ok I thought about this for long, and I currently feel there is nothing that can be done aka there is nothing mathematically superior in squares versus circle versus hexagons or randomly rotated squares or anything instead of fixed square lattice here. Everything mathematically will leak similar second order information to your corner case to various levels but all will end up in same attack level and if any slight benefits are only marginal and not so clean as square lattice. The biggest benefit to current static square cells lattice is we can always find exact feasible square (aka the true point is in this region) with F(z) alone when the z is the obscured coordinate of true coordinate x, while any other superior schemes definitely has to rely on F(z, x) for feasible region finding and record both this function output shape and z for visual indication and indexing and then should be redeployed to all obscured iNat records aka there is no single patch to fix corners data attack case.
But importantly this condition you found is only serious under specific other constraints (see below) as such attack is secured under another equally likely inference “maybe the user’s true X points ending up in those four cells have true coordinates in those four cells individually - this is an equal parity inference as all of them has to be at the center corner of those squares case” and assuming any other assumptions (like terrain decoding or decoding via species ranges to find correlations or such) should be outside of any such algorithm security guarantees in first place.
so in conclusion, I come with second mantra directly and highly relevant for obscure vs fudge discussion: “Dont naively fudge or keep open locations everywhere as one set while only obscuring some static locations always if those obscuring observations set coordinates follow the pattern of X.e ± 0.0001 on both lat/long” where X is lat/long integer range, e is single digit even number. This is a very subtle effect that effects in rare cases to you but it is nevertheless not an impossible scenario on iNat (note there are atleast 1.62+ Million locations in world that are going to get affected by this from simple geometry math and if we relax ±0.0001 home level to ±0.001 we reveal street level decoding)
to give a clear example again, I used to naively keep open locations always (inat will handle taxon privacy) and then I only naively “obscured” all my home observations but under the above mantra case if my true home happens to be unluckily (from algorithmic perspective) at say (17.60008, 83.19999) and by repeatedly creating footprint of such home observations around that corner point of ±0.0001 via simple obscure while keeping everything else in those regions open or fudge (and more worse, if genuine notes like “my garden” or “my ranch” will exacerbate this attack by grouping those observations), then I would fail the equal inference saviour I discussed above, and my unlucky home is now uniquely fingerprintable from a genuine and largely robust current obscure feature (as it is relying on static cells lattice). To get the benefits of obscurity in this case, the only saviour is I have to obscure some of my non-home observations seen around my home area, or fudge all my home observations and disable obscure.
and third mantra is dont do both “fudge to large radius+obscure”, if that is still a pending bug.