{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:W4SEUCLQTBXWU6NAQQ7PQ3IDVX","short_pith_number":"pith:W4SEUCLQ","canonical_record":{"source":{"id":"1709.09110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-26T16:16:15Z","cross_cats_sorted":[],"title_canon_sha256":"6008e4c820b289118d5e2fc742cef867fda613793cf6832910005cc91fedbb24","abstract_canon_sha256":"cd490524bd6d8d9dfa24d6567f1b08e81c64a5b8ba4c54a597edcebd0f880d11"},"schema_version":"1.0"},"canonical_sha256":"b7244a0970986f6a79a0843ef86d03adcee39240b2678d3392792b98d50207f9","source":{"kind":"arxiv","id":"1709.09110","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09110","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09110v2","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09110","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"W4SEUCLQTBXW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"W4SEUCLQTBXWU6NA","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"W4SEUCLQ","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:W4SEUCLQTBXWU6NAQQ7PQ3IDVX","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-26T16:16:15Z","cross_cats_sorted":[],"title_canon_sha256":"6008e4c820b289118d5e2fc742cef867fda613793cf6832910005cc91fedbb24","abstract_canon_sha256":"cd490524bd6d8d9dfa24d6567f1b08e81c64a5b8ba4c54a597edcebd0f880d11"},"schema_version":"1.0"},"canonical_sha256":"b7244a0970986f6a79a0843ef86d03adcee39240b2678d3392792b98d50207f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:06.225352Z","signature_b64":"HM3yVHy/svUXMsp9Gobf5Ff0BHsTekbOzzWp1e8VP1P21lo/XuiLpUCFPvfWZQRBIBtLg0gatkpINGslsVfEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7244a0970986f6a79a0843ef86d03adcee39240b2678d3392792b98d50207f9","last_reissued_at":"2026-05-18T00:33:06.224606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:06.224606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09110","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":"2026-05-18T00:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBIgpnWM6vxKRoGMQTYPf4LQcHQgDXTCJjlCf3UIPm39ai6nd5y3ZWYYkWpjIcflizqVk+k5Rufhbt+LmiG3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:44:13.261507Z"},"content_sha256":"c5ddc8d29f5d0e89182042ac4edab04bd416ed7493d71ef817a137be34dc3cec","schema_version":"1.0","event_id":"sha256:c5ddc8d29f5d0e89182042ac4edab04bd416ed7493d71ef817a137be34dc3cec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:W4SEUCLQTBXWU6NAQQ7PQ3IDVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circumcenter extension of Moebius maps to CAT(-1) spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kingshook Biswas","submitted_at":"2017-09-26T16:16:15Z","abstract_excerpt":"Given a Moebius homeomorphism $f : \\partial X \\to \\partial Y$ between boundaries of proper, geodesically complete CAT(-1) spaces $X,Y$, we describe an extension $\\hat{f} : X \\to Y$ of $f$, called the circumcenter map of $f$, which is constructed using circumcenters of expanding sets. The extension $\\hat{f}$ is shown to coincide with the $(1, \\log 2)$-quasi-isometric extension constructed in [biswas3], and is locally $1/2$-Holder continuous. When $X,Y$ are complete, simply connected manifolds with sectional curvatures $K$ satisfying $-b^2 \\leq K \\leq -1$ for some $b \\geq 1$ then the extension $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09110","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":"2026-05-18T00:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrsbLIdCfXFbwHCE0TdwKRdUr+qdJFRueZ0a07cwOoFore7KzTBk2SEdXVRbh9RrvQAS21aIzB3rVgJcWT/nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:44:13.262190Z"},"content_sha256":"6edeeddefd5e4c3b249e1c471766d710011b0183ccff55bdd6f2bba19bb497bf","schema_version":"1.0","event_id":"sha256:6edeeddefd5e4c3b249e1c471766d710011b0183ccff55bdd6f2bba19bb497bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX/bundle.json","state_url":"https://pith.science/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX/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":"2026-05-28T23:44:13Z","links":{"resolver":"https://pith.science/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX","bundle":"https://pith.science/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX/bundle.json","state":"https://pith.science/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W4SEUCLQTBXWU6NAQQ7PQ3IDVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W4SEUCLQTBXWU6NAQQ7PQ3IDVX","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":"cd490524bd6d8d9dfa24d6567f1b08e81c64a5b8ba4c54a597edcebd0f880d11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-26T16:16:15Z","title_canon_sha256":"6008e4c820b289118d5e2fc742cef867fda613793cf6832910005cc91fedbb24"},"schema_version":"1.0","source":{"id":"1709.09110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09110","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09110v2","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09110","created_at":"2026-05-18T00:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"W4SEUCLQTBXW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"W4SEUCLQTBXWU6NA","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"W4SEUCLQ","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:6edeeddefd5e4c3b249e1c471766d710011b0183ccff55bdd6f2bba19bb497bf","target":"graph","created_at":"2026-05-18T00:33:06Z","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":"Given a Moebius homeomorphism $f : \\partial X \\to \\partial Y$ between boundaries of proper, geodesically complete CAT(-1) spaces $X,Y$, we describe an extension $\\hat{f} : X \\to Y$ of $f$, called the circumcenter map of $f$, which is constructed using circumcenters of expanding sets. The extension $\\hat{f}$ is shown to coincide with the $(1, \\log 2)$-quasi-isometric extension constructed in [biswas3], and is locally $1/2$-Holder continuous. When $X,Y$ are complete, simply connected manifolds with sectional curvatures $K$ satisfying $-b^2 \\leq K \\leq -1$ for some $b \\geq 1$ then the extension $","authors_text":"Kingshook Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-26T16:16:15Z","title":"Circumcenter extension of Moebius maps to CAT(-1) spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09110","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:c5ddc8d29f5d0e89182042ac4edab04bd416ed7493d71ef817a137be34dc3cec","target":"record","created_at":"2026-05-18T00:33:06Z","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":"cd490524bd6d8d9dfa24d6567f1b08e81c64a5b8ba4c54a597edcebd0f880d11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-26T16:16:15Z","title_canon_sha256":"6008e4c820b289118d5e2fc742cef867fda613793cf6832910005cc91fedbb24"},"schema_version":"1.0","source":{"id":"1709.09110","kind":"arxiv","version":2}},"canonical_sha256":"b7244a0970986f6a79a0843ef86d03adcee39240b2678d3392792b98d50207f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7244a0970986f6a79a0843ef86d03adcee39240b2678d3392792b98d50207f9","first_computed_at":"2026-05-18T00:33:06.224606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:06.224606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HM3yVHy/svUXMsp9Gobf5Ff0BHsTekbOzzWp1e8VP1P21lo/XuiLpUCFPvfWZQRBIBtLg0gatkpINGslsVfEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:06.225352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5ddc8d29f5d0e89182042ac4edab04bd416ed7493d71ef817a137be34dc3cec","sha256:6edeeddefd5e4c3b249e1c471766d710011b0183ccff55bdd6f2bba19bb497bf"],"state_sha256":"2d080caee889a0aa07396531ad89a8400b4322f10139077e326068806863a0b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oavbgx4vLJ3vXgnalQ8npci4EI3nvwiqjFmoJq/t+tHZ24H9hUGePUiNBqbTVD3lTUTgnCjuMn2H4RV0zTLvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:44:13.265940Z","bundle_sha256":"fab779066bf625fce70e5f7fae48dd4c5c62ebe2b59bb98197bbfb243defcdea"}}