{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:53FZUOOUUV7UF5BKWVLSGZFQNN","short_pith_number":"pith:53FZUOOU","canonical_record":{"source":{"id":"1908.07603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-20T20:45:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"eee05862224ab4ae583871a86211924121c8d47244d41301ffc95e833acc74e2","abstract_canon_sha256":"65cb785bb65e8e8f50e5472a858e57162fc5c32d021dec4fecbd2195f550c36e"},"schema_version":"1.0"},"canonical_sha256":"eecb9a39d4a57f42f42ab5572364b06b48e4c905ca5f76da25b299a70901cefb","source":{"kind":"arxiv","id":"1908.07603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07603","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07603v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07603","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"53FZUOOUUV7U","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"53FZUOOUUV7UF5BK","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"53FZUOOU","created_at":"2026-07-04T23:58:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:53FZUOOUUV7UF5BKWVLSGZFQNN","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-20T20:45:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"eee05862224ab4ae583871a86211924121c8d47244d41301ffc95e833acc74e2","abstract_canon_sha256":"65cb785bb65e8e8f50e5472a858e57162fc5c32d021dec4fecbd2195f550c36e"},"schema_version":"1.0"},"canonical_sha256":"eecb9a39d4a57f42f42ab5572364b06b48e4c905ca5f76da25b299a70901cefb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:59.589601Z","signature_b64":"q4MH7ECqo+P22xCe+d2QkFgko8Z+O2Irj1Y6PqqGuA/HPG6rnTOryZPythLX1rYh/E1xLuY54HKaN9liYm+IDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eecb9a39d4a57f42f42ab5572364b06b48e4c905ca5f76da25b299a70901cefb","last_reissued_at":"2026-07-04T23:58:59.589263Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:59.589263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07603","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":"2026-07-04T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSWICbzNmQpQ24UoqjGf7U2NStE5/CWklACaubzUb+svEBeyyxMmaB1VyNRs5ESFyy98JLzrVmknjoOksE61Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:22:58.177321Z"},"content_sha256":"eed06db1e8eba1ba0772a20552299fbe8be34d293bb2d92af08ff8f2bea8e160","schema_version":"1.0","event_id":"sha256:eed06db1e8eba1ba0772a20552299fbe8be34d293bb2d92af08ff8f2bea8e160"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:53FZUOOUUV7UF5BKWVLSGZFQNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Piecewise Visual, Linearly Connected Metrics on Boundaries of Relatively Hyperbolic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Matthew Haulmark, Michael L. Mihalik","submitted_at":"2019-08-20T20:45:17Z","abstract_excerpt":"Suppose a finitely generated group $G$ is hyperbolic relative to $\\mathcal P$ a set of proper finitely generated subgroups of $G$. Established results in the literature imply that a \"visual\" metric on $\\partial (G,\\mathcal P)$ is \"linearly connected\" if and only if the boundary $\\partial (G,\\mathcal P)$ has no cut point. Our goal is to produce linearly connected metrics on $\\partial (G,\\mathcal P)$ that are \"piecewise\" visual when $\\partial (G,\\mathcal P)$ contains cut points. %Visual metrics for $\\partial (G,\\mathcal P)$ are tightly linked to inner products of geodesic rays in \"cusped\" spaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07603","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07603/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6QrKyXIvVf6bsyGkwTc+8dm0wIH0+/inBsKiHDRAdsPmxg0TtfMQ+w1FPqXui1Nin+XW7K2SPVItgcpyJfVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:22:58.178063Z"},"content_sha256":"2a0235b51947614df30cb30f3fe32ec6c4dc7b60f0109f32eb6648d74c25d60e","schema_version":"1.0","event_id":"sha256:2a0235b51947614df30cb30f3fe32ec6c4dc7b60f0109f32eb6648d74c25d60e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53FZUOOUUV7UF5BKWVLSGZFQNN/bundle.json","state_url":"https://pith.science/