A Framework Proposal for Structural Non-Separability: The Place of the Record v.14_Junghanna

A split divides a system's degrees of freedom into two parts, A and Ā, and a single split fixes self and other, so no observer is brought in from outside. Even for the same split, the amount actually read varies with the observation window W and with the environment-fragment size f. The paper therefore distinguishes three quantities: the amount of entanglement S_ent(A), the amount of record remaining in the medium S_rec, and the amount actually recovered through the observation window Q(W, f).

The upper bound on reading is S(ρ_diag), and it holds even when the window is the whole environment. And the paper defines window saturation as the regime in which widening the window changes Q(W, f) by less than ε.</p><p dir="ltr">In this structure the record and the reading are not symmetric. The recorded amount moves in one direction, whereas the amount read through a given window, once saturated, moves to another split and another window.

The cycle this paper proposes is therefore not a cycle in which the record itself returns to the origin, but one in which the readable structure saturates at one split and opens again through new records and new observation windows. This view distinguishes the formation time of a record from its retention time, and separates a record's physical existence from its present legibility.</p><p dir="ltr">The paper also treats the relation between information and recognition as a single pair, through the common notion of the split.

Information is structure present in systems and media; recognition is the process of reading part of that structure through a particular window and split. The two are read not as a one-way staircase but as mutually constraining. From this pair, one answer to the paper's question follows.

The record is what remains after coherence is gone; that is, the part on which all windows agree. Half of the answer is an established result and half is this paper's reading, and the reading holds when the dephasing basis and the medium's pointer basis are aligned. Time, space, and gravity are then examined as ways in which this pair is realized in different media.</p><p dir="ltr">Finally the paper compares the case in which a split appears inside a single object with the case in which it appears as a relation between objects, and examines the structural similarity between how string theory and loop quantum gravity count area and entanglement.

That the same mathematical form appears in two theories does not mean they count the same physical object, and the physical identity of this correspondence is left open. Each correspondence is accompanied by a result that would break it; of ten correspondences, three have been measured. The three correspondences this paper adds are as yet unmeasured.

The recorded amount accumulates, and the read amount cycles. The place where both stand is the cut.</p>