How do I keep track of connections between papers?

The appeal of linking papers to each other is obvious and the arithmetic is against it. Fifty papers have over a thousand possible pairs. You cannot evaluate them all, so you link the ones you happen to notice, which produces a network shaped by the order you read in rather than by the structure of the field.

Claims fix the arithmetic. A claim is a fixed point that many papers can attach to, so the number of things you maintain grows with the number of distinct assertions in your argument, which is small. Twenty claims can organize two hundred papers.

It also produces the connection type you actually want. Knowing that Fenton and Alvarez are related is not useful. Knowing that both support the three-year attenuation claim, and that Roy contradicts it using a different measure, is a paragraph.

The practical form is unglamorous. A table, one row per claim, with columns for the claim, the supporting sources, the contradicting sources, and your judgment. Every synthesis technique that works is a variation on this, and the elaborate versions add convenience rather than capability.

Add one more column than feels necessary, recording what each citation does rather than only that it exists. Greenberg's analysis of a claim about amyloid and inclusion body myositis classified every paper as primary data, review, or model, and every citation as supportive, neutral, or critical (Greenberg, 2009, p. 1). That distinction is what lets you tell corroboration from repetition. In that network of 242 papers, eight papers, seven of them from one research group, carried 97% of the citation traffic (Greenberg, 2009, p. 5). A table that only records who cites whom would show that cluster as overwhelming agreement rather than as a single group being cited many times.

Penders makes the same point from the writing end. The advice is to reprioritize your references for each publication and by section, using reviews for broad context in an introduction and empirical papers for detailed discussion, and preferring reviewed sources over preprints (Penders, 2018, p. 4). Citations can also signal allegiance to a school of thought rather than evidential support, which is a second reason to record the evidential status of a link and not just the link (Penders, 2018, pp. 4-5).

Do I need an atomic note system to do this?

No. Atomic notes solve this problem and bring a large maintenance cost, and many people spend more time tending the network than using it. A table with one row per claim and a column for sources does the same job for a literature review and can be read at a glance.

Atomic note systems earn their cost for long-running, wide-ranging intellectual work where you cannot predict which ideas will connect. A doctoral literature review is narrower than that. You know roughly what your argument is, and you need evidence organized against it.

If you already run such a system and it works, keep it. The failure mode to watch for is the same one as with any note system: when the network becomes the project, the thesis stops moving.

How do I see which papers speak to the same claim?

Group by claim and read the source column. If your records are one row per claim with sources attached, this is a sort. If they are one note per paper, there is no way to see it without rereading everything, which is the reason paper-shaped notes fail at synthesis.

Once grouped, the interesting rows are the ones with sources in both columns, supporting and contradicting. Those are where your chapter has something to argue about, and they are usually the paragraphs an examiner engages with.

The rows with a single source are worth a second look too. A claim your whole argument leans on that rests on one study is a risk you want to know about before someone else finds it.

Backward and forward citation searching is how you find the rest of the rows, but treat coverage as something to record rather than assume. Haddaway and colleagues compared Google Scholar against Web of Science across six environmental-management reviews and found it identified between 68.5% and 100% of the known studies, missing 31.5% in the worst case (Haddaway et al., 2015, p. 11). The evidence is genuinely mixed here. Gehano and colleagues found Google Scholar retrieved all 738 articles across 29 medical systematic reviews, while Boeker and colleagues found up to 34% missed across 14 reviews (Haddaway et al., 2015, p. 13). Finding a paper you already know about is an easier task than retrieving every relevant paper, which is why the two sets of results can both be right. Save the date, database, query, and exported records for each search, and use "cited by" as one route among several rather than the only one.