ψ–Armour: Structural Buffering Under Matched Timescale Coupling

ψ–Armour: Structural Buffering Under Matched Timescale Coupling When Systems Absorb Information Without Immediate Energetic Response Zenodo Canonical Edition ·Full-Form Archival Build ·v1.2 Ω Giovanni Esposito Independent Researcher Australia December 2025 Abstract Prior work established an empirical gate for detecting information–energy coupling: coupling becomes observable only when measurement cadence resolves system-internal informational timescales [ 3 ]. That result answers when coupling can be seen. Here we address the complementary question: once coupling is detectable, how do systems respond? Across eight astrophysical systems spanning stellar rotators, accreting compact objects, and pulsars, we observe a reproducible second-order response regime in which informational load increases while the externally observed energetic response is attenuated, delayed, and released in punctuated episodes under matched-timescale conditions. We term this conditional buffering regime ψ –armour. Importantly, ψ –armour is not defined by weak signals: highvariance systems can remain armoured when internal coherence is preserved. Neural analyses are included to validate regime discrimination rather than universality: an oddball EEG paradigm exhibits transparent first-order coupling ([E1]), while a motorimagery boundary case yields the predicted null ([E2]). Armoured neural regimes are stated as prospective ([P]) and are not claimed as established. We formalize ψ –armour as energy partitioning between internal and external channels governed by a regulation-depth proxy ψ7 , and provide a minimal saturating response model (Appendix S1) reproducing sigmoidal buffering and threshold release without violating global invariance. The contribution is a falsifiable separation between detectability and response: coupling can be observable while the system buffers, stores, and later discharges strain. 1 Introduction 1.1 Detectability is not response Empirical studies of complex systems increasingly report correlations between informational measures (e.g., transfer entropy, predictive information) and energetic proxies (e.g., flux, power, dissipation). A recurring failure mode in this literature is the conflation of (i) detectability of coupling with (ii) form of response. The matched-timescale law [ 3 ] isolates detectability: unless measurement cadence resolves characteristic driver timescales, coupling estimates collapse toward null even in strongly structured signals. However, the existence of a detectability gate does not specify how a system behaves once coupling is observable. This paper proposes and tests a second distinction: response regimes. Under matchedtimescale conditions, some systems transmit informational load directly to external energetic 1 output (transparent response), whereas others absorb load internally and suppress or delay external discharge. We term this latter conditional buffering regime ψ–armour. 1.2 The motivating paradox: visible coupling, muted discharge In multiple domains, systems appear to “know” more than they immediately “spend.” In astrophysical accretion, large variability in inferred inflow or state structure can coexist with extended quiescent radiative output punctuated by bursts. In engineered systems, strong informational shocks can be temporarily masked by internal buffering until saturation triggers rapid release. In neurophysiology, high-surprise paradigms can yield immediate energetic responses, whereas other tasks show null responses consistent with weak informational forcing or ambiguous commitment. These patterns invite a unifying question: If information–energy coupling is real and detectable, what determines whether energy is discharged immediately or buffered internally? 1.3 Core contribution The contribution of this manuscript is threefold: 1. Empirical response taxonomy under a verified detectability gate. We introduce a response classification (transparent, armoured, fragile, catastrophic) defined by the curvature and partitioning of the ∆ H→ ∆ Eobs mapping, explicitly conditioned on matched-timescale detection. 2. Astrophysical [E1] anchor across eight independent systems. Using the same R01– R08 system set as the preregistered predictive cascade analysis [ 4 ], we show cadence-gated detectability and systematic energetic attenuation/delay signatures in accreting systems, with amplitude-independent preservation in pulsars. 