{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZFMUCNQDIHTW4VIIFCFSLG7AJ2","short_pith_number":"pith:ZFMUCNQD","schema_version":"1.0","canonical_sha256":"c95941360341e76e5508288b259be04e8f2f3e045ef68e7ec283fa73637a79d6","source":{"kind":"arxiv","id":"1705.04767","version":3},"attestation_state":"computed","paper":{"title":"Metric-measure boundary and geodesic flow on Alexandrov spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Alexander Lytchak, Anton Petrunin, Vitali Kapovitch","submitted_at":"2017-05-12T23:16:37Z","abstract_excerpt":"We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The developed analytic tool has close ties to integral geometry."},"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":"1705.04767","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-12T23:16:37Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a865cb31bd7160835fccbf4e1f5de6d8a92b0d0c5fa3ac062b07ba7a4d7eb8db","abstract_canon_sha256":"0a12c2ba76eb56766cb4bab25a27166a6c98ff8fbba98632369b91df4f896875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:10:47.349454Z","signature_b64":"/UL53azt6hBLpVhQp3uMORecmQWO00QVVnMONFk8e4hg8y4CRz7hHdh0oQWgtI89zN2bQ+5xbCgXHf5/NZ9XCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c95941360341e76e5508288b259be04e8f2f3e045ef68e7ec283fa73637a79d6","last_reissued_at":"2026-07-05T02:10:47.349000Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:10:47.349000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metric-measure boundary and geodesic flow on Alexandrov spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Alexander Lytchak, Anton Petrunin, Vitali Kapovitch","submitted_at":"2017-05-12T23:16:37Z","abstract_excerpt":"We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The developed analytic tool has close ties to integral geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04767","kind":"arxiv","version":3},"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/1705.04767/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.04767","created_at":"2026-07-05T02:10:47.349062+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.04767v3","created_at":"2026-07-05T02:10:47.349062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04767","created_at":"2026-07-05T02:10:47.349062+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZFMUCNQDIHTW","created_at":"2026-07-05T02:10:47.349062+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZFMUCNQDIHTW4VII","created_at":"2026-07-05T02:10:47.349062+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZFMUCNQD","created_at":"2026-07-05T02:10:47.349062+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.00381","citing_title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","ref_index":36,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2","json":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2.json","graph_json":"https://pith.science/api/pith-number/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/graph.json","events_json":"https://pith.science/api/pith-number/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/events.json","paper":"https://pith.science/paper/ZFMUCNQD"},"agent_actions":{"view_html":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2","download_json":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2.json","view_paper":"https://pith.science/paper/ZFMUCNQD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.04767&json=true","fetch_graph":"https://pith.science/api/pith-number/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/action/storage_attestation","attest_author":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/action/author_attestation","sign_citation":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/action/citation_signature","submit_replication":"https://pith.science/pith/ZFMUCNQDIHTW4VIIFCFSLG7AJ2/action/replication_record"}},"created_at":"2026-07-05T02:10:47.349062+00:00","updated_at":"2026-07-05T02:10:47.349062+00:00"}