Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications
The article discusses growth dynamics in deterministic equational discovery substrates across three toy domains. It presents a model predicting saturating power-law growth, emphasizing that dynamics are conditional on the substrate used. The findings suggest that the preferred growth model varies by substrate and that the trajectories do not reach saturation in toy data.
- ▪The study investigates growth dynamics in three toy domains: arithmetic, boolean, and higher-order list.
- ▪A heuristic mean-field closure model predicts a saturating power-law growth pattern.
- ▪The dynamics are substrate-conditional, with different preferred functional families for growth observed.
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Record
| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.23983 |
| Publication time | Tue, 26 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-26T04:07:43.013Z |
| Last seen | 2026-05-26T04:07:43.013Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | zn7_djKEui9f |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Computer Science > Artificial Intelligence arXiv:2605.23983 (cs) [Submitted on 14 May 2026] Title:Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications Authors:Fabio Rovai View a PDF of the paper titled Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications, by Fabio Rovai View PDF HTML (experimental) Abstract:We investigate growth dynamics in deterministic equational discovery substrates. Across three toy domains (arithmetic, boolean, higher-order list; n=592 trajectories), short-range substrate sizes fit a power-law N(t) proportional to t^b.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
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