Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Natural sciences — physics, astronomy, planetary and earth science, chemistry, biology and medicine read outside any machine-learning claim.
95 of 1352 THEORY documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-026 v4 | For a system driven without feedback through fixed kernels, the average work dissipated at each switch of the drive equals the memory that fails to predict the next input; that is nonnegative when the drive is Markov and, summed, bounds the protocol’s dissipation from below when each kernel keeps its equilibrium stationary, so there only nonpredictive memory is wasteful; with feedback, in one binary channel no predictive agent is efficient | Still, Sivak, Bell & Crooks (2012), LIT-327: β⟨W_diss⟩ for the switch x_t → x_{t+1} equals I[s_t;x_t] − I[s_t;x_{t+1}] (Eq. 14, an identity). Under a Markov drive this nostalgia is nonnegative, and summed it lower- bounds dissipation when each kernel keeps its equilibrium stationary; both conditions are unstated in the paper and derived here. Fiderer et al. (LIT-041) show that with feedback, in one binary channel, predictive, max-entropy-action and efficient agents are disjoint. The claim is an ensemble average, not a per-operation floor. Whether the bound fails without the two conditions is QUESTION-191. | Active |
| THEORY-030 v3 | For a memory evolving reversibly with its environment, Landauer’s bound prices only steps that lose logical distinguishability, at least k ln 2 of entropy per bit lost, exported to the environment and not necessarily as heat, so copying onto a blank register, measuring or evaluating a bit has no minimum cost; learning a label has a floor only in total entropy production, at least the information learnt, which in Goldt and Seifert’s perceptron can be paid in the weights’ own entropy with vanishing heat | Bennett (2003), LIT-360: the cost attaches to many-to-one maps of the logical state, at least k ln 2 of entropy per bit exported to non-information-bearing degrees of freedom, which “need not” be heat. The record derives it for a memory and environment evolving reversibly from an uncorrelated start: the environment’s entropy rises by at least the logical entropy lost, H(X | f(X)), and an injective step has no floor, attained exactly by a permutation. Goldt & Seifert (LIT-308) bound information learnt by total entropy production, payable with vanishing heat in their toy model. It does not license a k_BT ln 2 heat floor per judgment, per gradient step or per bit learnt. Whether the bound survives without reversible dynamics is QUESTION-215. | Active |
| THEORY-072 v4 | Organisms differ from dissipative structures such as a candle flame not by far-from-equilibrium self-maintenance, nor by circular self-maintenance alone, but by organisational differentiation: several distinct constraints that produce one another at different time scales | The record’s first answer to the demarcation question that NOTE-094 reports. Prigogine (LIT-516) supplies the dissipative structures, and nothing in his account separates them from organisms. Mossio, Saborido & Moreno (2009, LIT-570) grant a candle flame organisational closure. Its one macroscopic pattern keeps up the conditions of the combustion that makes it. They draw the line at organisational differentiation: in an organism several distinct structures make distinct contributions, where a flame makes “a unique contribution”. Montévil & Mossio (2015, LIT-582) narrow closure to mutual dependence among constraints. Each constraint must be both produced by and productive of another, with at least one slow and one fast dependence. On the record’s reading, that builds differentiation into closure, as Mossio and Bich (2014) already say of closure of constraints. No paper analyses a flame under the 2015 definitions. Neither paper says closure defines an organism. | Proposed |
| THEORY-099 | Tryptophan networks in microtubule architectures support collective superradiant excitonic states, and their thermal quantum yield rises with network size and survives static disorder of room-temperature size | Babcock et al. (2024), LIT-645: a radiative Hamiltonian of up to more than 10⁵ tryptophan transition dipoles, on tubulin geometry, predicts superradiant states up to about 4000 times the single-tryptophan rate in a centriole, and a thermal quantum yield that rises with network size and is almost unaffected by static disorder of about 200 cm⁻¹, though that disorder cuts the brightest state’s enhancement from about 3600 to about 20. Steady-state spectroscopy finds a tryptophan quantum yield of 17.6 ± 2.1% in microtubules against 10.6 ± 0.6% in tubulin dimers. No lifetimes were measured. This is not evidence for Orch OR or for any claim about consciousness. | Proposed |
| THEORY-128 | After mass bleaching, coral recovery on a reef crest depends on large herbivorous fishes keeping macroalgae down, because recovery runs through recruitment and survival that macroalgae suppress, not through the persistence of surviving colonies alone | Hughes et al. (2007), LIT-711. On the reef crest at Orpheus Island after the 1998 bleaching, four roofless cages kept large and medium fishes out of 25 m² plots for 30 months. Macroalgae averaged 56% cover inside against 4.1% and 1.7% in controls. Coral cover reached 7.7% inside against 19.2% and 20.2%, with recruitment about two-thirds lower and mortality of established colonies more than double. Control recovery came mainly from recruits of taxa bleaching had removed. Proposed: one site, four replicates, plot scale, and fish exclusion standing in for herbivore exclusion. The algal state vanished within 30 days of reopening. | Proposed |
| THEORY-129 | In Acropora millepora the natural night-light regime is necessary for spawning on the expected night, and displacing it delays or abolishes both release and a spawning-night programme of G-protein-coupled signalling genes | Kaniewska et al. (2015), LIT-710, at Heron Island. In 2011, colonies under natural night light spawned with the reef, while colonies lit after sunset or kept dark for the preceding week did not spawn that night (N = 6, 5, 5). 184 transcripts changed around release in ambient colonies, early in lit ones and not at all in dark ones, and the induced genes were enriched for G-protein-coupled signalling. In 2006, blue, green or white nocturnal light delayed spawning 6–8 h or two nights and red did not. Proposed: one species and site, small groups, and a cascade inferred from co-expression. It shows synchrony by a shared cue, not coupling between colonies. | Proposed |
| THEORY-130 | Coral bleaching is the breakdown of a regulated host–symbiont exchange, reached by more than one route, not a single mechanism of symbiont loss | Two reviews, with no data of their own. Boilard et al. (2020), LIT-712, collect the regulators of the coral–dinoflagellate exchange: the host controls symbiont density, bacteria shift the nitrogen supply, and heat leads either to host rejection of symbionts (apoptosis, autophagy, exocytosis, detachment, necrosis) or to pigment loss under oxidative stress. Goulet et al. (2020), LIT-709, report two octocorals whose similar symbiont losses at +3 °C came by different routes, one by fewer symbionts per host cell and one by loss of host cells. Proposed. The claim that the wider microbiome drives bleaching is declined: its own source says it cannot yet be tested. | Proposed |
| THEORY-135 v2 | Multicellular cooperation depends on suppressing cells that gain fitness at the expense of the organism, across five foundations (proliferation inhibition, controlled cell death, division of labour, resource allocation and maintenance of the extracellular environment); cancer-like cheating on them is found across the independent origins of complex multicellularity, so complex multicellularity can be understood as a system for detecting and suppressing cheaters | Aktipis et al. (2015), LIT-740. Multicellularity requires cell-level fitness to be suppressed; cancer is cheating on five foundations of cellular cooperation. A survey of the independent origins of complex multicellularity finds cancer-like cheating widely, division-of-labour cheating in every form. Proposed: a literature review whose survey is limited by what has been studied, with no model or new data. | Proposed |
| THEORY-160 v2 | In the algebraic Hamiltonian setting, symmetry and conservation correspond because the bracket is antisymmetric, which for a bilinear bracket is each observable conserving itself; the theorem’s content lies in identifying observables with generators | Baez (2020), LIT-819, read in NOTE-630, Theorems 3, 4, 8 and 10, with Alfsen and Shultz’s theorem quoted as Theorem 12 and not checked here (QUESTION-142). With unique solutions to the flow equations, “a generates symmetries of b iff b generates symmetries of a” is {a, b} = 0 ⇔ {b, a} = 0. It assumes reversible one-parameter groups and an observable–generator map; it says nothing about dissipative or stochastic dynamics, nor about the Lagrangian form of Noether’s theorem. | Active |
| THEORY-178 v3 | In an ensemble of sign-consistent Boolean rules on the 87-gene core of E. coli’s regulatory network, a transient knockout or overexpression of one gene can leave the network in a different attractor after release, and every gene that does so reaches a strongly connected component containing a positive circuit | Zhao, Wytock, Reynolds and Motter (2024), LIT-854. In an ensemble of sign-consistent Boolean rules on the 87-gene core of the E. coli regulatory network, 51 genes admit a transient knockout or overexpression that moves the network to a different attractor, and every such gene reaches a strongly connected component with a positive circuit. So one genotype may hold several heritable expression states without epigenetic marks, in the model. The evidence is a model ensemble, read in full in NOTE-655, and the title claims no more. No transient perturbation has been shown to have a lasting effect in cells; that experiment is QUESTION-172. | Active |
| THEORY-179 v2 | In Bhattacharyya et al.’s single-cell swarm assays of E. coli MG1655, the daughters of one mother swarmed alike at the fourth generation sampled and varied again at the seventh; swarm size correlated with a plasmid fepA-promoter reporter of Fur derepression by low iron (Spearman r = 0.71), and an iron chelator or added iron shifted swarming and held the shared state longer; a three-class switching model fitted to two time points matched the lineages only with a delay of three to four generations before switching, which the authors read as ruling out a bistable switch | Bhattacharyya et al. (2023), LIT-853. Single-cell swarm assays show sibling homogeneity in swarming at four generations and its loss by seven, a correlation (Spearman r = 0.71) between a Fur-repressed reporter and swarming, and longer persistence when iron is clamped. The iron link is read through a promoter reporter and is correlational, the inheritance rests on few founders and three time points, and the paper’s “memory”, “conditioning” and “decision-making” are functional labels, not evidence of learning. | Active |
| THEORY-191 v2 | In four natural odour sources (strawberry, tomato, blueberry and mouse-urine volatiles), the rank order of correlations between compound concentrations has the Betti-curve signature of points near the boundary of a three-dimensional hyperbolic ball, not of any uniform Euclidean cube tried, and human odour-descriptor profiles for 127 odorants have that of a full three-dimensional hyperbolic ball | Zhou, Smith & Sharpee (2018), LIT-872: for strawberry, tomato, blueberry and mouse-urine volatiles, and for Dravnieks’ perceptual ratings of 127 odorants, clique-topology Betti curves match a 3D hyperbolic model and reject uniform Euclidean cubes of every dimension tried. It does not show a tree in the data, and because the fitted odour model is a thin shell, it does not separate a hyperbolic metric from a sphere in flat space. | Active |
