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Frank WapplerHeads-up! to <a href="https://arxiv.org/abs/2302.12209" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://arxiv.org/abs/2302.12209</a> "How to detect the spacetime curvature without rulers and <a href="https://mathstodon.xyz/tags/Clocks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Clocks</a>" (A. V. Nenashev, S. D. Baranovskii) -- which investigates the question (p. 2) "Is it possible to figure out that a spacetime [region] is curved [instead conformally flat] by testing <a href="https://mathstodon.xyz/tags/CausalRelations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CausalRelations</a> only ?" -- and provides proof of a positive answer through a criterion in terms of causal relations among any set of eight <a href="https://mathstodon.xyz/tags/events" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#events</a> (<a href="https://mathstodon.xyz/tags/StitchConfiguration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#StitchConfiguration</a>).Closely related is the question "Is it possible to figure out whether two (or more) participants are sitting still wrt. each other in a flat region (or whatever is equivalent in a conformally flat region) by testing causal relations only ?",(referring to the notion of <a href="https://mathstodon.xyz/tags/InertialFrame" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#InertialFrame</a> in the sense of W. Rindler as "set of point particles sitting still wrt. each other"; cmp. <a href="http://www.scholarpedia.org/article/Special_relativity:_kinematics" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://www.scholarpedia.org/article/Special_relativity:_kinematics</a>), -- which is presumably solved by <a href="https://mathstodon.xyz/tags/tetrahedral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tetrahedral</a>-octahedral <a href="https://mathstodon.xyz/tags/PingCoincidenceLattices" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PingCoincidenceLattices</a>, closely related to <a href="https://mathstodon.xyz/tags/OctetTruss" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OctetTruss</a> <a href="https://mathstodon.xyz/tags/PingCoincidenceLattices" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PingCoincidenceLattices</a>; see e.g. <a href="https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb</a> and <a href="https://www.google.com/search?q=%22octet+truss%22&tbm=isch&prmd=ivnbz" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.google.com/search?q=%22octet+truss%22&tbm=isch&prmd=ivnbz</a> -- and where, notably, eight events in one particular variant of the <a href="https://mathstodon.xyz/tags/StitchConfiguration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#StitchConfiguration</a> do indeed occur as integral part of those mentioned <a href="https://mathstodon.xyz/tags/PingCoincidenceLattices" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PingCoincidenceLattices</a> (namely, not surprisingly, depicted as <a href="https://mathstodon.xyz/tags/Octahedra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Octahedra</a> in the familiar drawings of the corresponding "plain 3D" lattices).<a href="https://mathstodon.xyz/tags/Relativity" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Relativity</a> <a href="https://mathstodon.xyz/tags/Spacetime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Spacetime</a>

aithir<a href="https://mstdn.social/tags/Octahedra" class="mention hashtag" rel="tag">#Octahedra</a>: ChephrenOscar van Dyk was one of the experts in the team of Carla Ruiz. They were responsible for the artefacts they called octahedra based on their form. There were four parts, almost identical and slightly imperfect. They were almost transparent except for a slight shimmer in different wavelengths. ...<a href="https://mstdn.social/tags/Space" class="mention hashtag" rel="tag">#Space</a>, <a href="https://mstdn.social/tags/Time" class="mention hashtag" rel="tag">#Time</a>, <a href="https://mstdn.social/tags/SciFi" class="mention hashtag" rel="tag">#SciFi</a>, <a href="https://mstdn.social/tags/Fantasy" class="mention hashtag" rel="tag">#Fantasy</a><a href="https://a.gup.pe/u/fantasy" class="u-url mention">@fantasy</a> <a href="https://a.gup.pe/u/scifi" class="u-url mention">@scifi</a> Full Post: <a href="https://octahedron.world/storylines/octahedra/02-chephren?c=mst" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://octahedron.world/storylines/octahedra/02-chephren?c=mst</a>

aithir<a href="https://mstdn.social/tags/Octahedra" class="mention hashtag" rel="tag">#Octahedra</a>: Udins StoneUdin found a stone. At first, it was fully covered with dirt. She only saw its beauty and quality because a small corner stood out. So she went to the river and cleaned it up. It was the most beautiful piece, she had ever seen. It had a perfect form. Except for a light blue shine, it was transparent and it had engravings on each side. ...<a href="https://mstdn.social/tags/Space" class="mention hashtag" rel="tag">#Space</a>, <a href="https://mstdn.social/tags/Time" class="mention hashtag" rel="tag">#Time</a>, <a href="https://mstdn.social/tags/SciFi" class="mention hashtag" rel="tag">#SciFi</a>, <a href="https://mstdn.social/tags/Fantasy" class="mention hashtag" rel="tag">#Fantasy</a><a href="https://a.gup.pe/u/fantasy" class="u-url mention">@fantasy</a> <a href="https://a.gup.pe/u/scifi" class="u-url mention">@scifi</a> Full Post: <a href="https://octahedron.world/storylines/octahedra/01-udins-stone?c=mst" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://octahedron.world/storylines/octahedra/01-udins-stone?c=mst</a>

mc ☕<a href="https://qoto.org/tags/Geometric" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometric</a> <a href="https://qoto.org/tags/Model" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Model</a> by A. Harry Wheeler, Five <a href="https://qoto.org/tags/Intersecting" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Intersecting</a> Regular <a href="https://qoto.org/tags/Octahedra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Octahedra</a> <a href="https://qoto.org/tags/Inscriptible" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Inscriptible</a> in a Regular <a href="https://qoto.org/tags/Dodecahedron" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Dodecahedron</a> <a href="https://www.si.edu/object/geometric-model-harry-wheeler-five-intersecting-regular-octahedra-inscriptible-regular-dodecahedron:nmah_1691577" rel="nofollow noopener noreferrer" target="_blank">https://www.si.edu/object/geometric-model-harry-wheeler-five-intersecting-regular-octahedra-inscriptible-regular-dodecahedron:nmah_1691577</a><a href="https://qoto.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a>

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