3. Mechanistic plausibility without overclaiming. We formalize ψ –armour as internal vs external energy partitioning governed by a regulation-depth proxy ψ7 (estimated via coherence/recurrence proxies; direct Janus operator computation is deferred) and provide a minimal saturating model (Appendix S1) that reproduces buffering and threshold release. 1.4 Relation to the ψ–GIE framework This work is compatible with, but not dependent upon, the broader ψ –GIE (Geometry– Information–Energy) framework [ 2 ]. In that framework, an invariant couples energetic expenditure to informational structure. The present paper does not modify any global invariants. Instead, it asks how energetic costs are distributed over time once coupling is observable. In other words, ψ–armour is a response classification, not an additional conservation law. 1.5 What this paper does not claim To prevent scope creep, we state explicit non-claims here: •We do not claim that ψ–armour is universal across all systems. •We do not claim that armouring implies resilience or desirability. •We do not claim direct numerical evaluation of the Janus operator Jin this manuscript. •We do not claim empirically established neural armour; neural armoured regimes are [P]. 2 1.6 Why astrophysics is the anchor domain Astrophysical systems provide a uniquely clean testbed for response classification: •Long baselines: months-to-years time series allow robust statistics and surrogate controls. • Dominant drivers: rotation, accretion, and spin-down define relatively interpretable timescales. •Low intervention confounds: no demand effects or experimental feedback loops. For these reasons, astrophysical results serve as the primary [E1] validation of ψ–armour. 2 Evidence Classification and Epistemic Discipline To ensure falsifiability and prevent domain leakage, every claim in this manuscript is bounded by an explicit evidence class. 2.1 Evidence classes [E1] Measured (Strong Evidence). Direct empirical validation across at least three independent systems or subjects, satisfying all of the following: 1. matched-timescale verification (cadence resolves the dominant driver), 2. appropriate statistical controls (e.g., HAC-robust regression), 3. surrogate/null testing that destroys coupling, 4. effect-size reporting with uncertainty. [E2] Partial (Boundary Evidence). Limited-sample or single-system validation confirming a specific prediction, diagnostic null, or regime boundary. These results are used to test discriminant validity, not to assert generality. [P] Prediction. Theoretically derived implication awaiting empirical test. Predictions are stated with explicit falsification conditions. 2.2 Interpretive rules The following rules are enforced throughout: 1. No bootstrapping across classes. A[P] claim may not be used as corroboration for any [E1] claim. 2. Boundary results do not generalize. [E2] results may validate regime boundaries or predicted nulls but do not establish laws. 3. Cross-domain consistency is suggestive, not confirmatory. Agreement across domains increases plausibility but does not upgrade evidence class. 4. Nulls are informative. Absence of coupling under violated conditions (e.g., cadence mismatch) is treated as diagnostic rather than as failure. 3 3 Operational Definitions and Measurement Proxies This section specifies how informational load, energetic response, and regulation depth are operationalized in each domain. Formal objects are clearly separated from their empirical proxies. 3.1 Informational load ∆H Conceptual role. ∆ H denotes deviation from baseline informational structure relative to a system’s equilibrium or steady regime. It is not defined as raw entropy alone, but as predictive or structural deviation capable of exerting energetic demand. Astrophysical proxies ([E1]). For time-domain astrophysical systems, ∆ H is estimated using variability-structure proxies implemented in the preregistered pipeline [4], including: •normalized flux variance and asymmetry, •entropy-like measures of light-curve structure, •regime transitions mapped to known state classifications (e.g., Belloni states [1]). Neural proxies ([E1]/[E2]). In EEG paradigms: •informational load is indexed by transfer entropy, surprise, or task-induced novelty, •energetic response is indexed by band-integrated spectral power or ERP magnitude. 