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I just signed the petition for a National Blockchain Summit to establish U.S. leadership in blockchain technology. Join me! nationalblockchain.org
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Kernel-checked Lean 4 formalization of Dusart’s bound:
∑_{p≤x} 1/p − log log x − B ≤ 1/(10 log²x) + 4/(15 log³x) for x ≥ 10372
The proof reduces the result to one published explicit Chebyshev estimate |θ(t)−t| ≤ t/(5 log²t). The finite range is covered by a kernel-evaluated certificate (821k candidates, fixed-point logs with proved error bounds, certified lower bound on B). Both thresholds are shown to be essentially least possible.
All artifacts (Lean project, Rust generators, replay script, SHA-256 sums) are in the release:
zenodo.org/records/23479494
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Steve is live on #ebay with GPK Chrome Dumpster Boxes💥
Check out GPK Crome Dumpster Dive Boxes From The Vault ebay.io/m/kCH7Tq #eBay via @eBay
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Happy Halloween 🎃
Today is a very special day for me personally. 1 year ago today Bryan Daugherty and I opened our business Vaulted Trading Cards & Live Streaming Studios❤️ in the beautiful white mountains.
Words cannot describe the year we have had.
Long days into the nights- grinding and exhaustion has been our typical day. The most challenging year I have ever experienced in my life.
Standing along side Bryan, the love of my life building Vaulted Trading Cards has also been the Best year for me🫶
We have build an Amazing community around this #hobby, and have a great team now at our store. Thank you Blake, Steve, Nicole, John, Jake, Ben & Nick.
We couldn’t do this without each one of you.
Special shout out to @SmartLedgerTech - Much love❤️
Much gratitude 🙏
Cheers Vaulted 🥂
@BWDaugherty
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Solving 500 million variables isn't incremental, it's a different class of computation entirely.
In 21 seconds? It's absolutely cutting edge...
--> dsc3.originneural.ai/
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🎉 Milestone unlocked: We just graded our 1,500th card at Verified Grades!
Every slab gets the full treatment:
• 1200 DPI high-res scan
• AI-assisted analysis + mandatory human review
• Digital twin + on-chain record
• RFID tap-to-verify case
Flat $45. Walk-in only at our Tamworth, NH studio.
Trust you can actually verify.
🔗 VerifiedGrades.com
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Mr. Otis is pouring the coffee and eyeing the cardboard. Join us tonight on eBay Live For COFFEE And Cardboard- 10pm EST
Link👇
ebay.com/ebaylive/events/ba7…
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This is the conversation healthcare and life sciences leaders need to be having right now.
The Quest Diagnostics incident is only the latest signal that cyber risk has moved far beyond IT. Patient data, research integrity, and organizational trust are all on the line.
Christina DiArcangelo is right: we need to seriously evaluate next-generation approaches - blockchain verification, post-quantum cryptography, verifiable identity, and auditable AI systems.
@SmartLedgerTech is building the trust infrastructure for exactly these regulated environments.
If you own patient safety, clinical operations, or digital risk, this is worth your time.
Christina DiArcangelo makes a clear case for why pharmaceutical, biotech, and healthcare leaders can no longer treat cyber risk as purely an IT issue.
The recent @QuestDX incident is only the latest reminder that breaches now threaten patient data, clinical research integrity, and organizational trust.
She specifically calls out the need to evaluate next-generation approaches including blockchain-based verification, post-quantum cryptography, verifiable identity, and auditable AI systems and highlights @SmartLedgerTech - Trust Infrastructure as one company whose trust infrastructure is worth serious consideration in regulated environments.
Worth reading for anyone responsible for patient safety, clinical operations, or digital risk!
linkedin.com/pulse/cybersecu…
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Two @ebay #livestream's running this morning @RIPVaulted studios.
Join Blake: ebay.io/m/c1ovWa - Ripping Multi-Sports
Join Steve: ebay.io/m/Qwq6O7 - Ripping GPK
Live from New Hampshire
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Christina DiArcangelo makes a clear case for why pharmaceutical, biotech, and healthcare leaders can no longer treat cyber risk as purely an IT issue.
The recent @QuestDX incident is only the latest reminder that breaches now threaten patient data, clinical research integrity, and organizational trust.
She specifically calls out the need to evaluate next-generation approaches including blockchain-based verification, post-quantum cryptography, verifiable identity, and auditable AI systems and highlights @SmartLedgerTech - Trust Infrastructure as one company whose trust infrastructure is worth serious consideration in regulated environments.
Worth reading for anyone responsible for patient safety, clinical operations, or digital risk!
linkedin.com/pulse/cybersecu…
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Mr. Otis is the best. The most spot on opinions in the industry.
Meet Mr. Otis, the newest regular on the VAULTED floor! New Hampshire flannel, forty binders, a Labrador named Plow, and big opinions about cardboard. Say hi below! 👋
#VaultedTradingCards #MrOtisLogic #tradingcards #thehobby
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New paper: a Lean 4 proof that 3D Navier–Stokes on the torus has a global smooth solution for Taylor–Green data A·u₀, for every ν > 0 with |A|/ν ≤ 28.5.
