AI / shareable research library / October 12, 2026
Companion library for the October 11 AI Search roundup.
Full mathematics collection — official catalogue · Watch the source video
Video topic
Interactive world model combining factorized action/semantic controls, compressed historical memory, and Stable Forcing distillation for real-time, longer-horizon generation. [1]
Limits: Characters can drift visually and semantically over long rollouts; infinite-horizon stability and geometric consistency remain unsolved.
Official original linked; summary PDF hosted
Video topic
Text-to-human-motion flow matching directly in full-resolution motion space without a learned encoder/decoder. Representation-aware attention and noise scaling support incremental and absolute-coordinate motion; the XYZ variant adds inference-time joint/frame constraints. [4]
Limits: Evaluated on HumanML3D and SnapMoGen only. Full-resolution sequences raise long-motion compute costs. Linear coordinate constraints do not guarantee physical feasibility, collision avoidance, contact, or joint limits.
Official original linked; summary PDF hosted
Video topic
A 3B Lite and 29B Pro diffusion-model family producing synchronized five-second audio/video. Dual-stream CrossDiT connects pretrained video and audio streams; super-resolution raises SD outputs to Full HD. [7]
Limits: Five-second duration, native SD resolution, and remaining visual/audio-quality gaps against leading proprietary systems. Full HD is upscaled rather than native. The same report covers the super-resolution model.
Hosted original: CC BY 4.0
Video topic
Adaptively looped diffusion language models at 1.7B and 8B scales. Shared-layer recurrence preserves unresolved token states, commits confident tokens, and learns token-specific compute allocation; authors evaluate eleven benchmarks. [10]
Limits: Longer time to first token can hurt short or latency-sensitive responses. Throughput depends on input difficulty and domain; underrepresented domains can erase or reverse speed advantages over optimized autoregressive baselines.
Official original linked; summary PDF hosted
Video topic
Test-time alignment framework for frozen SAM3D reconstruction, using geometry-grounded pose, visibility-aware observation fusion, rendering guidance, and optional refinement; supports monocular, multi-view and externally supplied dynamic geometry. [12]
Limits: Dynamic geometry depends on an external predictor. Coarse shape is not directly grounded in observed silhouette/depth. Rotation remains prior-driven, and errors in masks, depth or cameras can harm rendering supervision.
Official original linked; summary PDF hosted
Video topic
Multi-reference reinforcement-learning retargeting shares policies across human hand-object demonstrations to generate robot trajectories. Authors report 90% success on a 50-motion benchmark at roughly 30 GPU-hours, versus roughly 46% and 3,000 GPU-hours for CHORD. [14]
Limits: Needs relatively clean human hand-object trajectories, accurate geometry and privileged simulator information. Generalization to unseen motions/embodiments and observation-only real-world deployment remain future work; benchmark results are not universal robot competence.
Hosted original: CC BY 4.0
Video topic
A generative enzyme-design research pipeline reports experimentally tested catalysts for selected challenging chemistry, alongside improved performance on model reactions. [16]
Limits: Preprint; authors report commercial interests and a provisional patent. Selected laboratory demonstrations do not establish general performance for arbitrary reactions or industrial deployment.
Official original linked; summary PDF hosted
Video topic
Plant genomic foundation-model family; models evaluate genomic variation and support a generalist AI agent as a specialist analysis tool. [18]
Limits: Retrospective benchmarks and a known causal variant; prospective lab validation is still required. Case study starts with an already narrowed chromosome region; full-genome scoring ranked the true variant sixteenth, not first. Authors are or were employed by Living Models; model/weights restrictions are separate from the paper CC BY license.
Hosted original: CC BY 4.0
Video topic
AI-assisted DFT study proposes YBaMnFeO5 and re-identifies the previously synthesized KV[Cr(CN)6] as candidate Luttinger-compensated semiconductors. [20]
Limits: Neither band gap, conductivity nor spin polarization has been measured for these claimed properties. YBaMnFeO5 ordering may be inaccessible by standard synthesis; disorder destroys the proposed effect. KV[Cr(CN)6] evidence concerns one hydrated powder; hydration calculations differ by method. Ideal-crystal DFT omits reliably resolved spin–orbit/orbital effects and exact finite-temperature compensation.
Official original linked; summary PDF hosted
Video topic
Reconstructs task-relevant terrain from motion alone, retargets it to a musculoskeletal body and trains one muscle-actuated simulation policy using a 9.4-hour training split of an 11.3-hour library from five datasets. [22]
Limits: Evaluation is in simulation and on supported terrain families. Task-relevant support geometry from motion is not complete reconstruction of unseen scenery. Dynamic primitive geometry, online retargeting and moving surfaces remain open challenges (paper conclusion). Physiological comparison shows visible EMG timing/shape mismatches, not complete equivalence to measured human movement. Not best on every terrain: TERRA+Voronoi performed better on stairs in reported held-out tracking.
Official original linked; summary PDF hosted
Video topic
Multi-view RGB-to-simulation agentic pipeline reconstructs rigid and articulated objects plus deformable curves, surfaces and volumes, with simulated robot tests. [24]
Limits: Six scene reconstruction benchmarks (three Replica and three ScanNet++ scenes). Deformable results are capability demonstrations rather than a matched quantitative deformable benchmark. Agent-guided physical tests occur in simulation, not a demonstrated sim-to-real guarantee.
