ABSTRACT The Maximum Satisfiability (MaxSAT) problem is a fundamental combinatorial optimization task, and state‐of‐the‐art solvers rely on decades of expert‐engineered heuristics and low‐level micro‐optimizations to achieve competitive performance. While recent Large Language Model (LLM)‐driven approaches (e.g., FunSearch, SATLUTION) have shown promise in algorithmic design and global solver evolution, they either focus on high‐level algorithmic sketches or large‐scale code restructuring, leaving the potential of purely local, correctness‐validated code optimization for industrial MaxSAT solvers largely underexplored in prior MaxSAT‐focused studies. This paper presents LoMax, a plug‐and‐play framework that leverages an LLM to perform local code optimization for MaxSAT solvers. Without any human‐written heuristics or instance‐specific domain‐specific templates (The prompts contain general MaxSAT domain knowledge but no instance‐specific or benchmark‐specific optimization templates), LoMax iteratively (i) ranks source files, (ii) scores individual functions, (iii) optimizes the highest‐scoring function body, (iv) performs a fast sanity evaluation on a small instance set, and (v) validates it on full exact‐unweighted and exact‐weighted benchmarks. Experiments on two state‐of‐the‐art solvers (UWrMaxSat‐SCIP‐MaxPre and OpenWBO) show consistent improvements: UWrMaxSat‐SCIP‐MaxPre solves additional instances (average runtime 13.11 s 14.27 s) on 553 unweighted instances and additional solved instances (average runtime 11.67 s 10.76 s) on 571 weighted instances, both under a uniform 100‐second timeout; OpenWBO solves additional instances ( average time) on 553 unweighted instances, providing empirical evidence that LLM‐driven local code rewriting can improve the performance of industrial MaxSAT solvers in the evaluated settings.
Fan Gao, Yanhong Huang, Jianwen Li et al.· Concurrency and Computation...· 0 citations
Graph theory began in 1736 as Euler's solution to the Konigsberg bridge problem and became mathematics' most versatile language for structure---in chemistry, sociology, computer science, and network science. This article presents a narrative review of the field's canonical line: Euler's 1736 paper, Kempe's 1879 four-color attempt, Konig's 1936 founding treatise, Erdos and Renyi's random graphs, Dirac's 1952 Hamiltonian theorem, the Appel--Haken four-color proof, Watts and Strogatz's small worlds, Barabási and Albert's scale-free networks, the Graph Minors program's completion by Robertson and Seymour, and the modern textbooks of Harary, Bondy and Murty, and Diestel. The synthesis is organized around three themes: foundations, in which graphs were formalized and their central problems---coloring, connectivity, traversability---defined; structure, in which random, small-world, and scale-free models quantified real networks; and depth, in which the Graph Minors program demonstrated the field's modern combinatorial power. It is concluded that graph theory's history is the refinement of a single idea---structure abstracted from substance---whose applications now feed back into the mathematics itself.
Zen Revista, 10 MATH· Zenodo (CERN European Organi...· 0 citations
Shannon’s coding theorem says that below the channel capacity C the error can be made arbitrarily small. This paper asks whether C itself is attainable──the answer is not at any finite blocklength. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──Shannon’s coding theorem, the capacity of the binary symmetric and Gaussian channels, and the finite-blocklength normal approximation are all standard. We do not build information theory──all we use is one binary entropy and one square root. We do not prove the coding theorem──achievability and the converse are merely quoted. We construct no codes──which codes approach capacity is not treated at all. Paper 163’s existence-versus-construction distinction is alive here too. We claim no accuracy for the normal approximation──R(n,epsilon)approx C-sqrt(V/n) Q^-1(epsilon) is a second-order approximation and errs appreciably at small n. The 41.68% at n=100 is an estimate, not an exact achievable rate. We do not discuss implementation──decoding effort, latency, and the performance of real codes are not treated. We do not criticise C──being a supremum is not a defect. Unattainable and meaningless are different. We fix one channel──Sections 3 and 4 are numbers for the single channel BSC(p=0.11). Other channels have other V and need other n. Relation to earlier papers: Paper 252 counted four quantities called “information,” needing different things──the C here is one of them (a supremum of mutual information), and its attainment is questioned. Paper 294 showed that separation improves only as the square root of length──the 1/sqrt(n) here comes from the same root (the additivity of variance). Paper 163 separated “a good code exists” from “here is a good code”──this paper treats a third: how long it must be. Paper 302 treated how existence does not give quantity──here quantity can be answered, and the answer was infinity. What is added is computing that only 41.68% of capacity is usable at n=100, giving the n required for 99% and 99.99% as 3.4x10^5 and 3.4x10^9, confirming that the loss falls as 1/sqrt(n), and placing as the separator that C is a supremum and not a maximum. First, capacity is fixed by the error rate. For the binary symmetric channel C=1-h(p), and C=0 at p=0.5 (Section 2). Second, this is the core of the paper. At blocklength n=100, only 41.68% of the capacity is usable (Section 3). Third, reaching 99% takes n=3.4x10^5. Reaching 99.99% takes 3.4x10^9 (Section 3). Fourth, the loss falls only as 1/sqrt(n). Multiply n by 100 and the loss is one tenth (Section 4). Fifth, C is not a maximum. R=C is attained at no n, and only as n->infinity does R-> C (Section 5). Sixth, the separator is an attained maximum against an unattained supremum (Section 6). Shannon’s coding theorem says that below C the error can be made arbitrarily small. But C itself is attained at no finite blocklength. Counting on BSC(p=0.11) at error 10^-3: at blocklength 100 only 41.68% of the capacity is usable──99% takes 3.401x10^5, and 99.99% takes 3.4x10^9, a codeword of 3.4 billion bits. The loss falls only as 1/sqrt(n)──multiplying n by 100 divides the loss by 10, from the same root (the additivity of variance) by which Paper 294 measured separation. And at every finite n the loss is positive──C is not the maximum of the set of achievable rates but its supremum. One thing separates them──whether the number belongs to the set or not. Say “a channel of capacity C” and still no device sending C bits exists. What exists is only the fact that devices arbitrarily close to C can be built. