GIDS Study Guide / Cheat Sheet

This is the short working version of the manuscript: the hierarchy, the notation, the indispensable equations, and the tests that decide whether the theory survives. Every repeated equation keeps its canonical GIDS identifier and points back to the chapter in which it was originally explained; repetition here is retrieval, not a second derivation.

1. How to Read the Notation

A plain arrow gives the explanatory silhouette; a conditional kernel gives the probabilistically honest version. Read every equation from left to right and ask four questions: what object enters, what information is available at that time, what transformation occurs, and whether the output is an estimate, simulation, or observed trace.

2. The Philosophical Descent

GIDS–1 — Registration and lineage access.¹

Something exists in the mind-independent external domain; the model registers a difference inside God’s Infinite Dimensional Space; the actor class retains only what its access structure can make available. \(\mathcal G\) may be taken as an open-ended Hilbert arena for the first formalization, although the operational theory can inhabit a broader measurable state-space if later work requires it.

The same arena should be capable of representing phenomenal state at several actor scales: fish, human, ant colony, corporation, or another actor-observer. Phenomenal means the organized reality available to the actor as constructed at that scale; it does not, by itself, claim that every composite actor possesses one unitary human-like consciousness.

GIDS–4 — Two geometries.²

The first geometry asks whether registered distinctions overlap structurally; the second asks whether they bend this actor’s task-relevant next state in similar ways. They need not agree, which is why one universal dot product cannot carry every meaning we need.

GIDS–5 — Actor-relative object construction.³

Register the external difference, determine what reaches the actor, then organize it through the actor’s present state and context; the result is the object for this actor now. A proposition follows the same rule, therefore the external message and the experienced proposition are not the same model object.

3. From Inherited Actor to Operational State

GIDS–2 — The actor descent.⁴

• \(G_i\): inherited starting organization.
• \(T_{i,t}\): slowly changing realized actor after development and history.
• \(\phi_{i,t}\): complete phenomenal state now.
• \(Q_{i,t}\): general predictive response object.
• \(q_{i,t}^{(\tau,\Delta)}\): task-and-horizon summary, when one exists.
• \(\widehat s_{i,t}\): finite state estimated from traces.

These are not six names for the same thing; they mark a descent from actor as lived to actor as estimated.

The proposition-conditioned Chimera is the part of the person made active by this role, world, and proposition; role remains explicit context in the state, while its principal effect appears through proposition–actor interaction, so the same durable actor can therefore produce opposed responses without the model averaging the difference into noise.⁵

GIDS–11 — Slow and fast operational state.⁶

The slow vector approximates what the actor is generally like now; the fast state carries recent chronology; context and world remain explicit. A founder does not become another founder because one email arrived, although the local state may change completely because of that email.

The fast state is aligned to decision-time through GIDS–22:

Only records available before the decision may enter the state used to predict that decision’s consequences.⁷

4. Predictive State and Approximation

GIDS–13 — Predictive equivalence.⁸

Two information states count as the same predictive state when every admissible proposition sequence, horizon, and scenario in the declared family produces the same response law. If a biographical detail never changes any future we care about, it does not belong in the minimal state; if one forgotten event changes a single response ten steps later, it does.

GIDS–14 — State error plus model error.⁹

The first error means the state discarded predictive information; the second means the predictor failed to use retained information. Better training cannot recover what the representation threw away, while a richer representation does nothing if the predictive head cannot use it.

Memory is modeled as weighted traces whose availability changes under the present proposition; categorical evidence remains typed by source, role, and regime, because biography, stated language, observed behavior, and third-party inference are not interchangeable merely because they share a label.

5. Composite Actors and the World Model

A corporation is not an average of employees; the canonical composite institutional state preserves information access, authority, memory, incentives, coalitions, vetoes, missingness, and the way private organization-objects become coupled into one persistent higher-order actor.¹⁰

GIDS–17 — Filtered dyadic state.¹¹

containing two people, two institutions, one relationship, and a shared world.

GIDS–20 — Simulation and filtering.¹²

The first equation simulates what might happen; the second filters after real evidence arrives. Never write a model-generated future back as though it were evidence, and never mistake one observed trace for the whole state.

Proposition search evaluates candidate futures under the canonical predictive proposition value; the regime fixes continuation policy, future candidate sets, external scenario, and outcome convention, while forecasting predicts observed propositions, ranking compares simulated alternatives, and causal control requires intervention-grade evidence.¹³

6. Ontology Growth and the Four Tests

GIDS–7 — Cross-task ontology retention.¹⁴

A candidate distinction may split, merge, rotate, weaken, retire, restrict, or create a coordinate family; it survives when it improves held-out tasks after complexity and instability are counted, and—where intervention data exists—participates in the predicted change. The typed registry is chosen for debuggability, while reparameterizable latent blocks preserve continuity where discrete boundaries become artificial.

The four essential tests are:

1. Slow versus fast: remove each and verify that failure appears on the timescales its meaning predicts.
2. Actor, relationship, and institution: replace the structured state with flat metadata and shallow history.
3. Explicit construction versus monolithic sequence: provide the same information and comparable capacity; if the monolith wins everywhere, the ontology was a story.
4. Cross-task transfer: discover actor structure on one outcome family and test another without rebuilding the actor from scratch.

The program-level stopping rule is simple: after three materially different implementations across at least two independent temporal corpora, if the explicit decomposition cannot match a capacity-comparable monolithic model and produces no repeatable cross-task transfer, retire the decomposition for that actor class; keep the useful event discipline, stop calling the latent construction a stable ontology.

7. The Shortest Accurate Summary

External reality is larger than any actor’s experienced reality; actors inherit and develop methods for carving that reality into usable distinctions; a proposition is reconstructed inside the receiving actor; traces provide evidence about slow organization and fast state; memory, role, relationship, institution, and world alter the interaction; the interaction changes a recursively usable predictive state; visible behavior is one residue of that transition; candidate propositions can be compared by predicted trajectories; a new axis earns its place through cross-task transfer; the ontology is the product.