| _version_ | 1866901689182715904 |
|---|---|
| author | Doy, David Michael |
| author_facet | Doy, David Michael |
| contents | <p>Generative Calculus introduces a new differential framework grounded in the dynamics of possibility rather than geometric displacement. Building on the Generative Architecture of Reality, this report formalises the generative loop—activation, feedback, pattern formation, structured influence, development, identity, geometry, collapse, and agency—as a nonlinear, history‑sensitive operator acting on the possibility field.</p> <p>The calculus defines the generative derivative, generative differentials, and generative integrals, together with a full operator algebra governing thresholds, invariants, and non‑commutative interactions. These structures extend classical calculus by incorporating pattern accumulation, emergent geometry, identity dynamics, and thresholded reorganisation. The resulting framework provides a unified mathematical language for describing emergence across physical, cognitive, and cosmological systems.</p> <p>Applications include emergent curvature from development, stability and collapse of identity, formation of persistent patterns, and generative cycle integrals that quantify structural change. The report establishes the foundational theorems of Generative Calculus and positions it as a general system for modelling how structure arises, stabilises, reorganises, and transforms across scales.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19315416 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Generative Calculus: A Differential Framework for Possibility, Pattern, and Emergence Doy, David Michael generative calculus dynamics mathematical physics calculus nonlinear dynamics possibility possibility field pattern dynamics emergence opertator algebra differential framework phase architecture phase dynamics <p>Generative Calculus introduces a new differential framework grounded in the dynamics of possibility rather than geometric displacement. Building on the Generative Architecture of Reality, this report formalises the generative loop—activation, feedback, pattern formation, structured influence, development, identity, geometry, collapse, and agency—as a nonlinear, history‑sensitive operator acting on the possibility field.</p> <p>The calculus defines the generative derivative, generative differentials, and generative integrals, together with a full operator algebra governing thresholds, invariants, and non‑commutative interactions. These structures extend classical calculus by incorporating pattern accumulation, emergent geometry, identity dynamics, and thresholded reorganisation. The resulting framework provides a unified mathematical language for describing emergence across physical, cognitive, and cosmological systems.</p> <p>Applications include emergent curvature from development, stability and collapse of identity, formation of persistent patterns, and generative cycle integrals that quantify structural change. The report establishes the foundational theorems of Generative Calculus and positions it as a general system for modelling how structure arises, stabilises, reorganises, and transforms across scales.</p> |
| title | Generative Calculus: A Differential Framework for Possibility, Pattern, and Emergence |
| topic | generative calculus dynamics mathematical physics calculus nonlinear dynamics possibility possibility field pattern dynamics emergence opertator algebra differential framework phase architecture phase dynamics |
| url | https://doi.org/10.5281/zenodo.19315416 |