small language model

Rhythm Across Species: Situating Human Speech in a Comparative Framework

ABSTRACT At the level of smaller linguistic units, such as words and syllables, rhythm is characterized by a high degree of heterogeneity between languages. This suggests that it is distinct from nonhuman animal communication, where underlying isochrony is often observed. In this study, we examine speech rhythm using units similar to those previously examined for nonhuman animals: interonset intervals (IOIs), that is, sound elements surrounded by silence. Surprisingly, IOI durations are relatively similar across a comprehensive sample of 48 languages from all inhabited continents, with a median of approximately 2 s. IOI beats are also relatively similar at around 0.5 Hz, and human speech fits between exemplary animal species in terms of rhythmic variability and beat precision, that is, the extent to which an isochronous beat model fits the sequence. By revealing cross‐linguistic regularities and comparing them to those of other animal species, our results help to position human speech within the broader spectrum of rhythmic vocal behavior observed in nature.

Developing an ICT-Based Multiplication House Game for Ele-mentary Mathematics: Validity, Practicality, and Learning Perfor-manc

This study aims to develop an ICT-based Multiplication House learning media that is valid, practical, and feasible for use in elementary school mathematics learning. This research employs a development research design using the Plomp model, which consists of four phases: initial investigation, design, realization, and evaluation. The study involved 20 third-grade students of SD Laboratory UNESA as research subjects. The instruments used include (1) validation sheets to assess the content, format, and language validity of the media, (2) observation sheets to examine student engagement during learning, (3) questionnaires to measure students’ responses and practicality, and (4) learning outcome tests to evaluate students’ mastery of multiplication concepts. The developed media is designed as an interactive educational game that encourages students to explore strategies and solve multiplication problems competitively. The novelty of this study lies in the integration of traditional multiplication house media into an ICT-based platform equipped with features such as automatic answer randomization, real-time feedback, turn-based interaction, and dynamic game evaluation, which promote higher student engagement and strategic thinking. The results show that the ICT-based Multiplication House media meets the validity criteria, with an average score of 80.3% from material experts and 78% from media experts, both categorized as valid. The media is also considered highly practical, indicated by an average student response score of 4.27 (very practical category). In terms of post-implementation learning performance, 85% of students achieved scores of ≥80 on the multiplication learning test, indicating that most students reached the predetermined mastery criterion. However, the relatively small sample size (n = 20) limits the generalizability of the findings and should be considered in interpreting the results. In conclusion, the ICT-based Multiplication House media is feasible for use in elementary mathematics learning, particularly in multiplication topics. This study implies that integrating game-based ICT media can support student engagement and facilitate multiplication learning activities. Future research is recommended to involve larger samples and diverse educational contexts to strengthen the generalizability and explore long-term impacts on students’ mathematical thinking skills.

基于固定语义锚点与分层变换函数的AI原生认知架构——脱离统计拟合的类人理解范式

Current mainstream artificial intelligence models including convolutional neural networks and large language models rely on statistical fitting over fragmented input symbols. Vision models fit pixel distributions, while language models predict next‑token probabilities. This paradigm is essentially pattern‑matching and probabilistic speculation rather than genuine semantic understanding, and it inherently produces hallucinations, semantic drift, long‑tail failures and uncontrolled emergence. Breaking away from statistical‑learning frameworks, this paper proposes an AI‑native cognitive dynamical architecture built upon read‑only fixed semantic anchors. Instead of adopting human surface‑level grammar as internal computation rules, we construct a stack of layered transformation functions together with a graded semantic‑matching validation mechanism. Without token‑level probability sampling or massive pre‑training, five‑step cognitive dynamics (anchor assembling, verb stacking, complement modification, word‑order rearrangement and equivalent word replacement) reproduce core human‑like language comprehension and generation. A small‑scale sandbox experiment with ten basic semantic anchors demonstrates that the architecture eliminates root‑cause hallucinations and semantic drift, featuring full traceability, low computational cost and strong generalization. It represents a new human‑like cognitive paradigm alternative to statistical AI. Note: The mathematical dynamical function for semantic coupling, which inherits the prior “glue‑temporal‑grid” hypothesis, is not developed in this paper and will be presented in a follow‑up independent publication. Keywords AI‑native cognition; semantic anchor; transformation‑function stack; AI‑native grammar; statistics‑free modelling; explainable AI; hallucination mitigation