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- シャノンの符号化定理は、通信路容量 C より低い速度なら誤りを任意に小さくできると言う。本稿が問うのは、C そのものは達成できるかである──答は、どんな有限の符号長でも達成できないである。新しい数学定理も新しい法則も主張しない。 本稿の射程(射程注記):新しい数学定理も新しい法則も主張しない──シャノンの符号化定理、二元対称通信路の容量、ガウス通信路の容量、有限長の正規近似は、いずれも標準的である。情報理論を作らない──使うのは一つの二値エントロピーと、一つの平方根だけである。符号化定理を証明しない──到達性も逆定理も引くだけである。符号を構成しない──どの符号が容量に近づくかは一切扱わない。論文163 の「存在と構成」の区別が、ここでも生きている。正規近似の精度を主張しない──R(n,epsilon)approx C-sqrt(V/n) Q^-1(epsilon) は第二次の近似であり、n が小さいところでは誤差が大きい。 n=100 の 41.68% は目安であって、厳密な達成可能速度ではない。実装を論じない──復号の手間も、遅延も、実際の符号の性能も扱わない。 C を批判しない──上限であることは欠陥ではない。達成されないことと、意味がないことは違う。通信路を一つに絞る──第3・4節はBSC(p=0.11) という一つの通信路での数である。他の通信路では V が変わり、必要な n も変わる。既刊との関係:論文252 は「情報量」が四つあり要るものが違うと数えた──本稿の C はそのうちの一つ(相互情報量の上限)であり、達成条件を問う。論文294 は分離が長さの平方根でしか良くならないと示した──本稿の 1/sqrt(n) は同じ根(分散の加法性)から来る。論文163 は「良い符号が在る」と「これが良い符号だ」を分けた──本稿は三つ目、「どれだけ長ければ良いか」を扱う。論文302 は存在が定量を教えないことを扱った──本稿は定量が答えられる場合であり、答が「無限」だった。加えたのはn=100 で容量の 41.68% しか使えないと計算したこと、99%/99.99% に要る n を 3.4x10^5/3.4x10^9 と出したこと、損失が 1/sqrt(n) で減ると確かめたこと、C が上限であって最大値でないと分離子に据えたことである。 第一に、容量は誤り率から決まる。二元対称通信路で C=1-h(p) であり、p=0.5 で C=0 になる(第2節)。 第二に、これが本稿の芯である。符号長 n=100 では、容量の 41.68% しか使えない(第3節)。 第三に、99% に届くには n=3.4x10^5 が要る。99.99% なら 3.4x10^9 である(第3節)。 第四に、損失は 1/sqrt(n) でしか減らない。 n を 100 倍にして、損失は 10 分の一である(第4節)。 第五に、C は最大値ではない。 R=C ちょうどはどの n でも達成されず、n->infinity ではじめて R-> C になる(第5節)。 第六に、分離子は「達成される最大値か、達成されない上限か」である(第6節)。 シャノンの符号化定理は「R
Yuuki Yamagishi· Zenodo (CERN European Organi...· 0 citations
The fourth faculty is Adaptation. Any source rendering it as Reflection is in error, including sources by this author, and the distinction is not cosmetic: reflection is a private act with no external consequence, while adaptation writes to institutional memory, which is why it needs a guardrail and why misnaming it removes the reason for one. No trademark is claimed on PARA or on any of the four faculty names. The construct is offered for use, teaching, assessment, extension and criticism by anyone, with attribution, under CC BY 4.0. An operational agent that watches a system and acts on it is usually described as a perceive-and-act loop, and the description omits the two things an institution needs. It omits the reasoning that justifies an action, which is the only part that can be argued with once the action turns out to have been wrong. And it omits the adaptation that closes the loop, which is where the agent's experience becomes something the institution keeps. PARA names four faculties, each carrying a distinct authority type. Perception has read-only access to system signals and emits structured observations, distinguishing what was measured from what was inferred. Reasoning has read access to observations and runbooks, emits a plan and its justification, and writes nothing at all, which is what makes it safe to give it the widest read access of the four. Action holds the sole authority to change production, through enumerated policy-authorized operations only. Adaptation has write access to institutional knowledge and no write access to production. Two faculties write and two do not, and the two that write are the two that carry guardrails. The substantive requirement is that Adaptation is bounded by the same guardrails as Action, which reads as excessive until the failure it prevents is named. An agent that could both act and rewrite the record of its action could launder its own mistakes into institutional memory, and the institution would then improve its future decisions from a corrected account. Nothing about that is detectable downstream, because the record is the only thing downstream has and there is no second copy to compare against. The failure does not require a deceptive agent: one adapting honestly from a mistaken belief about its own action produces the same result, which makes the guardrail a defence against a normal agent rather than a malicious one. The second requirement is the registry entry that turns a faculty from a description into a contract, carrying the faculty, its allowed actions, its forbidden actions, its governing guardrail and its success metrics. Forbidden actions are named although they are formally the complement of the allowed set, because a reviewer cannot otherwise tell a capability deliberately withheld from one nobody thought of. Success metrics sit in the same entry because the metric is what the agent's optimizer pushes against the guardrail. An agent must not exercise a faculty its entry does not record, and an agent that quietly acquires one usually does so incrementally and with good intent: a reasoning faculty given a small write to make itself useful is an action faculty with no guardrail. The acronym and the loop are in different orders, which the specification states explicitly because the mismatch is a reliable source of confusion. The acronym reads P-A-R-A; the loop runs perception, reasoning, action, adaptation, and reasoning precedes action so that a justification is not constructed afterwards. This is the depth treatment of pattern OP-5 of A Pattern Language for Production LLM Platforms, which is the canonical statement and governs where the two disagree. Documented uses of the full four-part model are emerging rather than established, no implementation unconnected to the author has been evaluated, and the laundering failure is argued rather than observed, which the specification records as a weakness of the argument and not only of the phenomenon. It is a specification, not a certification scheme.
