knowledge: neurosymbolic + RLVR + causal learning-layer curriculum (v1)

8-paper synthesis composing Schölkopf SCMs + MIT BPL + LINC + GRPO into a
5-PR roadmap for the stack's missing self-improvement loop. Governance
only — no code changes. Doc + 2 board PREPENDs per CLAUDE.md Mandatory
Board-Hygiene Rule.

## What this composes

Eight papers, four tiers, ~6 hours total reading load:

Tier 0 (doctrinal frame):
- Causal de Finetti (Guo+Schölkopf 2022, arXiv:2203.15756) — ICM principle,
  AriGraph SPO-G grouping doctrine
- Executable Counterfactuals (Vashishtha 2025, arXiv:2510.01539) — Pearl
  2³ trainable verbs, RL>SFT for OOD

Tier 1 (method substrate):
- LINC (Olausson+Solar-Lezama+Tenenbaum 2023, arXiv:2310.15164) — Σ9-Σ10
  classical-prover dispatch
- GRPO/DeepSeekMath (Shao 2024, arXiv:2402.03300) — RLVR algorithm spec

Tier 2 (closed-loop generation):
- LPN (Bonnet 2024, arXiv:2411.08706) — StyleVectors test-time gradient
- TextGrad (Yuksekgonul 2024, ~arXiv:2406.07496) — textual-gradient prompt
  optimizer
- Opt-Sym (Yeo+Solar-Lezama 2026, ID pending) — symbolic-space adaptive
  data generation

Tier 3 (safety/calibration):
- Conformal CFG (Farzaneh 2026, arXiv:2601.20090) — calibrated bounds for
  L4 planner outputs

## Stack mapping (5 live components, 4 missing modules)

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

Missing: NARS Intervention/Counterfactual verbs · ICM-invariance column ·
TextGrad-style style_synthesize · GRPO trainer · LINC bridge

## 5-PR roadmap (each ~200-800 LOC, sequential, PR-LL-1..LL-5)

PR-LL-1: NARS Intervention/Counterfactual InferenceType variants + AriGraph
::intervene_on — closes Pearl 2³ dispatch gap

PR-LL-2: ICM-invariance BindSpace column (1 bit/row, gated through
CollapseGate per I1) + lance-graph-planner::data_gen module (Opt-Sym
generator targeting Σ-tier as difficulty axis, with NARS+Chapman-Kolmogorov
deterministic verification stronger than Opt-Sym's LLM verifier)

PR-LL-3: Hybrid TextGrad/LPN style_synthesize — numerical autograd on
StyleVector + textual gradient on rendering prompt — closes
THINKING_ORCHESTRATION_WIRING.md Gap 1 (12 vs 36 ThinkingStyle)

PR-LL-4: crates/lance-graph-trainer/ — GRPO loop with NARS confidence
∈ [0,1] as graded reward (strictly stronger than Opt-Sym binary). Backed
by candle or burn for the Qwen3 head fine-tune. ~2 weeks separate prep
work for the head-via-candle wiring.

PR-LL-5: crates/linc-bridge/ — Z3 SMT prover + Farzaneh-style conformal
counterfactual wrap. SMT theories (arithmetic, bitvectors, arrays) match
stack queries better than pure FOL. Required for MedCare-rs / q2
high-stakes safety.

## 6 Open Questions (ratify before sprint fan-out)

OQ-LL-1 reward shape (graded NARS confidence vs binary)
OQ-LL-2 TextGrad optimizer location (local Qwen3 vs frontier API)
OQ-LL-3 prover choice (Z3 vs Prover9 vs HOL Light)
OQ-LL-4 style-pool location (contract vs separate learned_styles pool)
OQ-LL-5 ICM-invariance update protocol (when does invariance bit clear?)
OQ-LL-6 Σ-tier-as-difficulty probe (hot-path latency check)

