Collaborator Review
This route packages the direction into one review surface: the live preview, the three simulated profile states, the system architecture, the anti-tacky product doctrine, the learning-signal ideas, the portfolio-plus-automation plan, and the actual repo integration path from foundations topics like ZFC and the axiom of choice through to ML-heavy overlays.
Knowledge State
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.
The learner has real foreground structure now, but one missing proof bridge still blocks a clean training-mechanics arc.
kolmogorov probability axioms is visible, but the proof bridge from sets functions and relations is not yet trustworthy.
The light should reveal names, nearby canonical edges, and exact state. It should never imply that dormant structure is already earned.
The page should still feel like a serious instrument before the learner has earned more than a foothold.
The learner has real foreground structure now, but one missing proof bridge still blocks a clean training-mechanics arc.
The graph is alive now because many bridges are genuinely supported, not because the UI is pretending density means mastery.
Monetization lanes
The revenue layer should preserve the brand logic: public theorem canon stays open, while the paid surfaces are private intelligence, stronger assessment, and serious workflow tooling.
The public site should stay trustworthy and indexable. The paid product is the private knowledge-state engine: diagnostics, proof history, adaptive review, and serious guidance.
The first paid surface should feel like a private instrument for serious learners: better diagnostics, adaptive next steps, exportable audits, and stronger review support.
Later expansion can support team diagnostics, weak-link reporting, and recruiter-facing technical evidence without turning the product into a leaderboard toy.
System design
The core mechanic is operational now, not just verbal: topics can be active without being trusted, canonical edges can be nearby without being earned, and the graph only turns solid where there is direct evidence.
This prototype uses a simple state machine instead of rating theater. Topic states, edge states, bottlenecks, and next proof points all derive from evidence events and the canonical prerequisite graph.
The graph spans ZFC, sets, relations, functions, and the axiom of choice through linear algebra, probability, optimization, and transformer mechanics. The product thesis is broader than a transformer explainer.
Current bottleneck, next proof point, why it matters, and expected unlocks are now the primary surface. Counts are secondary. This keeps the page out of generic dashboard territory.
Later AI should sharpen the same map rather than replace it: diagnostics, adaptive transfer prompts, review scheduling, source-grounded remediation, and skill audits all become evidence generators for the same graph.
The repo already has users, reading progress, review cards, assessments, and a canonical graph snapshot. The missing layer is the evidence ledger plus per-user topic and edge state derivation.
Signal ideas
Strong performance on repeated familiar checks paired with weaker transfer or portfolio prompts. The learner has fitted the surface but not the relation.
Persistent misses on easy and medium checks after exposure. The concept has not become a reliable support node yet.
A previously earned region weakens after time away. This should trigger review pressure and a fresh proof event, not punishment theater.
If the graph became a real product surface tomorrow, would you trust its claims, understand its next move, and want to keep it open while studying? That is the standard this concept has to hit.