Observer Series v1.1: Hidden World from a Single Point — Topology Recovery, Operational Worlds, and the Interiorization of Invisible Structure

Abstract

We present a systematic experimental study of what an observer with a restricted read channel can learn about a deterministic source whose full state is inaccessible to him. The source is a 12-node icosahedral cluster evolving under a discrete second-order update rule; the observer reads a subset of nodes through a fixed-width channel. All experiments are reproducible by seed. Main results: (1) Blind topology recovery: an algorithm not given the neighbor list reconstructs the full icosahedron from one-step counterfactual perturbation responses (12/12 nodes, 100% precision and recall, identical across 68 parameter configurations). (2) Operational worlds: a 4-node observer reconstructs the induced subgraph of his channel — a triangle — while node 0, whose five neighbors all lie beyond the channel, acquires no direct edges in the observer's one-step world. (3) Regime separation: in quiet (wrap-free) windows, an order-8 linear recurrence reproduces node 0's future exactly; in wrapping windows, the one-step AR(2) residual is dense, O(θP), scaling linearly with θ. (4) Spectral dimension method validated: return probability computed from exact Laplacian eigenvalues yields ds = 0.999 (cycle C200), 1.92 (2D torus), 2.78 (3D torus); applied to a periodic FCC lattice (k=12), ds = 2.8 at L=8 with a size series 2.25 → 2.82 converging toward 3. (5) Kick-response: the sum of the difference vector grows exactly linearly (Σ Di(n) = n+1; conserved discrete velocity), while node 0's share decays from 100% to 5% over 48 ticks, with the modal-interference zero-crossing at t ≈ 50 predicted by the spectral weights 1:3:5:3 of the Laplacian eigenspaces. Cross-layer checks: (6) Dimensional exclusion: the Planck constant h cannot be derived from the carrier building set (Kcell, φ, τ0), which contains no mass dimension; h is interface-native (the seam's per-tick bandwidth), not carrier-native. Closed negatively and constructively. (7) Spectral lattice check: the candidate identification of atomic spectra with the HK zero-lattice fails under the Illustrative length assignment ℓ(p) = p (lattice spacings grow as p/ln p; spectral energies decay as 1/n² — opposite monotonicities). Refined: the assignment must be superlinear in p. (8) Arrow of time: the hypothesis "time = accumulated information loss ΔI(n)" is falsified in both regimes (quiet: decreasing; wrapping: stationary); the correct formulation is projection irreversibility — the permanent non-invertibility of 133 → 4 — a property of channel width, not a temporal integral. Retractions: Six claims made during the series are withdrawn or corrected with full diagnostics. Keywords: observer, channel width, topology recovery, counterfactual perturbation, operational reality, linear recurrence, spectral dimension, FCC lattice, modular dynamics, interiorization, seam bandwidth, arrow of time