{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5UWYZAOOPQYY6RQFYTH2ZZR3ZR","short_pith_number":"pith:5UWYZAOO","canonical_record":{"source":{"id":"1612.05524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-16T16:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"f0acefb3afea0ccc9fea5686b8e64ac8dacd4dd551555cd15345030ec75dd52d","abstract_canon_sha256":"689e87c1774b4f39a6d42976f751ae9128b1482cf601d4ed31300be6e9d7748d"},"schema_version":"1.0"},"canonical_sha256":"ed2d8c81ce7c318f4605c4cface63bcc72734f31c74cdce041968cfbd4496837","source":{"kind":"arxiv","id":"1612.05524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05524","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05524v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05524","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"5UWYZAOOPQYY","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5UWYZAOOPQYY6RQF","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5UWYZAOO","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5UWYZAOOPQYY6RQFYTH2ZZR3ZR","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-16T16:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"f0acefb3afea0ccc9fea5686b8e64ac8dacd4dd551555cd15345030ec75dd52d","abstract_canon_sha256":"689e87c1774b4f39a6d42976f751ae9128b1482cf601d4ed31300be6e9d7748d"},"schema_version":"1.0"},"canonical_sha256":"ed2d8c81ce7c318f4605c4cface63bcc72734f31c74cdce041968cfbd4496837","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:51.606410Z","signature_b64":"ZFHO41ekPDZCcNSBa5zNHnxhtSsJxLPuET6hJkwqrAN5haYJsGV1vuQ2V5VWE1mElEn8HxpWNFworwM0rlalDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed2d8c81ce7c318f4605c4cface63bcc72734f31c74cdce041968cfbd4496837","last_reissued_at":"2026-05-18T00:54:51.605842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:51.605842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05524","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbEx8dvLFAUBah8xGHzf0YvgNj1nr1fP5DTkyg6315Jf61lN2qiwiuF4Et7GIVFm57It1OdTKlyW9rBvretjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:54:47.980338Z"},"content_sha256":"92f134783e2450461daf756dea6b08cb2cccb4505e22146456553d7a02da3501","schema_version":"1.0","event_id":"sha256:92f134783e2450461daf756dea6b08cb2cccb4505e22146456553d7a02da3501"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5UWYZAOOPQYY6RQFYTH2ZZR3ZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maciej Starostka, Marcin Styborski, Marek Izydorek, Robert C.A.M. Vandervorst, Thomas O. Rot","submitted_at":"2016-12-16T16:02:32Z","abstract_excerpt":"In this paper we introduce a new compactness condition - Property (C) - for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain the E-cohomological Conley index. We formulate a continuation principle for the E-cohomological Conley index and show that all LS-flows can be continued to LS-gradient f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05524","kind":"arxiv","version":1},"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":"2026-05-18T00:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6eIVjakEiESUliOdyApvCIwGWmunF6QZhOO74BwDV6+y2djaP2jNrenROwS1qRoVofTl7/DnbUOrL1adhcwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:54:47.980686Z"},"content_sha256":"0f7d7a0659789353dbf50ed4549bd4797e9edaeb4e0eb6910b29ea5126e50ca5","schema_version":"1.0","event_id":"sha256:0f7d7a0659789353dbf50ed4549bd4797e9edaeb4e0eb6910b29ea5126e50ca5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR/bundle.json","state_url":"https://pith.science/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR/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":"2026-06-01T07:54:47Z","links":{"resolver":"https://pith.science/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR","bundle":"https://pith.science/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR/bundle.json","state":"https://pith.science/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UWYZAOOPQYY6RQFYTH2ZZR3ZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5UWYZAOOPQYY6RQFYTH2ZZR3ZR","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":"689e87c1774b4f39a6d42976f751ae9128b1482cf601d4ed31300be6e9d7748d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-16T16:02:32Z","title_canon_sha256":"f0acefb3afea0ccc9fea5686b8e64ac8dacd4dd551555cd15345030ec75dd52d"},"schema_version":"1.0","source":{"id":"1612.05524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05524","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05524v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05524","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"5UWYZAOOPQYY","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5UWYZAOOPQYY6RQF","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5UWYZAOO","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:0f7d7a0659789353dbf50ed4549bd4797e9edaeb4e0eb6910b29ea5126e50ca5","target":"graph","created_at":"2026-05-18T00:54:51Z","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":"In this paper we introduce a new compactness condition - Property (C) - for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain the E-cohomological Conley index. We formulate a continuation principle for the E-cohomological Conley index and show that all LS-flows can be continued to LS-gradient f","authors_text":"Maciej Starostka, Marcin Styborski, Marek Izydorek, Robert C.A.M. Vandervorst, Thomas O. Rot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-16T16:02:32Z","title":"Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05524","kind":"arxiv","version":1},"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":"sha256:92f134783e2450461daf756dea6b08cb2cccb4505e22146456553d7a02da3501","target":"record","created_at":"2026-05-18T00:54:51Z","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":"689e87c1774b4f39a6d42976f751ae9128b1482cf601d4ed31300be6e9d7748d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-16T16:02:32Z","title_canon_sha256":"f0acefb3afea0ccc9fea5686b8e64ac8dacd4dd551555cd15345030ec75dd52d"},"schema_version":"1.0","source":{"id":"1612.05524","kind":"arxiv","version":1}},"canonical_sha256":"ed2d8c81ce7c318f4605c4cface63bcc72734f31c74cdce041968cfbd4496837","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed2d8c81ce7c318f4605c4cface63bcc72734f31c74cdce041968cfbd4496837","first_computed_at":"2026-05-18T00:54:51.605842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:51.605842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZFHO41ekPDZCcNSBa5zNHnxhtSsJxLPuET6hJkwqrAN5haYJsGV1vuQ2V5VWE1mElEn8HxpWNFworwM0rlalDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:51.606410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92f134783e2450461daf756dea6b08cb2cccb4505e22146456553d7a02da3501","sha256:0f7d7a0659789353dbf50ed4549bd4797e9edaeb4e0eb6910b29ea5126e50ca5"],"state_sha256":"738e9b1ad236aa212672e643469163e28b6fc007c567642b2f1c6595f14fb611"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hMjKQVG39ef3JPBxa8Npq8jYkcqbK+oPBC39g5s0XNUo7Kvp5pZopuvv4Hqbh8wAuna/iD+TmuJpIMjWQSpvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:54:47.982874Z","bundle_sha256":"885443e30b7f8407199f76529d8ee61b2626770b3e75a2e0e0b80446f4187aff"}}