The intricate decoding of star sequences demands not only the engagement of computational finesse but a dexterity in harmonizing the ancient protocol established by unknown celestial navigators. This paragraph serves to elucidate the steps, albeit convoluted and verbose, expected of the astute practitioner in the art of perpetration of the Star Sequence.

Step One: Acquisition of the Stellar Coordinates shall commence forthwith. The practitioner must ensure the input of hexadecimal values into the established grid within Quadrant Twelve (or your closest equivalency thereunto). The meticulous accuracy in the transmission of these coordinates is paramount and will correspond to the accuracy of requisite outcomes desired which by no means can be overemphasized.

            Example Coordinates:
            φ = 89.045d
            π = 64.835
            θ = (√7) / 14
        

Step Two: Proceed to initiate the Harmonious Computation Protocol whereby the star sequence algorithms engage recursively through layers of digital star maps, intersecting at factorial intersections. Each intersection is to be noted and duly recorded within the holographic membrane database, utilizing the cipher key assigned uniquely at the origin of stellar engagement.

Caution is advised: Disputations arising from intersecting values yielding a rational irreducible can exacerbate systemic anomalies.

Navigational Chart - Quadrant 12
Cipher Registry and Unique Keys

It is akin to an ancient wisdom inscribed within obelisks that our algorithms channel, thus it isn't merely a program but an homage to the celestial logic whose workings remain only partially illuminated within this codex-like manual.