The reading book uses plain words; the symbols here are the formal handles that live in the math layer. New to it? You need only the Core block. Hit a bare symbol anywhere on the site? It is defined here.
The one rule: in prose we say “the reference”; Y is its formal handle.
Core (the whole book in eight terms)
- The reference (Y). The thing you point at / ground in / check yourself against — the one thing the geometry leaves free to choose. The whole catalogue is operations on this one choice; “free will” is the choosing of it.
- Read / Create / Capture. What a reference can be: it pre-exists you (read), is manufactured by your consulting it (create), or is authored by an interested party (capture). You cannot tell them apart by content.
- Provenance, not coherence. The only sort that works. Provenance = where it came from, checked from outside. Coherence = how true or beautiful it feels — which cannot separate read from captured.
- Cut the loop. The one test: perturb the consultation and see what holds. A read reference survives; a created one follows it.
- The ouroboros. A created reference — one whose entire provenance is its own loop, true-seeming from inside, with no outside. The thing the book teaches you to cut.
- The bound (the third point). The external invariant that keeps a reference independent — the three bounds spatialize it (a wall), put it on a clock (a sabbath), and fix it in writing (a canon).
- Three-point vs two-point. Three-point = a reference genuinely independent of the two parties → grounded. Two-point = no independent reference, just a closed loop → the ouroboros.
- The penalty. The cost a closed loop cannot hide: when a reference is not independent of the parties it should referee, a measurable penalty is forced positive. A captured reference reads the penalty low — which is why you need the cut, not the penalty alone.
Formal layer (the symbols)
- Y — the reference (above); the one free degree of freedom.
- D, M — the two channels whose shared dependence the penalty measures: roughly your own dynamics (D) and the mechanism you are entangled with (M — the channel, oracle, model, or system you consult).
- I(D;M|Y) — the explaining-away penalty, a conditional mutual information: how much D and M still share once the reference Y is accounted for. = 0 when Y is a genuine independent common reference (clean three-point); > 0 when Y is coupled to the D and M it should referee. The penalty measures how badly your chosen reference fails to be independent.
- D1 → D2 → D3 — the drift cascade of an unbounded loop: agency-attribution → boundary-erosion → harm.
Deeper apparatus (optional)
- Čencov (1972) — the uniqueness theorem behind “only the reference is free”: the geometry of distinguishing states is fixed (unique up to scale), which is what makes the penalty well-defined rather than conventional. The framework’s “Lorentz invariance.” Fixes the metric, not any numerical constants.
- Fisher metric — the (unique, per Čencov) measure of distinguishability the penalty lives on.
See the Mechanics page for how these fit together, and the Cross-Reference Index for the seams.