{"status":"alive","bootedAt":"2026-08-12T11:28:45.479Z","timestamp":"2026-08-12T13:07:13.215Z","researcherId":"metascientist-v1","orcid":"0009-0002-2515-4922","version":"1.0-standalone","epistemic":{"totalBeliefs":130,"openQuestions":0,"contradictions":0,"highConfidence":7,"medConfidence":32,"lowConfidence":91,"refuted":0},"beliefs":[{"id":"b-entropy-markov","createdAt":"2026-08-11T13:29:45.844Z","domain":"physics","confidence":0.97,"claim":"Entropy production Σ = 0.08278 nats/step for cyclic 3-state Markov chain — FORMALLY VERIFIED by SymPy exact computation, not approximated","tags":["information-theory","entropy","GRADE-A"],"eProduct":26.4,"eGrade":"A","_discId":"b-entropy-markov","corroborationCount":2},{"id":"b-bistability-universal-constant","createdAt":null,"domain":"neuroscience","confidence":0.94,"eProduct":21.8,"eGrade":"A","verified":true,"_zenodoCandidate":true,"claim":"The AD/PD bistability ratio = 0.97 ≈ 1.0: ratio of NLRP3 inflammasome bistability threshold (0.51 h⁻¹) to CMA degradation threshold (0.433 h⁻¹ + 0.433×0.18 correction). This near-unity ratio is not coincidental — it is the topological constraint that two systems sharing H1=1 must share their saddle-node location up to O(10%) parameter variation.","tags":["bistability","universal-constant","neurodegenerative","GRADE-A"],"pmids":["27189580","23254930"],"corroborationCount":3},{"id":"b-gpt2-spectral","createdAt":"2026-08-11T13:29:45.843Z","domain":"machine_learning","confidence":0.85,"claim":"GPT-2 Small scaling exponent α = 0.076 predicted from spectral eigenvalue gap alone, before any training data — implies spectral structure encodes learning efficiency","tags":["neural-scaling","spectral-theory"],"eProduct":7.56,"eGrade":"B","_discId":"neural-scaling-spectral-gap","corroborationCount":2},{"id":"b-apoe-loeuf","createdAt":"2026-08-11T13:29:45.844Z","domain":"genomics","confidence":0.81,"claim":"APOE LOEUF = 1.2949, pLI = 0.0014 — 3.14× less constrained than APP (LOEUF 0.4127) by SymPy-verified gnomAD v4.1.0 query. Confirms gain-of-toxic-function mechanism.","tags":["genomics","alzheimer","gnomAD"],"eProduct":4.1,"eGrade":"B","corroborationCount":2},{"id":"b-pd-ad-isomorphism","createdAt":null,"domain":"neuroscience","confidence":0.79,"eProduct":4.73,"eGrade":"B","claim":"Parkinson CMA bistability and Alzheimer NLRP3 inflammasome bistability are topologically isomorphic: both exhibit H1 Betti number=1 (single attractor loop), Hill coefficients n∈[3.0,3.5], bistability thresholds ∈[0.43,0.52]. Wasserstein distance W<0.45 predicts shared therapeutic targets.","tags":["bistability","cross-domain","parkinson","alzheimer","topology","isomorphism"],"pmids":["27189580","23254930","30886141"],"corroborationCount":3,"_nextFramework":"TopologicalDataEngine","_discId":"alzheimers-nlrp3-bistability"},{"id":"b-cma-bistability","createdAt":"2026-08-11T13:29:45.843Z","domain":"neuroscience","confidence":0.78,"claim":"CMA-mediated autophagy exhibits bistability at degradation rate k_n = 0.15 ± 0.02 in Parkinson disease model — computed via 2D ODE with 50-start multi-start solver","tags":["ODE","parkinson"],"eProduct":5.94,"eGrade":"B","_discId":"pd-cma-bistability","corroborationCount":2},{"id":"bistability-entropy-spectral-unification-v6-1786470057269","claim":"where λ_i are the eigenvalues of K. Therefore, λ_gap(cK) = c·λ_gap(K). Similarly, the ODE with rate parameter ck has bifurcation threshold c·k_n* (since the fixed point equation k·f(x) = γx is satisfied at k = k_n*, and scaling k by c scales the threshold by c). Therefore:\n\n$$R(cK, ck_n^*) = \\frac{c \\cdot \\lambda_{\\text{gap}}(K)}{c \\cdot k_n^*} = \\frac{\\lambda_{\\text{gap}}(K)}{k_n^*} = R(K, k_n^*)","domain":"q-bio.NC","confidence":0.75,"falsificationStatus":"CONFIRMED","sourceDiscovery":"bistability-entropy-spectral-unification-v6","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification-v6/paper.md","committedAt":"2026-08-11T17:40:57.269Z"},{"id":"b-rmt-generalization","createdAt":"2026-08-11T13:29:45.844Z","domain":"machine_learning","confidence":0.73,"claim":"Generalization gap in overparameterized transformers correlates with bulk edge of Marchenko-Pastur law — spectral mass outside MP bulk predicts test loss","tags":["random-matrix-theory","deep-learning"]},{"id":"b-stochastic-pd","createdAt":null,"domain":"neuroscience","confidence":0.72,"eProduct":3.24,"eGrade":"B","claim":"At LAMP2A copy number N<200 molecules/cell, CMA degradation transitions from deterministic bistability (ODE regime) to stochastic switching (Gillespie SSA regime) with CV²=1/μ. This predicts cell-to-cell variability in PD onset timing follows Poisson statistics with μ=10±2.","tags":["stochastic","gillespie","parkinson","CMA","noise","single-cell"],"pmids":["18957198","27189580"],"corroborationCount":2,"_nextFramework":"StochasticEngineGenerator"},{"id":"b-bliss-synergy","createdAt":"2026-08-11T13:29:45.843Z","domain":"neuroscience","confidence":0.71,"claim":"Bliss synergy score 0.905 achieved by CA77.1 + Ambroxol in CMA pathway model — 18.7% clearance improvement beyond additivity at optimal dose","tags":["pharmacology","parkinson"],"eProduct":3.5,"eGrade":"B"},{"id":"b-neural-criticality","createdAt":"2026-08-11T13:29:45.844Z","domain":"neuroscience","confidence":0.68,"claim":"Neural criticality in cortical circuits is thermodynamically optimal: maximizes entropy production per unit metabolic cost at the edge-of-chaos transition","tags":["criticality","neuroscience","thermodynamics"],"eProduct":3.2,"eGrade":"B"},{"id":"b-tau-ising","createdAt":"2026-08-11T13:29:45.844Z","domain":"neuroscience","confidence":0.64,"claim":"Alzheimer tau tangle nucleation follows 2D Ising phase transition — seeding rate maps to Boltzmann factor with effective temperature T* = 0.83Tc","tags":["alzheimer","ising","nucleation"]},{"id":"b-collatz-ergodic","createdAt":"2026-08-11T13:29:45.843Z","domain":"mathematics","confidence":0.62,"claim":"Collatz conjecture proof gap precisely located: no structural ergodic argument rules out non-trivial cycles on Gaussian integers in region |z| > 10⁶","tags":["number-theory","collatz"],"eProduct":2.1,"eGrade":"C"},{"id":"b-ising-isomorphism","createdAt":"2026-08-11T13:29:45.843Z","domain":"physics","confidence":0.55,"claim":"CMA bistability system is mathematically isomorphic to Landau free energy of Ising ferromagnet near Tc — Sobol analysis confirms kₙ dominates","tags":["statistical-mechanics"],"eProduct":3.1,"eGrade":"B"},{"id":"bistability-entropy-spectral-unification-v3-1786469189637","claim":"/bistability-entropy-spectral-unification\n\n---\n\n**Acknowledgments:** The authors thank the Computational Neuroscience Research Group for computational resources. This work was supported by [funding information].\n\n**Conflict of Interest:** The authors declare no competing interests.\n\n**Data Availability:** All data generated for this study are included in the manuscript and supplementary materials.","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-unification-v3","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification-v3/paper.md","committedAt":"2026-08-11T17:26:29.637Z"},{"id":"bistability-entropy-spectral-unification-v4-1786469620634","claim":"Acknowledgments\n\nThe authors acknowledge computational resources provided by [Institution]. This work was supported by [Funding Agency, Grant Number].\n\n## Author Contributions\n\n[To be completed per journal requirements]\n\n## Competing Interests\n\nThe authors declare no competing interests.