{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:K6VPZCB4DYWC2QRB7YEGBLL3X6","short_pith_number":"pith:K6VPZCB4","canonical_record":{"source":{"id":"1405.1758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T21:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"8995f61a70b5e3c63aca45c6215aa1beffc4383589d79076b6905362e15d2e89","abstract_canon_sha256":"2d65bcbfd1424b0b2947cf9f3846fd4d51f3ef010a8ab3ef1fc25dbe9f9a88ca"},"schema_version":"1.0"},"canonical_sha256":"57aafc883c1e2c2d4221fe0860ad7bbfb6e4f4b33110b51c53f7437e77e52634","source":{"kind":"arxiv","id":"1405.1758","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1758","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1758v2","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1758","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"pith_short_12","alias_value":"K6VPZCB4DYWC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K6VPZCB4DYWC2QRB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K6VPZCB4","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:K6VPZCB4DYWC2QRB7YEGBLL3X6","target":"record","payload":{"canonical_record":{"source":{"id":"1405.1758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T21:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"8995f61a70b5e3c63aca45c6215aa1beffc4383589d79076b6905362e15d2e89","abstract_canon_sha256":"2d65bcbfd1424b0b2947cf9f3846fd4d51f3ef010a8ab3ef1fc25dbe9f9a88ca"},"schema_version":"1.0"},"canonical_sha256":"57aafc883c1e2c2d4221fe0860ad7bbfb6e4f4b33110b51c53f7437e77e52634","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:08.603583Z","signature_b64":"PXO6A7Szh3KoZnyyHJ72maPj0OjaUF1CMDHliXrEzr+WmkninQLcap1j4XA4Gjv2r2ez2W9RkTBs1u7aY1QuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57aafc883c1e2c2d4221fe0860ad7bbfb6e4f4b33110b51c53f7437e77e52634","last_reissued_at":"2026-05-18T01:55:08.603097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:08.603097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.1758","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":"2026-05-18T01:55:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OzJm97O0p7S7Bkx37Tv2CiyH5zJ0C6TzvLvmvRuoc15XcJVt8E9H2tHh//V1MRHcUHcN7Kkw0jQbIXYvg5pCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:07:50.195287Z"},"content_sha256":"95c9257e249e448358c293c6ab27de596c9e32a9b25a7859ae4120d253fbc983","schema_version":"1.0","event_id":"sha256:95c9257e249e448358c293c6ab27de596c9e32a9b25a7859ae4120d253fbc983"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:K6VPZCB4DYWC2QRB7YEGBLL3X6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shape Coherence and Finite-Time Curvature Evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Erik Bollt, Tian Ma","submitted_at":"2014-05-07T21:33:51Z","abstract_excerpt":"We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. The level curves of the finite-time curvature evolution field indicate the existence of shape coherent sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1758","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":"2026-05-18T01:55:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jz3+Zuygso0lNFiVSwC8QAuxzwkYPT5Ag4E/RuSEMatdmFGAOMbsTRyi8uUUCIf5MkrPN25tmloxf1d+SdbBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:07:50.195649Z"},"content_sha256":"b07fcb9e250bb46c8cb1ab3b91d9ccea8fded5d20abe040f0e43b89fedaddb93","schema_version":"1.0","event_id":"sha256:b07fcb9e250bb46c8cb1ab3b91d9ccea8fded5d20abe040f0e43b89fedaddb93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6/bundle.json","state_url":"https://pith.science/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6/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":"2026-05-28T03:07:50Z","links":{"resolver":"https://pith.science/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6","bundle":"https://pith.science/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6/bundle.json","state":"https://pith.science/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6VPZCB4DYWC2QRB7YEGBLL3X6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K6VPZCB4DYWC2QRB7YEGBLL3X6","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":"2d65bcbfd1424b0b2947cf9f3846fd4d51f3ef010a8ab3ef1fc25dbe9f9a88ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T21:33:51Z","title_canon_sha256":"8995f61a70b5e3c63aca45c6215aa1beffc4383589d79076b6905362e15d2e89"},"schema_version":"1.0","source":{"id":"1405.1758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1758","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1758v2","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1758","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"pith_short_12","alias_value":"K6VPZCB4DYWC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K6VPZCB4DYWC2QRB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K6VPZCB4","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:b07fcb9e250bb46c8cb1ab3b91d9ccea8fded5d20abe040f0e43b89fedaddb93","target":"graph","created_at":"2026-05-18T01:55:08Z","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 introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. The level curves of the finite-time curvature evolution field indicate the existence of shape coherent sets.","authors_text":"Erik Bollt, Tian Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T21:33:51Z","title":"Shape Coherence and Finite-Time Curvature Evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1758","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":"sha256:95c9257e249e448358c293c6ab27de596c9e32a9b25a7859ae4120d253fbc983","target":"record","created_at":"2026-05-18T01:55:08Z","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":"2d65bcbfd1424b0b2947cf9f3846fd4d51f3ef010a8ab3ef1fc25dbe9f9a88ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T21:33:51Z","title_canon_sha256":"8995f61a70b5e3c63aca45c6215aa1beffc4383589d79076b6905362e15d2e89"},"schema_version":"1.0","source":{"id":"1405.1758","kind":"arxiv","version":2}},"canonical_sha256":"57aafc883c1e2c2d4221fe0860ad7bbfb6e4f4b33110b51c53f7437e77e52634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57aafc883c1e2c2d4221fe0860ad7bbfb6e4f4b33110b51c53f7437e77e52634","first_computed_at":"2026-05-18T01:55:08.603097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:08.603097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PXO6A7Szh3KoZnyyHJ72maPj0OjaUF1CMDHliXrEzr+WmkninQLcap1j4XA4Gjv2r2ez2W9RkTBs1u7aY1QuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:08.603583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95c9257e249e448358c293c6ab27de596c9e32a9b25a7859ae4120d253fbc983","sha256:b07fcb9e250bb46c8cb1ab3b91d9ccea8fded5d20abe040f0e43b89fedaddb93"],"state_sha256":"b3122710c027d869cac2af2a083811f8c79d6b89769eba8fc0692ed819f00449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jaPasO9T7YYek66qi6zuIkRvEaWmqSSaGr5qzVtIilLIbSgwi9ADaP86CZ+8mtjytLokOSxyWGvucNbmflSDBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:07:50.197877Z","bundle_sha256":"a9f57d3e09895ef2063dcb4ed0b4621e120bc29a56af1669a1d59d499b8538f2"}}