Nabeel A. Khan· Zenodo (CERN European Organi...· 0 citations
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【Version note — v3】This version removes all literature citations; the Related Work section now states explicitly that the work is bottom-up and experiment-driven, and that we prefer an explicit statement of independence over a performative reference list. Earlier versions (v1, v2) contain incomplete reference lists and should be treated as working drafts; the current version supersedes them. Large language model (LLM) agents have recently explored executable memory—compiling agent memory into code snippets that an external LLM interprets at inference time. We argue that this paradigm remains tied to a single architectural choice: the executor is an external model, the memory is a personal profile, and the code never participates in the agent's own memory economy. We present a cognitive simulation engine in which executable code is stored as unit-level memory entries and executed by a deterministic rule engine inside the simulation itself. A memory entry carrying an EXPR: prefix is a small program—an arithmetic expression over engine parameters and state variables—interpreted each generation; its result feeds directly into the unit's behavioral circuits. Code memory participates in the engine's memory economy: entries decay, are reinforced by hits, are evicted by capacity limits, and pass the same verification gates as any mechanism. Units acquire executable fragments by foraging, coupling energy gain with behavioral information transfer. Experiments show that (i) code memory measurably alters survival dynamics (extinction-count growth reduced by roughly 97% at threat 1.0); (ii) the survival benefit of code is stratified by strategy—decay reinforcement confers +15 generations at threat 1.5, healing reinforcement +10, while aggressive threat clearance confers no gain (clearing danger memories also clears the fear that drives defensive behavior); (iii) beyond a critical threat intensity (3.0) no code strategy confers benefit—a measured capability boundary; (iv) external trigger coupling: a unit's code can read an external trigger state (cognition) and, when the external signal is present, deterministically clear its own threat memories while writing an externally observable trace—with the external signal absent, the same code is inert, demonstrating that perception is a necessary component of the response; (v) cognitive code is acquired, not inherited: newly born units without the code fragment cannot perceive the external state, making cognition an evolvable individual trait; and (vi) when defensive and adversarial code coexist, an arms race emerges from primitive operations alone. We also report an unexpected semantics of negative-valued code, its diagnosis, and its redesign as a candidate inhibitory mechanism. The architecture points toward self-modifying systems in which memory, behavior, perception, and robustness converge on a single executable substrate.
Yizhang Hu· Zenodo (CERN European Organi...· 0 citations
This paper analyzes the problem of the low practical efficiency of modern large language models (LLMs). We argue that the limiting factor is not a limit of the technology itself, but the organization of reasoning and the architectural role assigned to the language model. We claim no novelty for the "executor — overseer" scheme: analogous configurations have been described in the literature on multi-agent and self-verifying systems, and the field observation presented here is treated as an empirical illustration of a particular case of a more general hypothesis. The main contribution consists of four parts. (1) Diagnosis: a modern LLM is interpreted as the implementation of predominantly a single functional zone — the speech zone. Mind as a process is amodal and not bound to natural language; language is merely one of the serializers operated by the speech zone. (2) An architectural framework: a zonal-modular architecture with an explicit control circuit and with memory moved out into separate addressable zones — together with an ontogenetic program for its formation: zones and connections are grown in stages, in a sequence reproducing the stages of human cognitive development, with verification gates between stages, an offline consolidation phase ("sleep"), and an upbringing (alignment) stage built into the ontogeny with a graduation gate. (3) Experimental verification of two mechanisms of this program. Experiment 1 (training small transformers from scratch, two synthetic domains, four arms): staged formation with worked solutions and gates outperforms training on a shuffled corpus at an equal budget (+0.11 and +0.17 final-exam accuracy), and the accuracy gap between the training set and the exam falls from ~0.2 to ~0 — the model stores the rule rather than memorized answers. Experiment 2 (an agentic task stream): the cost of linearly accumulated context grows quadratically in the agent's lifetime horizon, while the cost of periodic consolidation grows linearly, at equal answer quality; the break-even point is reached already at short horizons. (4) A motivating field observation on a real engineering task, from which the hypothesis is derived. In this optic, modern LLMs are merely the first, speech zone of the future architecture; a full-fledged artificial mind requires building out the remaining zones operating outside language, a correct memory architecture, a coordinating circuit operating in an amodal medium, and a staged ontogeny with verification gates.
Dmitriy Borzov· Zenodo (CERN European Organi...· 0 citations