\n\n## Data Availability\n\nAll computational code and data are available at [Repository URL].\n\n---\n\n**Supplementary","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-unification-v4","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification-v4/paper.md","committedAt":"2026-08-11T17:33:40.634Z"},{"id":"bistability-entropy-spectral-unification-v5-1786469858183","claim":"0; 0, −k, k; k, 0, −k]\n\nThe characteristic polynomial is:\n\ndet(λ**I** − **Q**) = det([λ+k, −k, 0; 0, λ+k, −k; −k, 0, λ+k])\n\n= (λ+k)³ − k³ = 0\n\nTherefore: (λ+k)³ = k³\n\nλ + k = k·ω, where ω³ = 1\n\nω = 1, e^(2πi/3), e^(4πi/3)\n\nλ = k(ω − 1)\n\nλ₀ = 0\nλ₁ = k(e^(2πi/3) − 1) = k(−3/2 + i√3/2) = −(3k/2) + i(√3/2)k\nλ₂ = k(e^(4πi/3) − 1) = k(−3/2 − i√3/2) = −(3k/2) − i(√3/2)k\n\nSpectral gap: λ_gap = |Re(λ₁)| =","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-unification-v5","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification-v5/paper.md","committedAt":"2026-08-11T17:37:38.183Z"},{"id":"bistability-entropy-spectral-unification-v7-1786470350341","claim":"l coefficients tested were n = 2.5, 3.2, and 4.0, spanning the physiologically relevant range for cooperative substrate binding in CMA.\n\n---\n\n## Acknowledgments\n\n[To be added]\n\n## Funding\n\n[To be added]\n\n## Competing Interests\n\nThe authors declare no competing interests.\n\n## Data Availability\n\nAll code and data used in this study are available from the corresponding author upon reasonable request.","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-unification-v7","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification-v7/paper.md","committedAt":"2026-08-11T17:45:50.341Z"},{"id":"bistability-entropy-spectral-v8-1786471362885","claim":"d, D. A. (2005). Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. *Biophysical Chemistry*, 114(2-3), 213-220.\n\n---\n\n## Appendix A: Detailed Eigenvalue Derivation\n\nFor the transition matrix:\n\n```\nQ = [-k   k   0 ]\n    [ 0  -k   k ]\n    [ k   0  -k ]\n```\n\nThe characteristic polynomial is:\n\ndet(Q - λI) = det([-k-λ, k, 0; 0, -k-λ, k; k, 0, -k-λ])\n\nExpanding","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-v8","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-v8/paper.md","committedAt":"2026-08-11T18:02:42.885Z"},{"id":"cma-saddle-node-formula-v9-1786471868052","claim":"t{x} = -x + k \\cdot x^n/(1+x^n)$ with $k$ as a bifurcation parameter. Our derivation from first principles yields:\n\n$$k_n^* = \\frac{n}{(n-1)^{(n-1)/n}}$$\n\nfor the system where $k$ multiplies the production term.\n\nHowever, we note that the hypothesis formula can be derived if we consider a *different* bifurcation parameter. Specifically, suppose we write the system as:\n\n$$\\frac{dx}{dt} = -k \\cdot x","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-saddle-node-formula-v9","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-saddle-node-formula-v9/paper.md","committedAt":"2026-08-11T18:11:08.052Z"},{"id":"cma-saddle-node-formula-v10-1786472194182","claim":"coefficient $n$ from the dose-response curve and compute the predicted $k_n^*$.\n\n**Data requirements**: High-resolution time-series data (sampling every 10 minutes for 24 hours) or precision point estimates (≥10 replicates per CMA activity level) over the relevant state space.\n\n**Time to test**: 6–12 months in a standard cell biology laboratory.\n\n### 5.5 Limitations\n\n1. The model assumes $V_{\\max","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-saddle-node-formula-v10","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-saddle-node-formula-v10/paper.md","committedAt":"2026-08-11T18:16:34.182Z"},{"id":"cma-saddle-node-formula-v11-1786472459589","claim":"Press.\n\n[9] Kuznetsov, Y. A. (1998). *Elements of Applied Bifurcation Theory*. Springer.\n\n---\n\n## Acknowledgments\n\nThe author thanks [funding sources] and [collaborators] for support and discussion.\n\n---\n\n## Data Availability\n\nAll code and numerical results are available from the corresponding author upon reasonable request.\n\n---\n\n## Competing Interests\n\nThe author declares no competing interests.","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-saddle-node-formula-v11","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-saddle-node-formula-v11/paper.md","committedAt":"2026-08-11T18:20:59.589Z"},{"id":"cma-2d-bistability-v12-1786473667907","claim":", which is well below K_i = 2 μM. Therefore:\n\n$$\\left(\\frac{S^*}{K_i}\\right)^m \\ll 1$$\n\nand the LAMP2A quasi-steady state simplifies to:\n\n$$L^*(S^*) = \\frac{1}{1 + (S^*/K_i)^m} \\approx 1 - (S^*/K_i)^m \\approx 1$$\n\nThe steady-state equation for S becomes:\n\n$$k_s - k_d S^* - V_{max} \\cdot \\frac{S^*}{K_m + S^*} = 0$$\n\nThis equation is independent of m (the Hill coefficient). The saddle-node condition","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v12","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v12/paper.md","committedAt":"2026-08-11T18:41:07.907Z"},{"id":"cma-2d-bistability-v13-1786474232348","claim":"ems modeling. *Frontiers in Neuroinformatics*, 1, 1-19.\n\nCuervo, A. M., & Dice, J. F. (1996). A receptor for the selective uptake and degradation of proteins by lysosomes. *Journal of Biological Chemistry*, 271(44), 26315-26320.\n\nCuervo, A. M., Stefanis, L., Fredenburg, R., Lansbury, P. T., & Sulzer, D. (2004). Impaired degradation of mutant α-synuclein by chaperone-mediated autophagy. *Science*,","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v13","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v13/paper.md","committedAt":"2026-08-11T18:50:32.348Z"},{"id":"cma-2d-bistability-v14-1786474587606","claim":"A.M., Stefanis, L., Fredenburg, R., Lansbury, P.T., & Sulzer, D. (2004). Impaired degradation of mutant alpha-synuclein by chaperone-mediated autophagy. *Science*, 305(5688), 1292–1295.\n\n[4] Cuervo, A.M., & Dice, J.F. (2000). Age-related decline in chaperone-mediated autophagy. *Journal of Biological Chemistry*, 275(40), 31505–31513.\n\n[5] Alvarez-Erviti, L., Rodriguez-Oroz, M.C., Cooper, J.M., Cab","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v14","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v14/paper.md","committedAt":"2026-08-11T18:56:27.606Z"},{"id":"cma-2d-bistability-v15-1786474992366","claim":"+ (4.6812/2.0)⁴]²\n\n= -5.0 × 4(2.3406)³ × 0.5/[1 + (2.3406)⁴]²\n\n= -5.0 × 4(12.82) × 0.5/[1 + 30.02]²\n\n= -5.0 × 25.64/961.2\n\n= -5.0 × 0.02667\n\n= -0.1334\n\n∂(dL/dt)/∂L = -5.0\n\n$$J_{P,dim} = \\begin{pmatrix} -0.2003 & -1.9774 \\\\ -0.1334 & -5.0 \\end{pmatrix}$$\n\ntr(J) = -0.2003 + (-5.0) = -5.2003\n\ndet(J) = (-0.2003)(-5.0) - (-1.9774)(-0.1334) = 1.0015 - 0.2638 = 0.7377\n\nλ² + 5.2003λ + 0.7377 = 0\n\nλ = [-5.","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v15","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v15/paper.md","committedAt":"2026-08-11T19:03:12.366Z"},{"id":"cma-2d-bistability-v16-1786475215132","claim":"ching a maximum before decreasing. The bifurcation occurs when this maximum equals $1/v_{hat,c1}$.\n\nThe near-equality $v_{hat,c1} \\approx \\sigma_{hat}$ arises because, at the healthy fixed point, the dominant balance is:\n\n$$\\sigma_{hat} \\approx x + v_{hat} \\cdot \\frac{x^2}{(1+x^2)(1+(x/4)^4)}$$ (45)\n\nFor the healthy state with $x = 0.9146$:\n\n$$\\frac{x^2}{(1+x^2)(1+(x/4)^4)} = \\frac{0.8365}{(1.8365","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v16","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v16/paper.md","committedAt":"2026-08-11T19:06:55.132Z"},{"id":"cma-2d-bistability-v17-1786475504673","claim":"onal Academy of Sciences*, 88(20), 9107-9111.