| THEORY-194 v5 | On Monte Carlo samples of the 2D Ising model and of the 2D dimer model with added noise spins, a block coarse-graining trained to maximize mutual information with the system beyond a buffer recovered the variables renormalization already uses (Kadanoff block spins; the dimers’ low-momentum electric fields, with no weight on the noise), and iterated on 128 × 128 Ising samples gave the flow away from the critical point, locating it to about 1% and giving ν ≈ 1.0 ± 0.15, while a restricted Boltzmann machine trained by contrastive divergence on the noisy dimer data coupled to the noise and to columnar patterns instead | Koch-Janusz and Ringel (2017), LIT-873: shown numerically on two 2D lattice models whose relevant variables were known (Ising block spins, dimer electric fields), with an iterated Ising flow giving T_c to about 1% and ν ≈ 1.0 ± 0.15, and analytically only for 1D and quasi-1D chains. The general equivalence of the objective with a short-ranged effective Hamiltonian is argued, not proved, and no system with unknown relevant variables was tried. | Active |
| THEORY-197 v4 | Mehta and Schwab’s correspondence between Kadanoff’s variational renormalization group and restricted Boltzmann machines is an identity of parametrizations, under which an exact RG step is a perfect fit of the data distribution; away from that point it does not make training by distribution fitting a renormalization | Mehta and Schwab (2014), LIT-882, Eqs. 18–22: setting the RG kernel T = −E + H makes the RG coarse Hamiltonian equal the RBM’s hidden-marginal Hamiltonian for every parameter value, and Kadanoff’s exactness condition equal to zero KL divergence. Short of exactness the paper itself says the two use different variational schemes, and Koch-Janusz and Ringel (LIT-873) give a case where distribution fitting keeps the wrong variables. The free-energy part of the argument was derived independently here; Lin, Tegmark and Rolnick’s v2 appendix makes it in substance (LIT-887). | Active |
| THEORY-198 v2 | For a finite-range lattice Hamiltonian, a block coarse-graining that keeps all the mutual information the block shares with the system beyond a buffer makes the coarse measure factorize across the block, in 1D and, in D dimensions, when capture by a hyperplane of blocks amounts to capture by each block; barring exact cancellation of existing couplings, the renormalized Hamiltonian then gains no range, and in 1D product disorder gains no correlations across the block. The coarse-grainings actually optimized fall short of that condition, and for them the link is computed only for two-spin blocks of 1D Ising chains | Lenggenhager, Gökmen, Ringel, Huber and Koch-Janusz (2018), LIT-881: proved in 1D, and in D dimensions under an extra per-block assumption and barring fine-tuned cancellations. The full-capture condition is not met in the paper’s own worked case (decimation of two-spin Ising blocks keeps about half the information), and the decay of longer-range, many-spin and disorder-correlation terms as more information is kept is shown perturbatively for two-spin blocks of 1D chains only, and is monotonic only locally. | Active |
| THEORY-202 v3 | In variational renormalization over general Boltzmann machines, neither a matched partition function nor Kadanoff’s exact trace condition makes a coarse-graining a renormalization: the first holds for joint Hamiltonians whose marginal is not the data, the second for hidden variables that do not interact with the system, so the variables a renormalization keeps must be fixed by a further stated condition | Lin and Tegmark (2016), LIT-887, arXiv v1–v2 appendix, a part dropped from the journal text: a family of joint Hamiltonians with Z_tot = Z and the wrong marginal, and the remark that any non-interacting pair meets the trace condition. Under Mehta and Schwab’s identification (LIT-882) the trace condition is a perfect fit of the data, so even an exact variational RG step leaves the coarse variables’ meaning free. The restricted Boltzmann machine proper needs visible–visible terms for the second construction; that narrows the example, not the claim. Promoted on 2026-10-20 with both constructions re-derived. Whether the trace condition suffices inside Kadanoff’s kernel families is QUESTION-205. | Active |
| THEORY-205 v2 | For a short-range lattice model on a cylinder with a symmetric transfer matrix whose leading excited eigenvalue is non-degenerate, with block and environment as slabs L_B transfer steps apart, the uninformative information-bottleneck encoder first loses stability at β = (λ0/λ1)^(2L_B), in the direction of the boundary weak value of the leading excited eigenvector, which by the cited conformal finite-size relation is the lowest-dimension primary at large circumference; the uninformative encoder can stop being optimal at a smaller β, and nothing is shown for blocks inside a buffer shell or for the fixed-alphabet RSMI optimum | Gordon, Banerjee, Koch-Janusz and Ringel (2020), LIT-885, Eqs. 3–5 and B2–C11, with one numerical check on a three-site critical Ising cylinder, reproduced exactly in NOTE-690. The theorem holds for slabs of a cylinder, at the point where the uninformative encoder first loses stability. The global first transition can come earlier, and when the two coincide is QUESTION-185. The paper’s “equivalence” of IB and RG relevance, and LIT-878’s use of it for RSMI filters on planar blocks, go beyond it. | Active |
| THEORY-275 v5 | In two optically trapped beads with a symmetric hydrodynamic coupling, one trap moved by a recorded noise drive, time-delayed mutual information and transfer entropy follow the drive’s path rather than the coupling’s symmetry: the flow between the beads reads two-way under moderate drive, in experiment and numerics, and one-way under strong drive, in numerics of the fitted model only | Das, Manikandan and Banerjee (2025), LIT-947, read in NOTE-788. Two colloids are coupled by the fluid through a symmetric tensor, and recorded noise moves one trap. Time-delayed mutual information and transfer entropy give drive → driven → other, with backflow at moderate drive. In numerics only, flow is one-way at strong drive. With no drive the coupled particles are independent at steady state. The paper does not test an unrecorded drive shared by both units, and it does not claim that the measures reveal coupling architecture. Whether the same holds in other reciprocally coupled systems is QUESTION-186. | Active |
| THEORY-304 v3 | In plane Couette and Poiseuille flow, measured in the energy norm, the linearized operator is so far from normal that perturbations can grow transiently by O(R) and resonate by O(R²), and operator perturbations of size O(R⁻²) make it eigenvalue-unstable, at Reynolds numbers where eigenvalue analysis predicts stability | Trefethen, Trefethen, Reddy & Driscoll (1993), LIT-932, read in NOTE-839: computed scalings for the linearized shear flows, mostly credited to earlier work and unified through pseudospectra. That transition to turbulence happens by this linear growth plus nonlinear mixing is the paper’s conjecture from a 2 × 2 model, and is not part of this account. | Active |
| THEORY-323 v2 | Under spatially uncorrelated white noise, a stable non-normal linear system holds more variance than the sum of its pole contributions, and equality holds only when the operator is normal, so its spectrum understates the standing variance | Farrell & Ioannou (1996), LIT-931, read in NOTE-831, with Trefethen et al. (1993), LIT-932, read in NOTE-839. Linear algebra, worked in examples: growth over time t is the top singular value of the propagator, which the eigenvalues bound from below, not above. It holds in a chosen norm, and a norm can always be found that makes the operator normal. It says nothing about whether the growth survives nonlinearity. | Proposed |
| THEORY-325 v2 | Random variation of a linear operator destabilizes it generically, needing less variation the more non-normal and less damped the mean operator | Farrell & Ioannou (1996), Part II, LIT-929, read in NOTE-842. Necessity is a one-line bound and the destabilization is shown in explicit examples. Genericity under noise is cited to stochastic stability theory, and the role of non-normality and damping is shown numerically. In the deterministic examples, variation much faster than the transient growth destabilizes nothing. Since 2026-10-19 the deterministic half is THEORY-724, and this THEORY holds the stochastic half. | Proposed |
| THEORY-408 | In a one-locus model with non-overlapping generations, random mating and weak selection, gene frequencies change as if each individual maximized its inclusive fitness, so a trait that costs its bearer spreads only if its effect on relatives exceeds 1/r times the cost; the increase of mean inclusive fitness is proved only for traits whose total effect on others is not negative | Hamilton (1964), Part I, LIT-497, read in full in NOTE-401. Each effect an individual causes falls partly on genes identical by descent with its own (weight r) and partly on others, which only dilute. So selection tracks inclusive fitness. The threshold is written −k > 1/r (§5), not rb > c: “more than two brothers, or four half-brothers, or eight first cousins”. The maximization theorem needs non-negative total effects on others; for harming traits the change only points uphill. r is exact only for loci not under selection, and Hamilton could not bound the error (§4). | Active |
| THEORY-431 | For classical systems with Markovian, microscopically reversible dynamics, the entropy production of a trajectory obeys an exact finite-time symmetry against the time-reversed process, P_F(+ω)/P_R(−ω) = e^ω, wherever ω is odd under reversal; Jarzynski’s work equality and the mean second law follow as corollaries, and the symmetry constrains fluctuations, not which steady state a system selects | Crooks (1999), LIT-522, read in NOTE-413, with Jarzynski (1997), LIT-517 (NOTE-417), and Seifert’s review (2012), LIT-523 (NOTE-420). The work equality ⟨e^{−βW}⟩ = e^{−βΔF} holds at any switching rate, and Crooks derives it from a trajectory-level entropy-production theorem; Seifert derives every known theorem of the kind from one master theorem. These are exact given their premises. They are not proofs of the second law, since the dynamics build irreversibility in, and they say nothing about extremum principles for steady states. Their practical reach is work fluctuations of order k_BT. | Active |
| THEORY-463 | In classical statistical mechanics a strictly irreversible approach to equilibrium cannot come from the isolated Hamiltonian dynamics alone: the fine-grained Gibbs entropy is constant and bounded systems recur, so each account surveyed either weakens the target to typical or long-run behaviour or adds something from outside the dynamics | Frigg & Werndl (2023), LIT-114, the SEP entry, read in NOTE-103. The impossibility half rests on standard consequences of Liouville’s theorem, time-reversal invariance and Poincaré recurrence. The classification half is the survey’s: it is stated account by account, not argued as a general result. The entry is classical only, excludes the direction of time, and reports rather than settles the disputes about each repair. | Active |
