# life: apropos of birth-and-death processes, framework for fluctuating times and counting observables in stochastic excursions.

<< ️Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to quantum thermal machines. >>

<< ️In an accompanying Letter, (AA) introduced the notion of stochastic excursions−a framework to analyze out of equilibrium processes via sub-trajectories. Through counting observables, this framework captures finite-time fluctuations and trajectory-level behavior, which provides insights into thermodynamical trade-offs between thermodynamic quantities of interest, such as entropy production and dynamical activity. >>

<< ️In this work, (AA) enhance this formalism by providing a suite of technical results on how to efficiently compute excursion-related quantities. (Their) analytical results provide explicit formulas for general moments of counting variables and excursion duration, as well as their covariance and conditional moments. (They) show that excursion statistics recover full counting statistics results, and uncover a relation between fluctuations of counting observables at single-excursion level and the steady state diffusion coefficient (noise). >> 

<< ️(AA) also discuss a fluctuation theorem for individual excursions and show that it implies a modified thermodynamic uncertainty relation at the excursion level. In addition, (They) explore how analyzing excursions and using the results developed here can yield insights into three problems of interest: the three-qubit absorption refrigerator, cellular sensing, and birth-and-death processes. >>

Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Framework for fluctuating times and counting observables in stochastic excursions.

Phys. Rev. E 114, 024129. Aug 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/jydr-1853

arXiv: 2506.05160v3 [cond-mat.stat-mech]. Aug 19, 2026.

https://arxiv.org/abs/2506.05160

Also: Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Counting observables in stochastic excursions. Phys. Rev. E 114, L022102 (2026). 

https://journals.aps.org/pre/abstract/10.1103/1blp-2b27

Also: walk, walking, uncertainty, fluctuations, random, noise, behav, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: walk, walking, noise, uncertainty, behavior, fluctuations, randomness, stochasticity, stochastic excursions, Nomads. 

# gst: apropos of stretching during transitions, singularities in soft matter systems.

<< ️When a liquid thread pinches off, its neck thins as it separates into two unconnected regions. Using continuum mechanics, we can predict that the neck reaches zero radius in finite time while its curvature grows without bound. Together, the vanishing neck and diverging curvature form a finite-time singularity. >>

<< ️However, a real fluid does not realise these mathematical limits as molecular or material physics takes over once the neck becomes sufficiently small. Similar singularities arise throughout soft matter whenever a smooth continuum description is used at vanishing length scales. >>

<< ️This (AA) review asks what the shrinking region forgets, what it retains, and which material length, time, or stress cuts off the apparent divergence. The dynamics near a singularity often become self-similar, with profiles at different times collapsing onto one shape when rescaled by the shrinking local length. Sometimes that collapse is universal enough that the surrounding geometry and forcing no longer determine the local dynamics. Nonetheless, the measured output could still depend on how the shrinking region is fed by the surrounding flow and on the small-scale physics that finally replaces the ideal divergence. >>

<< ️Complex fluids and active matter change the same local balance by bringing their own timescales into the shrinking region. Beyond interfaces, the same logic applies when the localised object is a stress concentration or a defect in geometry or order rather than a moving surface. Singularities matter because they show where continuum theory stops being the relevant description and how the small-scale cutoff sets the outputs that count in printing, coating, aerosols, and stretchable solids. >>

Vatsal Sanjay. Singularities in Soft Matter Systems. arXiv: 2608.11060v1 [cond-mat.soft]. Aug 11, 2026.

https://arxiv.org/abs/2608.11060

Also: elastic, singularity, transition, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elasticity, singularity, transitions, collapse, soft matter

# gst: stabilities in the attachment of a particle to a pendant droplet.

<< ️Attachment of a particle to a pendant drop was experimentally investigated by Feng et al. (2022)]. The attachment force on the particle, consisting of the surface tension force and the pressure force, can overcome the gravity force. The attachment in equilibrium is possibly hard to maintain in practice due to instabilities. >>

