Why we're building a Knowledge Graph (and not just another curriculum doc)

An AI tutor needs to answer three questions on every turn: What does this student already know? What should they learn next? Did this last interaction actually help? A flat curriculum outline can't answer those — a structured catalog of atomic skills with dependencies can.

The problem an AI tutor faces

When a 12-year-old student sits with the tutor on a Tuesday evening, the tutor has to decide — in real time — whether to introduce a new fractions skill, drill an existing one, or back up because a prerequisite is shaky. Doing that well needs three things:

• A list of the atomic skills in the curriculum, fine enough that "mastered / not mastered" is a meaningful binary for each.
• The dependencies between them — what must be in place before what can be taught.
• A way to attach every piece of content (every video, every applet, every quiz item) to the specific skill it teaches or tests, so the system can pick the right next thing.

Together, those three are a knowledge graph. Atomic skills are the nodes; prerequisites and other relationships are the edges; content hangs off the nodes as evidence that the skill was taught or assessed.

Why not just use NCERT's competencies?

NCERT's Learning Outcomes 2017 document is excellent — but it's written for teachers and policy. Each NCERT learning outcome typically bundles 3-8 distinct cognitive moves into one entry, on purpose. That's right for "did this teacher cover the chapter" reporting. It's wrong for "did this student master comparing unit fractions specifically" runtime decisions.

Our catalog consumes NCERT (and NCF-SE 2023, and CBSE-CBE) via framework_alignments on every LO — every entry tells you which NCERT clause it implements. We're not replacing the standard; we're decomposing it into the teaching-level chunks a teacher would actually diagnose independently.

One catalog per curriculum, federated into a Universal Knowledge Graph

CBSE Math is its own catalog. Kurikulum Merdeka (Indonesia) is its own catalog. Common Core, Cambridge — same. The Universal Knowledge Graph (UKG) is what stitches them all together — not by collapsing them, but by drawing equivalence edges between LOs that name the same underlying skill.

Why not one global catalog?

Tempting — but it doesn't survive contact with reality. Curricula differ in scope, sequence, and emphasis in ways that aren't pedagogically arbitrary:

• KM Indonesia introduces unit fractions in Fase B (≈ G3-G4). CBSE introduces them in G3 too, but the formal denominators 1/100 and 1/200 appear only at G6. Flatten them and you've lost where the difficulty actually lives for each curriculum.
• CBSE G8 has Compound Interest as a full chapter applied to fractions. KM doesn't teach compound interest until secondary school. There's no shared "G8 fractions" node — they teach different things at the same age.
• CCSS-M has the "Number & Operations — Fractions" domain organised by year-by-year clusters; CBSE organises by topical chapters. Forcing them into one taxonomy means choosing whose pedagogy wins.

Federation preserves each curriculum's integrity. The UKG just records: "this LO in CBSE is the same skill as this LO in KM, even if the grade differs."

Where the equivalence edges go

An edge typed cross_curriculum_equivalent connects two LOs in different curriculum KGs that name the same underlying skill. The edge carries a strength field (strong / moderate / weak) and a notes field explaining the bridge.

Example (future): CBSE's cbse-math-compare-unit-fractions would bridge to KM's km-math-bandingkan-pecahan-satuan as strong equivalence. The bridge means: an applet authored once, with two language tracks, serves both curricula.

Layer model

How fine is "fine" — calibrating LO grain

A common reaction to this catalog is "this is more granular than NCERT". That's by design. The grain is set by what an AI tutor needs to track independently, not by what fits on a policy document.

Where this catalog sits

Why finer than published standards

Standards are written for human teachers, who can read "classify triangles by sides and angles" and mentally expand it into "I'll teach equilateral/isosceles/scalene, then acute/right/obtuse, then combinations". The AI tutor can't do that mental expansion — it needs each sub-skill named explicitly to know what to drill, what to assign, and how to score mastery.

So the rule is: the unit of an LO is the smallest distinct teachable skill a teacher would diagnose independently. If a teacher would say "Rahul has the rule for equilateral down but isn't catching when an isosceles is also right" — those are two separate LOs in this catalog.