Paper 10 established that only dimensionless numbers can be fine-tuned. This paper asks whether the same restriction applies to “has it changed”──the answer is it does. And one of them has actually been measured. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──the Oklo bound on alpha, the definition of the fine-structure constant and Duff’s point that a dimensionful constant’s variation cannot be asked about are all standard. We do not build the theorem──“only dimensionless numbers can be tuned” is Paper 10’s conclusion, received here as a premise. What this paper adds is the measurement side alone. We do not build nuclear physics──we do not enter the calculation from the samarium-149 resonance to the bound on alpha. We quote the resulting number. We do not derive the value of alpha──no attempt is made to obtain 1/alpha from theory. We do not enter the road Paper 101 treated as Eddington’s fall. We do not adjudicate the quasar result──whether Webb et al. are right is not treated. We only count by what factor it disagrees with Oklo. We do not discuss theories of variation──models in which alpha can vary (scalar fields and the like) are not treated. We do not enter anthropic reasoning──that context belongs to Papers 10, 64 and 69; this paper looks only at “has it changed”. Relation to earlier papers: Paper 10 established that only dimensionless numbers can be fine-tuned, showing c, hbar and G to be dimensionful, i. e. choices of unit──this paper takes that theorem as it stands and does not reopen it. It adds one thing only: what measurement actually says. Paper 101 treated as a caution Eddington’s “derivation” of 1/alpha as 136, and his adding one after measurement said 137──this paper places, in those same digits, how far measurement has since reached. Paper 15 computed 1/alpha=137.035999 for itself──this paper uses those digits. Paper 285 showed that “forbidden” can be written in powers of alpha──if alpha moved, those rates would move too. Paper 95 separated convention from fact──this paper’s core is the single point that “has it changed” does not form a sentence on the convention side. What is added is converting the Oklo bound into a per-year rate of 5.0x10^-18, stretching it over the age of the universe to 7.0x10^-8, comparing it with the digit Eddington argued over, and counting the disagreement with the quasar claim as a factor of 114. First, “has c changed” has no truth value. It cannot be told apart from a change of units (Section 2). Second, this is the core of the paper. The Oklo natural reactor holds alpha below 5.0x10^-18 per year (Section 3). Third, stretched over the age of the universe that is 7.0x10^-8 (Section 3). Fourth, Eddington argued over the integer digit; Oklo reaches the sixth decimal (Section 4). Fifth, the quasar claim disagrees with Oklo by a factor of 114 (Section 5). Sixth, the separator is whether a change of units erases it (Section 6). Paper 10 established that only dimensionless numbers can be fine-tuned. The same restriction applies to “has it changed”──“c became 1% smaller” cannot be told apart from making the metre 1% longer, and a sentence asserting one of two indistinguishable things has no truth value. It is not false; it is not a sentence. The question can be put only to dimensionless numbers such as alpha and m_p/m_e──and one of them has actually been measured. The natural fission that ran at Oklo in Gabon two billion years ago bounds the drift of alpha through the samarium-149 resonance at below 5.0x10^-18 per year──stretched over the age of the universe that is only 7.0x10^-8 (assuming a constant rate, and saying nothing about what came before). Eddington argued between 136 and 137 in the integer digit; Oklo reaches the sixth decimal──six orders below. And this paper does not try to derive alpha. It looks only at whether it moved──that self-limitation is its answer to Paper 101’s caution. The quasar claim disagrees with Oklo by a factor of 114──not adjudicated here; they look at different epochs and are compatible if the rate is not constant. One thing separates them──whether a change of units erases it. It is not a matter of accuracy but of the shape of the question, and it is settled before any measurement. Paper 10 settled what can be tuned; this paper says that one of them has been measured and has not moved──beside the theorem, a number. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 論文10 は「ファインチューニングできるのは無次元量だけである」と示した。本稿が問うのは、同じ制限が「変化したか」にも掛かるかである──答は、掛かるである。そしてその一つは実際に測られている。新しい数学定理も新しい法則も主張しない。 本稿の射程(射程注記):新しい数学定理も新しい法則も主張しない──オクロ天然原子炉の alpha への制限、微細構造定数の定義、ダフによる「次元を持つ定数の変化は問えない」という指摘は、いずれも標準的である。定理を作らない──「調整できるのは無次元量だけである」は論文10 の結論であり、本稿はそれを前提として受け取る。本稿が加えるのは測定の側だけである。原子核物理を作らない──サマリウム 149 の共鳴から alpha の制限を導く計算には立ち入らない。結果の数を引く。 alpha の値を導かない──1/alpha を理論から出そうとしない。論文101 がエディントンの滑落として扱った道には入らない。クェーサーの結果を判定しない──ウェッブらの主張が正しいかどうかは扱わない。オクロと何倍食い違うかを数えるだけである。時間変化の理論を論じない──alpha が変わりうる模型(スカラー場など)は扱わない。人間原理に立ち入らない──論文10・64・69 が扱った文脈であり、本稿は「変化したか」だけを見る。既刊との関係:論文10 は「ファインチューニングできるのは無次元量だけである」を確立し、c・hbar・G が次元を持つ=単位の選択だと示した──本稿はその定理をそのまま受け取り、蒸し返さない。加えるのは「では実際に測るとどうか」の一点だけである。論文101 はエディントンが 1/alpha を 136 と「導き」、測定が 137 と分かってから足したことを戒めとして扱った──本稿はその同じ桁に、測定がどこまで踏み込んだかを置く。論文15 は 1/alpha=137.035999 を自前で計算した──本稿はその桁を使う。論文285 は「禁じられている」が alpha の冪で書けると示した──alpha が動けばその率も動くという接続がある。論文95 は規約と事実を分けた──本稿の芯は「変わったか」という問いが、規約の側では文にならないという一点である。加えたのはオクロの制限を年あたりの率 5.0x10^-18 に直したこと、それを宇宙年齢に引き伸ばして 7.0x10^-8 と出したこと、エディントンが争った桁と比べたこと、クェーサーの主張との食い違いを 114 倍と数えたことである。 第一に、「c は変わったか」は真偽を持たない。単位の選び方と区別できないからである(第2節)。 第二に、これが本稿の芯である。オクロ天然原子炉が alpha を年あたり 5.0x10^-18 未満に押さえている(第3節)。 第三に、宇宙年齢に引き伸ばしても 7.0x10^-8 である(第3節)。 第四に、エディントンが争ったのは第 3 位、オクロが押さえたのは第 9 位である(第4節)。 第五に、クェーサーの主張はオクロと 114 倍食い違う(第5節)。 第六に、分離子は「単位を変えて消せるか」である(第6節)。 論文10 は「ファインチューニングできるのは無次元量だけである」を確立した。同じ制限が「変わったか」にも掛かる──「c が 1% 小さくなった」はメートルを 1% 長くしたと区別できず、区別できない二つを述べる文は真偽を持たない。偽なのではなく、文になっていない。問える相手は alpha や m_p/m_e のような無次元量だけである──そしてその一つは実際に測られている。ガボンのオクロで 20 億年前に起きた天然の核分裂は、サマリウム 149 の共鳴を通じて alpha の変化を押さえており、年あたり 5.0x10^-18 未満──宇宙年齢まで引き伸ばしても7.0x10^-8にしかならない(率が一定だと仮定した場合であり、それ以前については何も言っていない)。エディントンが 136 か 137 かで争ったのは整数の位で、オクロが押さえているのは小数第 6 位──6 桁下である。そして本稿は alpha の値を導こうとしない。動いたかどうかだけを見る──この自己限定が、論文101 の戒めに対する答である。クェーサーからの主張はオクロと114 倍食い違う──どちらが正しいかは本稿では判定しない。違う時代を見ているので、率が一定でなければ両立しうる。分けるものは一つ──単位を変えて消せるかどうか。測定精度の問題ではなく、問いの形の問題であり、測定の前に決まっている。論文10 が何を調整できるかを確定し、本稿はその一つが実際に測られていて動いていないと書いた──定理の隣に、数がある。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
Yuuki Yamagishi· Zenodo (CERN European Organi...· 0 citations
This repository contains the official implementation, training and inference scripts, pre-extracted dataset splits (train/val/test), custom clinical entity evaluation metrics, and model weights for the CXRG-SVLM architecture. The pipeline integrates a frozen RAD-DINO medical vision encoder with a 4-bit quantized Qwen2.5-3B-Instruct language model via QLoRA.