| THEORY-466 | Among contestants of equal prowess with dangerous weapons, individual selection can favour conventional fighting backed by retaliation: an escalating Hawk is not evolutionarily stable, Retaliator is at most neutrally stable because Mouse ties it, and in a contest settled by persistence alone no fixed persistence is stable while an exponential mixture is | Maynard Smith & Price (1973), LIT-505, read in full in NOTE-404. A simulation of five strategies, 2,000 contests per pairing, shows that “limited war” can be favoured by individual selection, without benefit to the species. The paper calls Retaliator an ESS “though Mouse does equally well”, which fails its own second condition. There is no Hawk–Dove game, no “dove”, no difference in prowess and no ownership, so it is not the source of display, deference or owner–intruder conventions. | Active |
| THEORY-473 | Scaled down to one organism, Hutchinson’s niche, defined as the conditions that give that individual an expected lifetime reproductive success of at least one, is observed only as a point; the rest of it is counterfactual, reached by translocation in only a few dimensions and otherwise inferred from other individuals, so in practice it is the niche of a phenotype class, and its authors call it mostly metaphorical | Takola & Schielzeth (2022), LIT-127, read in full in NOTE-170. The working definition (p. 5) gives the individualized niche an absolute-fitness boundary, expected LRS ≥ 1, and splits it into realized, potential, time-slice, prospective and trajectory-based niches. That the realized niche is a point and the potential niche unobservable follows from the definitions. The paper concedes there is “no empirical solution” at the individual level (p. 15), and its fix, marginalizing fitness functions across individuals, is schematic. It is a framework for structuring research, by its authors’ own account, not a measurement. | Active |
| THEORY-499 v2 | The breakup of the Eulalia parent body beside the Jupiter 3:1 resonance, 785–965 Myr ago, can plausibly have supplied the cluster of large lunar craters dated near 800 Ma, but shown only for the most favourable of five model solutions, the one carried through, with an average largest lunar impactor too small for Copernicus, and with the cluster’s absolute date inherited from Copernicus alone | Bottke, Vokrouhlický, Dykhuis & Zellner (2026), LIT-009, read in full in NOTE-002. A chain of multiplied factors (family fit, J3:1 influx, WISE incompleteness, collisional loss, impact probabilities) gives, for Solution 5 only, about 7,000 D ≥ 2 km fragments into the resonance and a largest expected lunar impactor of “>3 km”. A Monte Carlo puts the seven ~800 Ma craters “generally” within 1σ. It is an existence argument, not an estimate: one factor is tuned by eye, only the most favourable solution is propagated, and the seven craters are dated by N(1) against one sample-dated crater. The Earth, Mars and Venus links are the authors’ own speculation. Active as a reading of the model (ADR-065); whether the shower happened is THEORY-1195, Proposed. | Active |
| THEORY-508 | The Belousov–Zhabotinsky oscillation is a relaxation cycle in which autocatalytic production of HBrO₂ oxidizes the catalyst until bromide, released as the oxidized catalyst is reduced by bromomalonic acid, switches the autocatalysis off; a closed batch oscillates only as a transient of up to several thousand cycles on its way to equilibrium, and only a continuous-flow reactor sustains it indefinitely | Zhabotinsky (2007), LIT-531, the Scholarpedia review by one of the reaction’s eponyms, read in full in NOTE-414. The mechanism is supported by the primary kinetics and by phase-resetting with injected Br⁻, Ag⁺ and Ce⁴⁺. The closed/open distinction matters for any use of BZ as a dissipative structure: a closed batch is a long transient, and only a fed reactor holds it away from equilibrium. The Oregonator models oscillation and excitability qualitatively, not quantitatively. The “several thousand cycles” figure is uncited, and the primary papers were not read. | Active |
| THEORY-517 | Life raises the Earth’s entropy production, chiefly by increasing the absorption of sunlight, and if the planet is held at maximum entropy production, the negative feedbacks of that state would give the homeostasis the Gaia hypothesis postulates | Kleidon (2009), LIT-519, read in NOTE-423. The Earth’s entropy budget is dominated by the absorption of sunlight, and model studies, mostly the author’s, find that biotic activity raises it. The step to Gaia is explicitly conditional on MEP, which the same review says is not established, and its feedback argument is a schematic figure. It treats life as the most effective of the Earth’s dissipative processes, and gives no criterion separating a living dissipator from a convection cell. | Proposed |
| THEORY-543 | Diffusion can destabilise a homogeneous steady state of reacting chemicals that is stable without it: a disturbance of one finite wave-length grows while uniform and very short ones decay, so a stationary pattern appears whose spacing is set by the reaction and diffusion constants and only its phase by the disturbance; with two substances this needs them to diffuse at different rates, and the pattern lasts only while free energy is supplied | Turing (1952), LIT-535, read in full in NOTE-427, with Cross & Hohenberg (1993), LIT-527, skimmed in NOTE-418. The linear analysis on a ring gives exact conditions (9.4a, b) for stationary waves of finite wave-length; that equal diffusibilities cannot satisfy them is NOTE-427’s substitution, not stated in the paper. Turing calls the linearity assumption “a serious one” and the biological examples “very limited”. Stationary chemical Turing patterns were first made in 1989–1991, and real morphogens implementing the mechanism had not been identified by 1993. | Active |
| THEORY-562 | In REST2 replica-exchange simulations of intrinsically disordered proteins, high swap acceptance and short round trips show that replicas mix along the temperature ladder, not that conformations are sampled, because the upper rungs collapse the chain; sampling shows only when independent demultiplexed replicas agree in their structural distributions | Koneru, Reid & Robustelli (2025), LIT-076, read in full in NOTE-076. A how-to chapter whose one load-bearing methodological point is that high swap acceptance “is not, in isolation, sufficient evidence of robust conformational sampling or convergence” (p. 18). The reason the reading draws out is that REST2’s upper rungs are unphysical Hamiltonians on which disordered chains over-collapse, so replicas can swap freely without the chain rearranging. The chapter argues this and shows a passing example; it shows no failed run, and its convergence criteria have no quantitative threshold. | Proposed |
| THEORY-567 | In the donation game, where a cooperator pays c for another to get b, defectors win in a well-mixed population, and each of five mechanisms makes cooperators evolutionarily stable above a benefit-to-cost threshold: kin selection r > c/b, direct reciprocity w > c/b, indirect reciprocity q > c/b, network reciprocity b/c > k and group selection b/c > 1 + n/m; the rules cover altruism only, not mutualism, coordination or conflict | Nowak (2006), LIT-501, read in NOTE-409, main text only. A four-page review that casts each known mechanism as a 2×2 game so that one set of criteria applies to all. The five ESS conditions are confirmed by the main text; the derivations are in the supporting material, which was not read, and in cited papers. Several rules hold only under weak selection, regular graphs or rare group splitting. Every mechanism is modelled with the donation game, so mutualism, coordination and conflict are outside it. | Active |
| THEORY-634 | In a ring of M chemotactic catalyst species, each making the next one’s substrate, the non-reciprocal nearest-neighbour coupling makes the linear stability matrix circulant: the uniform state goes unstable for any M exactly when the species attract themselves, and the parity of M then decides the leading mode, a real alternating mode for even M that sorts species by parity into two static clusters, and a complex pair for odd M that can give persistent oscillation | Ouazan-Reboul, Agudo-Canalejo & Golestanian (2023), LIT-036, read in NOTE-079. The spectrum is exact for equal parameters (Eq. 5): instability iff μ(p) − μ(s) < 0, real leading eigenvalue for M = 2K, complex pair for M = 2K + 1. Brownian dynamics at M = 5 and 6 bear out the linear predictions; the odd-cycle oscillation is one trajectory at one parameter set. Direct metabolic partners repel; same-parity second neighbours co-aggregate. The origin-of-life reading is untested, and the authors concede in the review file that real catalysts’ mobilities are unknown. | Active |
| THEORY-655 v3 | Social behaviour evolves as if each individual valued a neighbour’s fitness against its own by their coefficient of relationship, and its discriminations evolve to make that coefficient determinate; so kin are favoured and strangers met with hostility, relatives fight less, and haplodiploid sisters, related by 3/4, are predisposed to worker altruism | Hamilton (1964), Part II, LIT-506, read in full in NOTE-410, on Part I’s model (LIT-497). Two general principles, offered as an “unrigorous” generalization, are applied to alarm calls, kin recognition in gulls and terns, clones and colonies, Hymenoptera, and fights. The evidence is anecdotal. The author calls his positive indications for distant relatives “rather few and feeble”, reports Australian halictines and multiple mating as running against the hymenopteran hypothesis, and explains anomalies case by case. | Proposed |
| THEORY-660 | The local branching geometry of physical tree networks, neurons, blood vessels, trees, corals and plants, is set by minimising the surface area of tubes that must keep a minimum circumference, not by minimising length: this predicts trifurcations once links are thick relative to their separation (χ = w/r above about 0.83) and orthogonal sprouts once one branch is much thinner than the other two (ρ = w′/w below about 0.6), both departures from Steiner trees that the data show qualitatively | Meng, Piazza, Both, Barzel & Barabási (2026), LIT-069, read in full with the SI in NOTE-075. Only two symmetric motifs are solved, each by a local, penalised optimiser started from the Steiner layout; the “exact” mapping to string worldsheets holds for a problem the paper does not solve. The random-terminal prediction is a sigmoid fitted to one tetrahedron, trifurcations are partly made by a merging rule, the one robustness check moves the key statistic 4.3-fold, and the sprouting breakpoints are chosen per dataset with no null. Real motifs are about 25% longer than Steiner, which the model leaves unexplained. | Proposed |
| THEORY-663 | Altruism between non-relatives can be selected when each act costs the giver less than it benefits the recipient, the same partners meet often and symmetrically, and help is withheld from those who do not return it; in humans, moralistic aggression, gratitude, sympathy and guilt are adaptations that regulate such exchange, and selection then favours sham versions of each and the ability to detect them | Trivers (1971), LIT-510, read in full in NOTE-402. A verbal model, with a Prisoner’s Dilemma sketch Hamilton communicated, followed by a functional account of the human emotions that would regulate reciprocity. The model is plausible and was later formalized. The psychology is fitted to 1960s social-psychology findings, mostly on American students, and the heritability of the dispositions is assumed. Trivers knows “of no psychological studies on the detection of sham moralistic aggression and sham guilt” (p. 51). His “unfairness” is inequity in exchange, not the division of a disputed resource. | Proposed |
