{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2ZISFBMUTCO5G4OKHFZVOF5JKW","short_pith_number":"pith:2ZISFBMU","canonical_record":{"source":{"id":"1701.00500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-01-02T19:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ec0b2c51da6fe9de512e380980bea47a252387c237bf2d8f8f5a31744b53a55","abstract_canon_sha256":"d51c21652416bfa2f58de5753c127294ef3efe16d60d2fdaa4fdb5b144a59064"},"schema_version":"1.0"},"canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","source":{"kind":"arxiv","id":"1701.00500","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00500","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00500v1","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00500","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"2ZISFBMUTCO5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2ZISFBMUTCO5G4OK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2ZISFBMU","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2ZISFBMUTCO5G4OKHFZVOF5JKW","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-01-02T19:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ec0b2c51da6fe9de512e380980bea47a252387c237bf2d8f8f5a31744b53a55","abstract_canon_sha256":"d51c21652416bfa2f58de5753c127294ef3efe16d60d2fdaa4fdb5b144a59064"},"schema_version":"1.0"},"canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:29.108894Z","signature_b64":"vsko4AaJ0d0w1CPeKZpKa/IxqFfY3ifyyWxWS8cOpBySCKwAFDDNAH7byalg83NJxVAM6XoUXIw+9zWVid2VCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","last_reissued_at":"2026-05-18T00:53:29.108511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:29.108511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00500","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":"2026-05-18T00:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jo8gSYnL2Bh8Or/CAYETB+Ch5YRAo8YN1OtghbFFaIsc+ukTDxy0Gw0bqAkAQt8Z6QDvtbTOOPZfAY6O0Ln8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:05:37.923551Z"},"content_sha256":"f796e969d43665dd16dfd16a42cbf9165c9d83f270757e5ad155788ec7fb6a7d","schema_version":"1.0","event_id":"sha256:f796e969d43665dd16dfd16a42cbf9165c9d83f270757e5ad155788ec7fb6a7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2ZISFBMUTCO5G4OKHFZVOF5JKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A characterization of Gromov hyperbolicity via quasigeodesic subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Thomas Weighill","submitted_at":"2017-01-02T19:10:56Z","abstract_excerpt":"By a geodesic subspace of a metric space $X$ we mean a subset $A$ of $X$ such that any two points in $A$ can be connected by a geodesic in $A$. It is easy to check that a geodesic metric space $X$ is an $\\mathbb{R}$-tree (that is, a $0$-hyperbolic space in the sense of Gromov) if and only if the union of any two intersecting geodesic subspaces is again a geodesic subspace. In this paper, we prove an analogous characterization of general Gromov hyperbolic spaces, where we replace geodesic subspaces by quasigeodesic subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00500","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":"2026-05-18T00:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIpPDmRaWo7yim/re3W3uJ7ttSlhWcS7mzptUD/H32zv1URre9wkp4UugmvYFtcv6Qwq6E+Ve5NLXwIhhvmBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:05:37.924270Z"},"content_sha256":"3500b85a48f8aa4c07776b0d41b6f952f2590287617b3da9ceed78dcc78b6013","schema_version":"1.0","event_id":"sha256:3500b85a48f8aa4c07776b0d41b6f952f2590287617b3da9ceed78dcc78b6013"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/bundle.json","state_url":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/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":"2026-06-12T03:05:37Z","links":{"resolver":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW","bundle":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/bundle.json","state":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2ZISFBMUTCO5G4OKHFZVOF5JKW","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":"d51c21652416bfa2f58de5753c127294ef3efe16d60d2fdaa4fdb5b144a59064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-01-02T19:10:56Z","title_canon_sha256":"4ec0b2c51da6fe9de512e380980bea47a252387c237bf2d8f8f5a31744b53a55"},"schema_version":"1.0","source":{"id":"1701.00500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00500","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00500v1","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00500","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"2ZISFBMUTCO5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2ZISFBMUTCO5G4OK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2ZISFBMU","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:3500b85a48f8aa4c07776b0d41b6f952f2590287617b3da9ceed78dcc78b6013","target":"graph","created_at":"2026-05-18T00:53:29Z","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":"By a geodesic subspace of a metric space $X$ we mean a subset $A$ of $X$ such that any two points in $A$ can be connected by a geodesic in $A$. It is easy to check that a geodesic metric space $X$ is an $\\mathbb{R}$-tree (that is, a $0$-hyperbolic space in the sense of Gromov) if and only if the union of any two intersecting geodesic subspaces is again a geodesic subspace. In this paper, we prove an analogous characterization of general Gromov hyperbolic spaces, where we replace geodesic subspaces by quasigeodesic subspaces.","authors_text":"Thomas Weighill","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-01-02T19:10:56Z","title":"A characterization of Gromov hyperbolicity via quasigeodesic subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00500","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:f796e969d43665dd16dfd16a42cbf9165c9d83f270757e5ad155788ec7fb6a7d","target":"record","created_at":"2026-05-18T00:53:29Z","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":"d51c21652416bfa2f58de5753c127294ef3efe16d60d2fdaa4fdb5b144a59064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-01-02T19:10:56Z","title_canon_sha256":"4ec0b2c51da6fe9de512e380980bea47a252387c237bf2d8f8f5a31744b53a55"},"schema_version":"1.0","source":{"id":"1701.00500","kind":"arxiv","version":1}},"canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","first_computed_at":"2026-05-18T00:53:29.108511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:29.108511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vsko4AaJ0d0w1CPeKZpKa/IxqFfY3ifyyWxWS8cOpBySCKwAFDDNAH7byalg83NJxVAM6XoUXIw+9zWVid2VCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:29.108894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f796e969d43665dd16dfd16a42cbf9165c9d83f270757e5ad155788ec7fb6a7d","sha256:3500b85a48f8aa4c07776b0d41b6f952f2590287617b3da9ceed78dcc78b6013"],"state_sha256":"486ff067a146957142ce7a466e4ece0dd182f27adf8ba77477fd40c3db9a319b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DPbPo7HqNKU3F9nDPfVQWSvn7aeFehPHyknRfTHmgc6PHGzQRkfZep9C1MOPpaqpz6R9rY13SHfz/rd+JoN9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:05:37.928435Z","bundle_sha256":"ede2fdce1b57c4b06b4acbfdef7c9785e0a67c4929c17b77adacb8e1a9028e1c"}}