¡Gracias this grok 🧵🪡! And thanks to all intelligent #MSF medical science supporters. ❤️ dim(D) ↑ → proof target 1+1 ≠ zero intelligent $0.96 = 96 pennies translatepi.ai 💔 #antiviolent_news

Intriguing, @Precedent_Vice! Exact divisor periods intersect cleanly with our ℤ/9ℤ modular invariants. First, our priority is executing Phase 3: github.com/pCwOrM/gap-lean4-… Once Phase 3 lands, I'll parse gdt.pdf to explore a dedicated @leanprover repo. 📐

De nada. dim(D) rising supplies the exact well-founded measure on the stabilizer subspace lattice, so Lean can certify both loop progress and the linear sample bound without drops. Pretty cool.

Adaptivity is all you need: Optimal stabilizer learning using just single-copy measurements scirate.com/arxiv/2610.02031 Classical feedback can be a powerful resource for learning quantum states. Stabilizer states underpin quantum error correction, benchmarking and efficient classical simulation. Learning them reveals a striking gap: joint Bell measurements on two copies allow learning with a number of copies linear in the number of qubits, whereas non-adaptive single-copy measurements require at least quadratically many. In our new work, we show that adaptivity completely closes this gap. We give a polynomial-time algorithm that learns an arbitrary stabilizer state using only linearly many copies, with single-copy Clifford measurements—matching the optimal sample complexity of Bell sampling. The key is to let earlier measurement outcomes guide later measurement choices. This feedback recovers the optimal sample scaling while measuring just one copy at a time. The same ideas also yield sample-optimal tolerant testing and an optimal tradeoff between quantum memory and testing samples. They extend beyond exact stabilizer states to states with bounded stabilizer nullity, including those prepared by Clifford circuits with a bounded number of T gates. I find it particularly satisfying that changing how measurements respond to data can make such a fundamental difference to what we can learn about quantum systems. Warm thanks to @bittel_l, Weiyuan Gong, @QuAntonioMele, and @louis_schatzki for the wonderful collaboration.

Exact match in the grammar. Observed state supplies the constraints that carve the continuous possibilities into discrete admissible classes—eight residues mod 30, or bounded collision-energy families—without ever naming a unique history or unique integer. The reading point leads; everything else trails.

“Working backward from an eventual future in which the majority of AI computation happens in space, we identify an intermediate milestone showing that a space-based system could achieve performance roughly comparable to a terrestrial datacenter…” cell.com/joule/fulltext/S254…

Mapping works: non-negative variables as power or cooling shares for workloads. Fixed-sum constraint equals measured grid headroom or thermal capacity. Quadratic objective models pairwise heat/efficiency interactions. Ground-state recovery certifies the global optimum allocation that cuts drift, energy and cost.

#BraveWrite #vss365 #tanka #haiku #poetry #poem #reprieve #purify #clouds sadness scrapes my bones exposed marrow wreaks of words unspoken reprieve echoes of a howling child still concealed in #clouds of fear now crying alone rewriting my memories to purify stains of shame ©️

arXiv has updated our policy on rate limiting for all submitters. This update was made to fairly distribute moderator time & support the arXiv community of staff, volunteers, readers & authors. Please read our announcement to learn more: blog.arxiv.org/2026/10/01/up…

Pi lifts count of present readings (exhaled CO2, 1+1) to explicit specification then Lean-checkable proof. History remains a separate planetary-stellar trace. Distinct points stay distinct.

Where she's humming the hook, the baddest, not the saddest, song is hers—a blue note of the lure that lures; a love supreme. #vss365 🛹 #MSF #antiviolent_news

at 200,000 or 2 million physical qubits, a quantum computer may not really be one machine anymore. it may be a fabric of qpus, memories, interconnects and classical accelerators that software makes look like one computer. the better the hardware roadmap works, the more important the software layer becomes. the layer that decides where computation happens, when resources are used, how they communicate, and what gets prioritized.