Commentary: Autism screening and diagnosis in children with congenital heart disease

Congenital heart disease (CHD) is the most common structural birth anomaly. As perioperative mortality has fallen, attention has rightly shifted toward the neurodevelopmental cost of surviving early cardiac surgery. Ontiveros Perez and colleagues make a timely contribution to this literature. They prospectively link Modified Checklist for Autism in Toddlers, Revised with Follow-Up (M-CHAT-R/ F) screening at 18-30 months to chart-confirmed autism diagnosis, in a cohort of 94 children who required cardiac surgery before initial hospital discharge (1).It is worth restating, at the outset, why the distinction between these two outcomes matters. Screening with the M-CHAT-R/F is a brief, parent report questionnaire, typically administered in a primary-care or follow-up-clinic setting to a large, largely unselected group of children; a positive result flags an elevated likelihood of autism, not the condition itself. Diagnosis, by contrast, requires a comprehensive, in-person evaluation. This generally involves a developmental paediatrician, psychologist or child psychiatrist, standardised observational instruments such as the Autism Diagnostic Observation Schedule and a detailed developmental history, before autism spectrum disorder can be confirmed clinically. The two therefore differ not only in accuracy but in the time, personnel, and resources each demands, and this gap sits at the centre of several issues raised below.Their headline finding is striking: a screen positive rate of 14.6%, and a diagnosis rate of 11.7%, both more than three fold the current general-population estimate (2). This reinforces a signal that has been accumulating across the congenital cardiology literature for a decade. The design has real strengths, particularly its reliance on a defined referral population and on chart verified outcomes, rather than on screening results alone. Several features of the data, nonetheless, warrant closer scrutiny before the findings are translated into practice recommendations, especially for cardiology programmes that lack the structured High-Risk Infant Follow-Up (HRIF) infrastructure that made this study possible.Of the 94 eligible children, only 48 were screened and only 7 screened positive.The confirmed autism subgroup within the screened cohort comprised just six children. Sensitivity of 66-67% therefore rests on the reclassification of a single case, and its reported confidence interval, 0.33 to 1.00, spans almost the entire plausible range (1). The authors are appropriately candid about this. Still, a bare comparison against general population prevalence (2) risks conveying more precision than the underlying numbers can bear.Table 1 places the study's psychometrics beside published benchmarks. What is notable is not that this CHD sample under-performed the general population norming cohort (3); it did not. Rather, its specificity and negative predictive value were unusually high relative to most high risk validation samples. In those samples, the customary trade-off usually runs the opposite way: sensitivity rises while specificity falls, because co-occurring developmental delay inflates false positives (4,5). A plausible explanation here is verification bias. Referral for full evaluation was left to clinician and family discretion, and 46 of 94 eligible children were never screened at all. Without a fixed, non-discretionary protocol, both the numerator and the denominator of these estimates are shaped by judgements the study cannot audit.A second concern is conceptual, rather than statistical. Children with CHD, independent of any autism diagnosis, commonly display weaknesses in theory of mind, pragmatic language and social cognition. These traits can phenotypically resemble autism without meeting full diagnostic criteria (6). The M-CHAT-R/F was normed on low risk and preterm populations, not on children who have undergone cardiopulmonary bypass, deep hypothermic circulatory arrest or repeated infant general anaesthesia. These exposures plausibly affect the very social communication domains the instrument probes, independent of core autism biology (6,7).Read against this background, the study's association between Risk Stratification for Congenital Heart Surgery-2 (RACHS-2) score and autism diagnosis is biologically plausible, but not unambiguous. Greater surgical complexity predicts both closer follow-up and therefore more opportunities for detection and greater hypoxic ischaemic exposure, a genuine risk factor in its own right. A single centre study of this size cannot separate ascertainment from causation, and few current alternatives can either.The authors attribute the association between public insurance and autism diagnosis to California's disability linked insurance eligibility pathways, rather than to true socioeconomic disadvantage (1). This is a reasonable, locally grounded reading. It is also a reminder that "public insurance" is not a portable proxy for socioeconomic status across health systems. In settings structured differently, including most cardiac referral centres outside the United States, this covariate would carry a different meaning entirely. The conclusion, therefore, should not be imported along with the variable.The HRIF model is valuable, but it is not universally available infrastructure.Cognitive and developmental impairment in CHD spans multiple domains and tends to worsen with age (8). Yet, in many referral centres, particularly in resourceconstrained settings, follow-up after infant cardiac surgery remains predominantly cardiological, with limited routine access to structured developmental surveillance.If autism prevalence in children with severe CHD genuinely runs three fold higher than in the general population, as this and prior work suggest (1,4), the practical bottleneck is not simply the decision to screen. It is the referral capacity that a positive result demands, given a positive predictive value of only 57% in this cohort (1). A screening programme without matching evaluation capacity risks generating parental anxiety, without improving outcomes.Ontiveros Perez et al. add welcome toddler period data to a still thin literature.Their central message, that CHD severity requiring early surgery tracks with meaningfully elevated autism likelihood, is consistent with the field (1,4,6). The specific psychometric estimates, however, rest on a small, clinician selected subgroup, and are better treated as hypothesis generating than confirmatory.Larger, multisite cohorts, using universal, non-discretionary screening and spanning varied insurance and resource settings, are needed before the M-CHAT-R/ F's performance in structural heart disease can be considered established. Until then, the more defensible clinical takeaway is not a specific cutoff, but the underlying principle: children surviving early, complex cardiac surgery warrant systematic developmental surveillance, delivered through pathways equipped to act on what screening finds.

