{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YUAD42NOBI4OENFAWHBGVGSCGW","short_pith_number":"pith:YUAD42NO","canonical_record":{"source":{"id":"1108.5830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-30T05:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"c22a7a5249f382b0b9a878dadf1e1283b0a56772ffe734b29489ee346ddb0b3a","abstract_canon_sha256":"8db2767121a91ef561668541d5c285b7b1d6a1ac42c4ac4d5792e2ec33b5a67b"},"schema_version":"1.0"},"canonical_sha256":"c5003e69ae0a38e234a0b1c26a9a42358fbd541ba7b5fbd32bcc67d618166ace","source":{"kind":"arxiv","id":"1108.5830","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5830","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5830v2","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5830","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"YUAD42NOBI4O","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YUAD42NOBI4OENFA","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YUAD42NO","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YUAD42NOBI4OENFAWHBGVGSCGW","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-30T05:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"c22a7a5249f382b0b9a878dadf1e1283b0a56772ffe734b29489ee346ddb0b3a","abstract_canon_sha256":"8db2767121a91ef561668541d5c285b7b1d6a1ac42c4ac4d5792e2ec33b5a67b"},"schema_version":"1.0"},"canonical_sha256":"c5003e69ae0a38e234a0b1c26a9a42358fbd541ba7b5fbd32bcc67d618166ace","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:07.368401Z","signature_b64":"2NjXFkJqUyr5E0dKvjHon4yOkzZ+9DFCsjOxbzm0DPZcG3uiyNGCMk54lXFk/JkAT7xUWpPhbnmNpE1J/t1qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5003e69ae0a38e234a0b1c26a9a42358fbd541ba7b5fbd32bcc67d618166ace","last_reissued_at":"2026-05-18T04:14:07.367885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:07.367885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5830","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lFK8OuUFvteOOp0EvhBEKZ6R5nKFDtze1igZYAB4DVCDeZlJ9WtvTp/5K8AkoZ7UcgTbShj6+n7Sre6vATLzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:25:01.169179Z"},"content_sha256":"4fec5ce49d4d56da57b8ac12a5db1a0ca29d83af0ac9e9b3691dac1ac18a9b57","schema_version":"1.0","event_id":"sha256:4fec5ce49d4d56da57b8ac12a5db1a0ca29d83af0ac9e9b3691dac1ac18a9b57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YUAD42NOBI4OENFAWHBGVGSCGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properties of isometrically homogeneous curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Enrico Le Donne","submitted_at":"2011-08-30T05:30:32Z","abstract_excerpt":"This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\\R$ that are translation invariant. We study possible values of various metric dimensions of such spaces. One of the main results is the equivalence of two properties: the first one is linear connectedness and the second one is 1-dimensionality, with respect to Nagata dimension. Several concrete pathological examples are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5830","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhChUOipacDP/zXKdWoR6HBIL4kSNTZdWTL30Oc4aVd+8nK0Jd8jsvKOx1IOTrnfTRqTG9E7Hon776i4xieaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:25:01.169540Z"},"content_sha256":"e6c47bdb5f0c7f324b590daaa12d26bbe471bb44e5b66872f2174191e07f0b5e","schema_version":"1.0","event_id":"sha256:e6c47bdb5f0c7f324b590daaa12d26bbe471bb44e5b66872f2174191e07f0b5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUAD42NOBI4OENFAWHBGVGSCGW/bundle.json","state_url":"https://pith.science/pith/YUAD42NOBI4OENFAWHBGVGSCGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUAD42NOBI4OENFAWHBGVGSCGW/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":"2026-07-03T10:25:01Z","links":{"resolver":"https://pith.science/pith/YUAD42NOBI4OENFAWHBGVGSCGW","bundle":"https://pith.science/pith/YUAD42NOBI4OENFAWHBGVGSCGW/bundle.json","state":"https://pith.science/pith/YUAD42NOBI4OENFAWHBGVGSCGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUAD42NOBI4OENFAWHBGVGSCGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YUAD42NOBI4OENFAWHBGVGSCGW","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":"8db2767121a91ef561668541d5c285b7b1d6a1ac42c4ac4d5792e2ec33b5a67b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-30T05:30:32Z","title_canon_sha256":"c22a7a5249f382b0b9a878dadf1e1283b0a56772ffe734b29489ee346ddb0b3a"},"schema_version":"1.0","source":{"id":"1108.5830","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5830","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5830v2","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5830","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"YUAD42NOBI4O","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YUAD42NOBI4OENFA","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YUAD42NO","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:e6c47bdb5f0c7f324b590daaa12d26bbe471bb44e5b66872f2174191e07f0b5e","target":"graph","created_at":"2026-05-18T04:14:07Z","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":"This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\\R$ that are translation invariant. We study possible values of various metric dimensions of such spaces. One of the main results is the equivalence of two properties: the first one is linear connectedness and the second one is 1-dimensionality, with respect to Nagata dimension. Several concrete pathological examples are provided.","authors_text":"Enrico Le Donne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-30T05:30:32Z","title":"Properties of isometrically homogeneous curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5830","kind":"arxiv","version":2},"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":"sha256:4fec5ce49d4d56da57b8ac12a5db1a0ca29d83af0ac9e9b3691dac1ac18a9b57","target":"record","created_at":"2026-05-18T04:14:07Z","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":"8db2767121a91ef561668541d5c285b7b1d6a1ac42c4ac4d5792e2ec33b5a67b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-30T05:30:32Z","title_canon_sha256":"c22a7a5249f382b0b9a878dadf1e1283b0a56772ffe734b29489ee346ddb0b3a"},"schema_version":"1.0","source":{"id":"1108.5830","kind":"arxiv","version":2}},"canonical_sha256":"c5003e69ae0a38e234a0b1c26a9a42358fbd541ba7b5fbd32bcc67d618166ace","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5003e69ae0a38e234a0b1c26a9a42358fbd541ba7b5fbd32bcc67d618166ace","first_computed_at":"2026-05-18T04:14:07.367885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:07.367885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2NjXFkJqUyr5E0dKvjHon4yOkzZ+9DFCsjOxbzm0DPZcG3uiyNGCMk54lXFk/JkAT7xUWpPhbnmNpE1J/t1qBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:07.368401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5830","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fec5ce49d4d56da57b8ac12a5db1a0ca29d83af0ac9e9b3691dac1ac18a9b57","sha256:e6c47bdb5f0c7f324b590daaa12d26bbe471bb44e5b66872f2174191e07f0b5e"],"state_sha256":"d833655f52419e6fe8ebb04050eec84cd57ae5a51ae01d0cf1fdfbc350aaa886"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LKYLcE81f1xA2I573QXBeNuScE3r7v+hNEpnwpF2cqu3aO93yGiUcG3vRy65uVm32fiRgBokJGUZ2TTBizG8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T10:25:01.171458Z","bundle_sha256":"bef46ef3eb5c2dfb8038568cf8d7feada6959e1b63edaf1a83321091158896db"}}