Foundational Thinking DPF Suite
Mathematical, physical and computational methods for entering unfamiliar problems, using their results and developing better ways of working.
- Author: Anatoly Levenchuk, with AI-assisted development and review
- Date: 16 September 2026
- Status: Eternal alpha. All five member DPFs are available and evolve with their methods, sources and uses.
- Publication: FPF repository
Start with the Suite Reference when you need to choose among these contributions or connect them. Open a DPF directly when you already know the contribution you need.
Start from a connected problem
You may know formulas or individual operations and still be unable to connect them into an answer. The Suite helps make those connections: what information a construction must retain, what another method can do with its result, and where a changed question makes earlier work worth revisiting.
| What you need to do | Follow the worked connection |
|---|---|
| Split or change a calculation while keeping its answer meaningful | Change a combining rule: expose the lost distinction, construct a summary and operation, prove their compatibility, then use and revise them. |
| Decide a question without reconstructing every hidden detail | Obtain a sufficient answer: expose what reduction loses, bound its effect, interpret the result and obtain more where it changes the answer. |
| Decide whether another observation will improve an action | Connect intervention, information and choice: derive the relevant consequences, compare the report’s benefit with its burden, and make the subsequent choice depend only on timely information. |
| Replace expensive component models and still obtain a usable joint answer | Replace and couple models: retain the required responses, connect their meanings and error bounds, and refine only what prevents the answer. |
| Develop a physical prediction and decide which observation matters | Connect physical accounts and observations: constrain the law, derive a consequence, compare the observations that matter and revise the affected premise. |
| Construct an algorithm and adapt it when the required answer changes | Keep construction and output consistent: construct the recurrence, share results, use bounds where they reduce search, and revisit what may be discarded. |
| Carry a changed instruction through several expressions | Keep meaning and change connected: recover references and interpretation, expose translation losses, and update the affected expressions. |
| Connect mathematics to changes in working methods | Understand and change a construction: retain the distinction a later operation uses and connect it to Method Engineering. |
| Make reasoning available to other contributors and develop its next use | Continue and distribute thinking: recover a missing relation, arrange explanation or support, change the work and preserve the method for further development. |
These examples use several patterns together. Their short sequences show dependencies; worked explanations give calculations and return points. Start at a later contribution when its inputs are available. Each DPF’s Table of Contents also gives direct help for other questions.
The vertical of ongoing work asks a complementary question: what larger work is being performed through this action now, and what constituent abilities and resources make it possible? It helps locate a missing intermediate Method or capability even when the elementary operations and the intended whole are familiar.
Use the publications
For use with an agent, follow Using FPF. Copy this whole folder beside FPF-Spec.md in your project’s reference folder. The root ecosystem Readme gives the other files to copy and a paragraph for the agent’s instructions. In GitHub, open an example above or a member link below.
Publications
This is the public constitution and membership account for the Foundational Thinking DPF Suite. The following product series belong to it as of the date above.
| Product series | Publication status | Useful contribution |
|---|---|---|
| Mathematical Thinking DPF | Published - 20 patterns | Construct objects, operations and arguments; derive and use consequences. |
| Mathematical Modeling DPF | Published - 14 patterns | Formulate questions, infer unknowns, construct causal comparisons, choose useful observations, construct continuing decisions, and change or combine models while retaining the needed answer. |
| Physical Thinking DPF | Published - 10 patterns | Construct physical accounts, derive their consequences, build observations and revise physical assumptions. |
| Computational Thinking DPF | Published - 14 patterns | Construct and transform algorithms; connect their meaning, representations, resource requirements and interactions. |
| Notational Engineering DPF | Published - 8 patterns | Design, interpret, transform and coordinate expressions, including temporal and embodied notation. |
| Foundational Thinking DPF Suite Reference | Published | Choose and connect available contributions, understand their organization and locate a missing contribution. |
Computational Thinking develops algorithmics within computer science; numerical computation is one of its applications. Notational Engineering develops the expression conventions that make operations interpretable and usable. Current editions and this Reference are published together in this Suite folder.
FPF supplies the common reasoning methods. The Engineering DPF Suite supplies collaborating domain methods, including Method Engineering and capability development. These publications can be used with this Suite without becoming its members.
Purpose and continuity
The Suite is constituted for people and teams working with theories, models, specialists and AI: enter an unfamiliar question, develop and connect mathematical, physical and computational contributions, interpret the consequence, and use it to continue inquiry or change a way of working. Its members may also be used independently.
A DPF series qualifies for inclusion when it develops a substantial repertoire contributing to that purpose, has a usable public edition, and explains the results and conditions another contribution can use. Subject examples demonstrate that reach. A collection concerned only with a particular device or chapter of a science needs its corresponding narrower publication boundary.
An accepted architecture decision adds or removes a product series and updates this account. A later edition of an included series replaces the edition presented here when it retains the series’ field purpose, identifies its changes, provides usable methods and source access, and states consequential limits. A substantially different field purpose requires a decision about the series itself. Changes to method details, pattern count, profiles or file arrangement can preserve the Suite’s identity while its shared purpose continues.
If an edition becomes unavailable or cannot support a previously advised use, the Reference must expose that limitation when presenting the affected answer. Direct use of another known contribution can continue. If a series ceases to serve the shared purpose, the architecture decision settles repair, relocation or removal; earlier editions and the reasons for changed advice remain identifiable through publication history. Ending the shared purpose retires this Suite. A later collection with a different purpose needs its own constitution.
The Reference and its editions
The Reference is separately constituted as a publication series belonging to this Suite. Its readers need a useful answer about selection, combination, shared architecture or an unavailable contribution. It returns to this membership account and to the publications that supply the answer. It is published as one Markdown file alongside the member DPFs.
A later Reference edition is admitted when its answers agree with the editions it presents, its available and planned contributions are distinguishable, and its readers can return to those sources. A different audience or use that defeats these conditions requires a decision about a different Reference series. A superseded or retired edition remains historical; its date alone cannot establish that its advice still applies.
Rights and citation
Copyright © 2026 Anatoly Levenchuk. This account and the author’s DPF publications are licensed under Creative Commons Attribution 4.0 International, except material carrying a separate notice. Cited sources retain their own rights. Independent authors choose the licenses for their own DPFs and LPFs.
Cite this account as: Anatoly Levenchuk. Foundational Thinking DPF Suite. FPF repository. Include the date shown at the start of this file. For a method, also cite its DPF edition and PatternID.