The exact value of the #Ramsey number R(3,10) rests on a single question: does a (3,10)-graph on 40 vertices exist? Our new paper tackles this boundary, closing a key structural case and mapping the exact computational road ahead.  We prove unconditionally that no (3,10)-graph on 40 vertices has a vertex of degree 4, meaning every such graph must have a minimum degree of at least 5. This removes the diameter-2 hypothesis required in prior work to exclude this degree.  We fixed the unique (3,9)-graph of order 35 as the dual neighborhood, leaving 140 undetermined adjacencies. This generated a 98,965-clause SAT instance that we refuted in just ten seconds on a single core. To eliminate solver doubt, the entire refutation is machine-checked with a DRAT proof.  Closing one case doesn't establish the Ramsey value, and we aren't claiming it does. Instead, we provide a complete audit of what remains: exactly 79 (order, edge-count) entries of (3,9)-graphs.  Here is the catch: exact numerical counts aren't enough. To close cases, we need the actual isomorphism-class representative graphs to run the refutations. Currently, 11 of these entries have been enumerated but not deposited, and 68 have not been enumerated at all.  This is no longer an insurmountable structural wall; it is a precise, distributed work order for the community. If you have heavy compute power or hold the 11 missing graph slices, the exact path forward is now defined.  Read the full paper and check out our 14-second reproduction pipeline here: zenodo.org/records/22945442 #RamseyTheory #GraphTheory #SATSolvers #MathResearch #Combinatorics

We hear a lot about the need to build thousands of miles of new power lines to support electrification and #AI #datacenters. But what if we could squeeze significantly more capacity out of the wires we already have? @SmartLedgerTech’s new paper on "DC Optimal Transmission Switching" (OTS) highlights a software-based approach that perfectly aligns with the Department of @Energy's grid modernization goals. OTS acts like a dynamic traffic cop for the power grid, selectively opening and closing existing transmission lines to reroute power away from bottlenecks.  The historical roadblock to this technology has always been reliability; operators are rightfully risk-averse when it comes to changing the grid's topology. This research solves that trust gap by introducing a "proof-tree certificate format" and an "exact-rational verifier". In plain English: it provides a mathematically rigorous, verifiable proof that a proposed grid configuration is completely connected, physically feasible, and respects all line capacities.  This framework is a game changer for adopting next-generation tech. It completely separates the search for solutions from the safety verification. Utilities can let untrusted, lightning-fast AI or advanced algorithms propose highly efficient new grid topologies. A small, trusted checker then independently verifies the math using exact rational arithmetic before anything is implemented. In several tested instances, this approach proved that the grid could operate at its absolute optimal "economic-dispatch bound" simply by flipping the right switches.  It is a blueprint for how we can safely deploy aggressive optimization algorithms in critical physical infrastructure. Where do you think software-based optimization will make the biggest physical impact next? @ENERGY

Play hard. Stack smart. Have fun doing it. The treasury is serious. The game shouldn’t be. Come for the run. Stay for the treasure. Risk it. Run it. Have fun.

Run the vault. Chase the treasure. Have some fun.

Very nice. Anytime , @WolfgangLohmann !

Bitcoin does not need a dedicated opcode for every cryptographic protocol. Sometimes the primitives are enough. medium.com/@codenlighten/bit… #bitcoin #postquantum #mathematical #bsv

web3co2.com/ Every Proof-of-Work transaction has a real carbon cost. WEB3CO2 measures it from live network data — and reveals how radically that cost differs between blockchains. It's 5,832 × more carbon-efficient to transact on BSV than BTC. @SmartLedgerTech

Very very excited to see this!!! Boom!

Yes. Every UUID along with identity, measurements, high resolution images, subgrades, and provenance is captured on chain.

linkedin.com/posts/jalexande… ProofOfProcess.ai/ #proofofprocess @jalexanderm @SmartLedgerTech

Haahaaahaaahaa

Tired of porch pirates? Postal workers feeling up your packages for rare Charizards? I have cracked the code. Everyone’s out here buying $80 lockboxes and camera doorbells when the real answer is psychological warfare. Porch pirates don’t want a felony and an aggressive bout of skin-rotting ringworm. 100% delivery success rate, zero stolen packages, and my mail carrier now drops my parcels off using 12-inch metal tongs and a hazmat suit. Work smarter, not harder. Follow for more elite logistics security hacks. @CardPurchaser

The AI Boom Is Quietly Becoming an Insurance and Credit Story Data centers, private credit, life insurers, offshore reinsurance, and decades-long debt are becoming deeply intertwined. The pieces are real... medium.com/@codenlighten/the…

Seems like an archaic way compared to VerifiedGrades.com