The series says the same thing four times — at four different resolutions. The claim is not that the books illustrate the math, or that the Lean files formalize what the chapters describe. The claim is that the fixed point x* is genuinely the same object in all four registers: the convergent narrative, the CEFR spiral, the formal proof, and the journey game all point at the identical mathematical structure from different approach angles.
This map tracks where each thread lives, which threads converge at each node, and what to do with overlaps — safe reinforcement vs. elevation opportunity vs. content to drop.
Chain.lean — G compositionChain.lean · fitribonacci.leanGeronoLemniscate.lean — 0 sorry ✓IterationGap.lean — CollatzLyapunov open axiomCrystal/G6.lean — PhaseVector (Fin 12 → ℝ)Crystal/G6.lean + Symmetry/D6.lean — crystal_lockin sorryOrdinal/MahloClosure.lean — g6_unconditional_closure sorryThreshold.lean — κ* threshold axiomTE.lean (book/gctc — stale; TE_odd sorry)Chain.lean — operator composition G = U∘F∘K∘CIterationGap.lean — attention protocol analogIterationGap.lean — CollatzLyapunov as self-limitOrbitLadder.lean — 0 sorry ✓ all decide ✓OrbitLadder.lean cajueiro orbit classDm3RHToy.lean Dm3NSToy.lean Dm3GoldbachToy.leanCrystal/G6.lean — PhaseVector formal upgradeIterationGap.lean — transmission = proof obligation handoffCrystal/G6.lean — η weighting in PhaseVectorThreshold.lean — κ* self-application| Lean File | sorry? | ch01 lemniscate | ch08 infinities | ch13 fixed pt | D2 academic | D2 Paraśurāma | Journey game |
|---|---|---|---|---|---|---|---|
| GeronoLemniscate.lean | 0 ✓ | ⬥ primary | — | — | — | — | ch01 node |
| Chain.lean (G, C,K,F,U) | 0 ✓ | — | — | ⬥ primary | §3 ops | §2 K-op | Pass 2 |
| Threshold.lean (K, κ*) | 0 ✓ | — | — | §K crossing | §5 | §1–2 primary | K event |
| OrbitLadder.lean | 0 ✓ | — | — | — | — | — | orbit nodes |
| Crystal/G6.lean | 1 (crystal_lockin) | — | ⬥ dm³ phase | — | §6 | §3 primary | — |
| Symmetry/D6.lean | 1 (d6_lockin) | — | ⬥ hexagonal | — | — | §3 Yantra | — |
| Ordinal/MahloClosure.lean | 1 (unconditional) | — | ⬥ primary ω^ω | — | §7 | §4 U-phase | — |
| IterationGap.lean | CollatzLyapunov open | — | — | §sorry map | §4 Metzinger | §5 transmit | §14 open |
| TE.lean (book/gctc — stale) | 1 (TE_odd) | — | — | — | §3 T=E | §2 TE dual | step weight |
| fitribonacci.lean | 0 ✓ | — | — | — | §3 orbit | — | Collatz steps |
What to drop from C1 scaffolding: The "Quantum Weave" framing using "quantum" loosely (Mini-Beast §4 seed text, pp. 48–51) should not be carried verbatim into D2. The Daśāvatāra-as-metaphor framing (avatar = adaptive stage, C1 convenience) should be replaced by the operator-sequence reading. These two items wear the right ideas in the wrong clothes.
What to elevate: The Daśāvatāra-as-operator-sequence (C→K→F→U→G maps to avatars I–X structurally, with Paraśurāma = K = threshold VI) needs its Lean grounding made explicit — Threshold.lean is the formal instance. The Metzinger no-self discussion in D2 §4 connects directly to IterationGap.lean's CollatzLyapunov as the formal limit of self-reference: mention this. The Quantum Weave upgrade is: replace the loose "quantum" with the formal PhaseVector from Crystal/G6.lean — 12 dimensions, D₆ symmetry, and the crystal_lockin sorry as an honest marker of what remains open in the formal theory.
Safe overlaps: The 112 Dhāraṇās as phenomenological protocol, the Cajueiro nut as resonant-chamber instantiation of the fixed point, the Seven Disciples transmission model, and the Varela/Maturana bridge all appear in multiple layers without contradicting each other. Reference but don't re-explain.
The core IKIGAI: x* · Collatz · lemniscate · K-crossing · sorry roadmap · Kālabhairava all have all four layers present. These are the load-bearing nodes. The ch-d2-parashurama.html full text should ensure §2 (K as formal hinge) cites Threshold.lean explicitly, §3 (Tantrāloka as field theory) grounds in Crystal/G6.lean PhaseVector, and §5 (transmission) closes by pointing at IterationGap.lean as the formal analogue of proof-obligation handoff from guru to disciple.