{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:G6PR7VNRFUV7N26DH4BO3GT4GL","short_pith_number":"pith:G6PR7VNR","canonical_record":{"source":{"id":"1102.2159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-02-10T16:17:11Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"39fd515b6beb14fd13b6f1a001cced77e438ca25ec37da0c0b257430ed182f93","abstract_canon_sha256":"847b39da921f3a48fd7c6dbcd61b204c33de3b5404cc7a7f6d4f46a709602a43"},"schema_version":"1.0"},"canonical_sha256":"379f1fd5b12d2bf6ebc33f02ed9a7c32d8e11c527073ed2e4049618cc0f14d1f","source":{"kind":"arxiv","id":"1102.2159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2159","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2159v1","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2159","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"G6PR7VNRFUV7","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G6PR7VNRFUV7N26D","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G6PR7VNR","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:G6PR7VNRFUV7N26DH4BO3GT4GL","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-02-10T16:17:11Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"39fd515b6beb14fd13b6f1a001cced77e438ca25ec37da0c0b257430ed182f93","abstract_canon_sha256":"847b39da921f3a48fd7c6dbcd61b204c33de3b5404cc7a7f6d4f46a709602a43"},"schema_version":"1.0"},"canonical_sha256":"379f1fd5b12d2bf6ebc33f02ed9a7c32d8e11c527073ed2e4049618cc0f14d1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:34.121133Z","signature_b64":"ILoe5rz5/WiCr9vDv3ehjXTMow2k8Mv79GSYpdLgEEVFoGuNyy3dxWHCRG0ylAKWWH66WF0RVRvqRa9QgqEBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"379f1fd5b12d2bf6ebc33f02ed9a7c32d8e11c527073ed2e4049618cc0f14d1f","last_reissued_at":"2026-05-18T04:29:34.120697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:34.120697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2159","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IfboQjguDLl4dTNXuQJjVbpjMfWvD9iPGDMfXfQ7SLk1Q8ROBCuOQTzA475PE4P0ueDAi0y4RC6n3/LSVIXSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:17:41.208089Z"},"content_sha256":"7ee160c05efe0254d82cc749b3f74a6a0d811dfce3bc3f8adf85dc4099f8f170","schema_version":"1.0","event_id":"sha256:7ee160c05efe0254d82cc749b3f74a6a0d811dfce3bc3f8adf85dc4099f8f170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:G6PR7VNRFUV7N26DH4BO3GT4GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The embedding structure for linearly ordered topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Alex Primavesi, Katherine Thompson","submitted_at":"2011-02-10T16:17:11Z","abstract_excerpt":"In this paper, the class of all linearly ordered topological spaces (LOTS) quasi-ordered by the embeddability relation is investigated. In ZFC it is proved that for countable LOTS this quasi-order has both a maximal (universal) element and a finite basis. For the class of uncountable LOTS of cardinality $\\kappa$ it is proved that this quasi-order has no maximal element for $\\kappa$ at least the size of the continuum and that in fact the dominating number for such quasi-orders is maximal, i.e. $2^\\kappa$. Certain subclasses of LOTS, such as the separable LOTS, are studied with respect to the to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2159","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQu6VPUII+ms6zBIPn0ifCr9FuDMla6yA8ntp/v4jsBCSnISSW2m6iX4gpp/3XOeHynSe1+iQyQOJkIN6fgABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:17:41.208964Z"},"content_sha256":"7cb29cc9a29689a3bd40d9d902c7643f3e5e112769281d6371208c314d0d9197","schema_version":"1.0","event_id":"sha256:7cb29cc9a29689a3bd40d9d902c7643f3e5e112769281d6371208c314d0d9197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6PR7VNRFUV7N26DH4BO3GT4GL/bundle.json","state_url":"https://pith.science/pith/G6PR7VNRFUV7N26DH4BO3GT4GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6PR7VNRFUV7N26DH4BO3GT4GL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T20:17:41Z","links":{"resolver":"https://pith.science/pith/G6PR7VNRFUV7N26DH4BO3GT4GL","bundle":"https://pith.science/pith/G6PR7VNRFUV7N26DH4BO3GT4GL/bundle.json","state":"https://pith.science/pith/G6PR7VNRFUV7N26DH4BO3GT4GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6PR7VNRFUV7N26DH4BO3GT4GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G6PR7VNRFUV7N26DH4BO3GT4GL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"847b39da921f3a48fd7c6dbcd61b204c33de3b5404cc7a7f6d4f46a709602a43","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-02-10T16:17:11Z","title_canon_sha256":"39fd515b6beb14fd13b6f1a001cced77e438ca25ec37da0c0b257430ed182f93"},"schema_version":"1.0","source":{"id":"1102.2159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2159","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2159v1","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2159","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"G6PR7VNRFUV7","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G6PR7VNRFUV7N26D","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G6PR7VNR","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:7cb29cc9a29689a3bd40d9d902c7643f3e5e112769281d6371208c314d0d9197","target":"graph","created_at":"2026-05-18T04:29:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, the class of all linearly ordered topological spaces (LOTS) quasi-ordered by the embeddability relation is investigated. In ZFC it is proved that for countable LOTS this quasi-order has both a maximal (universal) element and a finite basis. For the class of uncountable LOTS of cardinality $\\kappa$ it is proved that this quasi-order has no maximal element for $\\kappa$ at least the size of the continuum and that in fact the dominating number for such quasi-orders is maximal, i.e. $2^\\kappa$. Certain subclasses of LOTS, such as the separable LOTS, are studied with respect to the to","authors_text":"Alex Primavesi, Katherine Thompson","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-02-10T16:17:11Z","title":"The embedding structure for linearly ordered topological spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2159","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7ee160c05efe0254d82cc749b3f74a6a0d811dfce3bc3f8adf85dc4099f8f170","target":"record","created_at":"2026-05-18T04:29:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"847b39da921f3a48fd7c6dbcd61b204c33de3b5404cc7a7f6d4f46a709602a43","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-02-10T16:17:11Z","title_canon_sha256":"39fd515b6beb14fd13b6f1a001cced77e438ca25ec37da0c0b257430ed182f93"},"schema_version":"1.0","source":{"id":"1102.2159","kind":"arxiv","version":1}},"canonical_sha256":"379f1fd5b12d2bf6ebc33f02ed9a7c32d8e11c527073ed2e4049618cc0f14d1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"379f1fd5b12d2bf6ebc33f02ed9a7c32d8e11c527073ed2e4049618cc0f14d1f","first_computed_at":"2026-05-18T04:29:34.120697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:34.120697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ILoe5rz5/WiCr9vDv3ehjXTMow2k8Mv79GSYpdLgEEVFoGuNyy3dxWHCRG0ylAKWWH66WF0RVRvqRa9QgqEBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:34.121133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ee160c05efe0254d82cc749b3f74a6a0d811dfce3bc3f8adf85dc4099f8f170","sha256:7cb29cc9a29689a3bd40d9d902c7643f3e5e112769281d6371208c314d0d9197"],"state_sha256":"0e3693d1fe64d023b0f85ef5aa7f99d4e409d0a98824f4eee711dfc8d59d814c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZs7gAntJltXA/J+qWIq7IBlirbqLtYLljobTtUsEEgmqLNnb5Stkm14DaFdIUABOjp8Ja1fYyTL6x2CD7izBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:17:41.212803Z","bundle_sha256":"b1eb38640d9bcf67fc29af8f3a5009556399e14b78ab956b77bc48a9fe8d44ea"}}