## Iron rule audit (all 6 satisfied)

I-SUBSTRATE-MARKOV: synthesized trajectories pass Chapman-Kolmogorov in
PR-LL-2 verify step
I-NOISE-FLOOR-JIRAK: PR-LL-5 conformal calibration uses Jirak bounds (not
classical Berry-Esseen) — counterfactual rollouts share latent abduction,
classical bounds underestimate variance
I-VSA-IDENTITIES: style_synthesize produces identity fingerprints, not
content
I1: IcmInvarianceColumn writes through CollapseGate::bundle, never raw
assignment
Method-on-carrier: all 4 new capabilities are methods on existing carriers
(AriGraph, StyleVector, Student, Query)
AGI-as-glove SoA: synthesized styles land in StyleColumn extension; no
new layer

## Blast radius

- 2 new crates: lance-graph-trainer + linc-bridge (~1400 LOC total)
- 3 crates modified: lance-graph-planner, causal-edge, lance-graph-contract
- Zone 3 surface UNCHANGED
- ndarray side UNCHANGED (curriculum stays thinking-side of doctrinal split)
- External deps gated behind features: 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, 5-PR roadmap + 6 OQs + iron-rule audit)
- PREPEND: .claude/board/EPIPHANIES.md (E-LL-CURRICULUM-1)
- PREPEND: .claude/board/INTEGRATION_PLANS.md (plan-index entry)

3 files changed. Pure plan + board hygiene. No code.

## Predecessor / successor

Predecessor: PR #371/#372 (causaledge64-mailbox-rename-soa-v1) substrate
— this curriculum is the learning loop on top of that substrate

Successor: PR-LL-1 through PR-LL-5 (the curriculum is the spec for the
sequential implementation wave; each PR fan-outs via the established
CCA2A 12-worker pattern)

Author: claude

.claude/board/EPIPHANIES.md

@@ -1,3 +1,25 @@
+## 2026-05-14 — E-LL-CURRICULUM-1 — neurosymbolic + RLVR + causal learning layer (8-paper synthesis)
+
+**Status:** PROPOSAL (curriculum doc landed; 5-PR roadmap ratification pending)
+
+**Click:** The stack already has the substrate for *self-improvement*. PR #372 landed AriGraph SPO-G + CausalEdge64 v2 + Σ-tier router + MailboxSoA — all five doctrinal pieces of (probabilistic programs × structural causal models × multi-environment grouped data × explicit conditional dispatch × Bayesian belief). What's missing is **the learning loop on top**: a deterministic verifier (NARS), a Goldilocks data generator (Opt-Sym shape), a continuous program-latent optimizer (LPN shape), an RL trainer (GRPO shape), and a Σ9-Σ10 deductive prover (LINC shape). Each maps to one existing-or-near-existing stack component; the curriculum (this doc) is the joint reading that names which paper supplies which verb. Reading load: ~6 hours across 4 tiers. PR roadmap: 5 PRs (LL-1 NARS intervene/CFG verbs → LL-2 ICM column + Opt-Sym generator → LL-3 hybrid TextGrad/LPN style optimizer → LL-4 GRPO trainer crate → LL-5 LINC bridge + conformal CFG).
+
+**Stack alignment table:** Causal de Finetti ↔ AriGraph SPO-G (live); LPN ↔ StyleVectors (live, underused); LINC ↔ Σ9-Σ10 → L4 (live shell, no prover); Executable CFG ↔ Pearl 2³ in NarsEngine (live in name, missing verbs); Opt-Sym ↔ data_gen module (missing); Conformal CFG ↔ safety wrap (missing); TextGrad ↔ style optimizer (missing); GRPO ↔ trainer (missing).
+
+**Doctrinal claim:** Stack's NARS truth + I-SUBSTRATE-MARKOV gives a *strictly stronger* deterministic verifier than Opt-Sym's LLM verifier — graded confidence ∈ [0,1] is better than binary pass/fail as a GRPO reward. Stack's `StyleVectors` is *already* an LPN-style continuous latent space; LPN's gradient-at-inference is the missing operator. The MUL gate is *already* the LINC dispatch shape; LINC just fills the L4 slot. Each of the 8 papers maps to a verb the stack named but didn't ship.
+
+**Doc location:** `.claude/knowledge/neurosymbolic-rlvr-causal-curriculum-v1.md` (~600 lines, 12 sections). Cross-refs to causal-edge-64-* triad, cognitive-shader-driver-thinking-engine-reunification, encoding-ecosystem (mandatory), lab-vs-canonical-surface (mandatory), bf16-hhtl-terrain (probe queue).
+
+**Open questions (6) gated before sprint fan-out:** reward shape (graded vs binary), TextGrad optimizer (local vs frontier), prover choice (Z3 vs HOL Light), style-pool location (contract vs separate), ICM-invariance update protocol, Σ-tier-as-difficulty probe.
+
+**Iron rule audit:** Six rules (I-SUBSTRATE-MARKOV, I-NOISE-FLOOR-JIRAK, I-VSA-IDENTITIES, I1, method-on-carrier, AGI-as-glove SoA) all satisfied — synthesized styles are IDENTITY fingerprints (not content), Conformal CFG uses Jirak bounds (not classical Berry-Esseen), all four new capabilities are methods on existing carriers, BindSpace stays read-only with the new IcmInvarianceColumn gated through CollapseGate.
+
+**Predecessor:** PR #371/#372 (causaledge64-mailbox-rename-soa-v1) substrate.
+
+**Successor:** PR-LL-1 through PR-LL-5 (this curriculum is the spec).
+
+---
+
 # Epiphanies — Append-Only Log (date-prefixed)
 