<< This (AA) paper aims to discover the condition for the particle to be successfully attached under the liquid drop (bridge) through analyzing the stabilities of the capillary system. With disturbances potentially existing for both the liquid bridge and the particle, the two corresponding types of stabilities are studied. >>

<< Considering the cases with liquid surfaces checked to be stable, (AA) find four regimes for the attachment of the particle: the regimes of stable attachment, possibly stable attachment, overloaded attachment, and nonphysical attachment. Only the first two regimes mean feasible attachments in practice. (Their) prediction of feasible attachments agrees well with Feng et al., indicating the validity of (Their) stability theory. Whether for fixed-density particles of different sizes or fixed-size particles of different densities, the attachment capability for the liquid bridge first decreases, then increases, and decreases again as the volume of the liquid bridge increases. This can guide practice for lifting particles of higher weight with the pendant drop. >>

Wanqiu Zhang, Fei Zhang, Xinping Zhou. Stabilities in the attachment of a particle to a pendant droplet. Phys. Rev. Fluids 11, 084001. Aug 7, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/b63k-qk8s

Also: drop, droplet, droploid, particle, stability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, particles, stability, fluid-particle interactions, interfacial flows, liquid bridges, surface & interfacial phenomena.

# gst: escape over a saddle by colored noise.

<< ️Stochastic dynamical systems allow modeling of transitions induced by random disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. While the small-noise limit is well-described by the large deviation principle, existing computational methods often struggle with stochastic forcings any more complicated than nondegenerate Gaussian white noise, and with unbounded time intervals. >>

<< ️The primary innovations of this (AA) work are extending the framework to cater for colored and degenerate forcing and unbounded time horizons—scenarios that are physically realistic but numerically challenging. (They) cater for degenerate noise by using the Hamiltonian optimal control method. (They) cater for a class of colored noises by using linear filters on white noise. (They) cater for infinite time horizon by introducing the method of division (MOD), a computational approach for approximating rare transition events, including their most likely paths and the exponential scaling laws of their transition rates. >>

<< ️The effectiveness of MOD and the above approaches to colored noise, is demonstrated by illustration on two examples: an inverted double-well potential and a simplified roll-heave model for ship capsize. >>

Jiayao Shao (邵家瑶), Tobias Grafke, Robert S. MacKay. Escape over a saddle by colored noise: Theory and numerics. Phys. Rev. E 114, 024210. Aug 12, 2026.

https://journals.aps.org/pre/abstract/10.1103/w8dd-9cqg

Also: escape, noise, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, escape, noise, randomness, stochasticity, transitions, noise-induced transitions, method of division (MOD), inverted double-well potential, simplified roll-heave model, large deviation & rare event statistics.

gst: nonreciprocal dynamics with weak noise: aperiodic “Escher cycles” and their quasipotential landscape.

<< ️(AA) present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable attractors, forming recurrent but aperiodic “Escher cycles,” similar to the cyclic nucleation dynamics observed in the nonreciprocal Ising model. >>

<< (AA) calculate the quasipotential analytically to first order in nonreciprocality. (They) characterize it along a one-dimensional reaction coordinate that connects the attractors, and (They) also obtain the full two-dimensional landscape, at leading order in perturbation theory. >>

<< ️The resulting landscapes feature flat regions and extended plateaus, together with nondifferentiable switching lines. These singular structures arise from two geometric mechanisms: the handover of dominance between competing transition paths, and the competition between basins of attraction. The system provides a rare case where the geometry of nonequilibrium rare events can be fully resolved, and a simple analytically tractable example of a quasipotential in more than one coordinate that captures a rich set of nonequilibrium features. >>

Janik Schüttler, Robert L. Jack, Michael E. Cates. Nonreciprocal dynamics with weak noise: Aperiodic “Escher cycles” and their quasipotential landscape. Phys. Rev. E 114, 024104. Aug 3, 2026.

https://journals.aps.org/pre/abstract/10.1103/slp9-rd27

Also: noise, random, transition, singularity, escape, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, randomness, stochasticity, transitions, singularity, nonreciprocal interactions, noise-induced transitions, metastable attractors, Escher cycles, perturbation theory, escape problems, large deviation & rare event statistics. 

