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Knowledge State

Shareable noindex preview for the next-generation proof graph: same shell, three simulated maturity states, and the current direction for a more serious ML learning instrument.

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Profile state: active
Goal overlay: Optimization and transformer training
Current arc: Matrix multiplication -> Chain rule -> Backpropagation
Rule: No edge without proof

Knowledge State

Knowledge State Preview

TheoremPath separates canonical subject structure from what the learner has actually earned. A topic can be visible without being trusted; an edge only becomes real when there is evidence.

Simulated profile

The learner has real foreground structure now, but one missing proof bridge still blocks a clean training-mechanics arc.

Current bottleneck
Kolmogorov Probability Axioms is blocked by weak Sets, Functions, and Relations evidence.

kolmogorov probability axioms is visible, but the proof bridge from sets functions and relations is not yet trustworthy.

Expected unlocks
Common Probability Distributions, Empirical Risk Minimization, Empirical Risk Minimization, Expectation, Variance, Covariance, and Moments
4 earned
4 blocked
8 candidate
Next proof point
Sets, Functions, and Relations -> Common Probability Distributions
Proof event
definition_check ยท difficulty 3
Why this matters
This edge is part of the canonical TheoremPath dependency graph (snapshot version 2026-04-20). Earning it requires evidence that the source topic is understood well enough to support the target.
Missing evidence
No direct proof yet that sets functions and relations supports kolmogorov probability axioms.
Latent substrate
Move across the graph to reveal nearby canonical territory

The light should reveal names, nearby canonical edges, and exact state. It should never imply that dormant structure is already earned.

Kolmogorov Probability AxiomsSets, Functions, and RelationsMeasure-Theoretic ProbabilityVectors, Matrices, and Linear MapsMatrix Multiplication AlgorithmsInner Product Spaces and OrthogonalityCommon Probability DistributionsJoint, Marginal, and Conditional DistributionsVector Calculus Chain RuleConvex Optimization BasicsGradient Descent VariantsStochastic Gradient Descent ConvergenceFeedforward Networks and BackpropagationSoftmax and Numerical StabilityAttention Mechanism TheoryTransformer Architecture
Several mathematical supports are earned, yet backpropagation is still blocked because the system has not seen a convincing derivation edge.
Canonical
Candidate
Earned
Blocked
Earned bridges
4
Edges render as earned only when direct proof evidence exists.
Blocked bridges
4
These are the claims the learner can almost see, but has not yet justified.
Visible topics
16
Nearby territory can become visible before it becomes trustworthy.
Evidence events
18
The entire page should derive from evidence, not hand-authored progress flags.