Student research program planner
A cohort-ready pathway that selects accessible research targets, maps weekly exploration work, and keeps proof verification status honest from the first experiment to the final presentation.
Open the Research Lab
Use the internal lab to configure a cohort, select targets, generate assignment briefs, and track Lean/Python validation gates.
Recommended research targets
Each target includes exploration hooks, deliverables, MathScout assets, and verification gates.
Floor-sum count identity
Relate a modular pair count N_k(n) to F_k(n+1)-F_k(n), the finite difference of a floor sum for odd k.
First exploration moves
- Draw admissible lattice points for small odd k.
- Track which floor-sum terms increase when n changes to n+1.
- Build the pair-to-index bijection by hand.
Graph invariant game
Define a local move on a finite graph and determine which invariants decide whether a target state is reachable.
First exploration moves
- Play the move on paths, cycles, and grids.
- Record quantities that never change.
- Search for a complete invariant in small graphs.
Beatty-style partition explorer
Explore when two floor-generated sequences appear to partition a finite interval, then prove a parameter-restricted version.
First exploration moves
- Generate initial terms for rational slope pairs.
- Search for overlaps and gaps.
- State a finite version that is actually true.
Cohort program spine
Teachers can use these gates to pace teams without turning research into answer delivery.
Research orientation and tool setup
Set expectations: exploration is allowed, but proof claims need verification.
Verification gate
Students can explain experiment evidence, proof skeleton, and Level 5 verification.
Midpoint review and downselection
Choose the primary research target and archive the others as side explorations.
Verification gate
Primary target has a proof plan and a highest-honest verification goal.
Final exposition and verification report
Produce a student-readable paper, presentation, and verification appendix.
Verification gate
Final report states exactly what is proved, checked, or still open.
MathScout artifacts for Arcmath
The API returns the same contract shape for dashboards, assignments, and teacher-prep workflows.
API contract
GET /api/research-programPOST /api/research-programPOST accepts student level, weeks, interests, skill levels, formalization preference, and problem count.