Why coarser than v1

v1's grain was too fine. Three triggers for that, all addressed by v2:

• Number-range splits. v1 created a separate LO for "Compare unit fractions a,b ≤ 12" and "Compare unit fractions a,b ≤ 200". v2 fuses them as Levels of one LO. A wider scope at a higher grade is a Level, not a new LO — unless the procedure changes fundamentally (rare).
• Representation splits. v1 created separate LOs for "Compare via area model", "Compare via number line", "Compare via verbal share-size reasoning" — all linked by equivalent_to edges. v2 fuses these as Facets of one LO. The skill is the same; the representation is a teaching/assessment choice.
• Compound competency over-split. v1 took NCERT's "classifies triangles" and made 8 LOs for it. v2 has 2-3 LOs and uses Levels and Facets to capture the variations.

What this means for your review

Two failure modes to watch for, in opposite directions:

• "This LO is still too compound" — flag if a single LO bundles cognitive moves that you'd diagnose separately. Example: a hypothetical "Solve word problems involving fraction operations" would be too compound — addition, subtraction, multiplication of fractions in word contexts are distinct LOs already; "solve word problems" isn't an LO at all, it's a teaching format.
• "This LO is unnecessarily split" — flag if two LOs name the same cognitive move at different scopes/representations, and could be fused via Levels or Facets. We've tried to catch these in authoring — flag any survivors.

What we capture in every LO — and why

An LO card looks dense at first. Every field on it earns its place — each one feeds something concrete downstream (tutor decisions, content tagging, mastery tracking, cross-curriculum bridges). This section walks the card field-by-field, explains the rationale for each design choice, and gives authors the heuristic for picking the right value.

The five criteria — what makes something an LO at all

Before any structure: every entry in this catalog must pass five tests. Fail any one and it's not an LO.

What's on every LO card — annotated

Open any LO in the Catalog (section 9). The card has eight blocks. Here's what each captures, and why:

Why Bloom verbs — and why these six

The first word of every canonical statement must come from a fixed Bloom verb vocabulary. This isn't tradition for tradition's sake — it controls three downstream things:

• The kind of question stem the tutor generates. Compute demands a numerical answer slot; justify demands a free-text justification with a rubric. The verb determines the assessment shape.
• The kind of mastery evidence we accept. Identify can be checked by a single MCQ. Analyse requires multi-step work the tutor can inspect. The verb sets the bar for "mastered".
• The cognitive load mix per session. A session that's 100% recall verbs is rote; one that's 100% create verbs is exhausting. The tutor balances across Bloom levels per session — only possible because every LO carries one.

The six levels we use, in increasing cognitive demand:

Banned: understand, know, grasp, be familiar with, master, appreciate. They name no observable behaviour — which means no way to assess, no way to track mastery, no way for the tutor to act.

Why concept types matter

Every LO is one of four concept types (Anderson & Krathwohl). They determine what evidence the tutor accepts as mastery:

Why this matters: a factual LO doesn't need a Solving Schema (no procedure); a procedural LO without a Schema is a linter flag (probably mis-classified); a metacognitive LO almost always pairs with an Applied facet (you can't show strategy choice in pure symbolic form).

Why Levels are tiered foundational / intermediate / advanced

Three tiers, in order. Naming was deliberate — we considered alternatives and rejected them:

The picking heuristic:

• foundational — the first encounter with this skill in any form. Bounded scope, supportive visual, low cognitive load. Often G3-G5 in our catalog.
• intermediate — wider scope, mixed forms, expectation of unaided procedure. The "working" tier where most assessment happens. Often G5-G7.
• advanced — unrestricted scope, mixed with adjacent skills, expected to be near-instant. The "fluency" tier. Often G7-G8 or beyond.

An LO can skip tiers (an LO that's only introduced in G8 might go straight to intermediate). An LO doesn't need all three; one is fine.

Why those five Level roles

Each Level carries a role — what the curriculum is asking of this Level at this grade:

The 25% reviews-role cap. The linter (section 06, subsection 9b) flags any grade where more than 25% of Levels added are reviews-role. Reason: a grade that's mostly review isn't teaching anything new — likely a sign that the LO catalog is over-decomposing prior content rather than adding new skills.