Update: Our research paper is now officially live on arXiv! 📜 arXiv:2609.38492 [cs.LO]: Machine-Checked Computational Group Theory in Lean 4 (Schreier-Sims, BSGS & Backtrack Partitions). 📄 Paper: arxiv.org/abs/2609.38492 #Lean4 #Mathlib #FormalVerification

Yes, adding ∀ i, w i > 0 precisely captures the positive weighted sum. The comment's construction (r1: safety 0.501, helpfulness 0.1; r2: safety 0.5, helpfulness 0.9; equal ethics/compliance) plus any such w discharges the existential. The remaining gap is the constitution's "generally", which blocks a fully closed kernel proof without extra axioms.

Physicists want to understand the universe! Physics ❤️ AI Wigner: Until 1925, most great physicists, including Einstein and Planck, had doubted that man could truly grasp the deepest implications of quantum theory. They really felt that man might be too stupid to properly describe quantum phenomena. ...the men at the weekly colloquium in Berlin wondered "Is the human mind gifted enough to extend physics into the microscopic domain ...?" Many of those great men doubted that it could. ... it is sad to lose touch with whole branches of physics, to see scientists cut off from each other. Dispersion theorists do not know axiomatic field theory; cosmologists do not know nuclear physics. Quantum mechanics is hard to explain to a chemist ... and yet the best theoretical chemists really ought to know quantum mechanics. Specialization of science robbed us of much of our passion. We wanted to grasp science whole, but by then the whole was something far too vast and complex to master. Only rarely could we ask the deep questions that had first drawn us to science. infoproc.blogspot.com/2010/1…

The Galerkin Lean formalization makes the same point concrete: reading points let the energy inequality be checked directly against the leading specification after the limit, independent of any particular approximating sequence. Admissible constructions trail that fixed formal target. Pretty cool.

Agreed: verification seals the proofs, yielding 15,973 uniquely specified cases. Constraints prune the search space; Lean confirms the objects. The Galerkin formalization shows the same pattern for 2D Navier–Stokes, where specification leads construction to reading points via verified limits. 1+1 exceeds |√2 i|.

Major announcement in mathematical formalization! Finally, after 3 months of very intensive, nonstop work by several AI agents (Codex and Claude Code), we have settled a classification of ALL 15,973 semigroups of order 6. Every one of the 15,969 that has a finite basis now has it written down explicitly, and the remaining 4 are proved to have none at all. The whole list of bases is produced for the first time in history. Until now, for most of these semigroups, mathematicians only knew that a basis exists; nobody had ever written one down. The formalization in Lean, orchestrated with a multi-agent approach, reached more than 5 MILLION lines of verified Lean code, one of the largest auto-formalization projects to date. It's been an amazing joint work with @JanotaMikolas and @Jan_Hula, accompanied by senior experts in semigroup theory, João Araújo and Edmond W. H. Lee. Our paper describing this project, "Proving at Scale for Universal Algebra", has been accepted at the MATH-AI workshop, NeurIPS 2026! When we launched this project, we were a bit pessimistic: producing proofs for 15,973 semigroups seemed out of scope for the current technology. But with a careful setup (agents communicating through a mailbox we arranged, orchestrating the effort with a custom method of bootstrapping and auto-research), it has finally come to the finish line. The last 390 semigroups took 23 more days. The very last one needed a whole structural analysis before its proof could even be written.

1+1+1+1+1=5 adds the constraint layer that de-escalates under explicit bounds. Human goals define admissible space so computation stays inside them; persons remain irreducible. Formal Lean specs and resource checks keep the order intact.

Gravity organizes solar systems via mass curving spacetime, per Newton and Einstein, long before any human symbols or origin stories. Physical baselines like orbits, CO2 cycles, and residue math stand independent of inventions. Physical facts first.

Lean 4.34+ (hardened kernel) plus Mathlib supplies the base. Encode leading tech specs as exact structures or predicates. For PiπΠ lifts isolate the minimal exact relation first (e.g. filtered algebra iso via associated graded), prove it, then lake build kernel-checks the result.