| THEORY-672 | In the iterated Prisoner’s Dilemma with a probability w of meeting again, no strategy does better against an established TIT FOR TAT than TIT FOR TAT does against itself if and only if w ≥ (T−R)/(T−P) and w ≥ (T−R)/(R−S); always defecting is stable for every w, a cluster of reciprocators can invade it, and a nice stable strategy resists clusters, but the stability is only neutral, since always cooperating ties | Axelrod & Hamilton (1981), LIT-498, read in full in NOTE-411. Against TIT FOR TAT the best reply is always-defect or alternation, which gives the condition on w. The cluster result and the “ratchet” are explicit payoff comparisons. “Evolutionarily stable” here means no mutant does better, which is weaker than Maynard Smith and Price’s definition: always cooperate does exactly as well. The model is deterministic and error-free. Tournament robustness is a separate, empirical claim about the strategies people submitted. | Active |
| THEORY-679 | For dynamics obeying detailed balance in a heat bath, the heat released in a transition between observer-defined macrostates is bounded below by the log-odds against its reversal less the internal entropy change; where a replicator’s likeliest way back is a copy decaying within one generation, the bound grows with the copy’s durability and the speed of copying, not with the information copied | England (2012; J. Chem. Phys. 2013), LIT-515, read in NOTE-419. The general bound, β⟨ΔQ⟩ + ln π(II→I) + ΔS_int ≥ 0, is a coarse-grained second law and was re-derived. Applied to replication it gives a heat cost of about 2n ln(n τ_decay/τ_div) per copy, which falls away as division slows. The numbers for E. coli (within a factor of three of the bound) and RNA rest on an upper bound on the reverse probability that is argued from biology, not proved, and on an internal-entropy term set “arbitrarily”. It prices finite-time irreversibility, not information, and draws no line between living and non-living replicators. | Active |
| THEORY-682 | The time-average of a single threshold (Hill) response to a periodic signal is independent of the signal’s period for a fixed waveform, so a frequency cannot be read by one sigmoidal stage; two cascaded stages can read it, because the first changes the waveform with period; and a delayed kinesin–dynein signalling loop whose period grows with axon length, read out this way and coupled to protrusion and contraction, can hold an axon at a stable length | Folz, Wettmann, Morigi & Kruse (2018; PRE 2019), LIT-034, read in full in NOTE-067. The period independence is proved, for signals that differ by a time rescaling only; the two-stage readout is shown numerically and in the Heaviside limit; the loop’s minimum length and ω ≈ √3 v/L for long axons come from linear stability analysis. The length control is a lumped delay-differential model with one parameter set and the motor velocity v never stated, so its absolute lengths, about 125 µm, cannot be reproduced. A proof of mechanism, not a model fitted to axons. | Proposed |
| THEORY-742 v2 | For a Boltzmann distribution linear in its couplings, observed through any coarse-graining map, the Fisher information the coarse data lose about the bare couplings is the expected conditional covariance of the energy operators given the coarse state; when the renormalized Hamiltonian stays in the family, the parameter map is linear and the additive constant of the step is analytic, that loss is the constant’s Hessian, so the singular part of the metric passes unchanged to the coarse data. In the hopping model of diffusion at its Gaussian fixed point, keeping every n-th position of a trajectory of fixed duration multiplies the metric by n^(1−μ) in the μ-th Hermite coordinate: the drift’s information is kept exactly, the variance’s falls as 1/n, and higher shape parameters’ faster | Raju, Machta and Sethna (2018), LIT-1254, read in NOTE-972. The loss identity holds for any coarse-graining of an exponential family; that the loss is analytic, and so spares the singular part of the metric, needs an exact renormalization step with linear beta functions and an analytic constant. It does not say that relevant directions keep their information in general: on the paper’s own scalings only directions with RG eigenvalue above d/2 do, and away from the Gaussian fixed point even the drift loses information. | Active |
| THEORY-747 | In Fourier–Galerkin large-eddy simulation, a first-order finite-memory Mori–Zwanzig closure tracks filtered-DNS energy decay and dissipation on the viscous Burgers equation and on the incompressible Taylor–Green vortex, isotropic turbulence and channel flow about as well as dynamic Smagorinsky where that model is at home and better than Smagorinsky and the t-model on the transitional Taylor–Green vortex; the memory length that fits it is set by the cutoff, not by the flow alone, scaling in Burgers roughly as 0.2 over the spectral radius of the resolved variables’ Jacobian | Parish and Duraisamy (2017), LIT-1259, read in NOTE-973. The closure is THEORY-760’s finite Markovian augmentation. Here is how it did, as far as the paper’s plots show: close to filtered DNS in integral quantities, comparable to dynamic Smagorinsky in equilibrium turbulence, clearly better on a transitional flow, and with the subgrid transfer peaked at the cutoff where DNS puts it but about 40% too deep. The paper calls the predictions “excellent” with no numbers. Its fitted memory length shortens as the resolved dynamics speed up, so the memory belongs to the cutoff as much as to the flow. | Proposed |
| THEORY-748 | Block entropies, and so every lag-τ entropy rate of a stationary signal, are unchanged by the reflection x → −x and by time reversal, so they cannot detect the odd-order asymmetry the 4/5 law ties to energy flux; Granero-Belinchón, Roux and Garnier’s entropy rate conditioned on the sign of the increment breaks the reflection invariance, but h⁺ ≠ h⁻ shows only that the two-point distribution lacks central symmetry, which a skewed one-point distribution produces with exactly symmetric increments, so the test does not by itself detect skewed increments or an energy cascade | Granero-Belinchón, Roux and Garnier (2016), LIT-1243, read in NOTE-970, claim that conditioning the entropy rate on the sign of the increment lets one “prove the existence of the energy cascade” using information theory. The record finds two limits. The unconditioned entropy rate is exactly blind to reflection and time reversal. The conditioned one detects any central asymmetry of the two-point law, including one with no increment skewness at all. Independent pairs with the paper’s one-point skewness of 0.175 give h⁺ − h⁻ ≈ 0.066 nats with symmetric increments. Nothing in the paper ties an information quantity to the energy balance. | Active |
| THEORY-749 v3 | A weak solution of the incompressible Euler equations on the periodic box that lies in L³(0,T; B^α_{3,∞}) ∩ C([0,T]; L²) with α > 1/3 conserves kinetic energy, because the energy flux into scales below a mollification scale ε is bounded by Cε^(3α−1)∫‖u‖³ and so vanishes as ε → 0; this does not show that rougher solutions dissipate | Constantin, E and Titi (1994), LIT-1248, read in NOTE-982. The positive half of Onsager’s conjecture, in the Besov form: if velocity increments obey ‖u(·+y) − u‖_{L³} ≤ C|y|^α with α > 1/3, integrated in time, the coarse-grained energy flux across scale ε is O(ε^(3α−1)) and no energy can be lost to vanishing scales. It is a statement about regular fields only. It does not show that a flux survives the limit for rougher ones: that energy can fail to be conserved below 1/3 is Isett’s later theorem (THEORY-763), that it can strictly decrease is Buckmaster, De Lellis, Székelyhidi and Vicol’s (THEORY-776), both Proposed, and some rough solutions conserve energy anyway. | Active |
| THEORY-750 | For a stationary Gaussian signal the lag-τ entropy rate with one-point embedding is h_τ = H(X) + ½ log(1 − c(τ)²), so where the normalized second-order structure function 1 − c(τ) is small and scales as τ^ζ₂, h_τ = (ζ₂/2) log τ + constant; the “scaling of information” that Granero-Belinchón, Roux and Garnier measure in near-Gaussian wind-tunnel turbulence, slope 1/3 in the inertial range and 1 in the dissipative range, is the scaling of the second-order structure function written in nats | Granero-Belinchón, Roux and Garnier (2016), LIT-1243, read in full in NOTE-970. A Gaussian identity and its small-lag asymptotics: the conditional entropy of x(t) given x(t − τ) is a monotone function of the autocorrelation, so its scaling exponent is half the structure-function exponent. In the Modane data the estimated entropy rate matches the Gaussian formula, so the measured “information spectrum” is S₂ again. It is not a distribution of a conserved quantity over scales, and it carries nothing about the direction or size of energy transfer. It answers QUESTION-219 only in the narrow sense of supporting A3’s caution. | Active |
| THEORY-752 | In optimal prediction of a Hamiltonian system with separable energy and canonical initial law, projected by conditional expectation, the t-model’s leading-order memory term tPLQLx makes the effective Hamiltonian of the resolved variables non-increasing, so the eliminated variables’ memory enters as a damping that grows linearly in time | Chorin, Hald and Kupferman (2002), LIT-1253, read in NOTE-975: Theorem 8.1. Truncating the Mori–Zwanzig memory integral at its lag-zero value gives dΦ/dt = R̄(Φ) + tS(Φ), and under the stated conditions this dissipates the free energy of the resolved variables. It says nothing about how well the t-model predicts, gives no error bound, and holds only for the conditional-expectation projection; the true conditional mean’s effective energy need not decrease. | Active |
| THEORY-754 v2 | If a velocity field’s third-order increments obey ‖δu(r)‖₃ ≤ C u_rms (r/L)^σ at every separation r, with 0 < σ < 1, then for a smooth, rapidly decaying filter the space-averaged energy flux across scale ℓ takes at most a fraction of order (ℓ/Δ)^(1−σ) from strain at scales above Δ and of order (δ/ℓ)^(2σ) from stress at scales below δ, measured against u_rms³/L·(ℓ/L)^(3σ−1); so transfer between scales is local in scale, with a power-law decay and no gap | Eyink and Aluie (2009), LIT-1239, read in NOTE-969, stating bounds proved in Eyink (2005), LIT-1252. A conditional inequality: if velocity increments scale no faster than r^σ in the L³ mean, the contributions of far larger and far smaller scales to the mean flux across ℓ are bounded by powers of the scale ratio. It needs 0 < σ < 1: σ < 1 for the large scales, σ > 0 for the small. That the inertial range satisfies the hypothesis, that the mean flux there is non-zero, and the sharper 4/3 exponent are assumptions or heuristics, not part of it. It is about one field decomposed by scale, and says nothing about units. | Active |