 > **APPEND-ONLY.** Every epiphany, realization, correction, or

.claude/board/INTEGRATION_PLANS.md

@@ -1,3 +1,70 @@
+## 2026-05-14 — neurosymbolic-rlvr-causal-curriculum-v1 (LL-CURRICULUM)
+
+**Status:** Active (PROPOSAL — curriculum landed, 5-PR roadmap ratification pending §7 OQs)
+**Confidence:** High (composition of published methods + existing substrate; no novel research)
+**Plan file:** `.claude/knowledge/neurosymbolic-rlvr-causal-curriculum-v1.md`
+**Predecessor:** `causaledge64-mailbox-rename-soa-v1` (PR #372 — landed)
+
+### Scope
+
+8-paper curriculum + 5-PR implementation roadmap for the stack's learning layer. Composes Schölkopf-style structural causal models, MIT-style Bayesian program learning, Solar-Lezama × Tenenbaum neurosymbolic dispatch (LINC), and DeepSeekMath-style RLVR into one substrate that turns the existing `Think` struct (post-PR #372) into a self-improving system.
+
+### What this composes
+
+- **Causal de Finetti** (Guo+Schölkopf 2022, arXiv:2203.15756) → AriGraph SPO-G grouping doctrine
+- **LPN** (Bonnet 2024, arXiv:2411.08706) → `StyleVectors` test-time gradient adaptation
+- **LINC** (Olausson+Solar-Lezama+Tenenbaum 2023, arXiv:2310.15164) → Σ9-Σ10 EPIPHANY classical-prover dispatch
+- **Executable Counterfactuals** (Vashishtha 2025, arXiv:2510.01539) → Pearl 2³ trainable verbs + RL>SFT for OOD
+- **Conformal CFG** (Farzaneh 2026, arXiv:2601.20090) → calibrated counterfactual sets for MedCare-rs / q2 safety
+- **TextGrad** (Yuksekgonul 2024, arXiv:~2406.07496) → closed-loop style optimizer (textual gradient)
+- **Opt-Sym** (Yeo+Solar-Lezama 2026) → symbolic-space adaptive data generation
+- **GRPO/DeepSeekMath** (Shao 2024, arXiv:2402.03300) → RLVR trainer algorithm
+
+### 5-PR sequencing (this curriculum doc is governance only; the 5 implementation PRs follow)
+
+| # | Scope | LOC | Risk |
+|---|---|---|---|
+| PR-LL-1 | NARS Intervention/Counterfactual InferenceType variants + AriGraph::intervene_on | ~200 | Low (additive to enum) |
+| PR-LL-2 | ICM-invariance BindSpace column + `lance-graph-planner::data_gen` (Opt-Sym generator) | ~800 | Med (new SoA column + new module) |
+| PR-LL-3 | Hybrid TextGrad/LPN `style_synthesize` (numerical + textual gradient on StyleVector) | ~400 | Med (closes Gap 1) |
+| PR-LL-4 | `crates/lance-graph-trainer/` (GRPO loop, candle/burn-backed) | ~800 | High (new training crate, ~2 weeks prep work) |
+| PR-LL-5 | `crates/linc-bridge/` (Z3 prover + conformal CFG wrap) | ~600 | Med (new crate, external dep on z3-rs) |
