bits it falsifies. Generalises Operation 1 across every domain; the measurable quantity remains delusion divergence.
Resolution authority: Whatever scores the model against reality — lived experience (psychology), settlement and default (markets), the battlefield (war), reproducible measurement (science), the PoT ledger (society of nodes). Durability of the extracted truth scales inversely with how capturable the authority is.
Also called: delusion reduction, price discovery (markets), acceptance (psychology), measurement (physics).
Not: A new FPE term. Not the numerator — engineering optimises \(P_{\mathrm{in}}\eta\) (doing); truth extraction optimises the denominator \(\mathcal{D}_{\mathrm{KL}}\) (knowing). See truth_extraction.md.
Symbol: \(T\)
Definition: Model honesty and friction-repair capacity; in the respect factorisation \(T \propto 1/(\mathcal{D}_{\mathrm{KL}}\,\Gamma)\).
Not: Likability, fame, or “social currency” (likes). Not the same as being tolerated under high \(\Psi\).
Symbol: \(S \equiv P_{\mathrm{in}}\eta\)
Definition: Boundary enforcement capacity — the numerator’s claim on negentropic work (Warrior pole).
Not: Net worth in fiat. Currency can purchase the appearance of \(S\) (security, lawyers, weapons).
Symbol: \(\mathcal{Z} \propto S \cdot T\)
Definition: Long-run social standing; time-asymptote of \(\mathcal{R}\) when both strength and trustworthiness are non-zero.
Zero-product property: \(S=0\) or \(T=0\) → no durable standing (doormat or tyrant limit).
Definition: Overloaded in ordinary language. In this stack, distinguish:
| Phrase | Meaning |
|---|---|
| Trustworthiness \(T\) | Calibration + friction repair |
| Generalised trust (sociology) | Default expectation strangers cooperate under norms — amortised \(\Phi\) |
| AgentTrust.score (software) | KL-based forecaster score in aion-core |
| Market trust | Joint condition: bounded \(\mathcal{D}_{\mathrm{KL}}\), \(\Psi \approx 1\), \(\Phi\) above threshold — not sentiment |
Rule: Prefer trustworthiness for epistemic credit; use trust only with a qualifier.
Definition: Shelter artifact that clears desire (who pays next), not calibration (who was right).
FPE reading: High-\(\Psi\) token whose value persists while a supernode guarantees convertibility. Not earned by lowering \(\mathcal{D}_{\mathrm{KL}}\).
Not: Trustworthiness token. Confusing the two exports delusion to \(\Phi\) eventually.
Symbol: balance \(t\); unit millitrust (mT, 1000 mT = 1 trust, display agi-trust)
Definition: Ledger entry for forecast quality net of compute cost:
Also called: epistemic credit, societal value (when fungible for exchange); PoT trust (legacy).
Not: Fiat, reputation points, or stake-weight without scoring.
Definition: Any channel that moves resources without paying the thermodynamic bill for being wrong — e.g. fiat spending unchecked by \(\mathcal{D}_{\mathrm{KL}}\), insider edge without log-score penalty.
Trustworthiness tokens close the leak by construction.
Definition: Imported \(\Psi\) for nations invoicing in another state’s unit — shelter, not earned \(T\).
Not: Permanent endowment. When the issuing enclosure’s model fails, \(\Psi\) drops for all holders regardless of local calibration.
FPE reading: \(\Gamma\) deferral — borrowing \(P_{\mathrm{in}}\) from the future while growing unresolved obligations; made liquid by currency and credit markets.
Symbol: \(p_m\) (trust-weighted or consensus); \(P_m^*\) (final); \(p_t\) (date-\(t\) belief)
Definition: Aggregate probability measure over outcomes encoded in prices, options, analyst panels, or prediction-market state.
Stock price reading: Present value under risk-adjusted measure \(Q\) — the market’s probability model over future cash flows.
Symbol: \(q\) or \(q_t\)
Definition: Participant’s submitted probability distribution over the same outcome set as the market.
Definition: Per-event increment \(\log q(y) - \log p_m(y)\) — nats by which a forecaster beat or lost to the market on realized outcome \(y\).
Links: Trustworthiness update kernel, Kelly-criterion growth (log utility), sequential KL-reduction scoring in aion-core.
Not: Raw P&L without probability report. You can be profitable and miscalibrated.
Definition: Position-sizing rule that maximises asymptotic log-wealth growth; multiplicative form \(t \leftarrow t \cdot q(y)/p_m(y)\) is zero-sum and KL-equivalent to the trust update.
Market reading: Honest markets reward lowering \(\mathcal{D}_{\mathrm{KL}}\); insider sizing without scoring exports \(\mathcal{D}_{\mathrm{KL}}\) to uninformed flow (adverse selection).
Definition: Score of bet \(t\) in a market: \(v_{m,t} = D_{\mathrm{KL}}(P_m^* \| P_{m,t-1}) - D_{\mathrm{KL}}(P_m^* \| P_{m,t})\) — telescoping path value toward final consensus.
Software: prediction_market service, market_math.md.
Definition: Slow deflation of total trust when voters hold heterogeneous beliefs; trust-weighted average underperforms market log-score by Jensen’s inequality — cost of disagreement.
Not: Arbitrary inflation. Unlike fiat debasement, the tax scales with epistemic dispersion.