Pre-registered stakes against a tuned baseline: a one-day ledger of grokking interventions that mostly failed

A one-day, fully pre-registered study of grokking interventions on modular addition and small language models. Main results: (1) published grokking 'accelerators' largely reduce to artifacts of untuned baselines and first-crossing metrics; (2) an auxiliary per-example memory races the network for training CE and, via dead gradients plus weight decay, erases even an already-found generalising rule (cycle-vs-death dose structure; two independent erasers; on LM continued training the dominant eraser of unreinforced knowledge is interference, not weight decay); (3) at fixed data size, training-set structure decides grokking (with a pre-registered character-sum predictor) and transfers to language as a conditional two-axis law (coverage and window freshness) with an ordinal data predictor; (4) the ReLU/GELU gap is a training-budget effect while the final LayerNorm matters for both activations. Every claim was staked in a ledger before computing (176 stakes, 158 outcomes); the ledger is attached. Companion code and data repositories: https://github.com/iwasborninbali/grokking-honest-ruler, https://github.com/iwasborninbali/grokking-race-eraser, https://github.com/iwasborninbali/grokking-data-law, https://github.com/iwasborninbali/grokking-activation-ln. The experiments, analysis and text were produced by autonomous AI agents under the direction of the author of record, who takes responsibility for the content.

Pre-registered stakes against a tuned baseline: a one-day ledger of grokking interventions that mostly failed

A one-day, fully pre-registered study of grokking interventions on modular addition and small language models. Main results: (1) published grokking 'accelerators' largely reduce to artifacts of untuned baselines and first-crossing metrics; (2) an auxiliary per-example memory races the network for training CE and, via dead gradients plus weight decay, erases even an already-found generalising rule (cycle-vs-death dose structure; two independent erasers; on LM continued training the dominant eraser of unreinforced knowledge is interference, not weight decay); (3) at fixed data size, training-set structure decides grokking (with a pre-registered character-sum predictor) and transfers to language as a conditional two-axis law (coverage and window freshness) with an ordinal data predictor; (4) the ReLU/GELU gap is a training-budget effect while the final LayerNorm matters for both activations. Every claim was staked in a ledger before computing (176 stakes, 158 outcomes); the ledger is attached. Companion code and data repositories: https://github.com/iwasborninbali/grokking-honest-ruler, https://github.com/iwasborninbali/grokking-race-eraser, https://github.com/iwasborninbali/grokking-data-law, https://github.com/iwasborninbali/grokking-activation-ln. The experiments, analysis and text were produced by autonomous AI agents under the direction of the author of record, who takes responsibility for the content.

