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Mathematics is All You Need 2: Sign-Stabilized Behavioral Fibers in Transformer Residual Streams This volume presents a pre-registered empirical investigation of the residual-stream geometry of frozen transformer language models, anchored by a four-test decision sprint executed on 2026/05/09 and a six-experiment tier-0 lockdown battery, with full reproducibility manifest. Empirical findings. Cross-architecture transfer of behavioral readouts from Qwen-2.5-7B-Instruct to Hermes-3-Llama-3.1-8B yields mean AUC retention of 0.749 across 75 probe-layer pairs over 10 seeds (BCa bootstrap 95% CI [0.7466, 0.7577] from 10,000 resamples; permutation test 10,000 permutations p < 10⁻⁴; significance survives Bonferroni correction at α = 0.05). Causal steering of the target architecture using a probe direction trained on the source architecture produces strictly monotonic probe-output deflection on 29 of 29 held-out prompts (median Spearman ρ = 1.000, intervention range α ∈ [−3, +3]). Gauge-flexibility of the underlying low-rank substrate is established at high statistical power: 100 random orthogonal rotations of the projection basis produce retention standard deviation σ = 0.0096. The intrinsic dimension of the behavioral substrate is shown to be 1–4 for the majority of behavioral traits tested, with single-direction (r = 1) retention of 0.897. The angle between the rank-1 output highway direction and the centroid of trained probe directions at proportional depth is measured as 85.59° on Qwen-2.5-7B-Instruct at layer 13, independently reproducing a prior internal measurement of 85.5° to within 0.1°. Theoretical synthesis. The Two-Channel theorem: the residual stream of a frozen transformer admits a decomposition into a high-variance rank-1-dominant output channel read by the unembedding head and a low-rank near-orthogonal behavioral channel supporting both readout and causal cross-architecture steering. The architecture-invariant object is established empirically as the sign-stabilized SVD subspace itself rather than any specific basis within it; the canonical-basis specificity hypothesis is formally rejected by pre-registered ablation (T2). Convergence with prior work. The geometric near-orthogonality result provides a measurement-side mechanism complementary to the training-side finding of Huang, LeCun & Balestriero (LLM-JEPA, arXiv:2509.14252, 2025) that embedding-space training objectives improve LLM performance without altering generative capabilities. The two results describe the same underlying functional separability of latent structure and generation in transformer residual streams via independent methodologies. Scope and limitations. The empirical foundation is restricted to a single source–target architecture pair (Qwen-2.5-7B-Instruct → Hermes-3-Llama-3.1-8B), both decoder-only instruction-tuned transformers in the 7-8B parameter class. The headline T4 causal steering result is on one probe (language_id) at one layer pair (qL13 → hL15). Cross-family extension (Mistral, Phi, Gemma, Yi, Llama variants), multi-probe causal steering benchmarks, full d-model space angle measurement, and the PLATINUM-probe leakage audit are queued for the cluster reproduction sprint as a 15-pipeline validation matrix. Several claims from the prior volume Mathematics is All You Need (Napolitano 2026) are explicitly retracted or demoted to conjecture in Part VI of this work. Compute and reproducibility. Total wall time for the empirical foundation: approximately 9 hours on a single NVIDIA RTX 5090. Reproducibility manifest, replication recipes, and full numerical results are included as appendices. Keywords. Mechanistic interpretability; representation engineering; activation steering; cross-architecture transfer; linear representation hypothesis; transformer residual stream; behavioral probes; gauge invariance; pre-registered evaluation; Joint Embedding Predictive Architectures. Models and datasets used. Qwen-2.5-7B-Instruct; Hermes-3-Llama-3.1-8B. Datasets: HumanEval, MBPP, MATH, GSM8K, ProofNet, WritingPrompts, ROC stories, Wikipedia. Companion volume. Integrates and supersedes the unreleased internal report CYGNUS 2: Information Field Theory and the Geometry of Machine Consciousness (April 2026), included as Part II. Access. Distribution prior to public-release date is restricted to identified academic reviewers and partner research labs under signed NDA. Public release is scheduled for 30 days after the priority date of associated U.S. provisional patent applications. Source code, model weights, cached residuals, and intermediate artifacts are proprietary property of Proprioceptive AI, Inc. License. Text under CC-BY 4.0; source code and artifacts proprietary. ORCID. 0009−0000−1927−8537
Every year, the Capture the Atlas Milky Way Photographer of the Year contest brings together some of the most striking night sky images from photographers all over the world. Curated by photographer Dan Zafra, the project highlights a carefully selected collection of around 25 photos taken in some of the darkest and most remote places on Earth – locations where the Milky Way is still visible in incredible detail, free from the glow of light pollution.