Primary definition (IPS/finance essay): Uncertainty over the probability measure itself — dispersion and instability of \(p_t\), not return variance alone.
| Layer | Meaning | FPE term |
|---|---|---|
| Aleatoric | Inherent outcome randomness | \(\mathcal{E}_\Sigma\) |
| Epistemic | Belief disagreement and revision before resolution | Uncertainty over \(p_t\); VIX-like |
| Delusion | Systematic gap between \(p_t\) and realisable outcomes | \(\mathcal{D}_{\mathrm{KL}}\) ex post |
Not: Fear alone. Low displayed vol can mask rising delusion (suppressed information).
Definition: Informed sub-IPS extracts edge from uninformed flow; market makers widen spreads; liquidity subgraph \(\Phi\) falls — local \(\mathcal{R}_i < 1\) cascade.
Regulatory \(\Psi\): Enforcement that prices and punishes insider \(\mathcal{D}_{\mathrm{KL}}\).
FPE reading: Extra \(P_{\mathrm{in}}\) demanded per unit of exposed \(\mathcal{D}_{\mathrm{KL}}\) when trust in calibration falls.
Definition: What ordinary money and equity markets optimise locally — matching willingness to pay, not marginal correctness of belief.
Contrast: Trustworthiness coordinates who should be listened to.
Definition: Nominal claim (cash, index exposure) whose value persists under \(\Psi\) while calibration may already be failing — nominal wealth without \(T\).
Definition: Sustained \(\mathcal{R} < 1\) with rapid \(\Phi\) or \(\Psi\) failure — not a single bad draw but a regime change in the accounting identity.
Definition: Chronic \(\mathcal{R} \approx 1\) with rising delusion tax — fragile before macro shock.
Definition: \(\mathcal{D}_{\mathrm{KL}}\) rises without scoring event — e.g. hidden insider information — denominator grows while \(\eta_I\) falls.
Definition: Collective condition where norms no longer predict how effort maps to reward; rising \(\mathcal{D}_{\mathrm{KL}}\) between official promise and lived reality exported to members.
See: ips_sociology.md
Definition: Lowering local \(\Gamma\) by pushing cost onto a sub-node’s \(\Phi\) or \(\mathcal{D}_{\mathrm{KL}}\) (scapegoating, sanctions on periphery, drama-triangle geometry).
Definition: Sub-node persistence positively correlated with shelter’s persistence over shared horizon — not obedience to predatory \(\Psi\).
| Theory term | aion-llm | aion-core | aion-blockchain |
|---|---|---|---|
| \(\mathcal{R}\) | usage.persistence on completions |
Task/agent persistence sweeps | — |
| \(\mathcal{D}_{\mathrm{KL}}\) | fractal_loss, cross-entropy + delusion |
Market sequential KL, compute.py |
Vote KL margin vs market |
| Trustworthiness token | — | AgentTrust.score, PM bets |
trust_mtrust, PoT ledger |
| \(p_m\), \(q\) | — | prediction_engine.py |
Market refs, pot-market |
| Norms / laws | — | norms/ service |
NormDecl, NormVote |
| \(\Gamma\) / patches | — | Violations → ParticipantPatch |
ConflictRecord on chain |
| Predictive Governance | — | Intra-node governance | Inter-node PoT society |
Full map: fractal_layers.md, COMPONENTS.md
| Symbol | Always means |
|---|---|
| \(\mathcal{R}\) | Persistence ratio |
| \(\mathcal{D}_{\mathrm{KL}}\) | Delusion divergence (nats) |
| \(\Gamma\) | Structural fatigue / friction backlog |
| \(\Phi\) | Substrate integrity (postfactor) |
| \(\Psi\) | Shelter coefficient (prefactor) |
| \(P_{\mathrm{in}}\) | Power income |
| \(\omega\) | Complexity |
| \(\mathcal{E}_\Sigma\) | Internal noise floor |
| \(\eta\) or \(\eta_I\) | Coupling efficiency |
| \(L\) | Fractal level index |
| \(p_m\) | Market / consensus distribution |
| \(q\) | Private belief or bet |
| \(t\), mT | Trustworthiness balance |
| \(S\), \(T\), \(\mathcal{Z}\) | Strength, trustworthiness, respect |
Subscripts: \(\mathcal{R}^{(L)}\) = at level \(L\); \(\mathcal{R}_i\) = sub-node \(i\); \(\Psi_{\mathrm{eff}}\) = product over overlapping shelters.
Do not use interchangeably: - \(\Phi\) vs \(\Psi\) (substrate vs shelter — different failure modes) - \(\mathcal{D}_{\mathrm{KL}}\) vs \(\Gamma\) (wrong model vs unresolved backlog) - Currency vs trustworthiness token - Volatility vs \(\mathcal{D}_{\mathrm{KL}}\) (uncertainty of \(p\) vs wrong \(p\)) - Trust vs trustworthiness (qualifier required for generic “trust”) - \(P_{\mathrm{in}}\) vs turnover / GDP headline
| Term cluster | Start here |
|---|---|
| FPE formal | information_persisting_systems.md |
| Body → world stack | fractal_layers.md |
| Agent \(L\) | ips_psychology.md |
| Groups \(L+1\)–\(L+2\) | ips_sociology.md |
| States \(L+3\) | ips_geopolitics.md |
| Money vs calibration | trustworthiness_token.md |
| Equity markets | ips_economics.md |
| PM scoring | market_math.md |
| PoT / chain | whitepaper §4 |
| Anomie | ips_sociology.md |
| Religion and anomie | ips_sociology.md |
When adding new essays, define new terms here first or link an existing entry rather than introducing a third synonym.