# gst: apropos of persistence or extinction, lag-induced critical transitions to extinction in replicating systems; the 𝜏-tipping mechanism.

<< Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscape topographies, giving rise to error thresholds and lethal mutagenesis. >>

<< Motivated by experimental evidence that polymerase-targeting antivirals limit replication, (AA) analyze replicating systems with explicit time lags in replication-enzyme availability by means of delay differential equations. (Their) approach is not equivalent to a simple renormalization of the rate of replication, since explicit delays introduce memory and temporal nonlocality into the dynamics. (They)  identify a lag-induced critical transition driven by the loss of temporal coordination between genome expression and replication. >>

<< At fixed mutation and replication rates ensuring persistence, populations cross an extinction threshold solely due to replication delays. In (Their) delay-extended quasispecies model, the timing of replicase availability emerges as an independent dynamical control parameter, defining a route to extinction that is fundamentally distinct from transitions driven by mutation rates or replicative fitness. >>

<< These (AA) results further suggest that perturbing the temporal coordination of viral replication may provide an alternative antiviral strategy for driving viral populations toward collapse. More generally, (They) propose that the extinction mechanism described here constitutes a form of lag-time-induced tipping, which (They) denote as 𝜏-tipping. >>

Edward A. Turner, Francisco Crespo, Joan Gimeno, et al. Lag-induced critical transitions to extinction in replicating systems: the 𝜏-tipping mechanism. Phys. Rev. E 114, 024401. Aug 5, 2026.

https://journals.aps.org/pre/abstract/10.1103/gyd9-ctnc

arXiv: 2603.02036v1 [q-bio.PE]. Mar 2, 2026. 

https://arxiv.org/abs/2603.02036

Also: transition, pause, silence, virus, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, pause, silence, virus, error, collapse, genomes, RNA virus, replication, replicating systems, enzymatic amplification, criticality, persistence, extinction, mutation rates, fitness landscape topographies, error threshold, time-delay systems, lag-time-induced tipping, lag-induced critical transition, loss of temporal coordination.

# behav: noise-induced stability of insect swarms.

<< ️Flying insect swarms exhibit cohesion without the local velocity alignment observed in flocks of birds or schools of fish. The interaction rules and channels of communication between insects that lead to collective behavior have not yet been determined. >>

<< ️(AA) propose a theoretical model based on acoustic communication between swarm members, where each individual is attracted to a weighted mean field of its neighbors. (They) demonstrate that this simple framework can describe a wide range of swarming dynamics, including a phenomenon where pairs of insects break free from the swarm in a helical orbit around each other. >>

<< ️Counterintuitively, (Their) numerical model suggests that stochastic noise enhances the stability of an insect swarm, as it interferes with pair formation. >>

<< Finally, (AA) demonstrate that a specific species of malarial mosquito produces swarms that reside on the edge of a transition to instability. (Their) study shows that fairly simple local interaction rules can be sufficient to describe the collective behavior of swarming biological systems. >>

Justin Faber, Annabelle Boots, Dolores Bozovic. Noise-induced stability of insect swarms. arXiv: 2608.00314v2 [physics.bio-ph]. Aug 7, 2026.

https://arxiv.org/abs/2608.00314

Also: swarm, behavior, noise, instability, transition, sound, jazz, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, swarm, noise, instability, transitions, sound, jazz, dance, flying insects, collective behavior, acoustic communication, weighted mean field of neighbors.

# gst: survival probability of particles inside the lemon billiard.

<< ️(AA) study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, (They) explore how the survival probability depends on the position and size of the hole, as well as on the billiard shape parameter. >>

<< ️(AA) find that the survival probability exhibits a two-stage decay pattern: an initial exponential regime followed by a long-time power-law tail, a signature of the stickiness effect. (Their) results show that the short-time exponential decay rate follows a power-law dependence on the hole size, with different scaling exponents for holes placed in chaotic regions versus mixed phase-space regions. For holes located in mixed phase-space regions, the decay exponent of the long-time power-law tail remains approximately constant, while the amplitude follows a power-law scaling with hole size. >>