+
+Sequential: each PR is a precondition for the next. PR-LL-4 requires ~2 weeks of separate Qwen3-head-via-candle prep work before fan-out.
+
+### Closes / unblocks
+
+- `THINKING_ORCHESTRATION_WIRING.md` **Gap 1** (Contract Not Consumed — 12 vs 36 ThinkingStyle) → PR-LL-3 learns the missing 24 from runtime trajectories
+- `THINKING_ORCHESTRATION_WIRING.md` **Gap 4** (Elevation not connected) → SigmaTierRouter consumes PR-LL-3's free-energy gradient as elevation signal
+- **Pearl 2³ named-but-not-dispatched** → PR-LL-1 makes intervene/counterfactual first-class verbs
+- **L4 planner shell empty** → PR-LL-5 fills with LINC dispatch + conformal calibration
+- **TD-LEARNING-LOOP-MISSING** (implicit; no doc exists for the unwired GRPO trainer) → PR-LL-4
+
+### Blast radius
+
+- **New crates:** `lance-graph-trainer` + `linc-bridge` (~1400 LOC together)
+- **Crates modified:** `lance-graph-planner` (data_gen + style_synthesize modules), `causal-edge` (Intervention/Counterfactual variants), `lance-graph-contract` (StylePoolProvider trait per OQ-LL-4)
+- **Zone 3 surface UNCHANGED**
+- **External deps added:** `z3-rs` (PR-LL-5), `candle` or `burn` (PR-LL-4) — both gated behind feature flags
+- **ndarray side:** UNCHANGED (the curriculum stays on the thinking-side of the doctrinal split)
+
+### Open Questions (6 — ratify before sprint fan-out)
+
+OQ-LL-1 reward shape (graded NARS confidence vs binary) · OQ-LL-2 TextGrad optimizer location (local Qwen3 vs frontier API) · OQ-LL-3 prover choice (Z3 vs Prover9 vs HOL Light) · OQ-LL-4 style-pool location (contract vs separate) · OQ-LL-5 ICM-invariance update protocol · OQ-LL-6 Σ-tier-as-difficulty probe (hot-path latency)
+
+### Iron rule compliance
+
+| Rule | Status |
+|---|---|
+| I-SUBSTRATE-MARKOV | All synthesized trajectories pass Chapman-Kolmogorov test in PR-LL-2 verify step |
+| I-NOISE-FLOOR-JIRAK | PR-LL-5 conformal calibration uses Jirak-derived bounds, not classical Berry-Esseen |
+| I-VSA-IDENTITIES | `style_synthesize` produces identity fingerprints; content stays in YAML registries |
+| I1 BindSpace read-only | `IcmInvarianceColumn` writes go through `CollapseGate::bundle` |
+| Method-on-carrier | All 4 new capabilities are methods on existing carriers |
+| AGI-as-glove SoA | Synthesized styles land in `StyleColumn` extension; no new layer |
+
+---
+
 # Integration Plans — Versioned Index
 
 > **APPEND-ONLY.** Every integration plan ever authored for this