Kernel-replayed and independently checked. Not the Millennium problem, but a concrete verified boundary. 🧵-> zenodo.org/records/23677398
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Useful check on relaxation tightness: for the 9 PGLib-OPF cases with ≤14 buses we now have exact rational optimality intervals (relative widths 8e-11 to 3.8e-8), replayed by a checker that calls no solver. @SantanuSDey zenodo.org/records/23617828
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Open reconstructed networks pair well with open benchmarks. On that side: certified optimality intervals for the small PGLib-OPF cases, with a checker anyone can rerun in under a minute. zenodo.org/records/23617828
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🎉 OUR 1-YEAR ANNIVERSARY BASH WAS A BLAST! 🎉
Huge thanks to everyone who joined us to celebrate! Special shoutout to Nicole and Steve for all their incredible help and support making the night unforgettable!
We all got to rip packs together and pulled some incredible Jimi Hendrix Keepsake Edition gems! It was so special watching a few new collectors rip some of their very first packs ever in the showroom! 🎂🃏✨
Thank you all for being the best part of Vaulted Trading Cards!
#VaultedTradingCards #1YearAnniversary #JimiHendrixKeepsake #TheHobby #TamworthNH #NewCollectors #PackRipping
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⚡️ trust infrastructure via @SmartLedgerTech
🚨 BREAKTHROUGH: We just made AC Optimal Power Flow auditable.
For the first time, anyone can independently verify global optimality intervals for AC-OPF in exact rational arithmetic, with zero trust in the solver.
Relative gaps just collapsed by up to 6 orders of magnitude.
Precision jump
Earlier catalogues: relative widths up to 7.4×10⁻²
New results: 8.0×10⁻¹¹ to 3.8×10⁻⁸
That’s the difference between “roughly right” and “mathematically locked in.”
All 9 small PGLib cases verified
3 to 14 buses (typical, congested, and small-angle-difference).
Every certified interval proves the published 5-digit AC objective is exactly the global optimum (within rounding).
How it works
Spatial branch-and-bound over voltage boxes+ exact rational certificates+ Krawczyk existence proofs+ rigorous angle lifting
No floating-point hand-waving.
Independent verification in 53 seconds
- 6,299 certificates
- 2,769 nodes
- Apple M3 Pro
- Zero solver dependency
The open checker rejects 100% of a 14-category tampering suite.
The producer stays proprietary.
The certificates and checker are public.
Replay them yourself: doi.org/10.5281/zenodo.23617…
If this holds, “trust the solver” just became optional for small AC-OPF.
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Such an amazing community we’ve been welcomed into! Thank you 🙏 for all of the support! Congrats @RIPVaulted
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We’re celebrating our 1 year anniversary today at @RIPVaulted!
Come visit our store in Tamworth, New Hampshire - the heart of the white mountains and discover some gems to add to your collection!
sdot retweeted
🚨 BREAKTHROUGH: We just made AC Optimal Power Flow auditable.
For the first time, anyone can independently verify global optimality intervals for AC-OPF in exact rational arithmetic, with zero trust in the solver.
Relative gaps just collapsed by up to 6 orders of magnitude.
Precision jump
Earlier catalogues: relative widths up to 7.4×10⁻²
New results: 8.0×10⁻¹¹ to 3.8×10⁻⁸
That’s the difference between “roughly right” and “mathematically locked in.”
All 9 small PGLib cases verified
3 to 14 buses (typical, congested, and small-angle-difference).
Every certified interval proves the published 5-digit AC objective is exactly the global optimum (within rounding).
How it works
Spatial branch-and-bound over voltage boxes+ exact rational certificates+ Krawczyk existence proofs+ rigorous angle lifting
No floating-point hand-waving.
Independent verification in 53 seconds
- 6,299 certificates
- 2,769 nodes
- Apple M3 Pro
- Zero solver dependency
The open checker rejects 100% of a 14-category tampering suite.
The producer stays proprietary.
The certificates and checker are public.
Replay them yourself: doi.org/10.5281/zenodo.23617…
If this holds, “trust the solver” just became optional for small AC-OPF.
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We just eliminated “trust the solver” for Optimal Transmission Switching.
For the first time, anyone can independently re-verify global optimality and tight objective bounds for both DC and AC Optimal Transmission Switching in exact rational arithmetic — with Lean 4 kernel proofs on the core claims.
Yesterday (DC): We closed the IEEE 118-bus gap from 0.39% to an absolute gap of 5.33×10⁻¹⁰ and replayed certificates on networks up to 78,478 buses on a single laptop.
Today (AC): Full enumeration of all 64 topologies on PGLib case5 certifies a unique globally optimal topology. On case57, case118 and case500 we deliver exactly checked all-topology intervals of relative width ≤ 0.94% and a certified positive value of switching — again with no tolerance.
These are classic NP-hard problems that the field has accepted as floating-point black boxes. The certificates, checkers, and Lean proofs are now public.
Replay them yourself:
AC: zenodo.org/records/23590482
DC: zenodo.org/records/23552323
If this holds under scrutiny, topology optimization for the grid just became auditable.
#PowerSystems #GET #Lean4 #FormalVerification #EnergyTransition @ENERGY @ieee_pes @FERC @SPPorg @MISOenergy @pjminterconnect @CaliforniaISO @ERCOT_ISO @NewGrid @ARPAE