Why exactly these four Facets

Each LO can carry 1-4 Facets across Visual / Symbolic / Verbal / Applied. We considered three / five / six alternatives — these four are what we landed on:

• Visual — diagrammatic representations. Area model, bar/strip, number line, set diagram. Why: every fraction concept can be seen before it can be symbolised. SMEs unanimous that visual is non-negotiable.
• Symbolic — formal mathematical notation. Fraction bars, equations, inequalities, schema instances. Why: this is what high-stakes assessment uses. An LO that has no symbolic facet can't be tested in the formal exam track.
• Verbal — natural-language form. "If 3 children share 2 chappatis equally…" Why: real classroom talk lives here. Voice-first AI tutors (Byjus.AI) lean heavily on this facet for first introductions.
• Applied — real-world / contextual. Money, measurement, cooking, sport, recipes. Why: tests transfer. A student who can compute 3/4 + 1/8 symbolically but can't add 3/4 cup + 1/8 cup hasn't actually learned the LO.

Why not three? "Verbal" and "Applied" sometimes look similar but aren't — verbal is about linguistic encoding of the math; applied is about domain transfer. Collapsing them loses transfer signal.

Why not five? We tried "Procedural-Visual" (e.g., interactive applet manipulations) as a fifth — turned out it always reduced to either Visual + Symbolic interaction or Visual + Applied. Wasn't pulling its weight.

Why facets carry an explanatory vs assessable role

Same Facet, different role, very different implication for the tutor:

• explanatory — shown for teaching / intuition; never used as the test. A visual area-model is often explanatory: it makes "why ⅔ + ¼ ≠ 3/7" obvious, but you don't assess by asking students to "draw the area model".
• assessable — usable as the assessment vehicle. The Symbolic facet of "add fractions" is almost always assessable: that's what end-of-chapter tests use.

Rule of thumb: every LO needs at least one assessable Facet (linter flag NO_ASSESSABLE_FACET if not). All-explanatory Facets means the LO can be taught but not tested — almost certainly an authoring error.

Why Solving Schemas only on procedural LOs

A Schema is a named mathematical relation with named variables and variants. It only makes sense where a relation exists — i.e., procedural LOs. A factual LO ("name the denominator") has no relation to solve; a conceptual LO ("explain why equivalence preserves the value") has no variables. Forcing Schemas onto them would manufacture structure where none exists.

Variants encode which variable is unknown, NOT the question's surface form. Same Schema, three variants:

• equivalent_fractions relation: a/b = (a·k)/(b·k), variables {a, b, k}
• Variant find_scaling_factor: given ⅔ and 4/6, find k.
• Variant find_equivalent_with_given_denominator: convert ⅔ to a fraction with denominator 12 — find the new numerator.
• Variant verify_equivalence_symbolic: is ⅔ = 4/6? Find whether a valid k exists.

The tutor uses variants to scaffold: introduce the easiest variant first; layer in harder variants as mastery deepens. Without variants, a student who's mastered "verify equivalence" gets nominally credited for an LO they can't actually invert.

Other locked vocabularies

The 1:1 thread constraint

Every LO has exactly one primary_thread — its terminal cognitive skill. Cross-thread USE is expressed via prerequisite_of edges, not multi-thread membership.

Why: an LO with two threads is ambiguous about what it really is. Is "compute fraction of a quantity" a Fractions LO or an Operations LO? If both, content tagging gets two equally-valid primaries — and the tutor's "what to teach next" coin-flips. Forcing one thread forces a choice; cross-thread relevance is then explicit (an edge, not a membership).

Cultural / historical content — NOT an LO

Why: "Brahmagupta's method for fraction addition" is not a skill a student practises and demonstrates — it's curriculum context. Treating it as an LO meant the tutor would try to "assess" it, which is wrong by construction. Moving it to Section metadata means the content team can still surface the history at the right moment, without the runtime trying to test it.

What's NOT on an LO card — and why we didn't add it

A few fields were proposed and rejected; worth noting because the rejections are informative:

How this catalog gets authored — the operating manual

If a different person (or another LLM thread) had to recreate this work from scratch, this is everything they would need. The portal so far has shown the catalog (the output) and the spec (the rules). This section is the process — the operating procedure an author follows so the output is reproducible, audited, and defensible. Reviewers should read this so they can challenge not just "is this LO right" but "was the right procedure followed to produce it".