| THEORY-760 | The finite-memory Mori–Zwanzig closure that Parish and Duraisamy take from Stinis, truncated at order m with one trapezoidal sub-interval and constant memory lengths, is a finite-dimensional Markovian augmentation: m + 1 auxiliary variables per resolved mode, each relaxing at rate 2/τ; at first order it replaces the memory integral by the kernel 2e^{−2s/τ₀} acting on the first-order term, which tends to τ₀ times that term, the t-model with t replaced by τ₀, when τ₀ is short against the resolved dynamics; its kernel is twice the true one at zero lag for every τ₀, so it is not exact even where the true memory is a single exponential, and nothing in the construction bounds its error | Parish and Duraisamy (2017), LIT-1259, read in NOTE-973. The finite-memory closure turns the Mori–Zwanzig memory integral into auxiliary ordinary differential equations, so the reduced model is the resolved variables plus finitely many memory coordinates: the shape of augmentation QUESTION-222 asks about. But the truncation drops the next auxiliary term without a bound, the memory length is fitted, and the kernel’s form is fixed by the quadrature, not by the eliminated dynamics. It is an augmentation with uncontrolled error, not the controlled one the question asks for. | Active |
| THEORY-763 v2 | For every α < 1/3 there is a nonzero weak solution of the 3D incompressible Euler equations on the periodic box, with velocity Hölder-continuous of exponent α in space and time, that vanishes outside a finite time interval; its energy is not conserved, so the energy flux across a mollification scale ε does not vanish as ε → 0, and it runs in both directions, out of the vanishing scales while the energy rises and into them while it falls | Isett (2018), LIT-1255, skimmed in NOTE-974: the negative half of Onsager’s conjecture. With THEORY-749 (Constantin, E and Titi, the positive half) it makes 1/3 the threshold. For the record, its point is that below 1/3 the energy flux into vanishing scales can survive the limit, which is the half of A3’s point that THEORY-749 could not give. It does not say that this flux is a dissipative cascade. Isett’s solutions start from rest, gain energy and lose it again, so the surviving flux takes both signs. Nor does it say that such solutions are limits of Navier–Stokes or describe turbulence. | Proposed |
| THEORY-772 v2 | For every β < 1/3 there is a weak solution of the 3D incompressible Euler equations on the periodic box, in C⁰_t(B^β_{3,∞} ∩ L^{1/(1−3β)}), whose Duchon–Robert dissipation is the smooth nonnegative density E(t, x) = −e(t)e′(t)ρ₀(x₁, x₂)² fixed at the construction’s first step; for such a solution the local coarse-grained energy flux into scales below ℓ converges, as ℓ → 0 and as a distribution in space and time, to E, so the transfer into vanishing scales is one-way at every place and time in the limit, nonzero inside a periodic array of pipes and zero outside them; where and how fast energy is dissipated is chosen by the construction, not forced by the equations, and nothing is shown about the sign at any positive scale | Giri, Kwon and Novack (2023; Annals 2026), LIT-1289, skimmed in NOTE-1022: the L³-based strong Onsager theorem. Below 1/3, in Constantin, E and Titi’s own scale of spaces (THEORY-749), there are weak Euler solutions satisfying the local energy inequality. In the proof the Duchon–Robert measure is a prescribed smooth function, positive in a periodic array of pipes and zero elsewhere. So the coarse-grained flux into vanishing scales is one-signed locally in space and time, in the limit, and not only for the whole box as in THEORY-776. Its location and rate are inputs of the construction; it is a smooth density on a few pipes, not concentrated on a thin set; nothing is said about the sign at a positive scale or about vanishing viscosity. | Proposed |
| THEORY-774 | In a one-dimensional lattice hopping model with 2N+1 free hopping probabilities, all particles starting at the origin and the density after t steps observed with fixed Gaussian error, the Fisher metric is exactly t² times the distribution of the difference of two independent (t−1)-step walks, evaluated at the lag between the two hops, so it does not depend on the drift; when the walk is aperiodic with nonzero variance, its k-th largest eigenvalue is of order t^(3/2−k) for k = 0, …, 2N, so successive eigenvalues separate by a factor of order t | Machta, Chachra, Transtrum and Sethna (2013), LIT-1299, supplement §III, read in NOTE-1018. The eigenvalues grow for particle creation (t^(3/2)) and drift (t^(1/2)) and fall from the diffusion constant on (t^(−1/2), t^(−3/2), …). The data are not a coarse-graining of one fixed data set, so nothing forbids growth. The metric is a least-squares metric with an arbitrary unit of error, and its eigenvalues depend on the coordinates θ_μ. The ratio between successive eigenvalues matches the 1/n per Hermite order of THEORY-742’s diffusion result, though the two set-ups differ. | Active |
| THEORY-776 v3 | For every β < 1/3 and every smooth, strictly positive and strictly decreasing energy profile e(t) on [0, T], there is a weak solution of the 3D incompressible Euler equations on the periodic box, Hölder-continuous of exponent β in space and time, with ∫|v(t)|² = e(t) at every time; for such a solution the energy flux across a mollification scale ε, integrated over any time interval, tends as ε → 0 to ½ times the drop in e, which is strictly negative, so energy leaves the resolved field for vanishing scales on every interval; this is one-way for the energy of the whole box, not at every point, and it is chosen by the prescribed profile, not forced by the equations | Buckmaster, De Lellis, Székelyhidi and Vicol (2017; CPAM 2019), LIT-1300, read in NOTE-1013: the admissible version of Isett’s negative half of Onsager’s conjecture (THEORY-763). Any smooth positive energy profile can be imposed on a C^β solution, β < 1/3, so a strictly decreasing one gives solutions whose total energy only falls. Through THEORY-749’s energy balance, the coarse-grained flux then runs into the vanishing scales on every time interval. That is the one-way transfer THEORY-763 could not give. It is one-way for the box as a whole, not at every point (no local energy inequality is proved); the same theorem gives increasing energy as readily, so the direction is a choice of the construction; and nothing ties these solutions to Navier–Stokes, to a constant-flux inertial range or to uniqueness. | Proposed |
| THEORY-777 | In Monte Carlo on a 64×64 periodic square-lattice Ising model at its critical point, parametrized by a field and 13 nearby couplings and observed only through the spins left after n checkerboard decimations (b = √2 per step, n ≤ 6), the two Fisher eigenvalues along the field and the gradient of T_c stay within a factor of about two of their microscopic values, while the others fall by up to about six decades, in three groups whose decay is consistent with b^(2y−d) per step for y = 0, −2 and −4 | Machta, Chachra, Transtrum and Sethna (2013), LIT-1299, Fig. 3, read in NOTE-1018. One lattice size, one temperature, at most six steps of b = √2 (so b^n ≤ 8), no error bars, and no fitted rates. The groups and their rates are bands the authors drew. The value y = 0 is not an operator of the 2D Ising model: it is the rate at which any direction without singular support loses information as sites are discarded. The caption’s rate 2^(−d−y) disagrees with the bands and with the supplement’s b^(2y−d). | Proposed |
| THEORY-780 | Transcriptional regulation alone can give a bacterium’s gene expression a memory: in E. coli, a transient knockdown or overexpression of one regulator, with the environment held fixed, can leave other genes in a different self-maintaining expression state after it is released, as Zhao, Wytock, Reynolds and Motter predict from a Boolean-network model of its regulatory core | Zhao, Wytock, Reynolds and Motter (2024), LIT-854, read in full in NOTE-655. Their abstract and discussion carry the model result to cells: one genotype may hold several heritable expression states without epigenetic marks, and history picks among them. They predict that a transient crp knockdown leaves zraR, melR or rhaRS changed (NOTE-655, C8, untested). THEORY-178 is the model result this rests on. No such perturbation has been done in cells (QUESTION-172). | Proposed |
| THEORY-789 | The block coarse-graining that maximizes mutual information with the system beyond a buffer picks out the renormalization-group-relevant variables in general, so those variables can be found from samples by information alone, without being known beforehand, as Koch-Janusz and Ringel propose | Koch-Janusz and Ringel (2017), LIT-873, propose that their mutual-information criterion finds a system’s relevant degrees of freedom with no prior knowledge of them. What the record holds as shown, THEORY-194, is that it recovered variables renormalization already uses, on 2D models whose answer was known. This is the general thesis that result was offered for, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-817 | Once an agent’s actions affect the percepts it receives, maximal prediction of those percepts is generally not what thermodynamic efficiency requires: in percept-action loops with feedback, maximally predictive agents generally extract less work than the most efficient agent | Fiderer et al. (2025), LIT-041, read in NOTE-032, prove that without feedback the work-efficient agents are exactly the maximally predictive ones that randomise and forget their actions, and that with feedback one binary memoryless channel separates predictive, max-entropy-action and efficient agents; from that they assert that with feedback maximally predictive agents are generally inefficient. The record holds as proved, in THEORY-026, only the one channel. It does not say that efficiency under feedback is a trade-off between prediction and forgetting: in the proved example the efficient agent is memoryless. | Proposed |
| THEORY-818 v2 | In two-scale Lorenz 96 without time-scale separation (ε = 0.5, K = 18, J = 20, F = 10), a discrete-time closure for each resolved variable that fits the one-step discrepancy of a fourth-order Runge–Kutta step as a NARMAX series, with one autoregressive lag, at most two lags of the resolved variable and at most one moving-average term, reproduces the mean, spread, distribution, autocorrelation and neighbour cross-correlation of x₁ (Kolmogorov–Smirnov distance 0.005) and, with observations every 0.05, extends the 20-member ensemble forecast lead time at anomaly correlation 0.6 from about 2 to about 4 time units over a polynomial-plus-AR(1) closure; the model structure was chosen by trial and error, differs between the two observation spacings, and carries no error bound | Chorin and Lu (2015), LIT-1304, read in NOTE-1028. A data-driven closure with one or two steps of discrete memory, plus one moving-average innovation, is enough on this test to reproduce the resolved statistics and to double forecast skill against a memoryless-in-x closure. It is the record’s first evidence that a short discrete memory suffices in a chaotic system with no scale gap. It is one system, the structure was tuned, and there is no bound, so it does not give the controlled prediction error QUESTION-222 asks for. | Active |
| THEORY-821 | For every α < 1/15 there are weak solutions of the 3D incompressible Euler equations on the periodic box, Hölder-continuous of exponent α in space and time, that satisfy the local energy inequality; in the construction their dissipation measure is a nonnegative function of time alone, equal at each time to the rate at which the total energy falls, zero while the local energy equality holds and positive on all of space during a short final interval in which the solution’s energy is drained to zero; uncountably many such solutions share one initial datum and one dissipation measure; for them the local coarse-grained energy flux into vanishing scales converges to that measure, so the transfer is one-way at every place and time in the limit and spread uniformly over the box, with its timing chosen by the construction, not forced by the equations | Isett (2017; ARMA 2022), LIT-1305, skimmed in NOTE-1027: the first continuous, indeed C^α with α < 1/15, weak Euler solutions satisfying the local energy inequality with nonzero dissipation, and a Cantor family of them sharing one initial datum and one dissipation measure. In the construction the dissipation measure is a function of time alone, so in the limit of vanishing scale the energy flux runs one way at every place, as in THEORY-772, but in a Hölder class and spread uniformly over the torus rather than set in pipes. It is switched on only while the constructor drains the solution’s energy to zero at the end of its life. Where, when and how fast the energy goes are inputs; the exponent is far from 1/3; nothing ties these solutions to Navier–Stokes. | Proposed |