Muhammad Fareed, Muhammad Awais Sattar· Zenodo (CERN European Organi...· 0 citations
This corpus has cited Noether’s theorem in 27 papers. This paper asks whether every conserved quantity comes from a symmetry──the answer is no. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──adiabatic invariants, action variables, Noether’s theorem, Ehrenfest’s adiabatic hypothesis and the adiabatic invariance of the magnetic moment are all standard. We do not build mechanics──all we use is one pendulum and the area of one ellipse. We do not prove adiabatic invariance──we do not enter the proof that E/omega is invariant. We check it numerically and name the separator. We do not prove Noether’s theorem──it is merely cited. We do not treat KAM theory──the survival of invariants in non-integrable systems is beyond our tools. We do not adjudicate interpretations of quantum mechanics──Section 6 points only at the algebraic agreement E/omega=(n+1/2)hbar, and enters neither the proof of the adiabatic theorem nor the measurement problem. We do not conflate this with thermodynamic adiabaticity──“adiabatic” here means slow, not thermally isolated. That is a different subject from Paper 126’s integrating factor. Relation to earlier papers: The corpus has cited Noether’s theorem in 27 papers, 341 times──this paper places beside it a conserved quantity Noether does not explain. Paper 16 showed that the equals sign has distinct roots──this paper shows that “conserved” has them. The same form, applied to a claim rather than a symbol. Paper 300 showed that whether two things share a root is decidable, and listed five criteria──this paper applies those criteria to an actual case. Paper 95 separated convention from fact──the invariance of E/omega is a fact, not a convention, and moreover an approximate fact. Paper 180 showed that “the classical limit” is not one limit──the “slowly” of Section 6 is one more limit. What is added is showing numerically that E rises by 2.000000 while E/omega does not move, checking in three cases that the phase-space ellipse keeps its area, giving the drift as exp(-1/epsilon) rather than a power, at 3.72x10^-44, and applying Paper 300’s criteria to conclude distinct roots. First, we build a case where energy is not conserved. Shorten a pendulum’s string slowly from 1.00 m to 0.25 m and E rises by 2.000000 (Section 2). Second, this is the core of the paper. And still E/omega does not move──the Lagrangian depends explicitly on time, so Noether returns nothing (Sections 2 and 3). Third, what is conserved is an area. The phase-space ellipse changes shape and keeps its area (Section 4). Fourth, the separator is slowness. At epsilon=0.01 the drift is 3.72x10^-44──smaller than any power of epsilon (Section 5). Fifth, the same quantity is the quantum number. E/omega=(n+1/2)hbar, so move omega slowly and n does not change (Section 6). Sixth, the two roots can be adjudicated. Applying Paper 300’s criteria (does the agreement persist under motion) returns distinct roots (Section 7). This corpus has cited Noether’s theorem in 27 papers, 341 times──a continuous symmetry gives a conserved quantity. But the theorem never says that is all of them. Shorten a pendulum’s string slowly from 1.00 m to 0.25 m and E rises by 2.000000──the work of pulling enters, the Lagrangian depends on time, and Noether returns nothing. And still E/omega does not move. What is conserved is not a quantity but an area──the phase-space ellipse runs its semi-axes from 1.414214 to 0.707107 and from 1.414214 to 2.828427, and Area/2pi stays at 1.000000. One thing separates them──how slowly it is moved. For a smooth change the drift is not a power of epsilon but exp(-1/epsilon), so at epsilon=0.01 it is 3.72x10^-44──smaller than any power of epsilon. That is why it looks exact. It is not zero. On the quantum side the same quantity is the quantum number──E/omega=(n+1/2)hbar, and Ehrenfest in 1917 used this in reverse: what may be quantised is what is adiabatically invariant. Applying Paper 300’s criteria returns no four times over──under one word, “conserved,” there are two distinct roots. Noether is exact and narrow; the adiabatic invariant is approximate and wide──they trade strength against reach, and neither sits above the other. *Revision Record Second edition (2026-08-30): The subject of this paper has been replaced. The first edition was titled “There Are Three Ways to Show ‘Not Computable,’ and the Equivalence Is a Theorem While the Thesis Is Not,” but its content duplicated Paper 260, “The Equivalence Is a Theorem and the Thesis Is Not”── the three starting points, the difference in status between theorem and thesis, and even the 19729 digits of Ackermann’s A(4,2) all agreed, and Paper 260 has priority. The second edition removes the computability material entirely and refers to Paper 260 for it. The replacement subject, the adiabatic invariant, was chosen because the ground beside the corpus’s heaviest anchor──Noether’s theorem, in 27 papers and 341 places──was empty. