Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T16:44:32.324136Z
Paper Citation Record · LEDGER
As of 14 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 0 inbound Pith citation observations for arXiv:2412.09860.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T16:44:32.324136Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
65 of 65 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 890c2a49-4f8b-4716-a512-32b3c2f540d3 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Machine learning for combinatorial optimization: a methodol ogical tour d’horizon
Reference 1
Source-reported events for the cited work
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Observation e29e26b7-0ffc-4e1b-b069-c45374de1ce1 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Application of combinatorial optimization strategies in synthetic biology
Reference 2
Source-reported events for the cited work
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Observation d1f57b8a-0001-493e-a929-646951c0fe1e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Combinatorial optimization of mRNA structure, stability, and translation for RNA-based therapeutics
Reference 3
Source-reported events for the cited work
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Observation 06af4eff-7366-423c-81c7-692b04ce1fae · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Explicit Evolutionary Multitasking for Combinatorial Optimization: A Case Study on Cap acitated Vehicle Routing Problem
Reference 4
Source-reported events for the cited work
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Observation 89afb23e-5447-4030-937f-e8c0afa00f8a · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Reinforcement learning for combinatorial optimization: A survey
Reference 5
Source-reported events for the cited work
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Observation c69e3a40-9e86-4fd7-bf96-216033d439bb · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Pointer networks
Reference 6
Source-reported events for the cited work
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Observation 39541469-8b6a-4ba3-be3b-c705044e7c90 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Erdos goes ne ural: an unsupervised learning framework for combinatorial optimization on graphs
Reference 7
Source-reported events for the cited work
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Observation 9348086e-5ceb-44e3-af68-99c78d535f54 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Neural combinatorial optimization with reinforcement learning
Reference 8
Source-reported events for the cited work
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Observation 403da00b-3729-483a-933d-7af9035cd9a4 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Learning combinatorial optimization algorithms over graphs
Reference 9
Source-reported events for the cited work
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Observation 7af89ef1-7661-49da-a455-25ce1f5798f0 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization NeuroLKH: Combining deep learning model with Lin-Kernighan-Helsgaun heuristic for solving the traveling salesman problem
Reference 10
Source-reported events for the cited work
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Observation 8be4b9ef-c76c-4d60-8ecd-c2878ac24207 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization An effective implemen tation of the Lin–Kernighan traveling salesman heuristic
Reference 11
Source-reported events for the cited work
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Observation e30b63c4-0c71-4fe6-8cb1-76e7f3a8f9d4 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Combinatorial optimization with physics-inspired graph neural networks
Reference 12
Source-reported events for the cited work
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Observation c39a8ad3-8644-4df2-a870-e20596ede5c7 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Adam: A met hod for stochastic optimization
Reference 13
Source-reported events for the cited work
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Observation 579ca68d-b313-49b4-b223-024b38f96381 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Nonlinear dynamics and chaos with student solutions manual: With applications to ph ysics, biology, chemistry, and engineering
Reference 14
Source-reported events for the cited work
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Observation 96c20128-7bd0-43cf-818a-769ccdcf729e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Global searching ability of chaotic neural networks
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ed732396-9750-408e-bd89-819604ad9c9c · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Co mbinatorial optimization by simulating adiabatic bifurcations in non linear Hamiltonian systems
Reference 16
Source-reported events for the cited work
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Observation 7706e4a7-d48a-4a6f-a846-bba405aaeee6 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization High-performance combinatorial optimization based on classical mechanics
Reference 17
Source-reported events for the cited work
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Observation 2205b88a-090b-481f-b44d-b98e0fbe6a63 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Chaotic simula ted annealing by a neural network model with transient chaos
Reference 18
Source-reported events for the cited work
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Observation 78bd3f09-2815-485e-b35b-1dc49d8d0863 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Chaos and asymptot ical stability in discrete-time neural networks
Reference 19
Source-reported events for the cited work
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Observation 992b757a-e493-4e5e-a03c-8998f4108f5c · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Phas e locking, period-doubling bifurcations, and irregular dynamics in periodically stimul ated cardiac cells
Reference 20
Source-reported events for the cited work
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Observation d9902d7a-4b2f-4495-b079-e73d7f8b8872 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Subthreshold dynamics in periodically stimulated squid giant axons
Reference 21
Source-reported events for the cited work
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Observation 6fe2a2d8-fbd8-45c9-ac0c-9bec7b79a7f9 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Structures of attractors in periodically forced neural oscillators
Reference 22
Source-reported events for the cited work
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Observation 841e476f-c2cd-4b1d-8173-e961cfcee159 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization How brains ma ke chaos in order to make sense of the world
Reference 23
Source-reported events for the cited work
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Observation 736907bb-f8d2-485c-b616-03744f28fe96 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Is it healthy to be chaotic? Science 243, 604-607 (1989)
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 54d0f939-7436-4cf2-beb7-b59e65bee66e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization On chaotic dynamics in transcription factors and the associated effects in differential gene regulation
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b17c7ce4-5df9-4cd9-b00d-a09cb34a27fc · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Oscillations, complex spatiotemporal behavior, and information transport in networks of exci tatory and inhibitory neurons
Reference 26
Source-reported events for the cited work
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Observation 61861a16-8353-4e1d-990e-a6f3890f125c · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Evidence of chaotic dynamics of brain activity during the sleep cycle
Reference 27
Source-reported events for the cited work
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Observation 78d46817-7dfb-4c6e-b27b-e1747be42e4a · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Chaos and phase locking in normal squid axons
Reference 28
Source-reported events for the cited work
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Observation aae3197c-f15d-43e8-9cba-85987e668747 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Criticality between cortical states
Reference 29
Source-reported events for the cited work
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Observation 1b55b998-5fa6-4aaa-b39f-7192b5687246 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Evidence for quasicritical brain dynamics