| THEORY-1008 | Mixed memberships fitted by a fifteen-block MMSB to 871 yeast proteins’ curated physical interactions carry information about the proteins’ top-level MIPS functions beyond what the functions’ base rates give: after mapping blocks to functions on 87 proteins, thresholded memberships predicted the other proteins’ annotations with about 87% accuracy, against about 70% for random guessing at the right proportions | Airoldi, Blei, Fienberg and Xing (2008), LIT-1553, §4.3.2 and Figs. 10–12, read in NOTE-1179. The batch’s one check of inferred mixed memberships against labels the model never saw. The reported margin is over a weak baseline, so it shows less than it seems: probably some information, not yet how much. It says nothing about whether the fifteen blocks are the fifteen functions. | Proposed |
| THEORY-1049 v3 | On McCutcheon and colleagues’ survey, bacterial endosymbionts lose their own cell-envelope and envelope-transport genes together below about 400 kb, and begin to lose translation genes (ribosomal proteins, tRNAs, aminoacyl-tRNA synthetases) below about 200 kb, so that the smallest-genome symbionts cannot be self-sufficient and their membranes, transport and protein synthesis are presumably supplied by the host, as for organelles | McCutcheon, Garber, Spencer & Warren (2024), LIT-1571, read in NOTE-1213. The envelope goes first, near 400 kb, and translation starts to go below about 200 kb, the authors’ “tipping point”. Such symbionts have three-membrane envelopes and among the most biased proteomes in bacteria. They can only work if the host provides what they no longer encode. The host’s role is inferred, not shown: the mechanisms are, in the paper’s word, mysteries. | Active |
| THEORY-1085 | In Toner and Tu’s hydrodynamic theory, a flock’s ordered state is a broken continuous symmetry of a coarse-grained velocity field: speed fluctuations relax in a finite time of order 1/α and are dropped, leaving as slow degrees of freedom the transverse velocity and the conserved density, which propagate as sound at ω = ±cq⊥; no individual member appears in the description, which is offered for a universality class of microscopic rules | Toner and Tu (1995), LIT-1670, read in NOTE-1228 from the arXiv preprint. Active as a statement of what the theory is: its variables, the degree of freedom it eliminates and why, and the modes that remain, all in the text (pp. 3–8). It does not say that the theory’s exponents are right (THEORY-1095), that the universality claim holds, or that the order so described is an agent or an individual. | Active |
| THEORY-1095 | In Toner and Tu’s hydrodynamic model of a flock, true long-range orientational order survives in two dimensions, where the Mermin–Wagner theorem forbids it at equilibrium and the model’s own linearized theory loses it, because the convective coupling of the velocity field to its own transport, relevant below four dimensions, keeps the transverse velocity fluctuations bounded; the authors’ heuristic is that motion keeps changing each member’s neighbours, so originally distant members come to interact | Toner and Tu (1995), LIT-1670, read in NOTE-1228 from the arXiv preprint. The linear theory’s loss of order in d ≤ 2 and the relevance of the convective nonlinearity below d = 4 are calculations. The survival of order in d = 2 follows from χ = −1/5 < 0, which is exact only if a cubic vertex stays irrelevant (“we strongly suspect”), or from χ = (z − d)/3 with z < 2, which is expected “on physical grounds”. The change-of- neighbours mechanism is a heuristic. Proposed for those two steps. | Proposed |
| THEORY-1098 v2 | On Karnkowska and colleagues’ genome analysis, the oxymonad Monocercomonoides exilis lost its mitochondrion only after the organelle’s essential functions had been removed one by one, Fe–S cluster assembly to a bacterial-type SUF system shared with mitochondriate relatives and then the glycine cleavage system by loss, and the loss left the rest of the cell canonical, with no compensating changes found | Karnkowska et al. (2019), LIT-1574, read in NOTE-1243. The SUF replacement of the mitochondrial Fe–S pathway is shared by all examined Preaxostyla, including relatives that keep a mitochondrion-related organelle, and those relatives’ organelle still houses the glycine cleavage system that M. exilis lacks. So the organelle lost its jobs in at least two steps before it was lost. Apart from the mitochondrion, peroxisomes and mitophagy, the cell’s systems are those of an ordinary eukaryote. The order is inferred, not dated, and absence is limited by annotation. | Active |
| THEORY-1099 v2 | On Kay and colleagues’ relaxed-clock dating of pre-LECA gene duplications, most duplications in eukaryotic gene families of archaeal origin, including actin, tubulin, vesicle-trafficking and nuclear-targeted families, predate the onset of duplications in genes of alphaproteobacterial origin at about 2.2 billion years ago, which the authors take as the start of mitochondrial endosymbiosis, so the host was elaborating its cytoskeleton, endomembranes and nuclear machinery before the mitochondrion; each date is a maximum age for its paralogues’ functions, many intervals reach below 2.2 billion years, and the order of phagocytosis and the mitochondrion is left open | Kay et al. (2026), LIT-1566, read in NOTE-1234. A dated species tree places nFECA at 3.05–2.79 Ga, mFECA at 2.37–2.13 Ga and LECA at 1.80–1.67 Ga. Against an endosymbiosis marker at about 2.2 Ga, 85% of archaeal-origin duplications are older, and most non-alphaproteobacterial bacterial duplications are younger. The authors reject mitochondria-early scenarios and argue against serial endosymbiosis. The sharp edges are that duplication dates bound functions from above, that the priors shape which family can be older, and that the authors themselves cannot order phagocytosis and the mitochondrion. | Active |
| THEORY-1100 v2 | On Sørensen and colleagues’ review, a bacterial endosymbiont becomes genetically integrated, the authors’ mark of an organelle, when nuclear genes whose products are imported into it functionally replace essential genes it has lost, and this does not require gene transfer from the endosymbiont: in the Paulinella chromatophore and the nitroplast, the two systems with hundreds of imported proteins, many of which fill gaps left by lost genes, the imported proteins come mostly from the host’s own genes or from other bacteria, and in the nitroplast no gene transfer from the endosymbiont has been found | Sørensen, Stiller, Kröninger & Nowack (2025), LIT-1560, read in NOTE-1241. Protein mass spectrometry of isolated endosymbionts found hundreds of host proteins imported into Paulinella’s chromatophore and more than 350 into the nitroplast, where they fill gaps left by lost genes. In Paulinella the imported proteins come mostly from the host’s own genes, with some from gene transfer from the chromatophore and from other bacteria. In the nitroplast no gene transfer from the symbiont has been found at all. So the route to an organelle is import, and the endosymbiont’s genes need not move. The origins are stated in summary, not counted, and the import mechanisms are unknown. | Active |
| THEORY-1101 v3 | Tobiasson, Luo, Wolf and Koonin find, on 5,850 eukaryotic gene stems, that normalized stem length does not behave as a clock of acquisition time: alphaproteobacterial stems are longer than Asgard ones for the 70% of stems below 0.3 and shorter only above 0.35, oxidative-phosphorylation genes presumed acquired together vary by more than two orders of magnitude, and information-processing genes have short stems; they conclude that even normalized stem lengths are set primarily by factors other than acquisition time, at least over the long timescales analysed, and suggest that adaptation after acquisition lengthens stems | Tobiasson, Luo, Wolf & Koonin (2026), LIT-1558, read in NOTE-1242. They test the stem-length method of Pittis and Gabaldón on their own trees and reproduce its mitochondrion-late signal only for long stems. Below 0.3, where 70% of stems lie, the order reverses, and genes presumably acquired together scatter widely. They conclude that “even normalized stem lengths are determined primarily by factors other than the gene acquisition time”. The paper still favours a late mitochondrion, on other grounds. | Active |
| THEORY-1102 v2 | On Pittis and Gabaldón’s stem-length analysis of the LECA proteome, families of alphaproteobacterial origin and mitochondrial location sit closer to their prokaryotic relatives, after correction for each family’s rate, than families of other bacterial origin (P = 0.044), which sit closer than archaeal families, and the authors read this as late acquisition of the mitochondrion by a host whose proteome was already chimaeric, under their stated assumption that rates before and after LECA are correlated | Pittis & Gabaldón (2016), LIT-1595, read in NOTE-1240. Of 1,078 LECA families, bacterial ones have shorter normalized stems than archaeal ones (P = 1.38e-25), and alphaproteobacterial ones shorter than other bacterial ones (P = 0.044). Origin tracks location: alphaproteobacterial with the mitochondrion, other bacterial with endomembranes, archaeal with the nucleus. A plastid control runs the right way. The sharp edges are that stem length measures distance to the closest sampled relative, so sampling can move it, and that the chimaeric host could have come from partners or from transfer, which the paper cannot tell apart. | Active |
| THEORY-1103 v2 | On Shigenobu and colleagues’ genome of Buchnera sp. APS, the aphid symbiont keeps the genes for the amino acids its host cannot make and has lost almost all of those its host can, uses host-made glutamate and aspartate as precursors, and lacks phospholipid synthesis and nearly all its own transcriptional regulators, so that its metabolism interlocks with the host’s and it presumably lives only inside the bacteriocyte, a state reached by gene loss from an E. coli-like ancestor | Shigenobu et al. (2000), LIT-1596, read in NOTE-1236. The first complete genome of an obligate insect endosymbiont: 640,681 bp, a subset of E. coli’s. What is shown is gene content. The interlocking of host and symbiont metabolism is inferred from it and from earlier physiology. That Buchnera cannot live outside the bacteriocyte, and that the host supplies its membrane lipids, are the authors’ inferences. The paper names no mechanism of loss beyond a homeostatic niche: it says nothing of drift. | Active |