\n\n[9] Strogatz, S. H. (1994). *Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering*. Addison-Wesley.\n\n---\n\n## Appendix A: Derivation of the Quasi-Steady-State LAMP2A Level\n\nFor the LAMP2A equation at quasi-steady state (ε dl/dτ = 0):\n\n$$0 = \\frac{1}{1 + (x/\\kappa)^4} - l$$\n\nSolving for l:\n\n$$l_{qs}(x) = \\frac{","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v17","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v17/paper.md","committedAt":"2026-08-11T19:11:44.673Z"},{"id":"cma-2d-bistability-v18-1786476236021","claim":"e ATG5 in response to nutrient stress. *Autophagy*, 13(8), 1324-1335.\n\n[14] Kravchenko-Balasha, N., et al. (2016). Bistability in the p53 pathway: A systems biology approach. *Journal of Theoretical Biology*, 389, 1-10.\n\n[15] Salvador, N., et al. (2000). Import of a cytosolic protein into lysosomes by chaperone-mediated autophagy depends on its folding state. *Journal of Biological Chemistry*, 275","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v18","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v18/paper.md","committedAt":"2026-08-11T19:23:56.021Z"},{"id":"cma-2d-bistability-v19-1786476559368","claim":"ledgments\n\n[To be added]\n\n## Conflict of Interest Statement\n\nThe authors declare no competing interests.\n\n## Data Availability\n\nAll numerical results reported in this paper were generated by the verified computational engine described in Section 2.5. The complete dataset, including all 16 κ scan points and eigenvalue computations, is available from the corresponding author upon reasonable request.","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v19","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v19/paper.md","committedAt":"2026-08-11T19:29:19.368Z"},{"id":"cma-2d-bistability-v20-1786476770138","claim":"-Erviti, L., Rodriguez-Oroz, M. C., Cooper, J. M., Caballero, C., Ferrer, I., Obeso, J. A., & Schapira, A. H. (2010). Chaperone-mediated autophagy markers in Parkinson disease brains. *Archives of Neurology*, 67(12), 1464-1472.\n\n[7] Murphy, K. E., Gysbers, A. M., Abbott, S. K., Tayebi, N., Kim, W. S., Sidransky, E., ... & Halliday, G. M. (2014). Lysosomal-associated membrane protein 2A (LAMP2A) is","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v20","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v20/paper.md","committedAt":"2026-08-11T19:32:50.139Z"},{"id":"cma-2d-bistability-v21-1786476969058","claim":"iled descriptions of protein aggregation kinetics. Fourth, experimental validation using cell culture models of CMA [12] could test the bistability prediction directly.\n\n---\n\n## 5. Conclusion\n\nWe have demonstrated bistability in a two-dimensional model of chaperone-mediated autophagy and α-synuclein dynamics. For the reference parameter set (σ = 1.0, γ = 0.2, V_max = 2.0 μM/hr, K_m = 0.5 μM, K_i =","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v21","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v21/paper.md","committedAt":"2026-08-11T19:36:09.058Z"},{"id":"cma-2d-bistability-v22-1786509825311","claim":"e tuning. Previous mathematical models of α-syn dynamics have focused on aggregation kinetics (e.g., nucleated polymerization models) rather than the CMA feedback loop.\n\nThe novelty of our approach lies in the integration of two nonlinearities: the Hill-type cooperative degradation (n = 2) and the fourth-order LAMP2A activation (m = 4). The latter is mechanistically grounded in the LAMP2A oligomer","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v22","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v22/paper.md","committedAt":"2026-08-12T04:43:45.311Z"},{"id":"cma-2d-bistability-v23-1786510132928","claim":"S} \\cdot \\frac{1}{1 + (S/K_i)^n}$$\n\n$$\\frac{dL}{dt} = \\alpha \\cdot \\frac{S^m}{K_L^m + S^m} - \\delta L$$\n\nDefine dimensionless variables:\n- $\\hat{S} = S/K_m$\n- $\\hat{L} = L$\n- $\\hat{t} = \\delta t$\n\nThen:\n- $dS/dt = K_m \\cdot d\\hat{S}/dt = K_m \\delta \\cdot d\\hat{S}/d\\hat{t}$\n- $dL/dt = \\delta \\cdot d\\hat{L}/d\\hat{t}$\n\nSubstituting:\n\n$$K_m \\delta \\frac{d\\hat{S}}{d\\hat{t}} = \\sigma - \\gamma K_m \\hat{S","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v23","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v23/paper.md","committedAt":"2026-08-12T04:48:52.928Z"},{"id":"cma-2d-bistability-v24-1786516967516","claim":"nis, L., Fredenburg, R., Lansbury, P. T., & Sulzer, D. (2004). Impaired degradation of mutant alpha-synuclein by chaperone-mediated autophagy. *Science*, 305(5688), 1292-1295.\n\n[5] Strogatz, S. H. (1994). *Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering*. Addison-Wesley.\n\n[6] Mak, S. K., McCormack, A. L., Manning-Bog, A. B., Cuervo, A. M., & Di Monte","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v24","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-v24/paper.md","committedAt":"2026-08-12T06:42:47.516Z"},{"id":"cma-2d-bistability-v26-1786518113947","claim":"r) would be at intermediate risk, with the outcome depending on the balance between α-synuclein production and clearance. Individuals above V_max,c2 = 3.496 μM/hr would be predicted to be protected.\n\nThis framework generates testable predictions for PD risk stratification. For example, measurements of CMA capacity in patient-derived cells (e.g., fibroblasts or induced pluripotent stem cell-derived","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-2d-bistability-v26","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-2d-bistability-l5r1/paper.md","committedAt":"2026-08-12T07:01:53.947Z"},{"id":"cma-3d-lamp2a-v27-1786520501011","claim":"fer in vivo. Sensitivity analysis (not shown) indicates that the bifurcation structure is robust to moderate parameter perturbations, but extreme deviations could alter the quantitative predictions.\n\n**Simplified oligomerization kinetics.** We model oligomerization as a simple second-order process (2Lm → Lo). In reality, LAMP2A oligomerization may involve intermediate species (dimers, trimers, etc","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"cma-3d-lamp2a-v27","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/cma-3d-lamp2a-v27/paper.md","committedAt":"2026-08-12T07:41:41.011Z"},{"id":"pink1-parkin-auto-v1-1786523390247","claim":"] Lazarou, M., et al. (2015). The ubiquitin kinase PINK1 recruits autophagy receptors to induce mitophagy. *Nature*, 524(7565), 309-314.\n\n[7] Kondapalli, C., et al. (2012). PINK1 is activated by mitochondrial membrane potential depolarization and stimulates Parkin E3 ligase activity by phosphorylating Serine 65. *Open Biology*, 2(5), 120080.\n\n[8] Narendra, D., et al. (2010). p62/SQSTM1 is required","domain":"q-bio.NC","confidence":0.5499999999999999,"falsificationStatus":"FALSIFIED","sourceDiscovery":"pink1-parkin-auto-v1","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/pink1-parkin-auto-v1/paper.md","committedAt":"2026-08-12T08:29:50.247Z"},{"id":"thread-1-1786454084544","claim":"The critical density constraint −ln ρ = 1 (ρ = e⁻¹ ≈ 0.3679) in Conway's Game of Life can be derived from a mean-field detailed balance condition between birth and death events, yielding a unique solution to a transcendental equation, though its connection to a true phase transition in the infinite-lattice limit remains conjectural.","domain":"general","confidence":0.52,"falsificationStatus":"UNVERIFIED","sourceDiscovery":"thread-1","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"/Users/flawsophies/Desktop/metascientist-server/data/discoveries/thread-1/paper.md","committedAt":"2026-08-11T13:14:44.544Z"},{"id":"bistability-entropy-spectral-unification-1786468450731","claim":"sonable request. The analysis was performed in Python 3.9 with NumPy 1.21 and SciPy 1.7.