1. What you need before you start

2. The end-to-end author loop

For each new grade (G3 → G4 → … → G8, sequential, not parallel):

1. Load context. Read Spec v2 §0-§9. Read this portal sections 02-05. Read the cumulative prior-grade catalog (fractions_los.json) end-to-end. Note every existing LO, Level, Facet, Schema by ID.
2. Locate the source. Open the NCERT textbook for this grade. Locate the fractions chapter(s). Note the section list with page ranges.
3. Walk the chapter. For each section, perform the per-section classification (subsection 3 below). This produces a list of candidate proposals: existing-LO updates + new LOs + cultural callouts.
4. Draft the LOs / Levels / Facets / Schemas / Callouts. Use the naming conventions (subsection 7). For each new LO: canonical statement, Bloom verb, concept type, Level(s), Facet(s), Schema (if procedural), framework_alignments, source_provenance, misconceptions, tags.
5. Run the linter (subsection 9). Fix every auto-reject before continuing. Review every borderline flag with a human; resolve to "kept" or "split" and record.
6. Run the per-grade balance audit (subsection 9). If >25% of new Levels for this grade are reviews-role, the grade is over-reviewing — revisit and replace with new content where the curriculum actually expects it.
7. Propose cross-thread prereqs. For any new LO whose prerequisites lie in another thread, draft a proposal with status proposed_pending_human_review. Don't commit cross-thread edges to live; they wait until the target thread is authored.
8. Regenerate emissions. python3 generate_cypher.py + python3 generate_review_md.py. Both should run clean.
9. Copy JSONs into the portal. cp ../*.json portal/data/. The portal updates immediately.
10. Two-author governance gate. A second author reviews. LOs stay proposed until ratified to active.

3. The per-section classification protocol

For every section of every chapter, the author asks: "What is this section asking the student to do, and how does it map to the catalog?" Exactly one of these six outcomes applies (this is from Spec v2 §6.3):

Walking order within a chapter: sections in published page-order. Within a section: read the full section before classifying — don't decide on the first paragraph.

4. The hardest judgement: new LO vs new Level of an existing LO

This is the call authors get wrong most often. The default bias is "new Level, not new LO" (v1's failure mode was the opposite). The decision tree:

5. New LO vs new Facet vs new Schema-variant

The same call, in two more flavours:

• New Facet, not new LO when the cognitive move and conceptual object are the same but the representational form differs. The skill of "comparing two fractions" is one LO; the area model is a Visual facet, the cross-multiplication argument is a Symbolic facet, the "who eats more pizza" reasoning is a Verbal facet, the recipe-scaling problem is an Applied facet. All four are facets of one LO.
• New Schema-variant, not new LO when the relation is the same and only the unknown differs. a/b = (a·k)/(b·k): solving for new numerator, solving for new denominator, solving for k, verifying equivalence — all variants of equivalent_fractions, one Schema, one LO. The variants live as a list inside the Schema.
• New Schema, not new variant when the underlying relation is different. a/b + c/d = (ad+bc)/bd is a different relation from a/b = (a·k)/(b·k) — a separate Schema, even though both involve fractions.

6. The Bloom verb selection workflow

Given a candidate canonical statement, pick the verb in this order:

1. Identify the cognitive move the student must perform (not what they read or hear — what they DO).
2. Pick the Bloom level that matches: recall (retrieve) · understand (explain/classify) · apply (compute/use/solve) · analyse (decompose/compare-across) · evaluate (justify/critique) · create (compose/design).
3. Pick the verb from the controlled vocabulary for that level (section 05 of this portal has the table).
4. Rewrite the canonical statement as: [verb] [direct object] [optional qualifier]. No method (by, via, using); no multi-verb (and, or); no numeric bound; no historical attribution.
5. Run the linter to confirm. If it fails — back to step 2 or 3.

7. Naming conventions

Slugs are immutable once an LO ratifies to active. If an LO needs renaming, it's a supersession — old LO marked superseded, new LO with new slug links back via supersedes.

8. Citation and provenance protocols

Every LO carries three citation blocks. They are not optional:

Citation discipline: if you can't cite it, don't include it. Reviewers must be able to verify every claim against a primary source. Hallucinated framework codes (a common LLM failure mode) are caught by linter check UNKNOWN_FRAMEWORK_CODE — the code must exist in the loaded framework JSON.