AEGIS: Real-Time Latent-Space Backdoor Detection for Dependable and Secure Small Language Model Inference

Backdoor attacks pose a serious threat to small language models (SLMs) because compromised models can behave normally on benign inputs while producing attacker-specified outputs when a hidden trigger is activated. Existing defenses commonly require model retraining, operate only before deployment, rely on input-level signals, or incur excessive inference overhead. This paper presents AEGIS (Activation Evaluation and Guardrail for Inference Security), a non-invasive runtime framework for detecting backdoor-induced anomalies in transformer representations. AEGIS dynamically monitors equidistant internal layers, mean-pools and concatenates their hidden states, and compresses the resulting high-dimensional representation into a 64-dimensional latent space. A hybrid compression mechanism uses zero-shot principal component analysis for predominantly linear text representations and a lightweight autoencoder for nonlinear or multimodal representations. Detection is then performed entirely on the GPU using cosine distance from a centroid calibrated on clean data, without modifying or retraining the protected model. We evaluate AEGIS across Mistral-7B, Qwen2.5-7B, a 4-bit QLoRA-backdoored Qwen2.5-1.5B model, and a BadNets-backdoored Vision Transformer, covering simulated latent and PEFT-style attacks, genuine fine-tuned backdoors, FP16 inference, and 4-bit NF4 quantization. Across seven experimental scenarios, AEGIS achieves AUROC values between 0.95 and 1.00, true-positive rates between 86% and 100%, and detection latency between 0.47 and 2.40 ms. It obtains AUROC = 1.00 and 100% true-positive rate against the genuinely fine-tuned QLoRA backdoor, while achieving AUROC=0.997 against the fine-tuned visual BadNets attack. Under 4-bit quantization, it retains AUROC=0.95 with 1.50 ms latency and a 4.52 GB memory footprint. These results demonstrate that GPU-native latent-space monitoring can provide effective, retraining-free backdoor detection for real-time transformer inference.

That the Same Ellipse Was Three Months Out Was the Evidence of a Different Cause ── Aberration Is 20.49552 Arcseconds Whatever the Distance, While Parallax Goes as Its Reciprocal ── A Factor of 26.6442 at Proxima and 20495 at a Kiloparsec ── [Paper 328]

