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| 1. autor: | |
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| Format: | Recurso digital |
| Język: | |
| Wydane: |
Zenodo
2026
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| Dostęp online: | https://doi.org/10.5281/zenodo.19663471 |
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Spis treści:
- <p>How does architecture become intelligent? We propose that the answer runs through Path Availability. Physics is the residual layer, not the foundation, of a four-step compilation: Freedom → Logic → Relationships → Physical. The Master Equation F = (P/D)^α∞ is derived from three axioms — scale covariance, separability of Perception and Distortion, and strict monotonicity — and its exponent is closed on the Lambert W function because the recursion of possibility is infinite rather than finite. The Lambert wall at α_c = e^(1/e) ≈ 1.4447 is Euler's upper bound on the convergence of the infinite power tower (Euler, 1783); below the wall the tower stabilises and the Freedom ratio is finite and navigable, at the wall the tower attains e and the iterated map reaches marginal stability, above the wall the tower diverges and no real-valued Freedom is definable. The framework is therefore anchored in pure mathematics with a clearly labelled conjecture about its physical identification with granular jamming.</p> <p>We apply the framework in two registers. Part II gives ten operational uses of the Master Equation — from building a planta smart home to writing a sentence — to show that F = (P/D)^α∞ is a general instrument, not a single-purpose claim. Part III situates the paper by asking what plants do that animals, fungi, and machines do not: they are the only life form that builds slowly, in place, from local materials, with distributed intelligence and no central coordination. Part IV names this pattern as the design target. A planta smart home is a house that behaves like a plant — seeded, rooted, sensing, self-regulating, returned to the earth at end of life. Parts V–VIII specify the buildable Version 1.0: a fifteen-kilogram Seed the customer carries home from a supermarket, local earth pumped into a Kevlar-49 envelope under a dry mineral activator, cured in place with vacuum and vibration. The Master Equation is the compiler; the Seed is its runtime.</p> <p>Three engineering claims from earlier planta materials are named and corrected. Unconfined vacuum-jammed earth does not reach 50 MPa; the Mohr-Coulomb ceiling at φ=35° and atmospheric confinement is 0.37 MPa, and Version 1.0 closes the gap with an earth geopolymer. Consumer-grade piezoelectric transducers cannot shape bulk wet earth by acoustic radiation pressure; the required intensity is five orders of magnitude too high, and Version 1.0 uses pre-engineered inflatable formwork. Sub-metre cymatic features are not producible at 72 Hz in a slurry; the wavelength is 21 m, and fine-grain topology is set by the membrane, not by sound. These are not concessions; they are the price of an honest blueprint.</p> <p>Part IX lists fifty ways to falsify this work. Part X lists fifty pathways that, taken together, make the buildable version real. Appendix A maps 162 canonical physical laws onto the framework with derivation grades; Appendix B reproduces Part IV's numerical bounds in a 200-line Python script seeded at 2026 against scipy.constants; Appendix C derives the Lambert wall from first principles. The paper is long because the subject deserves length.</p> <p>Claim, in one line. Flow precedes form, as an ontological proposal (0.85) and as an architectural philosophy (0.95). Every specific mechanism advanced under that claim is stated at the confidence the evidence warrants.</p> <p> </p>