APOPHIS Projection-Memory Assumption Atlas V02

This research report develops a typed, falsifiable framework for studying whether the close Earth encounter of asteroid (99942) Apophis in April 2029 could activate internal degrees of freedom that are hidden by a purely barycentric or rigid-body reduction.

The work is developed within the Logic of Existence (LoE) research program by Krzysztof Sawa (Toonhai), in the Toonhai–AEon research line, and incorporates an additional variable-inertia mechanism proposed during parallel exploration with Gemini. The document does not claim that Apophis will undergo a neck-slip event, nor that LoE has been empirically confirmed. All new physical constructions remain MODEL_INFERENCE / TAU_ACTIVE with canon_commit:false.

The central conceptual repair is the replacement of the informal idea of an “unlocked barycenter” with Barycentric Fiber Unlocking. The barycenter itself is not treated as a physical lock. Instead, the full configuration space is projected onto a reduced observable state, and an encounter may increase the dimension of internal configurations accessible above the same or nearly the same barycentric state.

A corresponding Projection–Flow Defect is defined schematically as

D_{Π,F}(t,Z) = Π(F_full(t,Z)) − F_red(t,Π(Z)),

allowing the accuracy of a reduction to be evaluated separately for orbital motion, attitude, inertia, neck deformation and memory.

The report constructs a hierarchy of four competing dynamical models driven by the same Earth tidal forcing:

M0 — rigid-body rotational response;

M1 — Markovian viscoelastic neck dynamics;

M2 — hereditary neck dynamics with a non-Markovian memory kernel;

M3 — hereditary dynamics with threshold plastic return and persistent geometric change.

The memory branch is interpreted through a generalized projection formalism: elimination of unresolved internal contact modes may produce effective memory kernels and noise in the reduced dynamics. Within this restricted operational meaning, the term Bell-Swirl is used for a candidate projection-memory kernel rather than for an arbitrary delayed anomaly.

A key result of the V01 analysis is negative but informative: with a fixed bulk moment of inertia, internal neck relaxation does not generate delayed creation of total angular momentum after the external tidal torque has vanished. It may nevertheless preserve internal geometric offsets and shape-dependent observational residuals while respecting angular-momentum and energy ledgers.

Version V02 introduces the missing variable-inertia channel while explicitly preserving total angular momentum,

L = I(t) ω(t) = const.

Using the persistent plastic displacement generated by the M3 baseline trajectory and a first-order inertia map I(q), a fractional inertia change of 2 × 10⁻⁵ produces a secular rotational phase residual of approximately 0.0504° after 14 days and 0.108° after 30 days in the tested reduced scenario. The assumed 0.05° analysis threshold is crossed after approximately 13.9 days.

The same test shows that the transient M2 memory branch alone remains below that illustrative threshold, producing only about 0.0039° of accumulated phase residual after 30 days. In the current model, observability therefore arises primarily from a persistent geometry/inertia change, while the memory sector may contribute curvature to the early-time residual.

The V02 result is explicitly a first-order projection test, not a prediction for the real asteroid. The inertia–geometry coupling coefficient is not measured for Apophis, the neck geometry and constitutive law remain uncertain, and the current dynamical model is reduced rather than a full SO(3) non-principal-axis rotational reconstruction.

The report also identifies the backreaction required for a fully coupled V03 model. If I depends on an internal coordinate q, the neck dynamics must include the corresponding generalized inertial force and the pre-encounter equilibrium must be renormalized consistently. A naïve insertion of I(q) without this term creates an unphysical drift before the Earth encounter.

The principal scientific purpose of the atlas is therefore not to announce a specific 2029 outcome, but to formulate a hierarchy of distinguishable hypotheses that can eventually be confronted with radar, photometric, shape-model and spacecraft observations:

rigid response → Markov internal response → hereditary memory → threshold/plastic memory with variable inertia.

The framework requires every candidate explanation to preserve explicit energy and angular-momentum ledgers and to outperform simpler models before a delayed post-encounter residual can be interpreted as evidence for internal memory.

The report includes equations, assumption tables, competing-model architecture, numerical experiments, parameter sweeps, conservation checks, diagrams, reproducible code and machine-readable receipts.

Epistemic status:

MODEL_INFERENCE · IMPLEMENTATION · PUBLIC_CHECK_REQUIRED · TAU_ACTIVE

canon_commit:false

Primary research concepts:

Barycentric Fiber Unlocking; Projection–Flow Defect; Bell-Swirl memory; variable inertia under conserved angular momentum; tidal excitation; non-Markovian reduced dynamics; Apophis 2029; relational physicality; Logic of Existence (LoE).