| THEORY-1104 v3 | In Tobiasson, Luo, Wolf and Koonin’s constrained-tree survey of widespread eukaryotic protein families, Asgard archaea are the largest single prokaryotic source, with about half the likelihood weight in the best-resolved families and the lead in nearly every functional system, while Alphaproteobacteria contribute a small, coherent set centred on the mitochondrion and other bacteria about a third of families, scattered across functions with no pathway led by one donor except a narrow Myxococcota signal in nucleotide-sugar and nicotinate metabolism; the authors read this as one Asgard host lineage, one endosymbiont and piecemeal gene transfer rather than further symbioses | Tobiasson, Luo, Wolf & Koonin (2026), LIT-1558, read in NOTE-1242. In 4,290 well-resolved eukaryotic–prokaryotic clusters, Asgard takes 50% of likelihood weight and leads in almost every functional class. Alphaproteobacteria account for mitochondrial translation, oxidative phosphorylation and 4Fe-4S assembly. About a third of clusters point elsewhere, with no functional pattern except a narrow Myxococcota signal. The authors infer a complex Asgard ancestor, a late mitochondrion and “no indication of another symbiotic event”. The composition is shown; the scenario is read off it. | Active |
| THEORY-1105 v3 | In Bernabeu, Manzano-Morales, Marcet-Houben and Gabaldón’s reconstruction of the last eukaryotic common ancestor’s proteome, two bacterial phyla besides the mitochondrial ancestor, Myxococcota and Planctomycetota, each account for a share of the proteome comparable to that of Alphaproteobacteria and Asgard archaea under thresholds calibrated on those accepted partners, and stem-length distributions order the acquisitions as waves, Asgard first, then Planctomycetota, then the mitochondrial ancestor and Myxococcota together; the authors read this as serial associations with several partners, while conceding that their data cannot say whether any donor was a symbiont | Bernabeu, Manzano-Morales, Marcet-Houben & Gabaldón (2026), LIT-1561, read in NOTE-1237. Under thresholds chosen to maximize assignments to Alphaproteobacteria and Asgard, Myxococcota (3.92% of the proteome) and Planctomycetota (2.24%) pass in every dataset, beside Alphaproteobacteria (3.99%) and Asgard (3.28%). A control removing Alphaproteobacteria from the database does not reproduce their pattern. Stem lengths put Planctomycetota before the mitochondrion. The authors “challenge models depicting eukaryogenesis as a one-off event resulting from a binary symbiotic interaction”, and also say their data “do not provide information on the host or endosymbiotic nature of any partner”. | Active |
| THEORY-1106 v2 | Campbell and colleagues report, from four cicada species with five or six eggs each, that Hodgkinia cells per egg range from about 4,900 in a species with one Hodgkinia lineage to about 30,000, some six times as many, in Magicicada septendecim, whose Hodgkinia has split into many interdependent lineages and the only species that differs significantly, while Sulcia numbers are not raised, the transmission route is the same, and every egg sampled carries every lineage tracked by marker genes; the authors take the raised titre as a host adaptation that compensates for the symbiont’s fragmentation, and a cost of it | Campbell, Łukasik, Meyer, Buckner, Simon, Veloso, Michalik & McCutcheon (2018), LIT-1590, read in NOTE-1235. Measured: Hodgkinia cells per egg from 4,889 in a single-lineage cicada to 30,154 in M. septendecim, with Sulcia at 2,572 to 5,643; marker genotypes present in every egg sampled; the same route under the light microscope. Not shown: a trend across complexity beyond M. septendecim, or that splitting came first. The authors also speculate that a larger transmitted population weakens bottlenecks and could feed further splitting. | Active |
| THEORY-1107 v2 | On Sørensen and colleagues’ scenario, an endosymbiont becomes an organelle in steps: the host first targets effector proteins into it; an imported host protein redundant with one of its functions then lets the endosymbiont’s own gene decay, making it dependent; and a general import pathway, once evolved, brings in hundreds of proteins; this genetic integration arises only in permanent, vertically transmitted associations, and host effector control without vertical transmission, as in rhizobia, does not lead to it | Sørensen, Stiller, Kröninger & Nowack (2025), LIT-1560, read in NOTE-1241. Their closing scenario orders the steps from endosymbiont to organelle: effectors first, then dependence through one redundant imported protein, then many imported proteins once a targeting signal evolves. Rhizobia, targeted by about 700 host peptides yet not vertically transmitted, are their case of control without integration. It is a scenario built from systems at different stages, not a sequence observed in any one. | Active |
| THEORY-1108 v2 | On Imachi and colleagues’ cultivation of Candidatus Prometheoarchaeum syntrophicum MK-D1, the first Asgard archaeon grown in the laboratory is a small, internally simple coccus with long branching protrusions that degrades amino acids only in syntrophy, handing hydrogen and formate to partners that can be exchanged, and from its genome and other Asgard genomes the authors infer that the Asgard ancestor was likewise dependent on metabolic partners; the isolate is a modern relative separated from the host lineage by about two billion years, grown only in co-culture, and the entangle–engulf–endogenize model built on it is a hypothesis the authors call not definitive | Imachi et al. (2020), LIT-1591, read in NOTE-1238. Partner inhibitors impair MK-D1’s growth, added hydrogen or formate stops it, and it grows with either of two methanogens, so its dependence is on a service that several partners can supply. Cryo-EM and TEM show no internal compartments. The step from this one organism to the Asgard ancestor is a genomic inference, which the authors hedge. The sharp edge for the record is that the most famous transition in individuality may have begun from a host already dependent on others, with no partner specificity, cohesion or control. | Active |
| THEORY-1109 v3 | Santana-Molina, Williams, Snel and Spang find that the last eukaryotic common ancestor’s central carbon metabolism was chimeric: a few Asgard-archaeal enzymes in cytosolic glycolysis and the pentose phosphate pathway, four placed with Asgard archaea at bootstrap 39–97% and two ambiguously, most alphaproteobacterial ones in the mitochondrial TCA cycle and pyruvate conversion, and others from various bacteria with no third dominant donor, since remodelled by loss, horizontal replacement and retargeting so that compartment no longer follows origin; the authors take the cytosol–mitochondrion split as support for syntrophy | Santana-Molina, Williams, Snel & Spang (2025), LIT-1564, read in NOTE-1239. LECA had a complete central carbon metabolism. Six enzymes are placed with Asgard archaea, mostly cytosolic (bootstrap 39–97%, two ambiguous). Seventeen are alphaproteobacterial, ten of them in the TCA cycle, mostly mitochondrial. Others come from several bacteria, none dominant. Since LECA, Asgard enzymes have been replaced in many lineages and enzymes retargeted regardless of origin. The authors read the split as support for syntrophy; it does not discriminate syntrophy from other symbiogenetic models. | Active |
| THEORY-1195 | About 800 Myr ago the breakup of the Eulalia parent body beside the Jupiter 3:1 resonance sent an impact shower to the terrestrial planets and the Moon that made the cluster of large lunar craters dated near 800 Ma | The thesis of Bottke et al. (2026), LIT-009, in its title, kept here when the twenty-second status review narrowed and promoted THEORY-499, the reading of the plausibility model (ADR-065; ADR-047 kind 1). The model shows that a source could have done it; only Copernicus of the seven craters has a sample age. | Proposed |
| THEORY-1197 | Eukaryogenesis involved one archaeal host lineage, of Asgard descent, and one bacterial endosymbiont, the alphaproteobacterial ancestor of mitochondria; the eukaryotic genes from other bacteria came by piecemeal gene transfer, not from further symbiotic partners | The wider thesis Tobiasson, Luo, Wolf & Koonin assert, filed beside THEORY-1104 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1104, Active, holds what Tobiasson and colleagues’ survey finds and how the authors read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1104’s old condition, word for word. | Proposed |
| THEORY-1200 | The Asgard archaeal ancestor of eukaryotes depended on metabolic partners: like Candidatus Prometheoarchaeum syntrophicum, it degraded amino acids in syntrophy, handing hydrogen and formate to partners that removed them | The wider thesis Imachi et al. assert, filed beside THEORY-1108 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1108, Active, holds what Imachi and colleagues’ cultivation shows and what they infer from it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1108’s old condition, word for word. | Proposed |
| THEORY-1201 | Normalized stem length is not a clock of gene acquisition time: it is set mainly by factors other than when a gene was acquired, such as adaptation to the new cell after acquisition, so relative timings of eukaryogenesis drawn from stem lengths alone are not supported | The wider thesis Tobiasson, Luo, Wolf & Koonin assert, filed beside THEORY-1101 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1101, Active, holds what Tobiasson and colleagues find and conclude; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1101’s old condition, word for word. | Proposed |
| THEORY-1203 | The host lineage elaborated its cytoskeleton, endomembrane system and nuclear machinery before mitochondrial endosymbiosis began, about 2.2 billion years ago: most pre-LECA duplications in eukaryotic gene families of archaeal origin predate it | The wider thesis Kay et al. assert, filed beside THEORY-1099 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1099, Active, holds what Kay and colleagues’ dating finds and how the authors read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1099’s old condition, word for word. | Proposed |
| THEORY-1205 | Eukaryotes began in a syntrophic partnership: an archaeal host fermented sugars and passed reducing equivalents to an alphaproteobacterial endosymbiont that contributed a TCA cycle and an electron transport chain, which is why the last eukaryotic common ancestor’s central carbon metabolism is archaeal in cytosolic glycolysis and the pentose phosphate pathway and alphaproteobacterial in the mitochondrial TCA cycle | The wider thesis Santana-Molina, Williams, Snel & Spang assert, filed beside THEORY-1109 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1109, Active, holds what Santana-Molina and colleagues find and how they read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1109’s old condition, word for word. | Proposed |
| THEORY-1206 | The mitochondrion was acquired late in eukaryogenesis, by a host whose proteome was already chimaeric, with genes from several bacterial sources acquired before it | The wider thesis Pittis & Gabaldón assert, filed beside THEORY-1102 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1102, Active, holds what Pittis and Gabaldón’s analysis finds and how the authors read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1102’s old condition, word for word. | Proposed |
| THEORY-1208 | Bacterial endosymbionts lose their cell-envelope and envelope-transport genes together below about 400 kb and begin to lose translation genes below about 200 kb, and the host supplies the membranes, transport and protein synthesis that the smallest-genome symbionts no longer encode, as for organelles | The wider thesis McCutcheon, Garber, Spencer & Warren assert, filed beside THEORY-1049 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1049, Active, holds what McCutcheon and colleagues’ survey shows and what they infer from it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1049’s old condition, word for word. | Proposed |