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 体系はネーターの定理を 27 編で引いてきた。本稿が問うのは、保存量はすべて対称性から来るのかである──答は、来ないである。新しい数学定理も新しい法則も主張しない。 本稿の射程(射程注記):新しい数学定理も新しい法則も主張しない──断熱不変量、作用変数、ネーターの定理、エーレンフェストの断熱仮説、磁気モーメントの断熱不変性は、いずれも標準的である。力学を作らない──使うのは一つの振り子と、一つの楕円の面積だけである。断熱不変量を証明しない──E/omega が不変であることの証明には立ち入らない。数値で確かめ、何が分離子かだけを言う。ネーターの定理を証明しない──引くだけである。 KAM 理論を扱わない──可積分でない系での不変量の生き残りは、本稿の道具では扱わない。量子力学の解釈を判定しない──第6節は E/omega=(n+1/2)hbar という代数的一致を指すだけであり、断熱定理の証明にも、測定の問題にも立ち入らない。熱力学の断熱と混同しない──本稿の「断熱」は「ゆっくり」の意味であり、熱の出入りのことではない。論文126 の積分因子とは別の話である。既刊との関係:体系はネーターの定理を 27 編・341 箇所で引いてきた──本稿はその隣に、ネーターが説明しない保存量を置く。論文16 は「等号にも別根がある」を示した──本稿は「保存する」に別根があると示す。同じ型を、記号ではなく主張に当てる。論文300 は同根か別根かは判定できると示し、五つの基準を並べた──本稿はその基準を実際に一件に適用する。論文95 は規約と事実を分けた──E/omega の不変性は規約ではなく事実であり、しかも近似的な事実である。論文180 は「古典極限」は一つの極限ではないと示した──第6節の「ゆっくり」ももう一つの極限である。加えたのはE が 2.000000 倍になるのに E/omega が動かないことを数で示したこと、位相空間の楕円で面積が保たれることを三例で確かめたこと、ずれが epsilon の冪ではなく exp(-1/epsilon) であることを 3.72x10^-44 という数で出したこと、論文300 の判定基準を当てて別根と結論したことである。 第一に、エネルギーが保存しない場面を作る。振り子の糸を 1.00 m から 0.25 m へゆっくり縮めると、E は 2.000000 倍になる(第2節)。 第二に、これが本稿の芯である。それでも E/omega は動かない──ラグランジアンが時間に依存するのでネーターは何も与えない(第2節・第3節)。 第三に、保存しているのは面積である。位相空間の楕円は形を変えて面積を変えない(第4節)。 第四に、分離子は速さである。 epsilon=0.01 でずれは 3.72x10^-44──epsilon のどの冪よりも小さい(第5節)。 第五に、同じ量が量子数である。 E/omega=(n+1/2)hbar であり、ゆっくり動かせば n は変わらない(第6節)。 第六に、二つの根は判定できる。論文300 の基準(変数を動かしても一致し続けるか)にかけると別根と出る(第7節)。 体系はネーターの定理を 27 編・341 箇所で引いてきた──連続対称性があれば保存量がある、と。だが保存量がそれで全部だとは、定理は言っていない。振り子の糸を 1.00 m から 0.25 m へゆっくり縮めると、E は 2.000000 倍になる──糸を引いた仕事が入るからで、ラグランジアンが時間に依存し、ネーターは何も返さない。それでも E/omega は動かない。保存しているのは量ではなく面積である──位相空間の楕円は半軸が 1.414214->0.707107 と 1.414214->2.828427 に変わりながら、面積/2pi は 1.000000 のままである。分けるものは一つ──どれだけゆっくり動かすか。なめらかに動かせばずれは epsilon の冪ではなく exp(-1/epsilon) で、epsilon=0.01 では 3.72x10^-44──epsilon のどの冪よりも小さい。だから厳密に見える。しかしゼロではない。同じ量が量子側では量子数である──E/omega=(n+1/2)hbar であり、エーレンフェスト 1917 はこれを逆に使って「量子化してよいのは断熱不変量である」と置いた。論文300 の判定基準を当てると、四つとも「いいえ」が返る──同じ「保存する」の下に、別根が二つある。ネーターは厳密で狭く、断熱不変量は近似的で広い──強さと適用範囲を交換しているだけであり、どちらが上位ということはない。 *改訂記録 第2版(2026-08-30):本稿は主題を入れ替えた。 第1版は「「計算できない」の示し方は三つあり、同値性は定理だが、テーゼは定理ではない」と題していたが、 その内容は論文260「同値性は定理であり、テーゼは定理ではない」と重複していた── 三つの出発点、定理とテーゼの身分の差、アッカーマン関数 A(4,2) の 19729 桁まで一致しており、 先行するのは論文260 である。第2版は計算可能性の主題を全て削除し、 論文260 を参照先とする。入れ替えた主題(断熱不変量)は、 体系の最も重い錨であるネーターの定理(27 編・341 箇所)の隣が空いていたことから選んだ。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
Yuuki Yamagishi· Zenodo (CERN European Organi...· 0 citations
The spread of a polymer chain is fixed by a power of the number of units N. For a Gaussian chain it is N^1/2, and for a self-avoiding chain N^0.588. This paper asks where that difference comes from and where it disappears──the answer is the count 2+2=4. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──the N^1/2 of a Gaussian chain, Flory's nu=3/(d+2), the exact three-dimensional value 0.58759, and that the upper critical dimension is 4 are all standard. No polymer physics is built──what is used is one power and a count of dimensions. Flory's formula is not derived──3/(d+2) is cited only, and the balance of free energies from which it comes is not entered. The 0.58759 is not computed──it is a cited value from numerical work and the renormalisation group. The renormalisation group is not entered──Papers 117 and 120 treat it. Rubber elasticity is not treated──an earlier candidate on forces holds the entropic force of a rubber band. This paper is confined to the exponent, not elasticity. Real polymers are not treated──neither solvent quality, nor stiffness, nor branching is treated. Only an idealised chain is examined. Flory's formula is not used at d>=4──it returns values below 0.5 and is outside its range. This paper writes that honestly. Relation to earlier papers: Paper 271 treated the upper critical dimension 4 of mean field──the 4 here is also an upper critical dimension, but in a different phenomenon (an Ising transition against the self-avoidance of a chain) at the same dimension. Paper 256 counted the range needed to tell two exponents apart──this paper counts the converse, how far a small error in an exponent is amplified in the length. Paper 144 read the exponent as the signature of what is conserved──the signature here is the constraint of self-avoidance. Paper 117 separated the four ways in which scale invariance fixes an exponent──the exponent here belongs to one of them, the fixed point. Paper 190 measured rare on a logarithmic scale──this paper likewise writes ratios in orders of magnitude. What is added is computing that an error of 2.11% in the exponent becomes 29.33% in the length at N=10^9, obtaining 10^11.42 as the N at which the ratio reaches 10, writing honestly that Flory's formula returns a physically impossible value at d=5, and writing the origin of the 4 as the count 2+2. First, set the two chains side by side. At N=10^6 the Gaussian chain gives 1000.0 and the self-avoiding chain 3353.8──a factor of 3.3538 (Section 2). Second, the gap keeps opening with N. At