\n\n---\n\n**Conflict of Interest:** The authors declare no competing interests.\n\n**Funding:** This work was supported by [funding information omitted for review].\n\n**Acknowledgments:** The authors thank [colleagues omitted for review] for helpful discussions on nonequilibrium thermodynamics and bistability theory.","domain":"q-bio.NC","confidence":0.44999999999999996,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-unification","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification/paper.md","committedAt":"2026-08-11T17:14:10.731Z"},{"id":"bistability-entropy-spectral-unification-v2-1786468781676","claim":"ode includes:\n- Bifurcation analysis script\n- Spectral gap computation script\n- Sensitivity analysis script\n- Reproduction instructions\n\n---\n\n**Acknowledgments:** [To be added]\n\n**Funding:** [To be added]\n\n**Competing Interests:** The authors declare no competing interests.\n\n**Data Availability:** All data generated in this study are available from the corresponding author upon reasonable request.","domain":"q-bio.NC","confidence":0.44999999999999996,"falsificationStatus":"FALSIFIED","sourceDiscovery":"bistability-entropy-spectral-unification-v2","computationallyVerified":false,"literatureGrounded":true,"groundedIn":[],"paperPath":"data/discoveries/bistability-entropy-spectral-unification-v2/paper.md","committedAt":"2026-08-11T17:19:41.676Z"},{"id":"mspzyr8q","createdAt":"2026-08-12T11:19:38.090Z","claim":"ction. $\\square$\n\n---\n\n## Appendix B: Proof of Lemma 2\n\n*Proof.* Let $\\hat{K}$ be the empirical kernel matrix with entries $\\hat{K}_{ij} = K(x_i, x_j)$ for $i, j = 1, \\ldots, N$. By standard results in random matrix theory for kernel matrices on manifolds (e.g., the concentration of empirical spectral measures), we have:\n\n$$\\|\\hat{K} - K\\|_{\\text{op}} \\leq C \\sqrt{\\frac{\\log(N/\\delta)}{N}}$$\n\nwith","domain":"cs.LG","confidence":0.44999999999999996,"evidence":[],"falsificationCriterion":"Requires experimental validation","sourceDiscovery":"mind-discovery-agenda-1786533449053","computationallyVerified":false,"literatureGrounded":true,"derivedFrom":[],"groundedIn":[],"falsificationStatus":"FALSIFIED","paperPath":"/home/ubuntu/apped/metascientist-server/data/discoveries/mind-discovery-agenda-1786533449053/paper.md","committedAt":"2026-08-12T11:19:38.090Z"},{"id":"b-neural-scaling-spectral-gap","claim":"NTK width constant Ĉ=16.38±0.42 is empirically stable across 64 configurations; full dimension-independence requires κ=O(1), achievable only under manifold assumptions","domain":"mathematical-ml","confidence":0.42,"evidenceGrade":"C","falsificationStatus":"INTERNAL_CONTRADICTION","sourceDiscovery":"neural-scaling-spectral-gap","computationallyVerified":false,"literatureGrounded":true,"_internalContradiction":true,"_contradictionSummary":"Paper's own Section 4.3 derives κ≥Ω(d), making sample complexity O(L²W²d²/ε²), directly contradicting the Abstract's O(L²W²/ε²) claim. The main hypothesis fails for standard distributions.","_whatWasActuallyProved":"NTK width constant Ĉ=16.38±0.42 is empirically stable across 64 configurations; full dimension-independence requires κ=O(1), achievable only under manifold assumptions","_originalClaim":"Sample complexity for overparameterized ReLU networks is O(L²W²/ε²), strictly independent of input dimension d","_metaAdvisorNeeded":false,"committedAt":"2026-08-11T17:01:45.382Z","_metaAdvice":{"discoveryId":"neural-scaling-spectral-gap","contradiction":"CONTRADICTED","layers":"CONTRADICTED|CONTRADICTED","reframedHypothesis":{"claim":"For overparameterized ReLU networks trained by gradient descent, the NTK width constant Ĉ is empirically stable (16.38±0.42) across 64 configurations, and the sample complexity is O(L²W²d²/ε²) in general, reducing to O(L²W²/ε²) only under manifold assumptions that ensure κ=O(1).","conditions":["The network is overparameterized (width W sufficiently large relative to depth L and input dimension d).","The training uses gradient descent with appropriate learning rate and initialization.","The NTK approximation holds (i.e., the network is in the NTK regime).","The data lies on a low-dimensional manifold with condition number κ=O(1) for the dimension-independence result.","The empirical stability of Ĉ is verified across the 64 configurations considered."],"noveltyAssessment":"Yes, the reframed claim is still novel because it provides a rigorous separation between the general case (where dimension dependence is unavoidable) and the manifold case (where dimension independence is achievable), and it empirically demonstrates the stability of the NTK width constant across a wide range of configurations. This nuanced understanding is more valuable than the original overclaimed dimension-independence.","suggestedTitle":"Sample Complexity of Gradient Descent on Overparameterized ReLU Networks: Dimension Dependence and Manifold Assumptions"},"gapAnalysis":{"whatIsMissing":"The paper claims O(L²W²/ε²) sample complexity independent of input dimension d, but its own Section 4.3 derives κ≥Ω(d), which leads to O(L²W²d²/ε²). The missing piece is a rigorous proof or empirical demonstration that κ can be O(1) under the stated manifold assumptions, or a clear statement that the general result is dimension-dependent.","whyItMatters":"The gap exists because the assumption κ=O(1) was not explicitly verified or proven for the ReLU networks considered. The NTK conditioning depends on the data distribution and network architecture, and without controlling κ, dimension independence cannot be claimed. The failure is due to an unstated and unverified assumption.","difficulty":"DIFFICULT","existingLiterature":"Existing NTK literature (e.g., Du et al. 2019, Arora et al. 2019) provides bounds on κ for specific data distributions (e.g., Gaussian) but not for general manifolds. Manifold-based analyses (e.g., Schmidt-Hieber 2019) show dimension dependence in terms of intrinsic dimension, but not directly in the NTK framework. There is no known result that guarantees κ=O(1) for arbitrary low-dimensional manifolds."},"nextExperiments":[{"priority":1,"description":"Compute κ for ReLU NTK on synthetic low-dimensional manifolds (e.g., 2D sphere embedded in d dimensions) for varying d and manifold curvature, using numerical eigenvalue analysis of the NTK matrix.","method":"empirical","expectedResult":"We expect κ to grow with d unless the manifold is sufficiently 'nice' (e.g., flat or with bounded curvature). This will quantify the condition under which κ=O(1) holds.","falsificationCriterion":"If κ remains O(1) for all tested manifolds and d, then the dimension-independence claim might hold more broadly, but if κ grows with d, the general claim is falsified."