knowledge: neurosymbolic + RLVR + causal learning-layer curriculum (v1) — 8 papers, 5-PR roadmap, governance only

[AdaWorldAPI]

Summary

8-paper curriculum + 5-PR roadmap for the stack's missing self-improvement loop. No code changes — plan + board hygiene per CLAUDE.md Mandatory Board-Hygiene Rule (new integration plan → INTEGRATION_PLANS.md PREPEND + .claude/knowledge/<name>-v<N>.md + EPIPHANIES.md PREPEND).

What this composes

The substrate landed in PR #372 (causaledge64-mailbox-rename-soa-v1) — AriGraph SPO-G + CausalEdge64 v2 + Σ-tier router + MailboxSoA. What this curriculum adds is the learning loop on top of that substrate — the verbs that turn the existing Think struct into a system that trains itself.

8 papers in 4 reading tiers (~6 hours total):

Tier	Papers	Stack verb
0 — Doctrinal	Causal de Finetti · Executable CFG	ICM grouping, Pearl 2³ trainable
1 — Method	LINC · GRPO	Σ9-Σ10 prover dispatch, RLVR algorithm
2 — Generation	LPN · TextGrad · Opt-Sym	StyleVector test-time grad, hybrid prompt opt, symbolic data gen
3 — Safety	Conformal CFG	Calibrated bounds for L4 outputs

Stack mapping (5 live, 4 missing)

Live (PR #372): AriGraph SPO-G quads · StyleVectors · Σ9-Σ10 → L4 shell · MUL gate · Pearl 2³ in NarsEngine

Missing (this curriculum's PR roadmap fills): NARS Intervention/Counterfactual verbs · ICM-invariance column · TextGrad-style style_synthesize · GRPO trainer · LINC bridge + conformal CFG

5-PR sequencing

#	Scope	LOC	Risk
PR-LL-1	NARS Intervention/Counterfactual verbs + AriGraph::intervene_on	~200	Low
PR-LL-2	ICM-invariance column + lance-graph-planner::data_gen (Opt-Sym generator)	~800	Med
PR-LL-3	Hybrid TextGrad/LPN style_synthesize	~400	Med
PR-LL-4	crates/lance-graph-trainer/ (GRPO loop)	~800	High
PR-LL-5	crates/linc-bridge/ (Z3 prover + conformal CFG)	~600	Med

Sequential. PR-LL-4 requires ~2 weeks separate prep for the Qwen3-head-via-candle wiring.

Doctrinal claims worth flagging

1. Stack's NARS verifier is strictly stronger than Opt-Sym's LLM verifier — graded confidence ∈ [0,1] is better than binary commit/reject as a GRPO reward signal. The stack gets a free-quality improvement on the published method.
2. Stack's StyleVectors is already an LPN-style continuous latent space — the gradient-at-inference operator is what's missing, not the representation.
3. The MUL gate is already the LINC dispatch shape — LINC fills the "what does L4 actually compute" slot in the existing Σ9-Σ10 escalation path.
4. Conformal CFG with Jirak bounds, not Berry-Esseen — counterfactual rollouts share latent abduction; correlation makes classical bounds underestimate variance. The stack's I-NOISE-FLOOR-JIRAK iron rule already encodes this.

6 Open Questions (ratify before sprint fan-out)

• OQ-LL-1 reward shape (graded NARS confidence vs binary) — recommendation: graded
• OQ-LL-2 TextGrad optimizer location (local Qwen3 vs frontier API) — recommendation: local with frontier fallback
• OQ-LL-3 prover choice (Z3 vs Prover9 vs HOL Light) — recommendation: Z3 default, HOL Light for verified-code consumers
• OQ-LL-4 style-pool location (contract vs separate learned_styles) — recommendation: separate pool, contract exposes StylePoolProvider trait
• OQ-LL-5 ICM-invariance update protocol — recommendation: clear bit on counterfactual contradiction
• OQ-LL-6 Σ-tier-as-difficulty probe (hot-path latency)

Iron rule audit (all 6 satisfied)

Rule	Status
I-SUBSTRATE-MARKOV	All synthesized trajectories pass Chapman-Kolmogorov test
I-NOISE-FLOOR-JIRAK	Conformal calibration uses Jirak bounds, not Berry-Esseen
I-VSA-IDENTITIES	style_synthesize produces identity fingerprints, not content
I1 BindSpace read-only	IcmInvarianceColumn writes via CollapseGate::bundle
Method-on-carrier	All 4 new capabilities are methods on existing carriers
AGI-as-glove SoA	New styles land in StyleColumn extension, no new layer

Blast radius

• 2 new crates: lance-graph-trainer + linc-bridge (~1400 LOC)
• 3 crates modified: lance-graph-planner, causal-edge, lance-graph-contract
• Zone 3 surface UNCHANGED
• ndarray side UNCHANGED (curriculum stays thinking-side of the doctrinal split)
• External deps gated: z3-rs (PR-LL-5), candle/burn (PR-LL-4)

Files changed

• NEW: .claude/knowledge/neurosymbolic-rlvr-causal-curriculum-v1.md (~620 lines, 12 sections)
• PREPEND: .claude/board/EPIPHANIES.md (E-LL-CURRICULUM-1)
• PREPEND: .claude/board/INTEGRATION_PLANS.md (plan-index entry)

3 files changed, +617 lines. Zero code.

Test plan

• Knowledge doc renders cleanly (markdown)
• EPIPHANIES.md PREPEND format matches existing entries (append-only governance preserved)
• INTEGRATION_PLANS.md PREPEND format matches existing entries
• No code in this PR — nothing to compile or test
• Reviewer ratifies §7 OQ-LL-1 through OQ-LL-6 before sprint-11 worker fan-out
• Reviewer confirms §5 stack-substrate alignment table accurately reflects current state post-PR specs(sprint-10): 12-worker CCA2A fleet + meta-review (governance) #372

What this PR does NOT touch

• No code. Zero .rs / Cargo.toml changes.
• No new crates. All 5 PR-LL-* sub-PRs describe future crates; this PR does not create them.
• No ndarray changes. Curriculum is doctrinally thinking-side; ndarray stays as hardware substrate.
• PR-LL-1 through PR-LL-5 implementation workers — owned by the next sprint kick-off after this curriculum merges and OQs are ratified.
• Pre-training of foundation models — outside scope. Stack uses Jina v5 / Qwen3 / ModernBERT / etc. as frozen encoders; PR-LL-4 fine-tunes a head, not the foundation.

Predecessor

PR #372 (causaledge64-mailbox-rename-soa-v1) — the substrate this curriculum builds the learning loop on top of. Without PR #372's SPO-G quads, MailboxSoA, and Σ-tier router, the curriculum has nothing to wire into.

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