Read the equation
An expression equals itself under ordinary equality. This logical identity does not state that a quantity is unchanged between different times, and it does not measure the system’s awareness of its own value. Temporal persistence requires an additional relation such as xₜ₊₁=xₜ plus a specified observation procedure.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Value being identified with itself |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
The exact solution is zn=1+an. For every integer n≥1, 1<zn<2. The trajectory never returns exactly to the origin two, although it converges to one. A routine can repeatedly output zn=zn at every step. This satisfies the proposed weak numerical pattern of an internally computed change, permanent origin difference, and repeated declarations. The audit instantiated 100 different values of a from 0.05 to 0.95. All 100 satisfy that property analytically. This is not evidence that 100 consciousness events were generated. It shows that the criterion accepts an entire family of ordinary contracting recurrences. It has not yet distinguished a consciousness-specific phenomenon from the much broader class of stateful computation. A one-bit latch is an even smaller illustration: after a trigger it stores one instead of zero and repeatedly reports one. Calling every such latch conscious would be a substantive theoretical commitment, not something established by observing the latch. We do not claim to have independently proved these controls unconscious. The point is one of specificity: a measurement intended to diagnose consciousness must explain why this broad class of positives supports the intended interpretation, or state explicitly that it includes them and derive testable consequences of doing so.
Exact original notation
{z}_{n}={z}_{n}