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We present spectroscopic observations for quasars Q0107-025A, Q0107-025B, andQ0107-0232. For the first time, all data obtained with the Hubble SpaceTelescope's GHRS and FOS for these three quasars are combined. Ly-alphaabsorbers selected from the spectra can be used to trace the coherence of theintergalactic medium (IGM) on scales of 1-2 h_{70}^{-1} Mpc over the redshiftrange 0.4 < z_a < 0.9. A new analysis of double and triple absorbercoincidences derived from the improved spectra is performed. Automatedline-selection algorithms were used to detect absorption lines in the QSOspectra; coincident absorbers were identified across two and three sight linesbased on their proximity to each other in velocity space. A control simulationdesigned to generate artificial absorption-line spectra was used to gauge thesignificance of the coincidences. Four intervening metal line absorptionsystems are detected, with three of the four coincident to the A and B sightlines and one coincident across all three sight lines. This is evidence forsubstantial clustering among the objects responsible for the metal-enrichedgas. By contrast, large scale coherence of the IGM gas is detectable but weak.Fewer than half of the absorbers are coincident on scales of 1-2 h_{70}^{-1}Mpc, a result that is significant at the 99% confidence level, and coherencearises preferentially in the higher column density gas. Triple absorbercoincidences occur at a level that is significant at the 99% confidence level,which indicates that the higher column density gas has a planar geometry.Comment: Accepted for publication in the Astronomical Journal. 72 pages  including 13 figures and 19 table

Lyα Absorption in the Quasar Triplet Q0107-025A, Q0107-025B, and Q0107-0232: Data Calibration and Line Selection