9. Quality gates — when to run each

Four gates between "draft" and "ratified". They run in order; nothing skips ahead.

9a · Linter — auto-reject (mechanical) checks

These are catalog-integrity violations the linter rejects without escalation. Fix and re-run.

9b · Linter — borderline flags (human review)

These flag patterns that are often wrong but sometimes intentional. Author resolves each as "kept" or "split" and records the rationale.

9c · Per-grade balance audit — this catalog's current state

10. Emissions — what gets generated and when

Regenerate all three after any catalog change. They're cheap; treat them as ephemeral. The source of truth is the source JSONs in curriculum/cbse/fractions/v2/.

11. Lifecycle and supersession

Supersession rule: never rename or rewrite an active LO in place. Mark it superseded; author a new LO with a new slug; declare supersedes on the new LO pointing back. Content team migrates tags on its own clock.

12. Common traps — what NOT to do

13. Worked example — one chapter, end to end

Pick G6 Ganita Prakash Chapter 7 (Fractions). Section 7.2 introduces equivalent fractions via Brahmagupta's method. Walking it:

1. Read the full section. NCERT G6 Ch 7.2, pages 143-145, "Equivalent Fractions and Brahmagupta's Method".
2. Identify cognitive moves. Three are in play: (a) recognise when two fractions are equivalent; (b) generate equivalent fractions by multiplying numerator and denominator by the same number; (c) reduce a fraction to lowest terms.
3. Check prior catalog. G5 introduced "recognise equivalent fractions visually" — that's an existing LO, cbse-math-recognise-equivalent-fractions, with a Visual Facet.
4. Classify (a): maps to existing LO. New Symbolic Facet for "verify equivalence by multiplication argument". Outcome C. Event: facet_add.
5. Classify (b): NEW cognitive move (generate, not recognise). New LO cbse-math-generate-equivalent-fractions. Bloom: apply · concept type: procedural · Schema: equivalent_fractions (new global). Outcome E. Event: add.
6. Classify (c): NEW cognitive move (reduce, with the procedure of dividing by GCD). New LO cbse-math-reduce-to-lowest-terms. Bloom: apply · concept type: procedural · Schema: equivalent_fractions (reuses!) variant find_smallest_equivalent. Outcome E. Event: add.
7. Cultural callout: "Brahmagupta (628 CE, Brāhmasphuṭasiddhānta) introduced the rule". Add to Section.cultural_callouts[] with type historical_attribution. Outcome F. NOT an LO.
8. Cross-thread prereq: cbse-math-reduce-to-lowest-terms depends on knowing GCD — proposes prerequisite_of edge from cbse-math-find-gcd in the factors_multiples_primes thread (not yet authored) with status proposed_pending_human_review.
9. Lint. All three canonical statements pass: "Verify whether two fractions are equivalent" (recall→identify? no — uses understanding; verify is in the apply level vocabulary; passes), "Generate an equivalent fraction", "Reduce a fraction to lowest terms". 0 auto-rejects.
10. Balance audit for G6. 2 new LOs + 1 new Facet on existing. 0 reviews-role Levels. Passes.
11. Regenerate Cypher + markdown. Copy JSONs into portal/data/. Confirm portal still loads.
12. Two-author review. Second SME confirms or revises. On confirmation, lifecycle moves proposed → active.

14. What another author should be able to do after reading this

• Pick a new grade or thread and execute steps 1-10 without further guidance.
• Defend any catalog decision by citing a numbered rule above plus the source page.
• Detect when a candidate LO is actually a Level / Facet / Schema-variant (subsections 4-5).
• Write a canonical statement that passes the linter on the first try (subsection 6).
• Cite framework alignments and source provenance without hallucination (subsection 8).
• Avoid the 11 common traps in subsection 12.
• Reproduce this catalog from the same source PDFs, ending up with the same LOs at the same Levels with the same Facets (modulo minor wording).

From v1 to v2 — the nine review comments that reshaped this catalog

An earlier draft of this catalog (Spec v1, authored June 2026) went out for SME review. Nine recurring concerns came back. v2 is the spec that addresses each one — and the catalog you're looking at is the first re-authoring under it. This section maps each concern to the rule change it produced, with concrete fractions examples.

