# Proof的所有文章

在 HTX 新闻中心浏览与「Proof」相关的最新资讯与深度分析。潘盖市场趋势、项目动态、技术进展及监管政策，提供权威的加密行业洞察。

Zcash says Ironwood proof rules out undetectable counterfeiting bugs

Zcash researchers have completed formal verification of Ironwood, a new shielded pool introduced via the NU6.3 upgrade. They published a machine-checked proof, written in Lean and comprising over 2,700 theorems, that establishes the pool's "balance integrity." This proof confirms that, under its cryptographic assumptions, Ironwood cannot contain undetectable counterfeiting bugs, ensuring it cannot pay out more value than has publicly entered it. The verification, which took multiple teams over a month, covers the zero-knowledge proof system, circuit rules, and ledger accounting but not Ironwood's separate privacy guarantees. Ironwood was created in response to a theoretical vulnerability in the older Orchard pool that could have allowed undetectable counterfeiting, though there's no evidence of exploitation. Funds migrating from Orchard must pass through a public "turnstile" checkpoint, designed to prevent any hypothetical excess coins from entering the new pool and to provide evidence on whether the old pool was exploited.

cointelegraph昨天 01:15

Zcash says Ironwood proof rules out undetectable counterfeiting bugs

cointelegraph昨天 01:15

GPT-5.6 Cracks a 50-Year-Old Math Problem in 1 Hour, 64 AIs Claim the Crown Jewel of Graph Theory

OpenAI announced that its AI model, GPT-5.6 Sol Ultra, has successfully proved the 50-year-old Cycle Double Cover (CDC) conjecture in graph theory in under an hour. This long-standing problem, posed independently by several prominent mathematicians, states that every bridgeless finite undirected graph contains a set of cycles where each edge is covered exactly twice. The breakthrough was achieved using a novel "parallel test-time computation" (TTC) approach. Instead of a single AI working sequentially, the system deployed 64 concurrent AI agents, each exploring distinct proof strategies—from algebraic perspectives to structural induction. The process included strict protocols to avoid common research pitfalls: initial exploration of fundamentally different paths, preventing herd mentality by not revealing the most promising direction, and employing a "critic squad" of agents to rigorously attack and verify every proposed proof step. The system forbade vague assertions, demanding concrete lemmas and constructions. The resulting proof, generated by GPT-5.6 and formatted with Codex, employed a sophisticated multi-step strategy. It first reduced the general case to cubic graphs, then leveraged Tutte's group-flow theorem to establish the existence of a nowhere-zero 8-flow on the graph. A key inventive step was introducing a "two-element set" labeling scheme (Lemma 2.1), which, if satisfied, guarantees a cycle double cover. The AI then transformed this combinatorial condition into a large system of linear equations (Lemma 2.2), using linear algebra over finite fields to conclusively demonstrate that a solution always exists. Researchers highlighted that parallel TTC dramatically compressed the reasoning time, making deep, extended AI problem-solving practically feasible. While some observers marveled at the implications for mathematics and science, others questioned whether parallel breadth can fully substitute for deep, continuous logical chains. Nonetheless, this achievement marks a significant advance in AI's autonomous capacity for high-level abstract reasoning and complex proof generation.

marsbit07/15 07:57

GPT-5.6 Cracks a 50-Year-Old Math Problem in 1 Hour, 64 AIs Claim the Crown Jewel of Graph Theory

marsbit07/15 07:57

Tsinghua AI Mathematician Emerges: From Intuition to Theorem, Contributing to an 84-Page Quantum Algorithm Paper

Tsinghua University’s Intelligent Industry Research Institute (AIR) has developed an AI mathematician agent named AIM, designed not just to solve math problems but to actively participate in early-stage research. In a recent study, researchers collaborated with AIM to develop "Sign Embedding Quantum Algorithms," resulting in an 84-page paper on quantum algorithms for matrix equations and functions. The research began with a human researcher's intuition: can rational approximation serve as a design principle for quantum algorithms? AIM helped expand this idea into multiple candidate research directions. Human researchers then filtered and focused on the most promising path. AIM assisted in organizing theorems, generating proof drafts, and performing complexity analysis, while humans maintained oversight, auditing assumptions and refining derivations. This case illustrates a human-AI collaborative workflow: AI rapidly explores and expands research avenues, generates draft materials, and aids in checking derivations; human researchers provide critical judgment on direction, value, and validity. The process emphasizes "high-throughput candidate generation + human value gating + AI-assisted audit and repair + human final integration." The resulting quantum algorithm framework offers a unified approach to several matrix problems, advancing quantum linear algebra under more general conditions. This work suggests AI's role in theoretical research is evolving from task-specific assistance to supporting the entire research lifecycle—enhancing exploration and efficiency while keeping human expertise central to guiding inquiry and ensuring rigor. *Paper & System Links:* - AIM application report: https://arxiv.org/abs/2606.24899 - Quantum algorithm paper: https://arxiv.org/abs/2604.25333 - AIM repository: https://github.com/TheoryFoundry/AIMv2

marsbit07/10 02:53

Tsinghua AI Mathematician Emerges: From Intuition to Theorem, Contributing to an 84-Page Quantum Algorithm Paper

marsbit07/10 02:53

In the AI Era, What's Left for Bitcoin?