3.2 Energetic response ∆Eobs ∆Eobs denotes externally measurable energetic discharge: •radiative output or flux in astrophysical systems, •electrophysiological power in neural systems, •observable loss, instability, or intervention cost in engineered systems. Crucially, ∆ Eobs does not include internally sequestered energy or work; attenuation refers to redistribution, not disappearance. 3.3 Regulation depth and the coherence metric ψ7 Formal definition. Regulation depth is formalized via the coherence metric ψ7= 1 −ρ(J), where ρ ( J ) is the spectral radius of the Janus operator J in an irreversible extension of system dynamics [ 5 ]. This quantity captures divergence between forward and backward evolution and thus the reversibility/coherence of internal dynamics. Operational estimation. Direct computation of J is not performed here. Instead, ψ7 is estimated using empirically tractable proxies: •phase coherence across channels or modes, •recurrence stability in reconstructed state space, •persistence of dynamical motifs across windows. 4 3.4 Evidence Ledger Table 1 provides a compact ledger mapping each empirical component to its evidence class and interpretive role. Table 1: Evidence ledger for ψ–armour Domain System / Paradigm Class Role in argument Astrophysical R01–R08 systems [E1] Detectability gate + buffered response Neural Oddball EEG (N= 10) [E1] Transparent regime validation Neural Motor imagery (single subject) [E2] Predicted null (boundary regime) Neural Sustained conflict tasks [P] Armoured neural regime prediction AI / Institutional Various [P] Prospective applications 4 Response Regimes Under Matched-Timescale Coupling This section defines the core conceptual and mathematical object of the paper: the response regime. Response regimes describe how a system behaves after information–energy coupling has become empirically detectable. 4.1 Detectability is a prerequisite, not a response The matched-timescale law establishes that empirical coupling estimates collapse toward null unless ∆t≲τdriver,(1) where ∆ t is observational cadence and τdriver is the dominant informational timescale [ 3 ]. Throughout this section, we assume Eq. (1) holds. 4.2 First-order coupling is insufficient Under matched cadence, detectable coupling is often summarized by a first-order relation ∆E≈κψ∆H, (2) where ∆ H is informational load and κψ is a coupling constant. However, Equation (2) is silent on three empirically crucial questions: 1. Does response scale proportionally at high load? 2. Is energetic discharge immediate or delayed? 3. Can response be internally redistributed rather than externally expressed? 4.3 Energy partitioning framework We decompose energetic response into external and internal channels: ∆Etotal = ∆Eexternal + ∆Einternal,(3) where ∆ Eexternal ≡ ∆ Eobs is the measurable discharge channel, and ∆ Einternal denotes internally sequestered energetic cost (buffering, storage, internal work). 5 Total Invariant ˜ M=E/ψ Internal (Buffered) Einternal (ψ7↑) External (Observed) Eexternal (∆Eobs) Partitioning Figure 1: Thermodynamic Energy Partitioning. The global invariant is conserved, but systems with high regulation depth ( ψ7 ) divert flow to internal modes, reducing observable external energy. 4.4 Definition of ψ–armour Definition (conditional buffering). A system exhibits ψ –armour if, under matchedtimescale conditions: 1. informational load ∆Hincreases, 2. coupling remains detectable (κψ= 0), 3. externally observed energetic response satisfies ∆Eobs ≪κψ∆H, because a significant fraction of energetic cost is diverted into ∆Einternal. 4.5 Response taxonomy We distinguish four response regimes based on curvature and stability of the ∆ H→ ∆ E mapping. Table 2: Response Regimes Under Informational Load Regime Curvature Energetic Response Interpretation Transparent Linear ∆E≈κψ∆HDirect transmission Armoured Positive ∆Eobs < κψ∆HBuffered response Fragile Negative ∆Eobs > κψ∆HAmplified stress Catastrophic Divergent Runaway ∆EStructural collapse 6 Saturation Informational Load (∆H) Observed Energetic Response (∆Eobs) Transparent Armoured Fragile Boundary / Null Figure 2: Response taxonomy under matched-timescale coupling. Transparent systems scale linearly. Armoured systems attenuate and delay external discharge via internal buffering until saturation. Fragile systems amplify load. Boundary regimes show null response. 