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Stellar Cartography in a 2d universe

Given Oort's definition, if perigee is ≥5000 AU and the orbit isn't cleared, it's part of the Oort cloud.

There are multiple detected bodies matching that. Not as many as the Kuiper Belt, but it really only takes a handful to establish the pattern.

Actually, by the definition on phys.org, 2000 AU is sufficient.
2015-08-oort-cloudThe Oort Cloud is through to extend from between 2,000 and 5,000 AU (0.03 and 0.08 ly) to as far as 50,000 AU (0.79 ly) from the sun, though some estimates place the outer edge as far as 100,000 and 200,000 AU (1.58 and 3.16 ly). The Cloud is thought to be comprised of two regions – a spherical outer Oort Cloud of 20,000 – 50,000 AU (0.32 – 0.79 ly), and disc-shaped inner Oort (or Hills) Cloud of 2,000 – 20,000 AU (0.03 – 0.32 ly).

Read more at: https://phys.org/news/2015-08-oort-cloud.html#jCp

I don't know of any object with a perihelion of greater than 2000 AU - the most distant perihelion for a comet in wolfram is 11.78 au for 167P/CINEOS and the most distant perihelion for a minor planet is (note, edited: 80 au) for 2012 VP113. Wolfram is by no means exhaustive, however. I'm all but certain there are such objects, I just am unaware of them -
 
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For the record, I also searched horizons:

Horizons> QR > 50

Comet AND asteroid parameter search:
QR > 50.;
Continue [ <cr>=yes, n=no, ? ] :
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JPL/DASTCOM Small-body Search Results 2017-Sep-11 15:59:36

Comet AND asteroid parameter search:
QR > 50.;

Matching small-bodies:

Record # Epoch-yr Primary Desig Name QR
-------- -------- ------------- ------------------------- ------------
90377 2013 2003 VB12 Sedna 76.167690388
518113 2013 2004 XR190 [...unnamed...] 51.546397081
627070 2012 2012 VP113 [...unnamed...] 80.569027648
652439 2015 2014 FZ71 [...unnamed...] 55.938862957
652442 2014 2014 FC72 [...unnamed...] 51.696064661
691295 2015 2015 FJ345 [...unnamed...] 50.662808062

(6 matches. To SELECT, enter record # (integer), followed by semi-colon.)
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Select ... [F]tp, [M]ail, [R]edisplay, ?, <cr>:


Most distant perihelion in their database is 2012 VP113-
 
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There are quite a few, 113, that have aphelions over 5000 AU and are not on solar escape. I tried to paste them into a reply but the list was too long.
 
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