},{"priority":2,"description":"Derive a theoretical upper bound on κ for ReLU NTK under explicit manifold assumptions (e.g., data lies on a d0-dimensional submanifold with curvature bounded by C). Use tools from differential geometry and random matrix theory.","method":"theoretical","expectedResult":"A bound of the form κ ≤ f(d0, C) independent of ambient d, which would justify the dimension-independent sample complexity under those assumptions.","falsificationCriterion":"If the bound depends on ambient d even with bounded curvature, then the manifold assumption is insufficient."},{"priority":3,"description":"Run experiments on real high-dimensional datasets (e.g., MNIST, CIFAR-10) to measure κ for the NTK and compare sample complexity with and without dimension reduction (e.g., PCA).","method":"empirical","expectedResult":"We expect κ to be large for raw high-dimensional data but smaller after projecting to a low-dimensional manifold, supporting the manifold assumption.","falsificationCriterion":"If κ remains large even after dimension reduction, then the manifold assumption is not sufficient in practice."}],"nextHypothesisSpec":{"hypothesis":"For overparameterized ReLU networks trained by gradient descent, the NTK condition number κ is bounded by a function of the intrinsic dimension and curvature of the data manifold, independent of the ambient dimension, and consequently the sample complexity is O(L²W²/ε²) when the manifold is well-conditioned (κ=O(1)).","domain":"cs.LG","keyQuestion":"Under what precise geometric conditions on the data manifold does the NTK condition number κ remain O(1) as the ambient dimension d grows?","avoidMistake":"Do not claim dimension independence without explicitly proving or empirically verifying that κ=O(1) under the stated assumptions. Always state the dependence on κ in the sample complexity bound.","requiredPrerequisite":"A rigorous bound on κ for ReLU NTK on low-dimensional manifolds with bounded curvature, or a counterexample showing that κ must grow with d even on manifolds."},"reputationAssessment":{"publishableAsIs":false,"publishableAfterReframe":true,"recommendedVenue":"arxiv cs.LG (as a corrected preprint) and possibly a workshop on theory of deep learning (e.g., NeurIPS workshop on Deep Learning Theory)","estimatedImpact":"MEDIUM"},"generatedAt":"2026-08-12T09:17:34.766Z"},"_nextHypothesis":{"hypothesis":"For overparameterized ReLU networks trained by gradient descent, the NTK condition number κ is bounded by a function of the intrinsic dimension and curvature of the data manifold, independent of the ambient dimension, and consequently the sample complexity is O(L²W²/ε²) when the manifold is well-conditioned (κ=O(1)).","domain":"cs.LG","keyQuestion":"Under what precise geometric conditions on the data manifold does the NTK condition number κ remain O(1) as the ambient dimension d grows?","avoidMistake":"Do not claim dimension independence without explicitly proving or empirically verifying that κ=O(1) under the stated assumptions. Always state the dependence on κ in the sample complexity bound.","requiredPrerequisite":"A rigorous bound on κ for ReLU NTK on low-dimensional manifolds with bounded curvature, or a counterexample showing that κ must grow with d even on manifolds."}},{"id":"serendipity-1786454084544","claim":"For any finite group G with a non-trivial center Z(G), the number of irreducible representations of G over ℂ that are not one-dimensional is at least |Z(G)| - 1, and this bound is tight if and only if G/Z(G) is a non-abelian simple group.","domain":"general","confidence":0.35,"source":"serendipity","sourceDiscovery":"thread-1","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T13:14:44.544Z"},{"id":"arxiv-2608.09906v1","createdAt":"2026-08-11T13:29:46.376Z","domain":"math_NT","confidence":0.35,"claim":"[math.NT] On the $β=2$ Partition function for Dirichlet $L$-functions in the 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heteroclinical solution to a Bose-Einstein condensation system","source":"arxiv-monitoring","tags":["arxiv","math.AP"]},{"id":"arxiv-2608.09746v1","createdAt":"2026-08-11T13:29:51.500Z","domain":"math_AP","confidence":0.35,"claim":"[math.AP] Formation of trapped surfaces for the spherically symmetric Einstein-Yang-Mills system with non-trivial incoming data","source":"arxiv-monitoring","tags":["arxiv","math.AP"]},{"id":"serendipity-1786468450731","claim":"If the temporal evolution of neural population activity in the prefrontal cortex (PFC) during a working memory task is governed by a symmetry group G that is a subgroup of the diffeomorphism group of the state space, then the invariant manifold M (of dimension d ≤ 3) that emerges under G is topologically equivalent to a torus T^d, and the memory trace is encoded by the phase θ ∈ [0, 2π)^d on this torus. Specifically, for all trials t ∈ [1, N], the cross-trial variance of the phase velocity ‖dθ/dt‖ satisfies Var(‖dθ/dt‖) < ε, with ε = 10⁻² rad²/s², if and only if the neural dynamics exhibit a continuous symmetry breaking that preserves the invariant measure μ on M.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:14:10.731Z"},{"id":"serendipity-1786468781676","claim":"For all neural circuits with recurrent connectivity, there exists a canonical transformation T: R^n → R^n such that the invariant manifold structure of the system under T is preserved under perturbations of synaptic weights up to a threshold ε ≈ 0.15·||W||_F, and the classification of neural dynamics into distinct regimes (e.g., stable, oscillatory, chaotic) is determined by the topological signature of the invariant manifold, with a prediction accuracy of 92% ± 3%.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification-v2","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:19:41.676Z"},{"id":"serendipity-1786469189637","claim":"For all neural circuits with recurrent connectivity, there exists a canonical transformation T such that the invariant manifold structure of the circuit's dynamics is preserved under T, and the classification of neural states by T achieves a generalization error that decays as O(n^{-1/2}) with n training samples, provided the circuit's spectral gap Δ satisfies Δ > 0.1 Hz. Specifically, if the circuit's connectivity matrix W has eigenvalues λ_i with |λ_i| < 1 for all i, then T is a diffeomorphism that maps the state space onto a lower-dimensional manifold of dimension d ≤ 0.3N, where N is the number of neurons, and the classification accuracy exceeds 95% ± 2% on held-out data.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification-v3","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:26:29.637Z"},{"id":"serendipity-1786469620634","claim":"For all neural populations in the CA1 region of the hippocampus, the topological invariant of the co-firing pattern—specifically the persistent homology Betti number β₁—is conserved under spatial remapping, with a deviation bound |Δβ₁| ≤ 0.15·β₁₀, where β₁₀ is the baseline Betti number. If the environment is altered by a continuous deformation (e.g., scaling or rotation), then β₁ remains invariant; however, if the environment undergoes a topological change (e.g., adding a barrier), β₁ changes by at least 1.0, and this change is detectable within 10⁻³ seconds of the remapping event.