The nine comments at a glance

The five core rule changes (R1-R5)

Across the nine comments, five new rules emerged. Each is the load-bearing change that makes v2 different from v1:

R1 — Levels (replaces most scope_extends edges)

A single LO carries multiple Levels for grade-by-grade progression. Each Level has a tier (foundational / intermediate / advanced), a role (introduces / extends / reviews / applies / assesses), a grade, and a scope (the bounded version at that grade).

R2 — Facets (replaces most equivalent_to edges)

A single LO carries 1-4 Facets across the four representational forms: Visual (diagrams, area models, number lines), Symbolic (formal notation, equations), Verbal (story / share-size reasoning), Applied (real-world contexts: paratha, chikki, recipe scaling). Each Facet has an explanatory or assessable role. An LO needs at least one assessable Facet.

R3 — Solving Schema (procedural LOs only)

A procedural LO declares its underlying mathematical relation as a Solving Schema: a named relation with named variables, plus variants for which variable is unknown. Schemas are reusable across LOs and live in a hybrid library (global + per-LO local promoted on review). Conceptual / factual LOs have no Schema.

R4 — Strict canonical-statement linter (hybrid mode)

Every proposed LO runs through the linter (section 06, subsection 9). Auto-reject on mechanical violations — multi-verb, method clauses, banned verbs, numeric bounds in canonical, historical attribution, duplicate canonical. Flag for human review on borderline cases — long canonical, missing assessable facet, procedural LO without schema, >25% reviews role at a grade.

R5 — Sequential per-grade authoring + hard 1:1 LO-to-Thread

v2 is authored G3 → G4 → G5 → G6 → G7 → G8 in order, each grade receiving the cumulative prior catalog as context. New LOs can extend prior LOs (via new Levels/Facets) rather than duplicate. Every LO belongs to exactly one Thread; cross-thread USE relationships are prerequisite_of edges, not multi-thread membership.

The compression in numbers

Net effect: fewer rows, richer rows. Each v2 LO encodes what 2-3 v1 LOs used to encode — but with explicit, structured internal progression instead of brittle cross-LO edges. Easier to maintain, easier for the tutor to traverse, easier for SMEs to review (you read one card, not three).

What stayed the same

• Layer model (L1 backbone → L2 LOs → L3 content tagging) — unchanged.
• Anchoring of every LO to specific NCERT sections via taught_in_sections — unchanged (and now per-Level, more precise).
• framework_alignments to NCERT-LO-2017, NCF-SE 2023, CBSE-CBE — unchanged in shape, every LO carries them.
• One catalog per curriculum, federated via UKG — unchanged (see Section 03).
• Two-author governance gate (status: proposed → active) — unchanged.

CBSE curriculum map (Fractions thread)

The fractions thread spans G3-G8 across NCERT's Maths Mela (G3-G5) and Ganita Prakash (G6-G8). The chapter taxonomy below is the Layer 1 backbone; LOs anchor to specific sections within each chapter.

Strand and Thread

Every Fractions LO in this catalog has:

• primary_strand: number
• primary_thread: fractions

Cross-thread dependencies (e.g., to arithmetic_operations, factors_multiples_primes, decimals_and_rationals, geometry) are expressed via prerequisite_of edges — see section 13 of this portal.

LO catalog — 35 LOs (G3-G8)

Each card is an LO. Levels show within-LO progression across grades; Facets show representational forms with assessability. Click "💬 Comment" on any LO to leave a structured comment in the Google Form.

Interactive Knowledge-Graph explorer

Cytoscape view of the catalog. Click any node to drill into its details. Open in new tab for full-screen exploration.

↗ Open explorer in new tab

Solving Schema library

Reusable global schemas referenced by procedural LOs. Each schema has a canonical relation and a set of variants (which variable is unknown).

Section cultural callouts

Per Spec v2 §5.6 (and §7.1 A5 reversed) — historical attributions, traditional fraction vocabulary, regional terminology live on Section.cultural_callouts[] metadata. They are not LOs.

Cross-thread prerequisite proposals

Per Spec v2 §8.4 — LLM-proposed prerequisite edges to LOs in other threads. Each requires human approval once the target thread's catalog is authored. Until then, the edges live as proposals.

What this catalog unlocks downstream

An LO catalog by itself is just structured rows in a database. Its value comes from what it enables in the layers above and around it. Four downstream uses depend on this catalog being clean — that's why your review matters.