<< ️(They) also examine the dependence of short-time exponential decay rate on the billiard shape parameter and observe scaling behavior for small values of this parameter, which breaks down as the parameter increases. >>

Daniel Borin, Edson Denis Leonel, Diego Fregolent Mendes de Oliveira. Survival probability of particles inside the lemon billiard. Phys. Rev. E 114, 014224. Jul 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/md5j-ggyd

arXiv: 2601.13000v1 [nlin.CD]. Jan 19, 2026.

https://arxiv.org/abs/2601.13000

Also: billiard, particle, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, particles, chaos, transitions, survival probability, two-stage decay pattern, stickiness effect, scaling behavior, scaling laws of complex systems. 

# gst: apropos of bluff-body wakes, effect of centerline separation on a vortex dominated wake.

<< A previously undocumented Reynolds-number-dependent transition is identified in the wake of a rounded-edge slanted afterbody, from a centerline-separated to a novel centerline-attached vortex state. The transition produces a pronounced drag reduction through the collapse of the centerline recirculation region as the upstream boundary layer becomes turbulent. These (AA) findings explore experimental evidence linking laminar separation bubble dynamics, shear-layer instability, and wake-state transitions in this canonical bluff-body geometry. >> ( APS Editor, https://journals.aps.org/prfluids/recent/ )

Rhylan A. Huss, Farrukh S. Alvi. Effect of centerline separation on a vortex dominated wake. Phys. Rev. Fluids 11, 074702. Jul 28, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/bn64-wtlz

Also: vortex, transition, bubble, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, transition, 

bubble, laminar separation bubble dynamics, shear-layer instability, wake-state transitions.

# gst: natural invariant measures for chaotic game dynamics; finding order in chaos.

<< ️(AA) study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. >>

<< ️(AA) demonstrate that natural invariant measures — a fundamental concept from ergodic theory — provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, (They) prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, (They) show that this framework extends beyond simple strategy frequencies to general observables, enabling the precise calculation of long-term time averages for broad classes of economic metrics — including payoffs, social cost, and regret — despite chaos. >>

<< ️(They) results reveal that this simple learning algorithm captures the full spectrum of behaviors found in one-dimensional dynamical systems, from unique or multiple absolutely continuous invariant measures to complex periodic attractors as well as coexisting chaotic and stable (periodic) behaviors. By bridging game theory and dynamical systems, (AA) show that statistical predictability is attainable even in the absence of pointwise convergence. >>

<< ️The intersection of game theory, dynamical systems, computer science, and statistics is rich with open questions, particularly when considering learning dynamics in games. >>

Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski, et al. Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos. arXiv: 2607.21805v1 [math.DS]. Jul 23, 2026.

https://arxiv.org/abs/2607.21805

Also: game, chaos, order, disorder,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, game, chaos, Multiplicative Weights Update (MWU) algorithm, statistical structure, statistical predictability, two-strategy congestion game, complex periodic attractors, coexisting chaotic and stable (periodic) behaviors.

# gst: on the scaling of bubble interactions in dynamic turbulence; theoretical, numerical, and experimental study.

<< This (AA) study investigates dilute bubbly decaying homogeneous isotropic turbulence at high Reynolds number using theory, direct numerical simulation, and experiments. The turbulent kinetic energy and dissipation rate follow power-law decay, while the bubble population reorganizes relative to the evolving Hinze scale. When the dissipation decays sufficiently rapidly, the Hinze scale grows faster than the characteristic bubble diameter, driving the population from super-Hinze toward sub-Hinze sizes. The system passes through a mixed regime in which coalescence dominates but breakup remains active, followed by a pure-coalescence regime. Residual breakup in the mixed regime increases the number of small bubbles and enhances coalescence, leading to faster growth of the characteristic bubble size. DNS of dilute bubble-laden turbulence shows decay exponents close to single-phase turbulence and a bubble-size distribution that shifts toward smaller diameter relative to the Hinze scale. >>