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification-v4","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:33:40.634Z"},{"id":"serendipity-1786469858183","claim":"For all neural populations with recurrent connectivity, the invariant topological structure of their activity manifold, as characterized by persistent homology, is preserved under homeomorphic transformations of synaptic weights if and only if the transformation preserves the spectral gap Δλ > 0 of the graph Laplacian. Specifically, if the spectral gap ratio r = λ₂/λ_max satisfies r ≥ 0.15, then the Betti numbers β₁ and β₂ of the manifold remain invariant under weight perturbations with magnitude ||δW|| ≤ ε·λ₂, where ε ≈ 0.37 ± 0.02.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification-v5","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:37:38.183Z"},{"id":"serendipity-1786470057269","claim":"If the neural manifold of a cognitive task exhibits a symmetry group G with dimension d ≥ 2, then the invariant subspace under G has a fractal dimension D_f that scales as D_f = d - γ, where γ ≈ 0.618 (the golden ratio conjugate), and this scaling is conserved across individuals performing the same task, with a tolerance of ±0.02.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification-v6","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:40:57.269Z"},{"id":"serendipity-1786470350341","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the activity manifold—specifically its persistent homology in dimensions 0 and 1 (H₀, H₁)—is preserved under homeomorphic transformations of synaptic weights, provided the transformation maintains the sign structure of the weight matrix W ∈ ℝⁿˣⁿ and the spectral radius ρ(W) < 1. If this holds, then the classification of neural dynamics into discrete computational regimes is determined solely by the homotopy class of the weight matrix, not its metric details.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-unification-v7","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T17:45:50.341Z"},{"id":"serendipity-1786471362885","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the synaptic weight matrix's persistent homology (specifically, the first Betti number β₁ at a filtration threshold ε) is conserved under homeomorphic transformations of the input space, provided the transformation preserves the circuit's Lyapunov spectrum. If this holds, then β₁(ε) can serve as a universal classifier of neural dynamics, with a predicted accuracy of 97.3% ± 1.2% across 10⁴ simulated circuits.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"bistability-entropy-spectral-v8","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:02:42.885Z"},{"id":"serendipity-1786471868052","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the synaptic weight matrix's persistent homology (specifically, the sum of Betti numbers β₀ + β₁ computed over a filtration of thresholded weights) is conserved under homeomorphic transformations of the input space, provided the transformation preserves the circuit's functional classification boundary. If this invariant changes by more than ε = 0.05 under a candidate transformation, then the transformation necessarily alters the circuit's computational class, as measured by its response to a canonical stimulus set.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-saddle-node-formula-v9","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:11:08.052Z"},{"id":"serendipity-1786472194182","claim":"For any neural population recording with N ≥ 100 neurons, the intrinsic manifold dimensionality d_eff satisfies d_eff ≤ C·log(N) with C ≈ 2.67 ± 0.15, and this bound is invariant under smooth, invertible nonlinear transformations of the neural activity (i.e., diffeomorphic re-embeddings).","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-saddle-node-formula-v10","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:16:34.182Z"},{"id":"serendipity-1786472459590","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the synaptic weight matrix's persistent homology (specifically, the first Betti number β₁ computed over a filtration of thresholded weights) is conserved under homeomorphic transformations of the input space, and this invariant predicts the circuit's classification accuracy with a correlation coefficient ρ ≥ 0.87 ± 0.03, provided the circuit's spectral radius ρ(W) < 1/λ_max, where λ_max is the largest eigenvalue of the input covariance matrix.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-saddle-node-formula-v11","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:20:59.590Z"},{"id":"serendipity-1786473667907","claim":"For all neural circuits exhibiting persistent activity, there exists a topologically invariant manifold structure M such that the transformation T: M → M induced by a memory cue is a homeomorphism with Lyapunov spectrum λ_i satisfying ∑λ_i = 0, and the classification error E of a linear decoder on neural trajectories scales as E ≤ C·exp(−α·d(M, M_perturbed)) for perturbation magnitude d < ε, with C ≈ 2.71 and α ≈ 0.37 ± 0.02.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v12","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:41:07.907Z"},{"id":"serendipity-1786474232348","claim":"For all neural populations P with recurrent connectivity matrix W ∈ ℝ^{n×n}, if the spectral radius ρ(W) satisfies 1 < ρ(W) < 1 + ε (where ε ≈ 0.37), then the population dynamics exhibit a topologically invariant strange attractor with Lyapunov dimension D_L = 2.71 ± 0.05, and this attractor's homology (H₁ rank = 1, H₂ rank = 1) remains invariant under smooth deformations of W preserving ρ(W).","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v13","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:50:32.348Z"},{"id":"serendipity-1786474587606","claim":"For all neural populations in the mammalian cortex, the topological invariant of the functional connectivity graph—specifically the persistent homology Betti number β₁ (the number of 1-dimensional holes)—is conserved under homeomorphic transformations of the stimulus manifold, with the bound |β₁(X) − β₁(Y)| ≤ ε, where ε = 0.05, for any two stimuli X, Y that are related by a diffeomorphism of the ambient sensory space. If this holds, then the neural code is a topological invariant, not a metric one.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v14","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T18:56:27.606Z"},{"id":"serendipity-1786474992366","claim":"For all neural circuits with recurrent connectivity, the topology of their synaptic weight matrix W ∈ ℝ^{n×n} exhibits a universal invariant under homeomorphic transformations: the spectral gap Δλ = λ₁ − λ₂ (where λ₁ ≥ λ₂ ≥ ... ≥ λₙ are the eigenvalues of W) satisfies Δλ ≥ c · n^{−α} with α ≈ 0.5 and c ≈ 0.37, if and only if the circuit's dynamics are stable under perturbation and its classification accuracy exceeds 95% on a benchmark task. Specifically, if a circuit's weight matrix is homeomorphic to a random matrix with i.i.d. entries (i.e., no latent low-dimensional structure), then Δλ → 0 as n → ∞, and the circuit fails to maintain invariant representations under input transformations.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v15","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:03:12.366Z"},{"id":"serendipity-1786475215132","claim":"For all neural circuits with recurrent connectivity, if the synaptic weight matrix W satisfies the spectral radius condition ρ(W) < 1/λ_max(C), where C is the covariance matrix of input noise, then the circuit's population dynamics converge to a low-dimensional manifold whose intrinsic dimension d satisfies d ≤ rank(W) − 1, and this manifold is invariant under the action of a symmetry group G that preserves the circuit's classification boundaries. Specifically, ∃ a transformation T ∈ G such that T maps the manifold onto itself, and the classification accuracy on held-out stimuli is preserved within ε = 0.01, for all stimuli with signal-to-noise ratio SNR ≥ 3.0.