{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2S3CPA5Z6G5YSHTZDBIBRJ44XF","short_pith_number":"pith:2S3CPA5Z","schema_version":"1.0","canonical_sha256":"d4b62783b9f1bb891e79185018a79cb94c890ca6dcede186faa14450120776c5","source":{"kind":"arxiv","id":"1811.04185","version":2},"attestation_state":"computed","paper":{"title":"Siblings of an $\\aleph_0$-categorical relational structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Claude Laflamme, Maurice Pouzet, Norbert Sauer, Robert Woodrow","submitted_at":"2018-11-10T03:46:02Z","abstract_excerpt":"A sibling of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, in which $R$ can be embedded. Let $sib(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism. Thomass\\'e conjectured that for countable relational structures made of at most countably many relations, $sib(R)$ is either $1$, countably infinite, or the size of the continuum; but even showing the special case $sib(R)=1$ or infinite is unsettled when $R$ is a countable tree. This is related to Bonato-Tardif conjecture asserting that for every tree $T$ the numb"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.04185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-10T03:46:02Z","cross_cats_sorted":[],"title_canon_sha256":"64f4c019019cf5823f245ec8e9cd6a4c2acfcbf5b58d118c3f7ca9a285341abf","abstract_canon_sha256":"1d285e97ea870db3c39484d005759465db9257422e4191166788486829794c42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:58.574212Z","signature_b64":"KjWnGlcf4FGU5qSH9K9R4anxBCfwY5OfIxwP/ZsS68TCDk3eT2UxE32q7wtym06eedX4eu2TMfT/INi+2XRXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4b62783b9f1bb891e79185018a79cb94c890ca6dcede186faa14450120776c5","last_reissued_at":"2026-05-17T23:44:58.573795Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:58.573795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Siblings of an $\\aleph_0$-categorical relational structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Claude Laflamme, Maurice Pouzet, Norbert Sauer, Robert Woodrow","submitted_at":"2018-11-10T03:46:02Z","abstract_excerpt":"A sibling of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, in which $R$ can be embedded. Let $sib(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism. Thomass\\'e conjectured that for countable relational structures made of at most countably many relations, $sib(R)$ is either $1$, countably infinite, or the size of the continuum; but even showing the special case $sib(R)=1$ or infinite is unsettled when $R$ is a countable tree. This is related to Bonato-Tardif conjecture asserting that for every tree $T$ the numb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04185","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.04185","created_at":"2026-05-17T23:44:58.573854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.04185v2","created_at":"2026-05-17T23:44:58.573854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04185","created_at":"2026-05-17T23:44:58.573854+00:00"},{"alias_kind":"pith_short_12","alias_value":"2S3CPA5Z6G5Y","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2S3CPA5Z6G5YSHTZ","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2S3CPA5Z","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF","json":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF.json","graph_json":"https://pith.science/api/pith-number/2S3CPA5Z6G5YSHTZDBIBRJ44XF/graph.json","events_json":"https://pith.science/api/pith-number/2S3CPA5Z6G5YSHTZDBIBRJ44XF/events.json","paper":"https://pith.science/paper/2S3CPA5Z"},"agent_actions":{"view_html":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF","download_json":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF.json","view_paper":"https://pith.science/paper/2S3CPA5Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.04185&json=true","fetch_graph":"https://pith.science/api/pith-number/2S3CPA5Z6G5YSHTZDBIBRJ44XF/graph.json","fetch_events":"https://pith.science/api/pith-number/2S3CPA5Z6G5YSHTZDBIBRJ44XF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF/action/storage_attestation","attest_author":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF/action/author_attestation","sign_citation":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF/action/citation_signature","submit_replication":"https://pith.science/pith/2S3CPA5Z6G5YSHTZDBIBRJ44XF/action/replication_record"}},"created_at":"2026-05-17T23:44:58.573854+00:00","updated_at":"2026-05-17T23:44:58.573854+00:00"}