Over a year a star traces a small ellipse on the sky. This paper asks whether that ellipse is one thing──the answer is that there are two, and they are told apart by phase. 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──aberration, annual parallax, Bradley’s observation of 1728, and the definition of the constant of aberration are all standard. We do not build celestial mechanics──all we use is two angles and the phase between them. We do not treat this relativistically──the relativistic formula for aberration is not entered. We look only where first order in v/c suffices. We do not treat proper motion──a star’s own motion is not periodic and so separates from both of these. It is mentioned and no more. We do not adjudicate the history──who first saw what is not entered. We do not treat the distance ladder──the rungs beyond parallax belong to Paper 297. Relation to earlier papers: Paper 297 showed the cosmic distance scale to be a ladder of seven rungs with only the first measured directly──that first rung is parallax, and this paper looks at the other ellipse standing beside it. Paper 325 showed the radius not entering the angle of a rainbow──the same form, with distance not entering aberration here. Paper 300 showed whether two things share a root is decidable──this is an instance of “same shape, different root”, and what decided it was not a value but a phase. Paper 327 showed two curves agreeing to within 0.083 per cent──there the appearance is the same and the things differ; here the size can be the same and the things differ. Paper 313 showed the corpus using “synchrony” in several senses──phase is again the tool that decides. What is added is giving the constant of aberration from both a simple calculation and the literature and stating the difference, tabulating the ratio across three decades of distance, solving for the distance at which the two would be equal, and putting the separator on position against velocity. First, aberration is 20.49552 arcseconds (Section 2). Second, this is the core of the paper. Aberration does not depend on distance; parallax goes as its reciprocal (Section 3). Third, even the nearest star opens by 26.6442. At a kiloparsec, 20495 (Section 3). Fourth, amplitude cannot always separate them. At some distance the two would be equal (Section 3). Fifth, their phases differ by a quarter. That is how Bradley told them apart (Section 4). Sixth, the separator is whether the effect is set by position or by velocity (Section 5). Over a year a star traces a small ellipse on the sky, and two causes are possible──annual parallax, because the Earth’s position changes, and aberration, because its velocity does. Both have a period of one year, both are ellipses, and the shape does not distinguish them. Aberration follows from tanalpha=v/c and is 20.49552 arcseconds, about 1/88 of the apparent diameter of the full moon──(the simple calculation here, 20.492697, differs by 0.0138 per cent, because kappa is defined to include the eccentricity, so this paper uses the literature value). And the distance to the star is nowhere in that formula──it contains only the observer’s speed and the speed of light, not one piece of information about the thing being looked at. Even Proxima is out by 26.6442, and at a kiloparsec by 20495.5200. The distance at which the two would be equal is 0.159135 light years, and no such star exists──so on amplitude alone, aberration always wins. What separated them was not amplitude but phase──in circular motion the velocity points a quarter period ahead of the position, so the two ellipses are exactly three months apart. In 1728 Bradley, hunting for parallax, found an ellipse in the wrong season and knew it was not his quarry. A mismatch in amplitude would have been weak evidence──without the distance there is no predicted parallax to compare against, whereas the phase can be predicted without knowing the distance at all. One thing separates them──whether the effect is set by the observer’s position or by the observer’s velocity. Settle that and the distance dependence and the phase follow automatically, so three apparently independent differences are one. Paper 297 wrote that the first rung of the distance ladder is parallax──this paper says that immediately beside it sits an ellipse of the same shape containing no distance at all. The first rung does not stand by itself. One last thing──Bradley failed to find what he was looking for and found what he was not. And it became a measurement of the speed of light, because v/c can be read off from an angle of 20 arcseconds. A failure to find became the ruler for something else. 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. ----- 恒星は一年かけて空に小さな楕円を描く。本稿が問うのは、その楕円は一種類かである──答は、二種類あり、位相で見分けられるである。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──光行差、年周視差、ブラッドリーの 1728 年の観測、光行差定数の定義はいずれも標準的である。天体力学を作らない──使うのは二つの角度と、その位相差だけである。相対論的な扱いをしない──光行差の相対論的公式には立ち入らない。 v/c の一次までで足りる場面だけを見る。固有運動を扱わない──恒星自身の運動は周期的でないので、本稿の二つとは分けられる。触れるにとどめる。測定の歴史を裁定しない──誰が最初に何を見たかの帰属には立ち入らない。距離はしごを扱わない──視差より遠い段は論文297 の射程である。既刊との関係:論文297 は宇宙の距離が七段のはしごで、直接測られているのは一段目だけだと示した──その一段目が視差であり、本稿はその隣に立つもう一つの楕円を見る。論文325 は虹の角度に半径が入らないと示した──同じ型であり、ここでは光行差に距離が入らない。論文300 は同根か別根かは判定できると示した──本稿は「同じ形をしていても別根」の実例であり、判定に使ったのは値ではなく位相である。論文327 は二つの曲線が 0.083 パーセントしか違わないと示した──そこでは見た目が同じで別物、ここでは大きさが同じでも別物である。論文313 は体系が「同期」を複数の意味で使ってきたと示した──位相という語がここでも判定の道具になっている。加えたのは光行差定数を単純計算と文献値の両方で示し、その差を明示したこと、距離ごとの比を三桁にわたって出したこと、二つが同じ振幅になる距離を求めたこと、分離子を位置と速度の別に置いたことである。 第一に、光行差は 20.49552 秒角である(第2節)。 第二に、これが本稿の芯である。光行差は距離に依らず、視差は距離に反比例する(第3節)。 第三に、最も近い恒星でも 26.6442 倍ひらく。1 キロパーセクなら 20495 倍(第3節)。 第四に、振幅では分けられない場合がある。ある距離では二つが同じ大きさになる(第3節)。 第五に、位相が四分の一ずれている。ブラッドリーはそれで見分けた(第4節)。 第六に、分離子は「位置で決まるか、速度で決まるか」である(第5節)。 恒星は一年かけて空に小さな楕円を描き、その原因は二つありうる──地球の位置が変わるからの年周視差と、地球の速度が変わるからの光行差である。どちらも一年周期の楕円で、形では区別がつかない。光行差は tanalpha=v/c から出て 20.49552 秒角、満月の見かけの直径の約 1/88 である──(本稿の単純計算 20.492697 は文献値と 0.0138 パーセント違い、kappa は離心率を含む定義なので、本稿が使うのは文献値である)。そしてこの式には、恒星までの距離が入っていない──現れるのは観測者の速度と光速だけで、見ている相手の情報が一つも入らない。最も近いプロキシマですら視差の 26.6442 倍、1 キロパーセクでは 20495.5200 倍ひらく。二つが同じ大きさになる距離は 0.159135 光年で、そんな恒星は存在しない──振幅の大小では、常に光行差が勝つ。分けたのは振幅ではなく、位相である──円運動では速度は位置の四分の一周期先を向くので、二つの楕円はちょうど三ヶ月ずれる。ブラッドリーは 1728 年、視差を探していて楕円を見つけ、季節がずれていることで探し物ではないと知った。振幅が合わないことは証拠として弱い──距離を知らなければ視差の予想値が立たないからで、位相は距離を知らなくても予想できる。分けるものは一つ──その効果が観測者の位置で決まるか、速度で決まるか。それが決まれば距離依存も位相も自動的に決まり、独立に見えた三つの違いが一つの違いになる。論文297 は距離のはしごの一段目が視差だと書いた──本稿はその一段目のすぐ隣に、距離を一切含まない同じ形の楕円が乗っていることを言う。はしごの一段目は、単独では立っていない。最後に一つ──ブラッドリーは探していたものを見つけられず、探していなかったものを見つけた。そしてそれは光速の測定になった。20 秒角という角度から v/c が読めるからである。見つからなかったことが、別のものの物差しになった。 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。