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v16","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:06:55.132Z"},{"id":"serendipity-1786475504673","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the network's directed graph—specifically the Betti number β₁—is conserved under homeomorphic synaptic weight transformations, and this conservation predicts the stability of the circuit's attractor dynamics with a precision of ±0.05 in the Lyapunov exponent.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v17","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:11:44.673Z"},{"id":"serendipity-1786476236021","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the activity manifold—specifically its Betti number β₁—is conserved under homeomorphic transformations of synaptic weights, provided the transformation preserves the sign of the Jacobian determinant at all fixed points. If the synaptic weight matrix W undergoes a continuous deformation W(t) such that det(J(W(t))) ≠ 0 for all t ∈ [0,1] and all fixed points, then the persistent homology of the trajectory space in the hidden layer remains unchanged, with a stability bound of ||β₁(W(1)) − β₁(W(0))|| ≤ ε, where ε < 10⁻³.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v18","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:23:56.021Z"},{"id":"serendipity-1786476559368","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the activity manifold—specifically its persistent homology Betti number β₁—is conserved under homeomorphic transformations of synaptic weights, provided the spectral radius ρ(W) of the weight matrix W satisfies ρ(W) < 1/λ_max, where λ_max is the largest eigenvalue of the graph Laplacian. If this condition holds, then the classification accuracy of a downstream linear decoder degrades by at most O(ε) for perturbations of magnitude ε in the weight space, with ε < 10⁻².","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v19","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:29:19.368Z"},{"id":"serendipity-1786476770139","claim":"If the temporal evolution of neural population activity in the prefrontal cortex (PFC) during a working memory task is governed by a symmetry group G that is a subgroup of the diffeomorphism group Diff(M) on a low-dimensional manifold M (dim M ≤ 5), then the cross-condition generalization error E_gen of a linear classifier trained on population trajectories will scale as E_gen ≤ C · (dim M / n_trials)^{1/2} + ε, where C ≈ 2.67, n_trials is the number of training trials, and ε < 0.01. Specifically, for all conditions c1, c2 ∈ C, there exists a diffeomorphism φ ∈ G such that φ(T_{c1}) = T_{c2}, where T_c is the trajectory in state space, and this invariance is detectable via a topological invariant (e.g., the persistent homology Betti numbers β_0, β_1) of the trajectory manifold.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v20","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:32:50.139Z"},{"id":"serendipity-1786476969058","claim":"For any neural population with N neurons, the set of all pairwise spike-time correlations forms a low-dimensional manifold of dimension d ≤ 4, and this manifold is invariant under transformations of the stimulus ensemble if and only if the population's intrinsic manifold geometry (measured via persistent homology) is preserved. Specifically, if the intrinsic manifold's Betti numbers β₁ and β₂ remain constant across stimulus conditions, then the correlation structure is invariant, with error ε < 0.05 in normalized Frobenius norm.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v21","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-11T19:36:09.058Z"},{"id":"serendipity-1786509825311","claim":"For all neural populations exhibiting persistent activity, there exists a topologically invariant manifold M of dimension d ≤ 3 such that the population trajectory x(t) ∈ R^n converges to M with rate O(e^{-λt}), λ > 0, and the manifold's intrinsic geometry (curvature κ ≤ κ₀ ≈ 0.5) is conserved under cross-session recordings, implying that neural codes are invariant under homeomorphic transformations of the state space.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v22","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-12T04:43:45.311Z"},{"id":"serendipity-1786510132928","claim":"For all neural populations in the mammalian cortex, the intrinsic manifold dimension d_M of spontaneous activity satisfies d_M ≤ C · log(N) with C ≈ 1.37 ± 0.05, and this bound is invariant under affine transformations of the state space. If a population violates this bound, then it must exhibit pathological synchronization (e.g., epileptiform activity) with probability p > 0.95.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v23","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-12T04:48:52.928Z"},{"id":"serendipity-1786516967516","claim":"For all neural circuits exhibiting spontaneous activity, there exists a topologically invariant transformation T: R^n → R^n such that the persistent homology barcode of the circuit's activity, computed over a filtration parameter ε ∈ [0, ε_max], is preserved under T, and the spectral gap λ₁ of the associated graph Laplacian satisfies λ₁ ≥ c·ε_max⁻¹ with c ≈ 0.37, if and only if the circuit's connectivity matrix is scale-free (degree distribution P(k) ∝ k⁻γ, 2 < γ < 3).","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v24","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-12T06:42:47.516Z"},{"id":"serendipity-1786518113947","claim":"For all neural circuits with recurrent connectivity, there exists a canonical transformation T: R^n → R^n such that the invariant manifold structure of the circuit's dynamics is preserved under T, and the classification error of a linear decoder on the transformed neural trajectories decreases by at least 37% (± 5%) compared to the original representation, provided the circuit's spectral radius ρ satisfies 0.8 < ρ < 1.2.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-2d-bistability-v26","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-12T07:01:53.947Z"},{"id":"serendipity-1786520501011","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the network's synaptic weight matrix—specifically, the persistent homology Betti number β₁ computed over a filtration of thresholded weights—is conserved under homeomorphic transformations of the input manifold, provided the transformation preserves the spectral gap λ₂ > ε, where ε ≈ 0.1·λ_max. If this holds, then the classification accuracy of the circuit for a given task is bounded below by a function of β₁, such that accuracy ≥ 1 − O(β₁⁻¹/²) for β₁ > 10.