Timeless 2D Formation, Executed 3D Transition, and the Birth of Physical Time
Year: 2026
Type: preprint
Abstract: This paper proves a connected finite-pregeometry theorem in which a one-dimensional relational structure forms its first filled 2D cell without physical elapsed time, undergoes an explicitly executed transition to a filled 3D cell, and thereby produces the first irreversible physical ordering together with the capacity to produce, distinguish, and retain information. The result follows from the stated edge-dual restriction (EDR), route-specific gain law (GAIN), and fold-to-cone activation law (FCA), with every load-bearing identity reproduced by exact finite and matrix calculations. The first transition is exact. Five integer source events are allocated over seven relations of an open eight-vertex path. Among the 462 weak compositions, exactly 42 satisfy the two-sided hinge condition, and every firing configuration has one unique hinge. The selected adjacent relations retain their lineage; one transverse relation is created between their outer vertices; and the resulting three-cycle is filled by a two-simplex. The relation-count Gram rank changes from one to two, and the Cayley–Menger relation-count area diagnostic changes from zero to 3/16. A direct dependency analysis proves that the filled 2D formation uses no physical duration, clock, observer/record capacity, measurement channel, pointer/readout, or durable accessible event/measurement record. Its ordered construction remains exact after all temporal language and dλ/dt terms are deleted. Construction order is therefore retained without being renamed elapsed physical time. GAIN reaches its first fold exactly at x* = (1/2) ln 3. FCA then acts directly on the lineage-fixed triangle, creates a new apex and its three incident relations, creates three side faces, fills the resulting tetrahedron, and holds the fired sector. The executed 3D output has f = (4,6,4,1), nonzero C3, and the original filled 2D triangle literally survives as a boundary face. Physical time begins when FCA supplies the first nonempty irreversible ordering between the uncommitted 2D sector and the committed, retained 3D cell. This is the first physical ordinal, not yet a calibrated duration. Independently, the new apex and response packet satisfy a positive observer-capacity predicate and carry positive Holevo information, so the post-transition structure can produce, distinguish, and retain a result without requiring that an accessible first observation has already been performed. The theorem establishes timeless 2D formation, an executed 3D transition, and the birth of physical time and record capacity; it does not claim a calibrated clock, a completed observer engine, smooth spacetime, or empirical cosmology.
Author: Bulmash, Jacob
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203881031