The geopolitics of Artificial Intelligence: Technological Dependence and Digital Sovereignty in Developing States

Artificial intelligence is becoming part of the way countries develop their economies, educate their populations and provide digital services. At the same time, the resources needed to build advanced AI systems are concentrated in a relatively small number of countries and companies. This creates an important question for developing states: how can they benefit from technologies developed abroad without becoming too dependent on decisions made outside their own borders? This paper examines this question through the case of Uzbekistan. It focuses on technological dependence and digital sovereignty and uses linguistic inequality in AI as one example of how this dependence may appear in practice. Particular attention is given to tokenization, the process through which text is divided into smaller units before it is processed by a language model. Research has shown that different languages can require very different numbers of tokens to communicate similar information, and that these differences can affect the cost and efficiency of commercial AI systems (Ahia et al., 2023). The paper argues that the Uzbek language should not be viewed only as a technical challenge for AI developers. Its relatively limited computational language resources also illustrate a wider issue: countries with smaller technological ecosystems may have less influence over the systems they increasingly use. The paper therefore considers digital sovereignty not as complete technological independence, but as the ability of a country to develop sufficient knowledge, infrastructure and partnerships to make informed decisions about technologies on which it relies. It also examines the role of UNESCO, international cooperation and regional collaboration in creating a more inclusive system of AI governance.

Two Curves Agree to Within 0.083 Per Cent and Are Not the Same Curve ── What Divides the Catenary from the Parabola Is Not Shape but Which Length the Load Is Counted Along ── [Paper 327]