Official original linked; summary PDF hosted
Video topic
Single-image compositional 3D scene generation jointly represents environment and objects, then refines objects using scene context; trains using automatically assembled synthetic scenes distilled from an object generator. [26]
Limits: Indoor results may omit ceilings because training environment assets often omit them. Large outdoor scenes can have holes and lose fine geometry due to finite voxel resolution. Outdoor training corpus is smaller due to compute constraints; project lists code, checkpoints and dataset as coming soon.
Official original linked; summary PDF hosted
Video topic
A three-billion-parameter pixel-space image generator, with experiments in depth estimation and restoration. [28]
Limits: The paper reports no significant downstream improvement from a pixel-space generative prior; neither pixel model beats the compared latent fine-tune on the reported restoration experiment. This negative result matters more than gallery impressions.
Hosted original: CC0 1.0
Video topic
A modular multimodal embedding model maps text, images, audio and video into shared vectors for retrieval and classification. [31]
Limits: Vendor evaluations and device-specific resource measurements are not guarantees on every laptop or phone; data privacy still depends on the application architecture.
Official original linked; summary PDF hosted
Video topic
The release describes interactive interfaces in ChatGPT and related model availability. [33]
Limits: A product demonstration is not evidence that generated financial or other tools are validated for real-world decisions. No separate paper for this UI feature was located in the linked release.
Official original linked; summary PDF hosted
Video topic
Mistral announces a multimodal mixture-of-experts model and a public API preview, with coding, agent and enterprise evaluations. [34]
Limits: The announcement promises weights by the end of October; do not describe them as already released at the time of this review. Vendor benchmark results do not establish superiority across all workloads.
Official original linked; summary PDF hosted
Video topic
Google documents image-generation and editing capabilities, evaluations and safety measures for the Nano Banana 2.1 release. [35]
Limits: The source is a vendor model card rather than an independent evaluation; generated images and edits can still be inaccurate.
Official original linked; summary PDF hosted
Video topic
A system card reports the vendor's capability, safeguards and agentic-safety evaluations for its small model. [36]
Limits: The vendor describes omitted evaluations and a condensed testing approach. Benchmark scores, lower prices and improved injection robustness do not imply universal reliability or immunity to prompt injection.
Official original linked; summary PDF hosted
BSD principal
Claims full leading-term BSD only when some full q-power Selmer group has corank 0 or 1; not BSD for every elliptic curve. October 7 version removes an obsolete citation. [38]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
BSD companion
Companion: low Selmer corank implies analytic/algebraic ranks and finiteness of Sha, not by itself the entire leading-term formula. [41]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
BSD companion
Companion: concerns the two-primary part of the leading-term formula; do not equate a single prime component with all-prime full BSD. [42]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
quasi-Riemann direct match
Direct match to video 12.5%-edge claim: Re(s)>7/8. Not the full Riemann hypothesis. Formalization scope excludes later applications. [43]
Limits: Listed in formalization.yaml sources; artifacts inspected, not independently executed. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
quasi-Riemann alternate
Alternative weaker Re(s)>11/12 proof, not the 7/8 result illustrated in the video. README explicitly records human assistance. [44]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
quasi-Riemann companion
Companion excludes a uniform near-one real-zero region; does not exclude every real zero throughout (0,1). No explicit absolute constant supplied. [45]
Limits: Listed in formalization.yaml sources; artifacts inspected, not independently executed. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
Hilbert tenth direct match
Direct match at 18:50: undecidability of existence of a rational zero of arbitrary-variable integer-coefficient polynomials. Not merely a time-complexity lower bound or P versus NP. [46]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
Hilbert tenth companion
Supporting companion to Hilbert tenth family: elliptic curves with nonzero rational two-torsion and low 2-power Selmer corank, not a standalone general undecidability theorem. [47]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
BSD density-one companion explicitly implied by video
Needed with family 002 for the density-one quadratic-twist BSD claim. Ranks zero and one each density one half for signed squarefree twists ordered by absolute value; not all curves. [48]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
BSD mean-rank context
Related companion about the mean analytic rank tending to one half in the stated twist ordering; not itself a proof of the full BSD leading-term formula. [49]
Limits: Not listed in current formalization.yaml sources; no verified full-paper formalization established here. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
matrix direct match
Direct match to exponent 2.25: omega(C)<=9/4, asymptotic arithmetic-operation complexity with arbitrary positive exponent slack. Not a demonstrated practical GPU speedup or bit-complexity result. [50]
Limits: Listed in formalization.yaml sources; artifacts inspected, not independently executed. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
matrix secondary writeup
Secondary writeup with weaker square bound and rectangular bounds. Numerical integrity checks alone do not execute a proof; certificates do not certify tensor or limiting arguments. [51]
Limits: Listed in formalization.yaml sources; artifacts inspected, not independently executed. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted
matrix all-fields companion
Companion for every fixed field, with weaker exponent <2.371054886006746; do not substitute universal-field scope for the main complex-field 9/4 bound. [52]
Limits: Listed in formalization.yaml sources; artifacts inspected, not independently executed. No independent peer-review certification established by these repository materials. This brief reports the manuscript claim; it is not a verification of its proof.
Official original linked; summary PDF hosted