{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VNCFFAXTS66QZRL72EOFS364KK","short_pith_number":"pith:VNCFFAXT","canonical_record":{"source":{"id":"1708.00690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-02T10:31:37Z","cross_cats_sorted":[],"title_canon_sha256":"ec6a5775c29e21d2cb70acb98071c2cd3f0a7d5328ac6066370c8cdf796bca6e","abstract_canon_sha256":"cb3802705d6ea1a540a86350605a87f859f98bc2cf66d30206f30dd119389e77"},"schema_version":"1.0"},"canonical_sha256":"ab445282f397bd0cc57fd11c596fdc52afdc6e20ee2547f9b5b9bf8aaac0df70","source":{"kind":"arxiv","id":"1708.00690","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00690","created_at":"2026-05-18T00:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00690v3","created_at":"2026-05-18T00:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00690","created_at":"2026-05-18T00:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"VNCFFAXTS66Q","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VNCFFAXTS66QZRL7","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VNCFFAXT","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VNCFFAXTS66QZRL72EOFS364KK","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-02T10:31:37Z","cross_cats_sorted":[],"title_canon_sha256":"ec6a5775c29e21d2cb70acb98071c2cd3f0a7d5328ac6066370c8cdf796bca6e","abstract_canon_sha256":"cb3802705d6ea1a540a86350605a87f859f98bc2cf66d30206f30dd119389e77"},"schema_version":"1.0"},"canonical_sha256":"ab445282f397bd0cc57fd11c596fdc52afdc6e20ee2547f9b5b9bf8aaac0df70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:28.730132Z","signature_b64":"Aq2ct8ae6MEpk6nusy4RckS4hc9sa/uOFTNFe6BnuqdGZy+CWGcDjQ0+arBt/YRk7hnD2D8iA8k3QJXQRenjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab445282f397bd0cc57fd11c596fdc52afdc6e20ee2547f9b5b9bf8aaac0df70","last_reissued_at":"2026-05-18T00:22:28.729266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:28.729266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00690","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NooF31w2idN1/yMVihtYynN3p5agFBIBzs33qApBqlFt+STxzEK5UvR27b870j4a2ukE7NURAqa5JSp1YCXwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:04:01.618081Z"},"content_sha256":"d31364d671216e879f1a61c5a75f19e3cd0f2db73c8b26c47e1084a937fa5682","schema_version":"1.0","event_id":"sha256:d31364d671216e879f1a61c5a75f19e3cd0f2db73c8b26c47e1084a937fa5682"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VNCFFAXTS66QZRL72EOFS364KK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sturm 3-ball global attractors 3: Examples of Thom-Smale complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernold Fiedler, Carlos Rocha","submitted_at":"2017-08-02T10:31:37Z","abstract_excerpt":"Examples complete our trilogy on the geometric and combinatorial characterization of global Sturm attractors $\\mathcal{A}$ which consist of a single closed 3-ball. The underlying scalar PDE is parabolic, $$ u_t = u_{xx} + f(x,u,u_x)\\,, $$ on the unit interval $0 < x<1$ with Neumann boundary conditions. Equilibria $v_t=0$ are assumed to be hyperbolic. Geometrically, we study the resulting Thom-Smale dynamic complex with cells defined by the fast unstable manifolds of the equilibria. The Thom-Smale complex turns out to be a regular cell complex. In the first two papers we characterized 3-ball St"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00690","kind":"arxiv","version":3},"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":"2026-05-18T00:22:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7BlRdJAKXuoeTxd4hc6l9FXdu/UMdK/MRSs6JTvAMzLEHxTKAmwACFoDNXhe4xqAPEkYmxL1cuYcinpS1j2NBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:04:01.618448Z"},"content_sha256":"508bbda255e9b5cfad1562b7ca3f440633fd16e04fb14f549cf55436376a09a3","schema_version":"1.0","event_id":"sha256:508bbda255e9b5cfad1562b7ca3f440633fd16e04fb14f549cf55436376a09a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNCFFAXTS66QZRL72EOFS364KK/bundle.json","state_url":"https://pith.science/pith/VNCFFAXTS66QZRL72EOFS364KK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNCFFAXTS66QZRL72EOFS364KK/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":"2026-06-07T04:04:01Z","links":{"resolver":"https://pith.science/pith/VNCFFAXTS66QZRL72EOFS364KK","bundle":"https://pith.science/pith/VNCFFAXTS66QZRL72EOFS364KK/bundle.json","state":"https://pith.science/pith/VNCFFAXTS66QZRL72EOFS364KK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNCFFAXTS66QZRL72EOFS364KK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VNCFFAXTS66QZRL72EOFS364KK","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":"cb3802705d6ea1a540a86350605a87f859f98bc2cf66d30206f30dd119389e77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-02T10:31:37Z","title_canon_sha256":"ec6a5775c29e21d2cb70acb98071c2cd3f0a7d5328ac6066370c8cdf796bca6e"},"schema_version":"1.0","source":{"id":"1708.00690","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00690","created_at":"2026-05-18T00:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00690v3","created_at":"2026-05-18T00:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00690","created_at":"2026-05-18T00:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"VNCFFAXTS66Q","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VNCFFAXTS66QZRL7","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VNCFFAXT","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:508bbda255e9b5cfad1562b7ca3f440633fd16e04fb14f549cf55436376a09a3","target":"graph","created_at":"2026-05-18T00:22:28Z","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":"Examples complete our trilogy on the geometric and combinatorial characterization of global Sturm attractors $\\mathcal{A}$ which consist of a single closed 3-ball. The underlying scalar PDE is parabolic, $$ u_t = u_{xx} + f(x,u,u_x)\\,, $$ on the unit interval $0 < x<1$ with Neumann boundary conditions. Equilibria $v_t=0$ are assumed to be hyperbolic. Geometrically, we study the resulting Thom-Smale dynamic complex with cells defined by the fast unstable manifolds of the equilibria. The Thom-Smale complex turns out to be a regular cell complex. In the first two papers we characterized 3-ball St","authors_text":"Bernold Fiedler, Carlos Rocha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-02T10:31:37Z","title":"Sturm 3-ball global attractors 3: Examples of Thom-Smale complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00690","kind":"arxiv","version":3},"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:d31364d671216e879f1a61c5a75f19e3cd0f2db73c8b26c47e1084a937fa5682","target":"record","created_at":"2026-05-18T00:22:28Z","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":"cb3802705d6ea1a540a86350605a87f859f98bc2cf66d30206f30dd119389e77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-02T10:31:37Z","title_canon_sha256":"ec6a5775c29e21d2cb70acb98071c2cd3f0a7d5328ac6066370c8cdf796bca6e"},"schema_version":"1.0","source":{"id":"1708.00690","kind":"arxiv","version":3}},"canonical_sha256":"ab445282f397bd0cc57fd11c596fdc52afdc6e20ee2547f9b5b9bf8aaac0df70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab445282f397bd0cc57fd11c596fdc52afdc6e20ee2547f9b5b9bf8aaac0df70","first_computed_at":"2026-05-18T00:22:28.729266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:28.729266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aq2ct8ae6MEpk6nusy4RckS4hc9sa/uOFTNFe6BnuqdGZy+CWGcDjQ0+arBt/YRk7hnD2D8iA8k3QJXQRenjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:28.730132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00690","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d31364d671216e879f1a61c5a75f19e3cd0f2db73c8b26c47e1084a937fa5682","sha256:508bbda255e9b5cfad1562b7ca3f440633fd16e04fb14f549cf55436376a09a3"],"state_sha256":"d1db95fc8d9abff66ccb798e81a2f378380dd96fab66c8b357aa258de2475218"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyFXKmdcKnGHxFcEi2vkB3pK8dLZT1Y+wfdSGNrSAd+aNnOTWT9sSetvgxMI4JhXOILd/U6vGgNclYVGLWSIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:04:01.620840Z","bundle_sha256":"9f4df471fe236f794cb7bb72a8801f1333d017987910dfbe4bed8d5aeb1607cc"}}