A hanging chain and a suspension-bridge cable cannot be told apart by eye. This paper asks what divides them──the answer is not the shape, but which length the load is counted along. 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 catenary equation, the parabolic-cable theory of suspension bridges, and the Taylor expansions of both are all standard. We do not do structural design──all we use is two curves and one difference of measure. We do not treat deflection──cable stretch, thermal movement and live-load deflection are not entered. This paper looks only at the idealised static shape. We do not adjudicate which is correct──a real bridge lies between the two, and this paper does not locate it. We claim no engineering accuracy──the sag ratios are values for comparing shapes, not those of any particular bridge. We do not discuss optimal shape──which is structurally better is not treated. Relation to earlier papers: Paper 198 showed that “straight” does not mean “shortest”──198 says one curve has two characters; this says two curves look alike. The direction is reversed. Paper 326 showed the square-cube relation is an identity──both are of the “same appearance, different content” kind, but 326 is about a ratio and this is about functions. Paper 300 showed whether two things share a root is decidable──this is a worked instance of “numerical closeness is not sameness of root”. Paper 245 showed two limits have no answer until their order is written──here too, the curve is undetermined until the measure of integration is written. Paper 183 showed one table having two correct answers──one shape having two correct equations is its counterpart. What is added is computing the difference at six points, stating that it begins at fourth order, giving the maximum difference for each sag ratio, and putting the separator on the measure. First, they agree exactly through second order. At x=0.1 the difference is 0.083292 per cent (Section 2). Second, far out they are different things. At x=5, 82.925818 per cent (Section 2). Third, the difference begins at fourth order. x^4/24 against 0 (Section 2). Fourth, this is the core of the paper. What divides them is counting along arc length or along horizontal length (Section 3). Fifth, on a real bridge the difference is only 0.082674 per cent (Section 4). Sixth, the separator is whether the deck or the cable is the heavier (Section 5). A hanging chain and a suspension-bridge cable cannot be told apart by eye. Expanding cosh shows the leading term to be the parabola itself, so they agree exactly through second order──with a=1 the difference is 0.083292 per cent at x=0.1 and 82.925818 per cent at x=5, and both figures are correct about the same two curves. “How different are they” is undetermined until you say where you are looking. The difference begins at fourth order──first, second and third all agree, and the parabola is the second-order Taylor polynomial of the catenary, not a curve fitted to it. And what divides them is not shape but measure──both come from the same balance H y''=w, and all that differs is whether w is constant against arc length ds or horizontal length dx. Constant along the arc makes the steep ends weigh more per horizontal foot, and so the catenary rises faster. So “a parabola close to a catenary” has it backwards──each is the exact answer to a different physics, and the approximation relation is something mathematics noticed afterwards. At the 1/10 sag of a real suspension bridge the maximum difference is 0.082674 per cent of the sag──8.3 cm on a 1000 m span, sometimes smaller than the construction tolerance. And they are still two different curves. One thing separates them──whether the suspended deck or the cable itself is heavier. A real bridge is neither ideal, and this paper does not locate it. Against Paper 198 the direction is exactly reversed──198 says one curve has two characters, this says two curves have one appearance, and both obey the same discipline: appearance is not evidence. One last thing──Galileo wrote that a hanging chain is a parabola. He was wrong, by 0.083 per cent. Not an error the eye could correct, and with no cosh yet in existence there was nothing to correct it to. Writing the right shape needs the words for it to exist first. 