{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:44ZDDVTAKCOMDD3CFBYAJKUFCL","short_pith_number":"pith:44ZDDVTA","canonical_record":{"source":{"id":"1806.05812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-15T05:45:01Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"cfffc3e1c36d2b6ff9411b366f018cd731711074a87ba32f5417bc73c31e2173","abstract_canon_sha256":"a954e124c26fea230e4de9ea7546c98eb620204658c40a53a31209e96ba87964"},"schema_version":"1.0"},"canonical_sha256":"e73231d660509cc18f62287004aa8512ce9fa682b8f0693aa83e632bfae9362c","source":{"kind":"arxiv","id":"1806.05812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05812","created_at":"2026-05-18T00:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05812v2","created_at":"2026-05-18T00:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05812","created_at":"2026-05-18T00:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"44ZDDVTAKCOM","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"44ZDDVTAKCOMDD3C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"44ZDDVTA","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:44ZDDVTAKCOMDD3CFBYAJKUFCL","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-15T05:45:01Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"cfffc3e1c36d2b6ff9411b366f018cd731711074a87ba32f5417bc73c31e2173","abstract_canon_sha256":"a954e124c26fea230e4de9ea7546c98eb620204658c40a53a31209e96ba87964"},"schema_version":"1.0"},"canonical_sha256":"e73231d660509cc18f62287004aa8512ce9fa682b8f0693aa83e632bfae9362c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:49.230294Z","signature_b64":"0fP5krybK/f/Qdy1moXW5XCgcD/zwhaEbrD8JlkEB3E8iOZXdLbaNuAQXoQUdkjjzl6OoByd/wPxZmQexemXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e73231d660509cc18f62287004aa8512ce9fa682b8f0693aa83e632bfae9362c","last_reissued_at":"2026-05-18T00:07:49.229636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:49.229636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05812","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":"2026-05-18T00:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5aGJa/PzZAOkcJvEuPx0uVzGPbAF835RCwP/4+Rgb9TCaCieOe4IpLeTn6Bl5FwwVXecodX8sLo13xs7rPa9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:20:17.468243Z"},"content_sha256":"13a09d5c62a3d7d9d766738902a051edb450597fbe1a7771d61f862f1507ce25","schema_version":"1.0","event_id":"sha256:13a09d5c62a3d7d9d766738902a051edb450597fbe1a7771d61f862f1507ce25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:44ZDDVTAKCOMDD3CFBYAJKUFCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of combinatorial Ricci flows to degenerate circle patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Asuka Takatsu","submitted_at":"2018-06-15T05:45:01Z","abstract_excerpt":"We investigate the combinatorial Ricci flow on a surface of nonpositive Euler characteristic when the necessary and sufficient condition for the convergence of the combinatorial Ricci flow is not valid. This observation addresses one of questions raised by B. Chow and F. Luo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05812","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":"2026-05-18T00:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VI5FTnCYHz3L4zjEeycidXLVBeMCyIn7GwIBjVWkrW61pbJeIhA5EOyNMhfdYm4jq/JDChTWdNhZFMzQdiGhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:20:17.468988Z"},"content_sha256":"e5f738e0deac7cb987e830b8621f32a84477ab42c621e285502a1efb5b58dda5","schema_version":"1.0","event_id":"sha256:e5f738e0deac7cb987e830b8621f32a84477ab42c621e285502a1efb5b58dda5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL/bundle.json","state_url":"https://pith.science/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL/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":"2026-06-07T17:20:17Z","links":{"resolver":"https://pith.science/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL","bundle":"https://pith.science/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL/bundle.json","state":"https://pith.science/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/44ZDDVTAKCOMDD3CFBYAJKUFCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:44ZDDVTAKCOMDD3CFBYAJKUFCL","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":"a954e124c26fea230e4de9ea7546c98eb620204658c40a53a31209e96ba87964","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-15T05:45:01Z","title_canon_sha256":"cfffc3e1c36d2b6ff9411b366f018cd731711074a87ba32f5417bc73c31e2173"},"schema_version":"1.0","source":{"id":"1806.05812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05812","created_at":"2026-05-18T00:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05812v2","created_at":"2026-05-18T00:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05812","created_at":"2026-05-18T00:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"44ZDDVTAKCOM","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"44ZDDVTAKCOMDD3C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"44ZDDVTA","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:e5f738e0deac7cb987e830b8621f32a84477ab42c621e285502a1efb5b58dda5","target":"graph","created_at":"2026-05-18T00:07:49Z","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":"We investigate the combinatorial Ricci flow on a surface of nonpositive Euler characteristic when the necessary and sufficient condition for the convergence of the combinatorial Ricci flow is not valid. This observation addresses one of questions raised by B. Chow and F. Luo.","authors_text":"Asuka Takatsu","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-15T05:45:01Z","title":"Convergence of combinatorial Ricci flows to degenerate circle patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05812","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":"sha256:13a09d5c62a3d7d9d766738902a051edb450597fbe1a7771d61f862f1507ce25","target":"record","created_at":"2026-05-18T00:07:49Z","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":"a954e124c26fea230e4de9ea7546c98eb620204658c40a53a31209e96ba87964","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-15T05:45:01Z","title_canon_sha256":"cfffc3e1c36d2b6ff9411b366f018cd731711074a87ba32f5417bc73c31e2173"},"schema_version":"1.0","source":{"id":"1806.05812","kind":"arxiv","version":2}},"canonical_sha256":"e73231d660509cc18f62287004aa8512ce9fa682b8f0693aa83e632bfae9362c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e73231d660509cc18f62287004aa8512ce9fa682b8f0693aa83e632bfae9362c","first_computed_at":"2026-05-18T00:07:49.229636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:49.229636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fP5krybK/f/Qdy1moXW5XCgcD/zwhaEbrD8JlkEB3E8iOZXdLbaNuAQXoQUdkjjzl6OoByd/wPxZmQexemXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:49.230294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13a09d5c62a3d7d9d766738902a051edb450597fbe1a7771d61f862f1507ce25","sha256:e5f738e0deac7cb987e830b8621f32a84477ab42c621e285502a1efb5b58dda5"],"state_sha256":"50008ba475c470f43de56f0c2d98bc4a9b26a1726da25613bf095cf62641ca90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESlq3REAXaJKYBIbCMDBb0/g25s+Cz1Y9a7EkHMYWr4LtqiSFxFWOYKN0K74MI30tbYxab+gtKQXw9GrXLpgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:20:17.472659Z","bundle_sha256":"4cced741b7332dfca4ca0ebd817a5bd0f2fbc651aff8f81ceb72b79e0aef785e"}}