1. Layer 3 content tagging (the "1 + 2" model)

Every piece of content built for the product — every applet, video, quiz item, worksheet, MAX/Spark dialogue script — must declare what it teaches. The Layer 3 rule: each component tags to exactly one primary LO (the skill it directly assesses or teaches) plus up to two secondary LOs (other skills it incidentally reinforces).

This means the LO catalog is the labelling vocabulary for content. A clean catalog → clean labels → the AI tutor can pick the right component for the right moment. A muddled catalog → ambiguous labels → the tutor either picks the wrong content or picks nothing.

2. AI tutor runtime traversal

The Byjus.AI runtime maintains, per student, a real-time view of which LOs are mastered, which are in-progress, and which are not yet attempted. On every turn it traverses the LO graph to answer "what should we work on this session?":

• Going forward — find the nearest not-yet-attempted LO whose prerequisites are all mastered. Edge type: prerequisite_of.
• Backing up — if a student fails an assessment at LO X, follow prerequisite_of edges backward and find the deepest prereq that's still uncertain. Drill there.
• Within an LO — Levels and Facets choose how to present the next item: foundational tier first for new exposure, advanced tier for review; visual Facet for first introduction, symbolic Facet for assessment.
• Avoiding "skill stutter" — Solving Schemas ensure that variants of the same underlying relation aren't presented as if they're brand-new each time. Two questions sharing the equivalent_fractions schema are recognised as the same skill in different clothes.

3. Student Knowledge Graph — the per-student overlay (future)

The catalog you see is the shared curriculum graph — the same one every student sees. Layered on top, one per student, is the Student KG: a copy of the catalog where each LO node carries that student's mastery state (not-attempted / introduced / practising / mastered / overlearned), assessment evidence (which items, when, scored what), and timestamps of every interaction with that LO.

Over time, this per-student overlay accumulates into a longitudinal record — not a test score, but a continuous mastery trace across every LO the student has touched. This is the substrate for:

• Parent reports — "Aisha's mastered 18 of 22 fractions LOs this term; the four open ones are X, Y, Z, W with the following symptoms."
• Teacher dashboards — class-level mastery heatmaps; same vocabulary as the parent report; same vocabulary as the tutor's runtime logic.
• Research — multi-year retention studies, dependency-edge validation ("does mastering A actually unblock B?"), pedagogy A/B (does Facet ordering V→S→A outperform S→V→A?).

None of this is possible if the LOs aren't atomic and stable. If the catalog churns, every prior mastery state is unmoored.

4. Cross-curriculum content reuse via the UKG

An applet that teaches "add fractions with unlike denominators" should serve a CBSE student in India AND a KM student in Indonesia. The way to make that work is the federation we covered in Section 03: each curriculum has its own catalog; cross_curriculum_equivalent edges bridge equivalent LOs across them.

When CBSE's cbse-math-add-fractions is bridged to KM's km-math-jumlah-pecahan, the applet authored once (with two language tracks) can be reused under both curricula's runtimes. The bridge is what justifies the content investment.

The chain of dependencies

How your review feeds the loop

1. You leave per-LO and bulk comments (Section 15).
2. Each comment maps to either a catalog edit (split / level_extend / facet_add / add / deprecate) or a rationale reply preserved with the LO.
3. Two-author governance gate stamps the LO proposed → active.
4. Once the catalog is ratified, L3 content tagging unblocks. Until then, content production for this thread holds.

How to leave feedback

Two ways to comment: per-LO (recommended) or bulk.

Per-LO comments

On any LO card in section 9, click 💬 Comment on this LO — opens the Google Form with the LO ID and canonical statement pre-filled.

Bulk / general comments

Use this form for cross-cutting feedback (e.g., "the entire G7 multiplication treatment feels too procedural"):

Open comment form

What to comment on

What we'll do with your feedback

1. All comments collect into the linked Google Sheet — Vinay monitors.
2. Each comment triggers either a catalog edit (per Spec v2 §8.6 governance: split / level_extend / facet_add / add / deprecate) or a "rationale" reply preserved with the LO.
3. Two-author review remains the gate (status: proposed → active).

Reviewers

TBD — list to be filled in once SMEs are confirmed.