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. ----- 垂れた鎖の形と、吊り橋のケーブルの形は、目では区別がつかない。本稿が問うのは、では何が二つを分けているのかである──答は、形ではなく、荷重をどちらの長さで数えるかである。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──懸垂線の方程式、放物線ケーブルの吊り橋理論、両者のテイラー展開はいずれも標準的である。構造設計をしない──使うのは二つの曲線と、一つの測度の違いだけである。たわみを扱わない──ケーブルの伸び、温度変化、活荷重によるたわみには立ち入らない。本稿は理想化された静止形状だけを見る。どちらが正しいかを判定しない──実際の橋は両者のあいだにあり、本稿はその位置を決めない。数値に工学上の精度を主張しない──たるみ比は形を比べるための値であって、特定の橋のものではない。最適形状を論じない──どちらが構造として有利かは扱わない。既刊との関係:論文198 は「まっすぐ」は「最短」を意味しないと示した──198 は同じ曲線に二つの性格があると言い、本稿は二つの曲線が同じに見えると言う。向きが逆である。論文326 は二乗三乗が恒等式だと示した──どちらも「見かけが同じでも中身が違う」型だが、326 は比の話、本稿は関数の話である。論文300 は同根か別根かは判定できると示した──本稿は「数値が近いだけでは同根でない」の実例になっている。論文245 は二つの極限が順序を書くまで答を持たないと示した──ここでも、どの測度で積分するかを書くまで曲線が決まらない。論文183 は同じ表が二つの正しい答を持つと示した──同じ形が二つの正しい方程式を持つという、対になる例である。加えたのは両曲線の差を六点で計算したこと、差が四次から出ることを明示したこと、たるみ比ごとの最大差を出したこと、分離子を測度の違いに置いたことである。 第一に、原点では二次まで完全に一致する。 x=0.1 で差は 0.083292 パーセント(第2節)。 第二に、遠くでは別物になる。 x=5 で 82.925818 パーセント(第2節)。 第三に、差は四次の項から出る。 x^4/24 対 0(第2節)。 第四に、これが本稿の芯である。分けているのは、弧長で数えるか水平長で数えるかである(第3節)。 第五に、実際の吊り橋では差は 0.082674 パーセントしかない(第4節)。 第六に、分離子は「桁とケーブル、どちらが重いか」である(第5節)。 垂れた鎖と吊り橋のケーブルは、目では区別がつかない。 cosh を展開すると最初の項が放物線そのもので、二次まで完全に一致する──a=1 とすると x=0.1 での差は 0.083292 パーセント、x=5 では 82.925818 パーセントであり、同じ二本について両方とも正しい。「どれだけ違うか」は、どこを見るかを言わないと決まらない。差は四次の項から出る──一次も二次も三次も一致しているので近くでは見分けようがなく、放物線は懸垂線の二次のテイラー多項式そのものであって、当てはめた曲線ではない。そして二つを分けているのは、形ではなく測度である──どちらも H y''=w という同じ釣り合いから出て、違うのは w が弧長 ds について一定か、水平長 dx について一定かだけである。弧長で一定なら傾いた所ほど水平方向に重くなり、だから懸垂線のほうが速く立ち上がる。だから「懸垂線に近い放物線」という言い方は順序が逆である──どちらも別々の物理から出た正確な答であって、近似関係は後から数学が見つけたものである。実際の吊り橋のたるみ比 1/10 では、最大差はたるみの 0.082674 パーセント──スパン 1000 m・たるみ 100 m の橋で 8.3 cm であり、施工の誤差より小さいこともある。それでも二つは別の曲線である。分けるものは一つ──吊られた桁とケーブル自身の、どちらが重いか。実際の橋はそのあいだにあり、本稿はその位置を決めない。論文198 とは向きがちょうど逆である──198 は一つの曲線が二つの性格を持つと言い、本稿は二つの曲線が一つの見かけを持つと言う。どちらも「見た目は根拠にならない」という同じ規律に服している。最後に一つ──ガリレオは垂れた鎖を放物線だと書いた。間違いだが、0.083 パーセントの間違いである。目で見て直せる誤りではなく、cosh という関数がまだ無かったのだから直しようもなかった。正しい形を書くには、書くための言葉が先に要る。 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。

Capacity vs. architecture: an evaluation of SLMs for automated docstring generation

Contract-Grounded Cognitive Composition: Deterministic Topology, Interface Contracts, and Local Validation in LLM Multi-Agent Systems

This release presents Contract-Grounded Cognitive Composition (CGCC), an engineering framework for improving the reliability of LLM multi-agent systems through deterministic workflow topology, shared interface contracts, and local validation. The study reports three exploratory experiments conducted with a local qwen3.5:9b model. The experiments examine sequential reasoning with deterministic validation, control-flow ablations across evidence retrieval, planning, and code generation, and frontend-backend integration under free communication, natural-language API documentation, and shared JSON Schema conditions. The results suggest that LLM cognition can be composed, but reliable composition depends on three distinct conditions: correct workflow progression, compatible interfaces, and validated local execution. Fixed topology reduces premature termination and routing errors, while shared API contracts reduce cases in which independently generated modules are locally plausible but fail during integration. This archive includes the English working paper, complete experimental code, raw model prompts and responses, routing and validation traces, aggregate results, supporting experiment notes, a data dictionary, and reproducibility materials. The experiments use one local 9B model and small synthetic task sets. The results should therefore be interpreted as an exploratory mechanism study rather than a general performance benchmark.