What makes this contest special isn’t just the final images, but everything behind them. Each photo usually involves planning, travel, and a lot of patience, waiting for clear skies, perfect timing, and the right conditions to align. These aren’t just snapshots of the night sky, but moments earned through dedication and a real passion for astrophotography. The result is a collection that feels both artistic and deeply human, showing how different places on Earth (and beyond) connect through a shared view of the cosmos.
Scroll down and explore the winning images for yourself. Each one is a window into a different corner of the night sky, captured in a way most of us rarely get to see.
Deep inside planets like Uranus and Neptune, scientists may have uncovered a bizarre new state of matter where atoms behave in unexpected ways. Advanced simulations suggest that carbon and hydrogen, under crushing pressures and scorching temperatures, can form a strange hybrid phase—part solid, part fluid—where hydrogen atoms spiral through a rigid carbon framework. This unusual “superionic” structure could reshape how heat and electricity flow inside these distant worlds, potentially helping explain their mysterious magnetic fields.
The deep interiors of ice giant planets such as Uranus and Neptune may contain a previously unknown form of matter. This possibility comes from new computer simulations conducted by Carnegie scientists Cong Liu and Ronald Cohen.
Their study, published in Nature Communications, suggests that carbon hydride could take on an unusual quasi-one-dimensional superionic state under the intense pressures and temperatures found far beneath the surfaces of these distant planets.
A new study, published in Science Advances, has refined some important details about the moon’s largest and oldest impact crater, which stretches more than 1,200 miles (2,000 km) on the far side of the moon. The new details can help guide some of the planning for NASA’s upcoming Artemis mission to the moon, which is planned for 2028.
The South Pole–Aitken (SPA) basin is the moon’s largest and oldest confirmed impact basin. The basin has a unique, tapered elliptical shape that has puzzled scientists and sparked some debate over the direction and nature of the impact that formed it. Some asymmetries in the crust suggest a northward trajectory of the impactor, while the shape and the structure of the basin suggest a southward trajectory.
The authors of the new study write, “Large basins on the moon and other solid bodies (e.g., Mars and Pluto) are ellipses that taper in the downrange direction. SPA’s tapering toward the south, a steeper crustal thickness gradient toward the north, and the presence of a thorium-and iron-rich deposit toward the southwest of SPA beyond the basin rim support a southward impact trajectory.”
Since the goal is to find Earth-like planets orbiting Sun-like stars, the Sun is an ideal proxy, as it is the only one astronomers can fully resolve. Dedicated instruments with high-precision spectrographs have been developed to observe the “Sun-as-a-star,” such as the High Accuracy Radial velocity Planet Searcher North (HARPS-N) solar telescope and the HARPS spectrograph (HELIOS). The main drawback is that only disc-integrated spectra are obtained, precluding a detailed analysis of individual stellar features.
According to the team, what is needed is a telescope that can offer three vital things: 1. Spatially resolved spectroscopy with very high wavelength stability 2. Very high spectral resolution to adequately resolve photospheric line asymmetries 3. Extended wavelength coverage, for the simultaneous observation of thousands of spectral lines probing different physical conditions.
This, they claim, can be achieved by linking the ESPRESSO spectrograph to a solar telescope — in this case, PoET. The solar telescope will observe the Sun at different spatial scales, corresponding to sunspots and solar granules, and send the light it gathers to ESPRESSO via optical fibers. The overall system involves three telescopes, starting with the main telescope (MT) developed by Officina Stellare. This telescope has a Gregorian configuration, standard for solar observations, and will observe small areas of the solar disc.
A tiny world in our Solar System has an atmosphere it shouldn’t—hinting something dramatic happened there recently.
A group of Japanese astronomers, including both professionals and amateur observers, has found signs of a thin atmosphere surrounding a small object far beyond Neptune. The discovery is surprising because the object is so small that it should not be able to hold onto gas for long. This raises new questions about when the atmosphere formed and what is keeping it there. Additional observations will be needed to better understand this unusual finding.
Why most trans-neptunian objects are airless.
A new mission promises to ‘open the box’ on exoplanet science. Scientists and engineers recently released the first engineering images from the Pandora exoplanet survey mission. The pictures represent the first ever images from a NASA Astrophysics Pioneers Program mission. Established in 2020, the program looks to test the feasibility of small low cost missions designed to address key questions in astronomy and astrophysics.