{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SCAXGBT4F6OMW23ENC23ZJFG6G","short_pith_number":"pith:SCAXGBT4","canonical_record":{"source":{"id":"1806.04767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T21:04:31Z","cross_cats_sorted":[],"title_canon_sha256":"4d07bbb06ccb1a542ab55640258a0694439ac310c87cc9ad3eecf1b85f363dba","abstract_canon_sha256":"f7780077c2dbadcc5bd1495bc78d6d65bc1a9035444e6d81cfa773a4f846935a"},"schema_version":"1.0"},"canonical_sha256":"908173067c2f9ccb6b6468b5bca4a6f1b954fe1a3e38d961948868b5cbc598f6","source":{"kind":"arxiv","id":"1806.04767","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04767","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04767v2","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04767","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"SCAXGBT4F6OM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SCAXGBT4F6OMW23E","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SCAXGBT4","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SCAXGBT4F6OMW23ENC23ZJFG6G","target":"record","payload":{"canonical_record":{"source":{"id":"1806.04767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T21:04:31Z","cross_cats_sorted":[],"title_canon_sha256":"4d07bbb06ccb1a542ab55640258a0694439ac310c87cc9ad3eecf1b85f363dba","abstract_canon_sha256":"f7780077c2dbadcc5bd1495bc78d6d65bc1a9035444e6d81cfa773a4f846935a"},"schema_version":"1.0"},"canonical_sha256":"908173067c2f9ccb6b6468b5bca4a6f1b954fe1a3e38d961948868b5cbc598f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:03.805405Z","signature_b64":"BR4f0IYFpreP4vuBOWOslSevXWUdCma3DZgjesGivjniGBbY/loGdzayEBoNnFsQomXdxkAd4NvYsW3b3oJyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"908173067c2f9ccb6b6468b5bca4a6f1b954fe1a3e38d961948868b5cbc598f6","last_reissued_at":"2026-05-18T00:13:03.804723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:03.804723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.04767","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":"2026-05-18T00:13:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCCvNo29jpbAfAVx+A0wFl+GVlfo0RQ2pT/md6SFqU3VHtQtHN2IcfG6FRBQUMHPrm2m8SAPl3Ln008EqJy0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:14:53.828865Z"},"content_sha256":"9c884159a96b77bcc16138a948b80f20add1bbae7de8baa06d6fb327661dc906","schema_version":"1.0","event_id":"sha256:9c884159a96b77bcc16138a948b80f20add1bbae7de8baa06d6fb327661dc906"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SCAXGBT4F6OMW23ENC23ZJFG6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Keeping it together: a phase field version of path-connectedness and its implementation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Patrick Dondl, Stephan Wojtowytsch","submitted_at":"2018-06-12T21:04:31Z","abstract_excerpt":"We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are presented. First, a discrete steepest decent of a phase field version of a bending energy with spontaneous curvature and additional surface area penalty is shown, which leads to disconnected surfaces without our topological constraint but connected surfaces with the constraint. The second application is the segmentation of an image into a connected component "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04767","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":"2026-05-18T00:13:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzyNr11qPLy5z3vIRJch4weEOJAZ7rvCUsYBR/Amv390eWEBpq0Ogj2sEhNLoUFm/IxTbpsvhCSmnNCkNYF8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:14:53.829214Z"},"content_sha256":"0df09c4182b7b270704ecf0b57f35bc3840623765a7b88c29bec0dbd566821e4","schema_version":"1.0","event_id":"sha256:0df09c4182b7b270704ecf0b57f35bc3840623765a7b88c29bec0dbd566821e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCAXGBT4F6OMW23ENC23ZJFG6G/bundle.json","state_url":"https://pith.science/pith/SCAXGBT4F6OMW23ENC23ZJFG6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCAXGBT4F6OMW23ENC23ZJFG6G/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":"2026-06-20T14:14:53Z","links":{"resolver":"https://pith.science/pith/SCAXGBT4F6OMW23ENC23ZJFG6G","bundle":"https://pith.science/pith/SCAXGBT4F6OMW23ENC23ZJFG6G/bundle.json","state":"https://pith.science/pith/SCAXGBT4F6OMW23ENC23ZJFG6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCAXGBT4F6OMW23ENC23ZJFG6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SCAXGBT4F6OMW23ENC23ZJFG6G","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":"f7780077c2dbadcc5bd1495bc78d6d65bc1a9035444e6d81cfa773a4f846935a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T21:04:31Z","title_canon_sha256":"4d07bbb06ccb1a542ab55640258a0694439ac310c87cc9ad3eecf1b85f363dba"},"schema_version":"1.0","source":{"id":"1806.04767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04767","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04767v2","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04767","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"SCAXGBT4F6OM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SCAXGBT4F6OMW23E","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SCAXGBT4","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:0df09c4182b7b270704ecf0b57f35bc3840623765a7b88c29bec0dbd566821e4","target":"graph","created_at":"2026-05-18T00:13:03Z","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 describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are presented. First, a discrete steepest decent of a phase field version of a bending energy with spontaneous curvature and additional surface area penalty is shown, which leads to disconnected surfaces without our topological constraint but connected surfaces with the constraint. The second application is the segmentation of an image into a connected component ","authors_text":"Patrick Dondl, Stephan Wojtowytsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T21:04:31Z","title":"Keeping it together: a phase field version of path-connectedness and its implementation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04767","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":"sha256:9c884159a96b77bcc16138a948b80f20add1bbae7de8baa06d6fb327661dc906","target":"record","created_at":"2026-05-18T00:13:03Z","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":"f7780077c2dbadcc5bd1495bc78d6d65bc1a9035444e6d81cfa773a4f846935a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T21:04:31Z","title_canon_sha256":"4d07bbb06ccb1a542ab55640258a0694439ac310c87cc9ad3eecf1b85f363dba"},"schema_version":"1.0","source":{"id":"1806.04767","kind":"arxiv","version":2}},"canonical_sha256":"908173067c2f9ccb6b6468b5bca4a6f1b954fe1a3e38d961948868b5cbc598f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"908173067c2f9ccb6b6468b5bca4a6f1b954fe1a3e38d961948868b5cbc598f6","first_computed_at":"2026-05-18T00:13:03.804723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:03.804723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BR4f0IYFpreP4vuBOWOslSevXWUdCma3DZgjesGivjniGBbY/loGdzayEBoNnFsQomXdxkAd4NvYsW3b3oJyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:03.805405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c884159a96b77bcc16138a948b80f20add1bbae7de8baa06d6fb327661dc906","sha256:0df09c4182b7b270704ecf0b57f35bc3840623765a7b88c29bec0dbd566821e4"],"state_sha256":"b62f6c13ce7bb047ca08ccf6a11dd76e503123a1299ab2dca35a8b75c470f866"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohdVdaqyYixTG0HDxoPOpLrGdZxcGEK2J8k8gbeeRQvoxIkpGHF/4IX56QHOmD3xBOQLMF4Uu9EvU6EM9x+RCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:14:53.831168Z","bundle_sha256":"66ecbbe1a015f414a2e7afdacfb5d5e4447171d6b29b1e5f0beba52d1ef07ee7"}}