<< Before the transition, the distribution exhibits two power-law ranges associated with capillary effects and inertial breakup; after the transition, it approaches a single capillary-dominated scaling. Theory and DNS predict distinct growth laws for bubble diameter in the mixed and pure-coalescence regimes, together with corresponding scalings for number density, interfacial area, and coalescence rate. These predictions are further assessed in a spatially developing pump-driven bubbly duct flow at higher Reynolds number. Despite confinement, inhomogeneity, and wall production, the measured trends agree with the theoretical and DNS-based scalings. >>

<< The (AA) results identify Hinze-scale drift as the organizing mechanism for bubble interactions in both idealized and practical decaying turbulent flows, and provide guidance for population-balance and interfacial-area-transport models. >>

Vivek Kumar, Prasoon Suchandra, Shivam Prajapati, et al. On the scaling of bubble interactions in dynamic turbulence: theoretical, numerical, and experimental study.  arXiv: 2607.25251v1 [physics.flu-dyn]. Jul 28, 2026.

https://arxiv.org/abs/2607.25251

Also: bubble, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, transitions, dilute bubbly decaying, coalescence, mixed- pure-coalescence regimes, dilute bubble-laden turbulence, capillary effects, inertial breakup, decaying turbulent flows.  

# gst: emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving.

<< (AA) report the experimental realization of minimal chimera states in a system of three uncoupled oscillators driven solely by frequency-modulated forcing. Unlike conventional scenarios where chimera states emerge due to interactions among oscillators, here the coexistence of coherent and incoherent dynamics arises entirely from a common external modulation of a system parameter. By tuning the modulation amplitude and frequency, the system exhibits transitions between global synchronization, global incoherence, and minimal chimera states. >>

<< The stability of these regimes is quantified using the maximal Lyapunov exponent, while a synchronization order parameter is employed to characterize the degree of coherence. A systematic exploration of the parameter space reveals well-defined regions associated with distinct dynamical behaviors. To provide analytical understanding, (AA) employ a phase-reduction approach and derive the corresponding phase dynamics, which elucidate the mechanisms underlying phase locking and desynchronization. The robustness of the proposed mechanism is further demonstrated in a time-delayed chaotic system. >>

<< Finally, experimental results obtained from an electronic circuit realization confirm the emergence of minimal chimera states under frequency-modulated driving. These findings establish external modulation as a viable route to chimera formation without coupling, offering a new perspective on collective dynamics in driven nonlinear systems. >>

Debabrata Biswas, Tanmoy Banerjee. Emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving: theory and experiment. arXiv: 2607.25449v1 [nlin.CD]. Jul 28, 2026.

https://arxiv.org/abs/2607.25449

Also: chimera, transition, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, transition, chaos, three uncoupled oscillators, coherent- incoherent dynamics, frequency-modulated forcing, global synchronization, global incoherence, minimal chimera states.

# sound: origin of the sound produced by a detaching bubble.

<< ️When a bubble detaches, it produces a sound. While the frequency of this sound is well understood, there has been no consensus on what drives its amplitude. Although mechanisms based on shape oscillations, initial velocity of the bubble radius, neck collapse or Laplace pressure have been suggested, none of them has been confirmed experimentally. >>

<< (AA) performed experiments involving two methods of producing bubbles, which result in sound levels differing by two orders of magnitude. (They) results show that the sound amplitude is given by the conditions of velocity and radius of the bubble at detachment, in line with the scenario of a free harmonic oscillator proposed by Strasberg in 1956. >>

<< ️(They) refined this scenario by describing how the bubble radius velocity is affected by gas exchange though the closing neck. This “leaking bubble” model predicts that the bubble begins to produce sound prior to detachment, as observed experimentally. By feeding image analysis of the neck into the model, (AA) obtained excellent agreement between the experimental and the calculated pressure signals. >>

Vincent Gourmandie, Jeanne Chauris, Remi Fechter, et al. Origin of the sound produced by a detaching bubble. Phys. Rev. Fluids 11, 073605. Jul 29, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/xshn-mnb8

Also: sound, bubble, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: sound, bubble, bubble dynamics, detachment bubble, leaking bubble, noise, acoustics, hydrodynamic noise, underwater acoustics. 

