Large Signal Model · A theoretical atlas
See what a predictive state must preserve
Seventeen visual plates connect realization, predictive closure, memory, and certified probability domains. Start with the four contracts, follow a short route, or choose a question below.
Start with the four contractsTry two states with the same observation
Build a predictive state
Begin with the obstruction, then add the observable directions needed for closure.
Understand lost paths and memory
Follow discarded contributions through composition, history, and error propagation.
Follow probability certificates
Move from behavior coordinates to domains, matrix witnesses, and statistical guarantees.
Plate 10 · Plate 11 · Plate 12 · Plate 13 · Plate 14 · Plate 15 · Plate 16 · Plate 17
Choose a plate
17 plates
- Plate 1 · P1
Realizable coefficients form a subspace
Can every stored coefficient vector represent an observation?
- Plate 2 · P2
One operation, several coordinates
Do two coordinate descriptions describe the same operation?
- Plate 3 · P6–P7
The obstruction lives in a fiber
Can the same current summary lead to two different futures?
- Plate 4 · P8, P14
Refinement closes an observable space
Which extra observable directions make the state close?
- Plate 5 · P3–P5, P20
Packets decompose operations too
What changes when interactions cross packet boundaries?
- Plate 6 · P7
Compression can erase a return path
Can a discarded coordinate matter after a round trip?
- Plate 7 · P10, P19
Memory is an exact elimination
What does eliminating the discarded state leave behind?
- Plate 8 · P18
A local defect needs a propagation law
Will a local defect shrink or grow as it propagates?
- Plate 9 · P14–P17
What four observations identify
What does a finite set of observations actually identify?
- Plate 10 · P27–P28
Behavior can supply the coordinates
Can future tests themselves supply predictive coordinates?
- Plate 11 · P29, P39–P40
Probability meaning is geometric
What makes every observation record a valid probability?
- Plate 12 · P46, P50–P51
A curved domain can have a finite witness
How can a curved domain have a finite matrix certificate?
- Plate 13 · P56–P59
Integration retains a covariance term
What is lost by averaging before a quadratic action?
- Plate 14 · P72, P83
Uncertainty on a curved domain
Which uncertainties preserve the supplied curved geometry?
- Plate 15 · P66, P68, P81–P84, P87
A confidence set can meet an exact certificate
How do statistical coverage and exact validity work together?
- Plate 16 · P85–P87
Choose the future quantity before its bound
Are we bounding a whole record or one future observation?
- Plate 17 · Navigation
From the atlas to the proofs
Where are the full statements, proofs, and recorded scopes?
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This is a visual companion to the mathematical volume. Exact identities, geometric obstructions and worked rational examples connect the theory to its formal proofs. The source scope notes remain with every plate; the finite explorer illustrates the declared example.
Read the original 19-page PDF · Conversion record · Retained exact-example receipt