As Bitcoin falls below $60,000, the author reflects on the relationship between AI and Bitcoin, seeing them as two sides of the same coin. In the AI era, the cost of generating content has plummeted, making fake text, images, and videos increasingly easy and cheap to produce. This has led to a fundamental shift: while AI dramatically lowers the cost of information production, it also undermines trust and authenticity online. What becomes truly valuable is not more content, but the ability to verify what is real—"verifiability." This perspective offers a new lens for Bitcoin. Its massive energy consumption, often criticized as wasteful, is reinterpreted. While AI burns energy to enhance "capability" and efficiency, Bitcoin burns energy to produce "verifiability." Its purpose is not to be trusted but to enable a system where no trust in intermediaries—banks, platforms, or developers—is needed. Every transaction and the entire ledger's history is secured by cryptography and a decentralized network of nodes, making it independently verifiable. AI cannot forge a transaction on the Bitcoin network because the system is designed for proof, not generation. The author draws a historical parallel to the Renaissance: the printing press drastically reduced the cost of copying knowledge, while double-entry bookkeeping reduced the cost of trust in commerce. Today, AI is the new printing press, reducing content creation costs to near zero. Blockchain, and Bitcoin as its pioneer, may be the modern equivalent of double-entry bookkeeping—a foundational technology for verifying digital asset ownership and historical records without centralized authorities. Thus, AI and blockchain are not competitors. AI lowers the cost of creation; blockchain lowers the cost of verification. In an age where AI can generate anything, true scarcity may lie not in more content, but in independently verifiable facts. Whether the market will reprice Bitcoin accordingly remains uncertain, but its core value proposition as a "machine for producing verifiability" becomes strikingly relevant.

marsbit06/30 15:57

In the AI Era, What's Left for Bitcoin?

marsbit06/30 15:57

The Crypto Industry Enters the 'Show Me' Era: Vision Alone Is No Longer Enough

The crypto industry has entered a "Show Me" era, where grand visions and white papers are no longer sufficient to gain traction. This shift is driven by increased skepticism, high-profile bad actors, and notably, the serious entry of traditional finance (TradFi) institutions like BlackRock, Fidelity, and JPMorgan Chase, which are launching real, scaled products such as tokenized funds and blockchain-based settlement. This raises the bar for what constitutes a credible project. The communication dynamic has fundamentally changed. The focus is no longer on "what you are building" but on "what you have built and who is using it." Startups must now provide a "proof stack": verifiable data like mainnet transaction volume and active wallets, genuine partnerships with signed contracts, and evidence of organic product-market fit from real users, not just investors. Announcements must be backed by concrete, chain-verifiable evidence. For communication strategies, this means leading with proven facts and hard data—even if modest—rather than speculative narratives. A compelling story must be grounded in demonstrated results. While vision remains important, the balance has inverted from 80% vision/20% substance to the opposite. This higher threshold ultimately benefits builders with genuine traction, filtering out noise and allowing their real signals to stand out clearly. The "Show Me" era is a permanent maturation, demanding that communication strategies prove value, not just promise it.

链捕手06/25 06:20

The Crypto Industry Enters the 'Show Me' Era: Vision Alone Is No Longer Enough

链捕手06/25 06:20

Michael Saylor Vows ‘We Buy Real Bitcoin,’ No Rehypothecation

Michael Saylor's firm MicroStrategy reaffirmed its Bitcoin acquisition strategy, stating it buys "real bitcoin" and does not engage in rehypothecation. This came in response to skepticism from Casa CTO Jameson Lopp, who questioned whether the company verifies that its Bitcoin holdings are not being rehypothecated by third-party custodians. The debate highlights concerns about transparency and proof of reserves for institutional Bitcoin custody. MicroStrategy disclosed purchasing 2,932 BTC for $264.1 million, bringing its total to 712,647 BTC. While some critics demanded public proof of addresses, others argued that traditional auditing and corporate controls provide sufficient validation. Saylor emphasized that the company audits its custodians and advised others to avoid rehypothecation. Bitcoin was trading at $88,001 at the time of reporting.

bitcoinist01/30 05:01

Michael Saylor Vows ‘We Buy Real Bitcoin,’ No Rehypothecation

bitcoinist01/30 05:01

MEXC Begins 2026 With Strong Reserves: January Audit Shows BTC Coverage at 158%

MEXC has released its January 2026 Proof of Reserve Audit Report, showing strong reserve ratios for all major assets. BTC coverage increased to 158%, while USDC rose to 140%. USDT and ETH remained at 127% and 107%, respectively. The exchange holds 6,172.88 BTC, $2.24 billion USDT, $111.54 million USDC, and 61,729.67 ETH in reserves. The audit, conducted by blockchain security firm Hacken, uses a Merkle Tree system to allow users to independently verify their balances. MEXC emphasizes its commitment to user asset security through excess reserves and regular third-party audits to ensure transparency and trust.

TheNewsCrypto01/14 10:16

MEXC Begins 2026 With Strong Reserves: January Audit Shows BTC Coverage at 158%

TheNewsCrypto01/14 10:16

活动图片

热门分类right-arrow

热门标签right-arrow

Technology Trendsright-arrow

Industry Newsright-arrow