Generative Calculus: A Differential Framework for Possibility, Pattern, and Emergence
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2026
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| _version_ | 1866901691059666944 |
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| author | Doy, David Michael |
| author_facet | Doy, David Michael |
| contents | <p>Generative Calculus introduces a 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. It extends classical calculus by incorporating pattern accumulation, emergent geometry, identity dynamics, and thresholded reorganisation, and by integrating smooth continuation with discrete collapse events into a unified hybrid dynamical system.</p> <p>The report establishes the foundational theorems of Generative Calculus—including conservation, accumulation, emergent geometry, identity stability, and generative stability—and introduces a phase‑aware extension in which the system adapts its own mode of evolution. Applications include emergent curvature from development, stability and collapse of identity, formation of persistent patterns, and generative cycle integrals that quantify structural change across physical, cognitive, and cosmological regimes.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19357790 |
| 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 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. It extends classical calculus by incorporating pattern accumulation, emergent geometry, identity dynamics, and thresholded reorganisation, and by integrating smooth continuation with discrete collapse events into a unified hybrid dynamical system.</p> <p>The report establishes the foundational theorems of Generative Calculus—including conservation, accumulation, emergent geometry, identity stability, and generative stability—and introduces a phase‑aware extension in which the system adapts its own mode of evolution. Applications include emergent curvature from development, stability and collapse of identity, formation of persistent patterns, and generative cycle integrals that quantify structural change across physical, cognitive, and cosmological regimes.</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.19357790 |