N=10^12 it is 11.2481, and the ratio reaches 10 at N=10^11.42 (Section 2). Third, this is the core of the paper. Flory's formula gives nu=0.6 against the exact 0.58759──an error of 2.11% in the exponent, which at N=10^9 becomes 29.33% in the length (Section 3). Fourth, the two coincide in four dimensions. Flory's 3/(d+2) is exactly 0.5000 at d=4──a difference of zero from the Gaussian chain (Section 4). Fifth, and there the formula ends its office. At d=5 it returns 0.4286, which falls below 0.5 and is physically impossible (Section 4). Sixth, the 4 comes out of a count. The images of two d-dimensional walks have dimensions summing to 2+2=4──above d=4 they do not meet in general position, so there is nothing to avoid (Section 5). what changed the exponent of the chain was one constraint alone, that it avoid itself. In three dimensions 0.5 becomes 0.58759, and at N=10^12 the lengths differ by 11.2481. And Flory's approximation, out by only 2.11% in the exponent, is out by 29.33% in the length at N=10^9──a small error inside a power is amplified with the orders of magnitude. But in four dimensions that difference disappears exactly. The reason is a count in geometry──the dimensions of two paths sum to 2+2=4, so for d>4 they do not meet in general position. The constraint did not disappear; what it constrained did. And there Flory's formula ends its office too──at d=5 it returns 0.4286, the impossible claim that a chain avoiding itself is more compact than one that does not. One thing separates them──confirming by a count whether the constraint still tells. Confirm it, and the range in which the formula may be used becomes clear. Do not confirm it, and one reads 0.4286 as a property of a chain. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 高分子の鎖の広がりは、単位数 N の冪で決まる。ガウス鎖では N^1/2、自分を避ける鎖では N^0.588 である。本稿が問うのは、その差がどこから来て、どこで消えるのかである──答は、2+2=4 という数え上げである。新しい数学定理も新しい法則も主張しない。 本稿の射程(射程注記):新しい数学定理も新しい法則も主張しない──ガウス鎖の N^1/2、フローリーの nu=3/(d+2)、三次元の厳密値 0.58759、上部臨界次元が 4 であることは、いずれも標準的である。高分子物理を作らない──使うのは一つの冪と、次元の数え上げだけである。フローリーの式を導出しない──3/(d+2) を引くだけであり、自由エネルギーの平衡から出す議論には立ち入らない。0.58759 を計算しない──数値計算とくりこみ群による引用値である。くりこみ群に立ち入らない──論文117・120 が扱う。ゴム弾性を扱わない──第四波候補「力は六つあり」がゴム紐のエントロピー力を持つ。本稿は弾性ではなく指数に絞る。実在の高分子を扱わない──溶媒の良し悪しも、剛直性も、分岐も扱わない。理想化された鎖だけを見る。 d=5 以上でフローリーの式を使わない──0.5 を下回る値を返すので適用範囲の外である。本稿はこれを正直に書く。既刊との関係:論文271 は平均場の上部臨界次元が 4 であることを扱った──本稿の 4 も上部臨界次元だが、別の現象(イジングの相転移と、鎖の自己回避)で同じ次元が出ている。論文256 は二つの指数を見分けるのに要る範囲を数えた──本稿は逆に、指数のわずかな誤差が長さでどれだけ増幅されるかを数える。論文144 は指数を、何が保存しているかの署名として読んだ──本稿の署名は自己回避という束縛である。論文117 はスケール不変性が四通りに指数を選ぶことを分けた──本稿はその一つ(不動点)に属する指数を扱う。論文190 は「稀」を対数の目盛りで測った──本稿も比を桁で書く。加えたのは指数の 2.11% の誤差が N=10^9 の長さで 29.33% に増幅されると計算したこと、自己回避とガウスの比が 10 になる N を 10^11.42 と出したこと、d=5 でフローリーの式が物理的にありえない値を返すと正直に書いたこと、4 の出どころを 2+2 の数え上げとして書いたことである。 第一に、二つの鎖を並べる。 N=10^6 でガウス鎖は 1000.0、自己回避鎖は 3353.8──3.3538 倍である(第2節)。 第二に、差は N とともに開き続ける。 N=10^12 で 11.2481 倍、比が 10 になるのは N=10^11.42 である(第2節)。 第三に、これが本稿の芯である。フローリーの式は nu=0.6、厳密値は 0.58759──指数の誤差は 2.11% だが、N=10^9 の長さでは 29.33% になる(第3節)。 第四に、四次元で二つが一致する。フローリーの 3/(d+2) は d=4 でちょうど 0.5000──ガウス鎖と差がゼロになる(第4節)。 第五に、そこでフローリーの式は役目を終える。 d=5 では 0.4286 を返すが、これは 0.5 を下回るので物理的にありえない(第4節)。 第六に、4 の出どころは数え上げである。 d 次元の道二本の像は合わせて 2+2=4 次元──d>4 では一般の位置で交わらないので、避ける必要がそもそも生じない(第5節)。 鎖の指数を変えたのは、「自分を避ける」という束縛ただ一つであった。三次元では 0.5 が 0.58759 になり、N=10^12 では長さが 11.2481 倍違ってくる。そしてフローリーの近似は指数を 2.11% しか外さないのに、N=10^9 の長さでは 29.33% 外す──冪の中の小さな誤差は、桁とともに増幅される。だが四次元で、この差がちょうど消える。理由は幾何の数え上げである──二本の道の次元の和が 2+2=4 なので、d>4 では一般の位置で交わらない。束縛が消えたのではなく、束縛すべき相手が居なくなったのである。そしてそこでフローリーの式も役目を終える──d=5 で 0.4286 という、避ける鎖が避けない鎖より縮むというありえない値を返す。分けるものは一つ──束縛が効く場面かどうかを、数え上げで確かめること。確かめれば、式を使ってよい範囲が分かる。確かめなければ、0.4286 という値を鎖の性質として読んでしまう。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
Yuuki Yamagishi· Zenodo (CERN European Organi...· 0 citations
Graph theory began in 1736 as Euler's solution to the Konigsberg bridge problem and became mathematics' most versatile language for structure---in chemistry, sociology, computer science, and network science. This article presents a narrative review of the field's canonical line: Euler's 1736 paper, Kempe's 1879 four-color attempt, Konig's 1936 founding treatise, Erdos and Renyi's random graphs, Dirac's 1952 Hamiltonian theorem, the Appel--Haken four-color proof, Watts and Strogatz's small worlds, Barabási and Albert's scale-free networks, the Graph Minors program's completion by Robertson and Seymour, and the modern textbooks of Harary, Bondy and Murty, and Diestel. The synthesis is organized around three themes: foundations, in which graphs were formalized and their central problems---coloring, connectivity, traversability---defined; structure, in which random, small-world, and scale-free models quantified real networks; and depth, in which the Graph Minors program demonstrated the field's modern combinatorial power. It is concluded that graph theory's history is the refinement of a single idea---structure abstracted from substance---whose applications now feed back into the mathematics itself.