5 Astrophysical Systems and Observational Pipeline [E1] This section describes the astrophysical datasets, preprocessing pipeline, and cadence-manipulation tests used to establish detectability as a necessary precondition for response classification. 5.1 System set (R01–R08) We analyze eight independent astrophysical systems, denoted R01–R08, identical to those used in the preregistered Predictive Cascade analysis [4]. Table 3: Astrophysical systems and dominant driver timescales ID System class Dominant driver τdriver Instrument class R01 Stellar rotator Rotation ∼2.1 h TESS R02 Stellar rotator Rotation ∼3.4 h TESS R03 Stellar rotator Rotation ∼1.8 h K2 R04 Accreting BH Accretion cycle ∼1.2 d Swift/XMM R05 Accreting NS Accretion cycle ∼0.8 d Swift/XMM R06 Accreting system Accretion cycle ∼1.5 d Swift R07 Pulsar Spin-down ∼33 ms Radio PTA R08 Pulsar Spin-down ∼89 ms Radio PTA 5.2 Cadence-gated detectability Across all eight systems, coupling is consistently detectable only at matched cadence. 7 Time State Timescale Matching Logic Figure 3: The Matched-Timescale Gate. Information flow (gray wave) is only detectable if sampling cadence (blue dots) satisfies the Nyquist condition. Sparse sampling (red dots) perceives the dynamic system as static (null result). Table 4: Cadence dependence of coupling strength System class Matched cadence κψMismatched cadence κψ Stellar rotators 0.54 ±0.08 −0.02 ±0.11 Accreting systems 0.66 ±0.13 0.07 ±0.18 Pulsars 0.61 ±0.12 ≈0 6 Astrophysical Response Signatures [E1] Having established cadence-gated detectability, we now characterize how astrophysical systems respond once coupling is active. 6.1 Attenuation in accreting systems Accreting systems (R04–R06) exhibit the strongest buffering signatures. Large fluctuations in informational structure are not accompanied by proportional energetic discharge. •Informational variability: 50–77% RMS •Energetic variability: 18–31% RMS •Mean attenuation ratio: 0.62 ±0.08 6.2 Punctuated release When buffering capacity is exceeded, release is rapid and nonlinear. In GRS 1915+105 (R04), we observe: •prolonged quiescent phases under rising accretion entropy, •sudden, high-amplitude X-ray flares, •flare duration ≪accumulation duration. 6.3 High-variance yet armoured: pulsars Pulsars (R07–R08) provide a critical control case. They show RMS variability > 70% yet coupling remains robust under matched cadence. This demonstrates that buffering is not equivalent to low variability or damping. 8 7 Neural Systems as Regime Discriminators Neural systems offer a stringent test of the ψ –armour framework because they combine fast timescales, dense feedback, and experimentally controllable informational forcing. 7.1 Transparent regime: oddball paradigm [E1] We analyzed a public EEG oddball dataset (OpenNeuro ds004621, N = 10). A robust first-order coupling is observed: κEEG ψ= 81 ±13 µV2/bit, t = 6.0, p < 0.001. Neural response scales proportionally with informational load, consistent with a ψ –transparent regime. 7.2 Boundary regime: motor imagery [E2] We analyzed the PhysioNet EEG Motor Imagery dataset (BCI2000), subject S001. Imagined movement induces weak informational gradients. Results show no detectable coupling ( p = 0 . 426), which is predicted: insufficient ∆Hplaces the system in a boundary regime. Table 5: Neural regime discrimination Property Oddball Motor imagery Armoured (predicted) Informational gradient High Low High Timescale ∼450 ms ∼4 s ≫30 s Energetic commitment Transient Minimal Sustained Observed response Proportional Null Attenuated/delayed Evidence [E1] [E2] [P] 8 Mechanism: Timescale Gating and Regulation Depth This section formalizes the mechanisms underlying the empirical observations. 8.1 Control-Theoretic Interpretation In control-theoretic terms, ψ-armour describes the plant, not the controller. ΣController Plant (ψ-Armour) e∆H∆Eobs − Ref Internal ψ7 Figure 4: Control-Theoretic Interpretation. ψ -Armour resides in the Plant. High ψ7 absorbs the control signal (∆ H ) without changing the output (∆ Eobs ), masking strain from the Controller. 8.2 Why ψ7is the correct control variable Empirically: •attenuation correlates with coherence, not amplitude, 9