Reference 30
Source-reported events for the cited work
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Observation e284c125-e6c3-4ee4-b390-dad0e8fe8c36 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization On redefining a snap-back repeller
Reference 31
Source-reported events for the cited work
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Observation e342a16d-96b5-42a3-92a6-36e6f04f06f3 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Ising formulations of many NP problems
Reference 32
Source-reported events for the cited work
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Observation 9ff97712-6f2b-4ce1-a499-a808f84f6cd7 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Analysis of the relation between quad ratic unconstrained binary optimization and the spin-glass ground-state problem
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 445d4cfa-f729-4a82-8b27-2ba248762afa · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Semi-supervise d classification with graph convolutional networks
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b830aad3-4533-4ca7-b472-3477c4ce486e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization I nductive representation learning on large graphs
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 72691e88-c1ed-47fe-8c95-9b97adb8d357 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Graph attention networks
Reference 36
Source-reported events for the cited work
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Observation f30a89c5-9be7-4dc8-8b3a-85f9f3e86bac · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Brain-in spired chaotic backpropagation for MLP
Reference 37
Source-reported events for the cited work
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Observation 558b30ca-154b-48b9-aa6e-ddb95f0bce5e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization On a response char acteristic of a mathematical neuron model
Reference 38
Source-reported events for the cited work
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Observation 0dfbe42c-fc6c-4b05-9536-ae80d3bbd8e6 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Chaotic neural networks
Reference 39
Source-reported events for the cited work
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Observation 899d5fe0-e5c8-4a3e-ae43-5cdd8d277f77 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization On the importance of initialization and momentum in deep learning
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d3a03b3b-63ca-4f81-8420-7005952e0a15 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Ex tremal cuts of sparse random graphs
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 060393fc-06ea-48c6-856e-772c1ff147de · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Solvable model of a spin-glass
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f368f1d3-6cef-4622-b11f-23b359b4962e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Im proved approximation algorithms for maximum cut and satisfiability proble ms using semidefinite programming
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 6a12d66e-7a02-47dc-99a3-4493a194037e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Breakout lo cal search for the max-cutproblem
Reference 44
Source-reported events for the cited work
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Observation 24e2c7e5-12ee-4036-b24b-bf84143fca27 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Solving sparse semi definite programs using the dual scaling algorithm with an iterative solver
Reference 45
Source-reported events for the cited work
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Observation fb8348d1-351b-486e-a0d1-cc4b1cf11f70 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Solving large scale max cut problems via tabu search
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9d122098-1a68-482a-995e-4caaad5e6f08 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Graph neural networks for maximum constraint satisfaction
Reference 47
Source-reported events for the cited work
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Observation 33dca0a6-7062-4f9d-9c04-2075865810a1 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Graph coloring with physics-inspired graph neural networks
Reference 48
Source-reported events for the cited work
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Observation 28c74dde-e068-4fea-8305-ce344c858fae · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Automating the construction of internet portals with machine learning
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 44c99077-d48b-4389-8598-484b665eea2f · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Collective classification in network data
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 22c40b5d-c5ce-4d62-99e7-8ac400d63da1 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Query-driven active surveying for collective classification
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 57c664f3-67b9-4164-be54-da0ed8425675 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Using tabu s earch techniques fo r graph coloring
Reference 52
Source-reported events for the cited work
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Observation c5c6c696-5e25-4d19-a742-e74954b40dfb · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Rethinking Graph Neural Networks for the Graph Coloring Problem
Reference 53
Source-reported events for the cited work
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Observation 55a6fb35-a041-489c-97ef-d5bb14e7585e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Back-propagation with chaos
Reference 54
Source-reported events for the cited work
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Observation 44cf1eb7-9e0a-4b35-97bb-834d0021c14a · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Self-backpropagation of synaptic modifications elevates the effici ency of spiking and artificial neural networks
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4f735c35-5707-4f10-b61b-911e8fffb744 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization The forward-forward algor ithm: Some preliminary investigations
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9e0d0da7-ed5e-4ecb-a545-9a96fdcf0532 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Adabelief optimizer: Adapting stepsizes by the belief in observed gradients
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 986fb905-83b4-4a1b-806e-fec8e947b6dd · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Adan: Adaptive Nesterov Momentum Algorithm for Faster Op timizing Deep Models
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b657e858-5f9d-487e-a182-c13f594cee42 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Sparse graph attention networks
Reference 59
Source-reported events for the cited work
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Observation 4a80610e-c880-47b6-adf4-b65e4278bbc1 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Deep graph library: Towards efficient and scalable deep learning on graphs
Reference 60
Source-reported events for the cited work
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Observation ed6e822c-ad3a-4086-a2e2-5d7b44422871 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Rectified lin ear units improve restricted boltzmann machines
Reference 61
Source-reported events for the cited work
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Observation 7df6e5ff-c499-433b-9d1f-1b092bebb2fe · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Dropout: a simple way to prevent neur al networks from overfitting
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d4e5e94f-0060-4496-9bb2-d947fe5e9d1f · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Batch normaliza tion: Accelerating deep network training by reducing internal covariate shift
Reference 63
Source-reported events for the cited work
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Observation fcee2eee-822c-4a85-becf-b0a9e8f2e784 · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Pytorch: An imperative style, high-performance deep learning library
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation faaae027-9705-47cb-a9b1-a45f1a0ab23e · outbound
Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization Making a science of model search: Hyperparameter optimi zation in hundreds of di mensions for vision architectures
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
No inbound Pith citation observations are available.