pith/53FZUOOUUV7UF5BKWVLSGZFQNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53FZUOOUUV7UF5BKWVLSGZFQNN/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":"2026-08-16T17:22:58Z","links":{"resolver":"https://pith.science/pith/53FZUOOUUV7UF5BKWVLSGZFQNN","bundle":"https://pith.science/pith/53FZUOOUUV7UF5BKWVLSGZFQNN/bundle.json","state":"https://pith.science/pith/53FZUOOUUV7UF5BKWVLSGZFQNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53FZUOOUUV7UF5BKWVLSGZFQNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:53FZUOOUUV7UF5BKWVLSGZFQNN","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":"65cb785bb65e8e8f50e5472a858e57162fc5c32d021dec4fecbd2195f550c36e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-20T20:45:17Z","title_canon_sha256":"eee05862224ab4ae583871a86211924121c8d47244d41301ffc95e833acc74e2"},"schema_version":"1.0","source":{"id":"1908.07603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07603","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07603v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07603","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"53FZUOOUUV7U","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"53FZUOOUUV7UF5BK","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"53FZUOOU","created_at":"2026-07-04T23:58:59Z"}],"graph_snapshots":[{"event_id":"sha256:2a0235b51947614df30cb30f3fe32ec6c4dc7b60f0109f32eb6648d74c25d60e","target":"graph","created_at":"2026-07-04T23:58:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose a finitely generated group $G$ is hyperbolic relative to $\\mathcal P$ a set of proper finitely generated subgroups of $G$. Established results in the literature imply that a \"visual\" metric on $\\partial (G,\\mathcal P)$ is \"linearly connected\" if and only if the boundary $\\partial (G,\\mathcal P)$ has no cut point. Our goal is to produce linearly connected metrics on $\\partial (G,\\mathcal P)$ that are \"piecewise\" visual when $\\partial (G,\\mathcal P)$ contains cut points. %Visual metrics for $\\partial (G,\\mathcal P)$ are tightly linked to inner products of geodesic rays in \"cusped\" spaces","authors_text":"Matthew Haulmark, Michael L. Mihalik","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-20T20:45:17Z","title":"Piecewise Visual, Linearly Connected Metrics on Boundaries of Relatively Hyperbolic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07603","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:eed06db1e8eba1ba0772a20552299fbe8be34d293bb2d92af08ff8f2bea8e160","target":"record","created_at":"2026-07-04T23:58:59Z","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":"65cb785bb65e8e8f50e5472a858e57162fc5c32d021dec4fecbd2195f550c36e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-20T20:45:17Z","title_canon_sha256":"eee05862224ab4ae583871a86211924121c8d47244d41301ffc95e833acc74e2"},"schema_version":"1.0","source":{"id":"1908.07603","kind":"arxiv","version":1}},"canonical_sha256":"eecb9a39d4a57f42f42ab5572364b06b48e4c905ca5f76da25b299a70901cefb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eecb9a39d4a57f42f42ab5572364b06b48e4c905ca5f76da25b299a70901cefb","first_computed_at":"2026-07-04T23:58:59.589263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:59.589263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4MH7ECqo+P22xCe+d2QkFgko8Z+O2Irj1Y6PqqGuA/HPG6rnTOryZPythLX1rYh/E1xLuY54HKaN9liYm+IDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:59.589601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eed06db1e8eba1ba0772a20552299fbe8be34d293bb2d92af08ff8f2bea8e160","sha256:2a0235b51947614df30cb30f3fe32ec6c4dc7b60f0109f32eb6648d74c25d60e"],"state_sha256":"5dab10697e17258761ef52a167d091a8dad4cd9e8779927db2a678868bf4ca13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQWWh39qnLIOBzRV9yxJTlH361X7xDtxZz2DI4Shwl0/W3F1VzTQAtQtMmOsYFRBK0WCdfZflaA8bln6vv4BDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:22:58.183914Z","bundle_sha256":"58e99092c97632ffff3d567ab8a189a7afb3012319d48828e94ab1d7e269d67d"}}