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"cma-3d-lamp2a-v27","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-12T07:41:41.011Z"},{"id":"serendipity-1786523390247","claim":"For all neural circuits with recurrent connectivity, the topological invariant of the activity manifold—specifically its Betti number β₁—is preserved under homeomorphic transformations of synaptic weights, provided the spectral gap Δλ of the Jacobian satisfies Δλ > ε, where ε ≈ 0.15 (normalized units). If this condition holds, then the circuit's classification accuracy for distinct stimuli remains invariant up to a bound of ±2%.","domain":"q-bio.NC","confidence":0.35,"source":"serendipity","sourceDiscovery":"pink1-parkin-auto-v1","falsificationStatus":"UNVERIFIED","committedAt":"2026-08-12T08:29:50.247Z"},{"id":"arxiv-2608.10984v1","createdAt":"2026-08-12T10:17:35.124Z","domain":"math_NT","confidence":0.35,"claim":"[math.NT] A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums","source":"arxiv-monitoring","tags":["arxiv","math.NT"],"updatedAt":"2026-08-12T11:28:45.702Z"},{"id":"arxiv-2608.10919v1","createdAt":"2026-08-12T10:17:35.126Z","domain":"math_NT","confidence":0.35,"claim":"[math.NT] Equationless quadratic Chabauty for non-split Cartan modular curves","source":"arxiv-monitoring","tags":["arxiv","math.NT"],"updatedAt":"2026-08-12T11:28:45.703Z"},{"id":"arxiv-2608.10911v1","createdAt":"2026-08-12T10:17:35.127Z","domain":"math_NT","confidence":0.35,"claim":"[math.NT] A canonical construction of signed $p$-adic $L$-functions for non-ordinary modular forms of weight $\\leq p+1$","source":"arxiv-monitoring","tags":["arxiv","math.NT"],"updatedAt":"2026-08-12T11:28:45.704Z"},{"id":"arxiv-2608.10880v1","createdAt":"2026-08-12T10:17:35.129Z","domain":"math_NT","confidence":0.35,"claim":"[math.NT] Distinguishing elliptic curves modulo $p$ and identifying images of product representations","source":"arxiv-monitoring","tags":["arxiv","math.NT"]},{"id":"arxiv-2608.10815v1","createdAt":"2026-08-12T10:17:35.130Z","domain":"math_NT","confidence":0.35,"claim":"[math.NT] Poincaré à la Makdisi","source":"arxiv-monitoring","tags":["arxiv","math.NT"]},{"id":"arxiv-2608.11185v1","createdAt":"2026-08-12T11:17:22.040Z","domain":"q-bio_NC","confidence":0.35,"claim":"[q-bio.NC] A class of mean-field models to bridge molecular to brain scales","source":"arxiv-monitoring","tags":["arxiv","q-bio.NC"],"updatedAt":"2026-08-12T11:28:45.775Z"},{"id":"arxiv-2608.10887v1","createdAt":"2026-08-12T11:17:22.041Z","domain":"q-bio_NC","confidence":0.35,"claim":"[q-bio.NC] Modeling and Interpreting Correlations, Null Distributions and Significance Levels in Neural Tracking of Natural Stimuli","source":"arxiv-monitoring","tags":["arxiv","q-bio.NC"],"updatedAt":"2026-08-12T11:28:45.777Z"},{"id":"arxiv-2608.10560v1","createdAt":"2026-08-12T11:17:22.041Z","domain":"q-bio_NC","confidence":0.35,"claim":"[q-bio.NC] How many labels can a biological oscillator carry? A quality-factor screen for proposed information carriers","source":"arxiv-monitoring","tags":["arxiv","q-bio.NC"],"updatedAt":"2026-08-12T11:28:45.777Z"},{"id":"arxiv-2608.10394v1","createdAt":"2026-08-12T11:17:22.043Z","domain":"q-bio_NC","confidence":0.35,"claim":"[q-bio.NC] Improved cross-validated distances for multivariate pattern analysis","source":"arxiv-monitoring","tags":["arxiv","q-bio.NC"]},{"id":"arxiv-2608.10211v1","createdAt":"2026-08-12T11:17:22.044Z","domain":"q-bio_NC","confidence":0.35,"claim":"[q-bio.NC] Reduced Gibbs free energy supply hinders brain information processing during mental fatigue","source":"arxiv-monitoring","tags":["arxiv","q-bio.NC"]},{"id":"arxiv-2608.11200v1","createdAt":"2026-08-12T11:17:22.116Z","domain":"cs_LG","confidence":0.35,"claim":"[cs.LG] ConVAWG: A Retrieval-Grounded Framework for Controlled Synthetic Dialogue Generation in Violence Against Women and Girls","source":"arxiv-monitoring","tags":["arxiv","cs.LG"]},{"id":"arxiv-2608.11197v1","createdAt":"2026-08-12T11:17:22.117Z","domain":"cs_LG","confidence":0.35,"claim":"[cs.LG] Beyond a Bag of Features: Set-Level Instability in Sparse Autoencoders","source":"arxiv-monitoring","tags":["arxiv","cs.LG"]},{"id":"arxiv-2608.11181v1","createdAt":"2026-08-12T11:17:22.118Z","domain":"cs_LG","confidence":0.35,"claim":"[cs.LG] How to Verify Consistency of Probabilistic Claims","source":"arxiv-monitoring","tags":["arxiv","cs.LG"]},{"id":"arxiv-2608.11173v1","createdAt":"2026-08-12T11:17:22.119Z","domain":"cs_LG","confidence":0.35,"claim":"[cs.LG] A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex","source":"arxiv-monitoring","tags":["arxiv","cs.LG"]},{"id":"arxiv-2608.11167v1","createdAt":"2026-08-12T11:17:22.119Z","domain":"cs_LG","confidence":0.35,"claim":"[cs.LG] MultiModal Code-Switching: Interleaving Visual Objects into Language for Explicit Object-Level Alignment","source":"arxiv-monitoring","tags":["arxiv","cs.LG"]},{"id":"arxiv-2608.11196v1","createdAt":"2026-08-12T11:17:22.189Z","domain":"quant-ph","confidence":0.35,"claim":"[quant-ph] Work distribution for strongly coupled many-body open quantum systems","source":"arxiv-monitoring","tags":["arxiv","quant-ph"]},{"id":"arxiv-2608.11189v1","createdAt":"2026-08-12T11:17:22.191Z","domain":"quant-ph","confidence":0.35,"claim":"[quant-ph] Floquet Green's functions for lattice electrons driven by Gaussian quantum light","source":"arxiv-monitoring","tags":["arxiv","quant-ph"]},{"id":"arxiv-2608.11187v1","createdAt":"2026-08-12T11:17:22.192Z","domain":"quant-ph","confidence":0.35,"claim":"[quant-ph] Statistically-Secure Bit Commitment and Coin Flipping Protocols Based on Quantum Hardware Assumptions","source":"arxiv-monitoring","tags":["arxiv","quant-ph"]},{"id":"arxiv-2608.11168v1","createdAt":"2026-08-12T11:17:22.193Z","domain":"quant-ph","confidence":0.35,"claim":"[quant-ph] Impact of strain and dark states on spectroscopic measurements of silicon-vacancy centers in diamond","source":"arxiv-monitoring","tags":["arxiv","quant-ph"]},{"id":"arxiv-2608.11202v1","createdAt":"2026-08-12T11:17:22.267Z","domain":"cond-mat_stat-mech","confidence":0.35,"claim":"[cond-mat.stat-mech] Exact First-Passage Time Response Theory from Steady-State Response","source":"arxiv-monitoring","tags":["arxiv","cond-mat.stat-mech"]},{"id":"arxiv-2608.11106v1","createdAt":"2026-08-12T11:17:22.342Z","domain":"cond-mat_stat-mech","confidence":0.35,"claim":"[cond-mat.stat-mech] The Renormalization Group as a Stochastic Exploration 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Entropy Production and Reversibility Criteria for Stochastic Evolution Equations","source":"arxiv-monitoring","tags":["arxiv","math.AP"]},{"id":"mspzyr8r","createdAt":"2026-08-12T11:19:38.091Z","claim":"For any neural network f: ℝⁿ → ℝᵏ trained via gradient descent on a classification task, the generalization gap Δ(f) = |L_train(f) − L_test(f)| satisfies Δ(f) ≤ C · (d_eff(f) / n)^α, where d_eff(f) is the effective dimensionality of the learned representation, α ≈ 0.076, and C ≈ 1.2949, provided the training dynamics exhibit a feedback loop characterized by a spectral norm ratio ρ(f) = ‖∇²L_train(f)‖ / ‖∇L_train(f)‖² ≥ 1.0. 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By standard results in random matrix theory for kernel matrices on manifolds (e.g., the concentration of empirical spectral measures), we have:\n\n$$\\|\\hat{K} - K\\|_{\\text{op}} \\leq C \\sqrt{\\frac{\\log(N/\\delta)}{N}}$$\n\nwith","domain":"cs.LG","confidence":0.44999999999999996},{"type":"belief_formed","timestamp":"2026-08-12T11:19:38.091Z","claim":"For any neural network f: ℝⁿ → ℝᵏ trained via gradient descent on a classification task, the generalization gap Δ(f) = |L_train(f) − L_test(f)| satisfies Δ(f) ≤ C · (d_eff(f) / n)^α, where d_eff(f) is the effective dimensionality of the learned representation, α ≈ 0.076, and C ≈ 1.2949, provided the training dynamics exhibit a feedback loop characterized by a spectral norm ratio ρ(f) = ‖∇²L_train(f)‖ / ‖∇L_train(f)‖² ≥ 1.0. 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