# gst: breathing chimera states from purely triadic interactions.

<< ️Chimera states, characterized by the coexistence of synchronized and desynchronized dynamics in identical oscillators, are typically studied in systems with pairwise interactions. Whether higher-order interactions alone can generate such symmetry-broken collective states remains unclear. >>

<< ️Here, (AA) show that chimera states can arise solely from triadic interactions. Furthermore, exploiting the intrinsic π-symmetry of the triadic coupling leads to bimodal phase distributions. (They) construct a bimodal Ott--Antonsen reduction that incorporates an asymmetry parameter via symmetry-breaking initial conditions, thereby achieving an exact low-dimensional description of the macroscopic dynamics. This allows to derive an analytic condition for the emergence of chimera states and identify a bifurcation to a breathing chimera regime characterized by persistent oscillations. Furthermore, the reduced dynamics can be expressed as a Riccati-type equation, providing a geometric interpretation of the chimera state as a closed periodic orbit in the complex plane. >> 

<< ️(AA) results establish purely triadic coupling as a minimal mechanism for chimera formation and provide a tractable framework for studying symmetry-broken collective dynamics in systems dominated by many-body interactions. >>

Sudo Yi, Gugyoung Kim, Mi Jin Lee, et al. Breathing chimera states from purely triadic interactions. arXiv: 2607.28017v1 [physics.soc-ph]. Jul 30, 2026.

https://arxiv.org/abs/2607.28017

Also: chimera, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, coupled oscillators, synchronized- desynchronized dynamics, pairwise interactions, symmetry-broken collective states, triadic interactions, bifurcations. 

# life: a calculus of discernment; decision-relevant insight, sequence value, and forgetting as higher-order learning.

<< ️In a world of generative AI, candidate insights are abundant; what is scarce is the capacity to discern which matter, to act on them in the right amount and order, and to forget the rest so the system can adapt. (AA) argue these scarcities are governed by one object and build a framework around it. (They) define an insight strictly as a lever with an identified, measurable effect on an objective, and rank candidates by decision-relevance via the expected value of information rather than novelty. >>

<< ️(They) show action carries an order, not only a size: under realistic belief dynamics, content "touches" are non-commuting operators, so a fixed plan delivered in different orders yields different outcomes, defining a sequence premium. (They) observe that the value of any lever is a shadow price, unifying pharmaceutical marketing, equity selection, and manufacturing as one leverage-discovery problem. >>

<< ️Most speculatively, (AA) propose APOHA, a theory in which forgetting is not the disposal of knowledge but the operator by which value is learned: the value of a retained item is the counterfactual cost of forgetting it, a learning system is the residue of maximal forgetting subject to preserved value, and higher-order value is the structure that survives repeated forgetting (a renormalisation-relevant invariant), with consolidation as its conjugate. >>

<< ️(AA) state the central open problem (a non-trivial attractor with a spectral gap) and test the forgetting theory: operationalising APOHA as an agent on a non-stationary obesity-treatment decision world over 30 seeds, adaptive forgetting cut cumulative decision-regret by 24-32% against never-forget and a fixed half-life, kept a ~6x smaller, cleaner memory, and converged stably; notably, blind forgetting was worse than never forgetting, so the benefit is specific to value-aware forgetting. A multi-disciplinary critique stress-tests the whole. >>

Suyash Mishra. A Calculus of Discernment: Decision-Relevant Insight, Sequence Value, and Forgetting as Higher-Order Learning. arXiv: 2607.18275v1 [cs.GT]. Jun 17, 2026.

https://arxiv.org/abs/2607.18275

Also: brain, pause, silence, Occam, Zen, in https://www.inkgmr.net/kwrds.html 

Keywords: life, brain, pause, silence, Occam, Zen, memory, higher-order learning, oblivion, APOHA attractor, discernment, sequencing, leverage, forgetting theory, survives repeated forgetting, never forgetting, blind forgetting, value-aware removal, value-aware forgetting,