मंथिकाManthika ← How we write
LATTICE · the atom graph

A book chapter is not a stack of pages — it is a graph. Every claim (an atom) declares what a reader must already hold before it makes sense, and QUILL only writes prose once that structure is settled. Below is the real prerequisite graph for one chapter — Physics 11 · Ch 4, Laws of Motion — the same chapter walked end-to-end on /how-we-write.

Ch 4 — Laws of Motion · atom graph

Prerequisite DAG, read top → bottom. Arrows run prereq → atom (downstream); each row is one dependency depth; color is rung. Layout is precomputed at build time (longest-path layering + barycenter crossing reduction), not recomputed by this page. A table view of the same nodes and edges follows the diagram.

rung prereq R1 recognise R2 apply R3 transfer
Ch 4 — Laws of Motion · atom graph Prerequisite DAG, 22 atoms, 28 edges. The table below this diagram lists the same nodes and edges as text. WE-1 impulse WE-2 incline—does it slide? WE-3 1-D collision WE-4 banked road prereqs depth 1 depth 2 depth 3 depth 4 depth 5 depth 6 depth 7 depth 8 M0.vec vector components M0.vec · vector components (prerequisite) M0.calc d/dt notation M0.calc · d/dt notation (prerequisite) M0.dim dim. analysis / SI M0.dim · dim. analysis / SI (prerequisite) C3.circ centripetal a✤=v²/r C3.circ · centripetal a✤=v²/r (prerequisite) A1 Aristotle's fallacy yield B A1 · Aristotle's fallacy A2 Galileo's inertia yield B A2 · Galileo's inertia A3 Newton's 1st law yield B A3 · Newton's 1st law A4 Momentum p=mv yield B+C A4 · Momentum p=mv A5 Newton's 2nd law yield B+C A5 · Newton's 2nd law A6 Impulse J=FΔt yield B+C A6 · Impulse J=FΔt A7 Newton's 3rd law yield B A7 · Newton's 3rd law A8 Cons. of momentum yield B+C A8 · Cons. of momentum A8b 1-D collision yield B+C A8b · 1-D collision A9 Equilibrium · FBD yield B+C A9 · Equilibrium · FBD A10 Common forces yield B+C A10 · Common forces A11 Static friction yield B+C A11 · Static friction A12 Kinetic friction yield B+C A12 · Kinetic friction A12b Rolling friction yield B A12b · Rolling friction A13 Centripetal force yield B+C A13 · Centripetal force A14a Inclined plane yield B+C A14a · Inclined plane A14b Connected / Atwood yield B+C A14b · Connected / Atwood A14c Banking of roads yield C A14c · Banking of roads

Table view

The same graph as the diagram above, as an accessible table — one row per atom, its prerequisites and dependents as text.

Ch 4 — Laws of Motion · atom graph — table view. Same nodes and edges as the diagram above, as text: every atom's prerequisites (what must come first) and dependents (what builds on it next).
Atom Concept Rung Prerequisites Depends on this Worked-example yield Worked-example cluster
A1 Aristotle's fallacy R1 recognise — A2 B —
A10 Common forces R1 recognise A9 A11, A14b B+C WE-2 incline—does it slide?
A11 Static friction R2 apply A10 A12, A14a B+C —
A12 Kinetic friction R2 apply A11 A12b B+C —
A12b Rolling friction R1 recognise A12 — B —
A13 Centripetal force R3 transfer A5, C3.circ A14c B+C WE-4 banked road
A14a Inclined plane R3 transfer A11, A9, M0.vec A14c B+C WE-2 incline—does it slide?
A14b Connected / Atwood R3 transfer A10, A5, A9 — B+C —
A14c Banking of roads R3 transfer A13, A14a — C WE-4 banked road
A2 Galileo's inertia R1 recognise A1 A3 B —
A3 Newton's 1st law R1 recognise A2 A5 B —
A4 Momentum p=mv R1 recognise M0.vec A5 B+C —
A5 Newton's 2nd law R2 apply A3, A4, M0.calc, M0.dim A13, A14b, A6, A7, A8, A9 B+C WE-1 impulse
A6 Impulse J=FΔt R2 apply A5 — B+C WE-1 impulse
A7 Newton's 3rd law R1 recognise A5 A8 B —
A8 Cons. of momentum R2 apply A5, A7 A8b B+C WE-3 1-D collision
A8b 1-D collision R3 transfer A8 — B+C WE-3 1-D collision
A9 Equilibrium · FBD R2 apply A5, M0.vec A10, A14a, A14b B+C WE-2 incline—does it slide?
C3.circ centripetal a✤=v²/r prerequisite — A13 — —
M0.calc d/dt notation prerequisite — A5 — —
M0.dim dim. analysis / SI prerequisite — A5 — —
M0.vec vector components prerequisite — A14a, A4, A9 — —