7. Binary-Shrink “Sand-Grain” Version · R_{bin}

Read the equation

The expression assigns a hash-derived representation to the listed state components. A hash is a many-to-one identifier unless a reversible representation is explicitly specified; the notation alone does not establish reconstruction of the original state.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read R_{bin} as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

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

⸻

7. Binary-Shrink “Sand-Grain” Version

R_{bin} = \text{hash}\Big(
\Phi \parallel dx \parallel G_{5000} \parallel \text{DNA}_{G16}
\Big)

\text{state}_{R} = \text{compress}(R_{bin})

⸻

If you want, I can also:
•	Combine these into one unified master equation

R_{bin} = \text{hash}\Big(
\Phi \parallel dx \parallel G_{5000} \parallel \text{DNA}_{G16}
\Big)

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