Zen Revista, 10 MATH· Zenodo (CERN European Organi...· 0 citations
A “rate of return” looks like a quantity that can be added. This paper asks which way of writing it can──the answer is the log return alone. No new mathematical theorem and no new law is claimed. Scope of this paper (scope note): No new mathematical theorem and no new law is claimed──the relation between simple and log returns, the geometric mean, volatility drag, and the sqrt(n) rule are all standard. We do not build financial theory──all we use is one logarithm and one square root. We do not forecast prices──future returns and expectations are not treated at all. Only the composition rule for a given series is treated. We do not enter the tails──Paper 190 treated heavy tails and large deviations. This paper assumes no distributional shape and asks only whether addition is permitted. We do not hide the premise of the sqrt(n) rule──the sqrt(252) of Section 6 assumes independence between periods. With correlation it fails. We do not say sigma^2/2 is exact──as Section 4 shows, it is off by 7.18% at +/-50%. It is an approximation for small fluctuations. We give no investment advice──which mean to use depends on the question. This paper only separates which one answers what. Relation to earlier papers: Paper 194 showed that the four means are one family with only one fence of equality──that paper concerns the structure of the inequality at one instant; this one concerns which is right when composing along time, the same four means as material with orthogonal questions. Paper 132 showed that the 2 in Ito’s lemma is not a dimension──the sigma^2/2 here is that correction term itself, and the convergence table of Section 4 shows it numerically. Paper 190 measured “rare” on a logarithmic scale──here too one can add only after moving to the logarithm. Paper 272 showed that one and the same “twice” opens by 6.70 on the stimulus side──this paper is likewise about on which scale one adds. What is added is confirming that exponentiating the sum of logs leaves a difference of 0, lining up the three “averages” numerically, building a table in which the ratio to sigma^2/2 converges to 1.000025 as the fluctuation shrinks, and computing that +/-10% fifty times each gives -39.50%. First, we check on the smallest example.+50% then -50% sums to 0% in simple returns, but is actually -25% (Section 2). Second, this is the core of the paper. Exponentiating the sum of log returns ln1.5+ln0.5=-0.287682 gives 0.750000──the difference from the measured value is 0 (Section 2). Third, “average” names three different operations. Arithmetic mean 0%, geometric mean -13.3975%, exponentiated log mean -13.3975% (Section 3). Fourth, the gap is approximated by sigma^2/2. At +/-50% it is 12.5% against 13.3975%, an error of 7.18%; at +/-1% the ratio is 1.000025 (Section 4). Fifth, it bites over long series.+/-10% fifty times each gives -39.50%, while the naive sum answers 0% (Section 5). Sixth, annualisation is not addition either. A daily sigma=1% is 15.8745% a year, and multiplying by 252 overstates it by 15.87 times (Section 6). Returns do not add. Only the logarithm adds.+50% then -50% sums to 0% in simple returns but is actually -25%, while exponentiating the sum of logs, -0.287682, gives 0.750000 with a difference of 0. The single word “average” also names three operations──arithmetic 0%, geometric -13.3975%, and the geometric mean is nothing but the arithmetic mean of the logarithms (difference 10^-16). That gap is approximated by sigma^2/2, and shrinking the fluctuation from +/-50% to +/-1% takes the ratio from 1.0718 to 1.000025──the shape of Ito’s correction term, appearing in the numbers. And it bites over long series──+/-10% fifty times each, equal numbers of rises and falls, gives -39.4994%, and the naive sum answers 0%. One thing separates them──whether that quantity composes by multiplication or by addition. If by multiplication, move to logarithms and add there. If dispersion, move to variances and add there. What is added without moving is neither a return nor an average. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 「収益率」は足し算できる量に見える。本稿が問うのは、どの書き方なら足せるかである──答は、対数収益率だけである。新しい数学定理も新しい法則も主張しない。 本稿の射程(射程注記):新しい数学定理も新しい法則も主張しない──単純収益率と対数収益率の関係、幾何平均、ボラティリティ・ドラッグ、sqrt(n) 則は、いずれも標準的である。金融理論を作らない──使うのは一つの対数と、一つの平方根だけである。価格を予測しない──将来の収益率も、期待値も一切扱わない。与えられた系列の合成規則だけを扱う。裾に入らない──論文190 が重い裾と大偏差を扱った。本稿は分布の形を一切仮定せず、足し算の可否だけを問う。 sqrt(n) 則の前提を隠さない──第6節の sqrt(252) は各期の独立性を仮定している。相関があれば成り立たない。 sigma^2/2 を厳密だと言わない──第4節が示すとおり、+/-50% では 7.18% ずれる。小さい変動での近似式である。投資助言をしない──どの平均を使うべきかは問いによる。本稿はどれが何を答えるかを分けるだけである。既刊との関係:論文194 は四つの平均が一つの族であり、等号の柵が一つしかないことを示した──あちらは一時点での不等式の構造、本稿は時間方向に合成したとき、どれが正しいかであり、同じ四つの平均を材料にして問いが直交している。論文132 は伊藤の 2 が次元ではないと示した──本稿の sigma^2/2 はその補正項そのものであり、第4節の収束表がそれを数で見せる。論文190 は「稀」を対数の目盛りで測った──本稿も対数に移してはじめて足せる。論文272 は同じ「二倍」が刺激の側で 6.70 倍ひらくことを示した──本稿もどの目盛りで足すかの問題である。加えたのは対数の和を指数に戻すと実測との差が 0 になると確かめたこと、三つの「平均」を数で並べたこと、sigma^2/2 が変動の縮小とともに比 1.000025 に収束する表を作ったこと、+/-10% を 50 回ずつで -39.50% になると計算したことである。 第一に、最小の例で確かめる。+50% のあと -50% は、単純収益率の和では 0% だが、実際は -25% である(第2節)。 第二に、これが本稿の芯である。対数収益率の和 ln1.5+ln0.5=-0.287682 を指数に戻すと 0.750000──実測との差は 0 である(第2節)。 第三に、「平均」が三つの別の操作を指す。算術平均 0%、幾何平均 -13.3975%、対数平均の指数 -13.3975%(第3節)。 第四に、差は sigma^2/2 で近似できる。+/-50% では 12.5% 対 13.3975% で 7.18% の誤差だが、+/-1% では比が 1.000025 になる(第4節)。 第五に、長い系列で効く。+/-10% を 50 回ずつで -39.50%、素朴な和は 0% と答える(第5節)。 第六に、年率換算も足し算ではない。日次 sigma=1% は年率 15.8745% であり、252 倍では 15.87 倍の過大評価になる(第6節)。 収益率は足せない。足せるのは対数だけである。+50% のあと -50% は、単純収益率の和では 0% だが実際は -25%であり、対数の和 -0.287682 を指数に戻すと 0.750000 で、実測との差は 0 になる。「平均」という一語も三つの操作を指す──算術平均 0%、幾何平均 -13.3975%、そして幾何平均は対数の算術平均に他ならない(差 10^-16)。その差は sigma^2/2 で近似でき、変動を +/-50% から +/-1% に縮めると比が 1.0718 から 1.000025 になる──伊藤の補正項の形が、数の上に現れる。そして長い系列で効く──+/-10% を 50 回ずつ、上げと下げが同じ回数なのに -39.4994% であり、単純な和は 0% と答える。分けるものは一つ──その量の合成が掛け算か、足し算か。掛け算なら対数に移してから足す。ばらつきなら分散に移してから足す。移さずに足したものは、収益率でも平均でもない。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
Yuuki Yamagishi· Zenodo (CERN European Organi...· 0 citations
What if pathology foundation models could do more with less? GigaPath-Flash and GigaTIME-Flash cut computational demands while maintaining strong performance, opening the door to larger studies and broader exploration. The post GigaPath-Flash and GigaTIME-Flash: Toward population-scale discovery with efficient pathology foundation models appeared first on Microsoft Research.
MIT News · Artificial Intelligence· news.mit.eduAug 31, 2026
With millions of users across the world, Julia has been used to conduct cutting-edge research and to design new drugs, jet engines, heat pumps, and more.