Series Layer Map · Principia Orthogona · G6 LLC · 2026

Four Registers, One Fixed Point Philosophical · Didactic · Formal · Experiential — convergence at x*

Pablo Nogueira Grossi (Sri Brodananda) · G6 LLC · Newark, NJ
Companion to: D2 · Evolutionary Epistemology · and the Paraśurāma Hinge

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.

x* The Fixed Point · Center of the Ikigai
G(x*) = x*  ·  K-crossing = Paraśurāma hinge  ·  sorry roadmap = honest boundary of x*
L1 · Philosophical (books / papers)
L2 · Didactic (CEFR chapters / course)
L3 · Formal (Lean files)
L4 · Experiential (journey game / Collatz orbits)
IKIGAI — all 4 layers present: reinforce explicitly
SAFE — 2–3 layers: acknowledge the parallel, don't repeat
ELEVATE — strong in 1 layer, needs formal or experiential grounding
DROP — C1 scaffolding that doesn't survive D2 scrutiny
OPEN — Lean sorry; keep claim honest
FILTER:
Node Map — 22 convergence points
Concept / Node
Layers
Verdict
L1 Source
L3 File
L4 Event
Fixed point x* = G(x*)The series center; convergence criterion
Ikigai
D2 §3, ch13, Mini-Beast §5
Chain.lean — G composition
Journey node §13 · "Fixed Point"
Collatz orbit as Pass 2Journey game: odd/even orbit = C→K→F→U
Ikigai
D2 §1 · Paraśurāma = K-crossing
Chain.lean · fitribonacci.lean
Journey Pass 2 · Collatz orbit animation
Figure-eight / Lemniscate / AnalemmaSelf-intersection as the hinge geometry
Ikigai
ch01-one-equation · analemma intro
GeronoLemniscate.lean — 0 sorry ✓
Journey ch01 · "One Equation" node
Sorry roadmap = honest incompletenessWhat remains open is the product, not a failure
Ikigai
D2 §4 · Metzinger boundary; Mini-Beast §6
IterationGap.lean — CollatzLyapunov open axiom
Journey §14 · "AXLE" node · open doors
Bindu / PhaseVector initializationThe pre-operator state; 12-dim rest point
Ikigai
D2 Paraśurāma §2; Mini-Beast §4 Quantum Weave seed
Crystal/G6.lean — PhaseVector (Fin 12 → ℝ)
Journey "Bindu" entry-point node
Shree Yantra / hexagonal D₆ structureg⁶ = 33 crystal law; 6-fold symmetry
Safe
Mini-Beast §4 Quantum Weave; D2 Paraśurāma §3
Crystal/G6.lean + Symmetry/D6.leancrystal_lockin sorry
Nested infinities / ω^ω closureG6Ordinal = Mahlo-like transfinite lift
Open
ch08-nested-infinities; Mini-Beast §4 Quantum Weave
Ordinal/MahloClosure.lean — g6_unconditional_closure sorry
K-operator = Paraśurāma hingeAvatar VI = threshold crossing; κ* curvature
Ikigai
D2 Paraśurāma §1–2; ch-d2-academic §5
Threshold.lean — κ* threshold axiom
Journey Pass 2 · K-crossing event
TE operator: T = E = log 3 − v₂(n)·log 2Conformal time / entropic cost — dual reading
Ikigai
D2 academic §3; Mini-Beast §3 TE section
TE.lean (book/gctc — stale; TE_odd sorry)
Journey weight annotation on each Collatz step
Daśāvatāra as evolutionary metaphor (C1 framing)Avatar = adaptive stage — pop-science level
Drop
Mini-Beast §2 C1 scaffold version
Daśāvatāra as operator sequence (D2 framing)C→K→F→U→G as formal Daśāvatāra map
Elevate
D2 Paraśurāma §1; ch-d2-academic §6
Chain.lean — operator composition G = U∘F∘K∘C
needs journey node
112 Dhāraṇās as phenomenological protocolVBT as laboratory; Varela/Maturana bridge
Safe
D2 academic §2; Paraśurāma §3 (Tantrāloka)
IterationGap.lean — attention protocol analog
Metzinger / no-self / transparencyPhenomenological boundary; epistemic humility
Elevate
D2 academic §4; ch-d2-academic §4
IterationGap.lean — CollatzLyapunov as self-limit
OrbitLadder: 6 orbit classesSchumann · Hypogeum · φ-helix · dm³ · Cajueiro · G-series
Safe
Mini-Beast §3; ch05-oscillations
OrbitLadder.lean — 0 sorry ✓ all decide ✓
Journey oscillation chapter nodes
Cajueiro nut / resonant chamberPhysical instantiation of the fixed point
Safe
Mini-Beast §4 Resonant Chamber Extend
OrbitLadder.lean cajueiro orbit class
Toy proofs: RH / NS / GoldbachDm3RHToy · Dm3NSToy · Dm3GoldbachToy — all sorry=0
Open
Dm3RHToy.lean Dm3NSToy.lean Dm3GoldbachToy.lean
Quantum Weave — C1 pop-science framing"quantum" used loosely; C1 reader convenience
Drop
Mini-Beast §4 Quantum Weave seed pp.48-51
Quantum Weave — D2 upgrade: dm³ phase spaceReplace "quantum" with formal PhaseVector / bindu
Elevate
D2 Paraśurāma §3 · Tantrāloka territory
Crystal/G6.lean — PhaseVector formal upgrade
Seven Disciples transmission modelGurukula → śaktipāta → second-order didactics
Safe
D2 Paraśurāma §5; D2 academic §5
IterationGap.lean — transmission = proof obligation handoff
n-Bonacci Pass 3 / Tribonacci η = 1.839Journey game mode 3; η as G-series attractor
Safe
Crystal/G6.lean — η weighting in PhaseVector
Journey Pass 3 · n-Bonacci mode
Varela / Maturana autopoiesis bridgeEnactivism as D2 philosophical framework
Safe
D2 academic §2; ch-d2-academic §2
Kālabhairava / operator at the hingeDestroyer of time = K applied to itself
Ikigai
D2 Paraśurāma §2; Mini-Beast epilogue
Threshold.lean — κ* self-application
Journey hinge-crossing event · node §8
Lean File → Chapter Map
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
D2 Writing Strategy

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.

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