A Survivability Framework for Time-Mass-Gravity Systems: Constraint-Based Dynamics Across Scales
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2026
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| author | Broomhead, Geoffrey Sovereign Trust Node: Broomhead Private Sovereign Trust geoffreybroomhead.eth |
| author_facet | Broomhead, Geoffrey Sovereign Trust Node: Broomhead Private Sovereign Trust geoffreybroomhead.eth |
| contents | <p>The framework introduces three principal mathematical objects: coherence functionals measuring information-preservation efficiency, memory operators encoding history-dependent dynamics, and constraint enforcement mechanisms governing admissibility.</p> <p> </p> <p>Main results: (1) existence and uniqueness of weak solutions for a broad class of systems satisfying regularity, positivity, and coercivity assumptions (Theorems 8.1-8.2); (2) forward invariance of the survivability region R under bounded forcing via Nagumo's theorem (Theorem 8.5); (3) complete characterisation of three collapse modes — constraint breach, mass overload, and memory horizon failure (Theorems 9.1-9.3).</p> <p> </p> <p>The framework recovers classical stability theory in the Newtonian limit and admits relativistic extension via covariant formulation. Discrete analogues preserve forward invariance under CFL-type conditions. Falsifiability is ensured through explicit counterexample templates violating each assumption.</p> <p> </p> <p>The survivability functional S(t) and the conserved product Q(t)S(t) are adopted from the recursive geometry framework of R1 (Broomhead 2025, DOI: 10.5281/zenodo.17959914). The present paper demonstrates that the conservation law QS = const actively prevents silent exit from the survivability region (Theorem 8.5, Remark), providing the formal mathematical backbone for the non-Markovian discriminator programme established in Papers B and C.</p> <p> </p> <p>No claim is made to replace existing physical theories. The framework provides structural conditions for persistence and collapse in constrained dynamical systems, complementing the geometric foundations of the R-series.</p> <p> </p> <p><span>MSC 2020: 35Q75, 37L05, 35B35, 83C05, 70H45.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19344228 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | A Survivability Framework for Time-Mass-Gravity Systems: Constraint-Based Dynamics Across Scales Broomhead, Geoffrey Sovereign Trust Node: Broomhead Private Sovereign Trust geoffreybroomhead.eth survivability constrained dynamics forward invariance viability theory memory operators gravitational collapse non-Markovian dynamics Nagumo theorem coherence functional time-mass-gravity Broomhead Sovereign Private Trust <p>The framework introduces three principal mathematical objects: coherence functionals measuring information-preservation efficiency, memory operators encoding history-dependent dynamics, and constraint enforcement mechanisms governing admissibility.</p> <p> </p> <p>Main results: (1) existence and uniqueness of weak solutions for a broad class of systems satisfying regularity, positivity, and coercivity assumptions (Theorems 8.1-8.2); (2) forward invariance of the survivability region R under bounded forcing via Nagumo's theorem (Theorem 8.5); (3) complete characterisation of three collapse modes — constraint breach, mass overload, and memory horizon failure (Theorems 9.1-9.3).</p> <p> </p> <p>The framework recovers classical stability theory in the Newtonian limit and admits relativistic extension via covariant formulation. Discrete analogues preserve forward invariance under CFL-type conditions. Falsifiability is ensured through explicit counterexample templates violating each assumption.</p> <p> </p> <p>The survivability functional S(t) and the conserved product Q(t)S(t) are adopted from the recursive geometry framework of R1 (Broomhead 2025, DOI: 10.5281/zenodo.17959914). The present paper demonstrates that the conservation law QS = const actively prevents silent exit from the survivability region (Theorem 8.5, Remark), providing the formal mathematical backbone for the non-Markovian discriminator programme established in Papers B and C.</p> <p> </p> <p>No claim is made to replace existing physical theories. The framework provides structural conditions for persistence and collapse in constrained dynamical systems, complementing the geometric foundations of the R-series.</p> <p> </p> <p><span>MSC 2020: 35Q75, 37L05, 35B35, 83C05, 70H45.</span></p> |
| title | A Survivability Framework for Time-Mass-Gravity Systems: Constraint-Based Dynamics Across Scales |
| topic | survivability constrained dynamics forward invariance viability theory memory operators gravitational collapse non-Markovian dynamics Nagumo theorem coherence functional time-mass-gravity Broomhead Sovereign Private Trust |
| url | https://doi.org/10.5281/zenodo.19344228 |