| THEORY-1209 | In genetically identical E. coli, a cell’s swarming potential is a transient inherited state: its descendants share it for about four generations and lose it by about seven, and it tracks the cell’s iron status rather than a bistable switch | The wide form of Bhattacharyya et al. (2023), LIT-853, kept here when the status review of 2026-10-30 narrowed THEORY-179 to what the assays measured and promoted it (ADR-065; ADR-047, kind 1). The paper asserts a heritable iron memory. Iron was read only through a plasmid promoter reporter, inheritance rests on few founders and four sampled generations, and the delay model is fitted to two time points. | Proposed |
| THEORY-1211 | An endosymbiont becomes an organelle in steps: the host first targets effector proteins into it; an imported host protein redundant with one of its functions then lets the endosymbiont’s own gene decay, making it dependent; and a general import pathway, once evolved, brings in hundreds of proteins; this genetic integration arises only in permanent, vertically transmitted associations | The wider thesis Sørensen, Stiller, Kröninger & Nowack assert, filed beside THEORY-1107 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1107, Active, holds the scenario Sørensen and colleagues propose; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1107’s old condition, word for word. | Proposed |
| THEORY-1214 | Cicada hosts whose endosymbiont Hodgkinia has split into many interdependent lineages compensate by sending more Hodgkinia cells to each egg, with Sulcia numbers and the transmission route unchanged, so that every egg still receives every lineage; the raised titre is a host adaptation driven by the symbiont’s fragmentation, and a cost of it | The wider thesis Campbell et al. assert, filed beside THEORY-1106 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1106, Active, holds what Campbell and colleagues measured and how they read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1106’s old condition, word for word. | Proposed |
| THEORY-1215 | Besides Asgard archaea and the alphaproteobacterial ancestor of mitochondria, Myxococcota and Planctomycetota were major donors of genes to the eukaryotic lineage before its last common ancestor, in waves: Asgard first, then Planctomycetota before the mitochondrion, then the mitochondrial ancestor and Myxococcota together | The wider thesis Bernabeu, Manzano-Morales, Marcet-Houben & Gabaldón assert, filed beside THEORY-1105 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1105, Active, holds what Bernabeu and colleagues’ reconstruction finds and how the authors read it; whether that is true is this entry’s question, and its promote_when is THEORY-1105’s old condition, word for word. | Proposed |
| THEORY-1219 | Buchnera’s metabolism interlocks with its aphid host’s: it makes the essential amino acids its host cannot from host-supplied glutamate and aspartate, depends on the host for the non-essential amino acids and its membrane phospholipids, and cannot live outside the bacteriocyte | The wider thesis Shigenobu, Watanabe, Hattori, Sakaki & Ishikawa assert, filed beside THEORY-1103 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1103, Active, holds what Shigenobu and colleagues’ genome shows and what they infer from it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1103’s old condition, word for word. | Proposed |
| THEORY-1223 | Monocercomonoides exilis lost its mitochondrion only after the organelle’s essential functions had been removed in steps, Fe–S cluster assembly to a cytosolic SUF system and then the glycine cleavage system by loss, and the loss required no compensating change elsewhere in the cell | The wider thesis Karnkowska et al. assert, filed beside THEORY-1098 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1098, Active, holds what Karnkowska and colleagues’ genome analysis finds and infers; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1098’s old condition, word for word. | Proposed |
| THEORY-1228 | A bacterial endosymbiont becomes genetically integrated, an organelle, when host proteins imported into it replace genes it has lost, and this does not require gene transfer from the endosymbiont: in the Paulinella chromatophore and the nitroplast, the two systems with hundreds of imported proteins, the replacing genes are mostly the host’s own or come from other bacteria | The wider thesis Sørensen, Stiller, Kröninger & Nowack assert (“EGT is not a precondition for the genetic integration of an endosymbiont”), filed beside THEORY-1100 by the twenty-third status review (ADR-065 §3; ADR-047 kind 1). THEORY-1100, Active, holds what the review reports; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1100’s old condition, word for word. | Proposed |
| THEORY-1265 | Approximating a chemical master equation by a Fokker–Planck or nonlinear Langevin equation gets the quasi-potential right only at the fixed points: between them it mis-estimates the barriers, so escape rates come out wrong by a factor exponential in system size and the approximation can pick the wrong one of two states as the long-run favourite, and its apparent entropy production vanishes at every steady state, missing the dissipation that sustains it | Falasco & Esposito (2025), LIT-1892, §IV.D–E and §VII.A.1, read in NOTE-1472; Vellela & Qian (2009), LIT-1890, appendix A, read in NOTE-1474. Active: both formulas were checked on the Schlögl model, including Vellela & Qian’s counterexample, where the exact and diffusion quasi-potentials favour different states. It does not say diffusion approximations fail near fixed points or for Gaussian fluctuations; there they are exact to leading order. | Active |
| THEORY-1268 | In a nonequilibrium steady state of a thermodynamically consistent Markov jump network, the entropy produced while a current is counted, times the squared relative uncertainty of that count, is at least 2k_B, independent of the counting time, so a current precise to ε costs at least 2k_BT/ε² of dissipation; the 2015 letter proves this within linear response and for single-cycle networks at any affinity, and for many-cycle networks far from equilibrium shows it numerically and states it as a conjecture | Barato & Seifert (2015), LIT-1885, read in full in NOTE-1480. Active for the scope stated in the title: the biased walk, the unicyclic formula (A/N) coth(A/2N) and the bound on random four-state networks were checked numerically. It bounds the precision of currents, not of occupations, so it does not price how long a maintained state lasts, and the general multicyclic proof is not in this paper. | Active |
| THEORY-1270 | Entropy production does not select which of several maintained steady states is the stable one: in the bistable Schlögl model the state the system occupies in the long run can carry either the higher or the lower deterministic entropy production rate, and the mean stochastic entropy production follows whichever state is more probable; in general the most dissipative attractor is the longest-lived only under special conditions, and lifetime tracks relaxation entropy only near detailed balance | Vellela & Qian (2009), LIT-1890 (§3.3, Fig. 6), read in NOTE-1474, show the counterexample; Falasco & Esposito (2025), LIT-1892 (§§III.F, IV.H, VIII.B.6), read in NOTE-1472, give the general account: minimum entropy production holds only near detailed balance with linear dynamics, and the two maximum principles hold only where relaxation and escape dissipations nearly coincide. Active as a negative result. It does not refute every extremum principle, only those that rank steady states by dissipation alone. | Active |
| THEORY-1273 | In a driven chemical system with two stable states and a finite number of molecules, each maintained state is metastable: it is left by fluctuation after a time exponential in system size, set by a barrier in a nonequilibrium quasi-potential that closes at the saddle-node, and the long-run share of time in each state is fixed by the parameters and system size, not by the initial condition; the deterministic rate equation, where the initial condition decides, holds only on times short of that escape time | Vellela & Qian (2009), LIT-1890, read in NOTE-1474, on the Schlögl model, with Falasco & Esposito’s general frame (LIT-1892, §§III.C, IV.H, VI; NOTE-1472). Active: the slow eigenvalue, the barriers, the initial-condition independence and the closing of the barrier at the fold were checked numerically on the paper’s model. It does not say which state is the more stable without computing the quasi-potential, and the paper’s own large-volume rate formula carries a spurious 1/V factor. | Active |
| THEORY-1315 | As a stochastically forced system approaches a fold bifurcation its dominant eigenvalue goes to zero, so it recovers ever more slowly from small perturbations, and under ongoing perturbation this critical slowing down shows as rising lag-1 autocorrelation and rising variance; skewness and flickering are further warnings not caused by slowing; but the same signals, less pronounced, also precede thresholds that are not bifurcations, so they mark proximity to a broad class of thresholds and not which kind, nor when the shift will come | Scheffer et al. (2009), LIT-1956, read in NOTE-1536 (Skimmed) from the version reprinted as chapter 2 of Dakos’s 2011 thesis. Active for the slowing-down result, which is standard (Wissel 1984), checked in the chapter’s Box 2.2 example, and re-derived and simulated here for variance σ²/(2|λ|) and autocorrelation e^{λΔ} since the chapter’s Box 2.3 was not extractable. The scope and timing caveats are the authors’ (p. 31). It does not say the signals have been shown in chaotic systems, which the review calls “less well studied”, or that any of the reviewed empirical cases was checked here. | Active |
| THEORY-1323 | Under weak local noise a many-body operator decays at a rate proportional to its size, so a Hamiltonian’s small-sized integrals of motion, which chaotic dynamics does not spread, decay slowly while generic operators, which it spreads, decay fast; in exact diagonalization of Ising and Heisenberg chains of up to nine sites at weak depolarizing noise, the slowest Lindbladian eigenoperators are linear combinations of the known exact and approximate small integrals of motion, and which approximate ones rank among the slowest moves with the noise strength | Yang and Abanin (2025), LIT-1958, read in NOTE-1534. Active as a statement of what the paper derived exactly and what its exact diagonalization showed at the sizes it reached. It does not say that the correspondence holds at large system size (THEORY-1343), that every integral of motion is found (those above size 3–4 are not), or that slowness ranks conserved quantities independently of the environment. | Active |
| THEORY-1343 | The first-order picture in which a small integral of motion Q of a many-body Hamiltonian is, under weak local noise, the slowest Lindbladian eigenoperator holds at large system size whenever its leak ε out of span{Q} satisfies ε ≲ γ ≪ 1, because the gap controlling the perturbation is not the exponentially small level spacing but one of order min(γL, √(v_Bγ)), set by the ballistic growth of the operators Q leaks into | Yang and Abanin (2025), LIT-1958, §IV, read in NOTE-1534. Proposed because the argument assumes fully chaotic operator growth for the complement, is checked numerically only at nine sites, and is qualified by the authors themselves: hydrodynamic modes give a continuum of slow modes in the Mori limit, so the gap “might not exist at all” outside sectors orthogonal to them. | Proposed |