{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DF22FYTOGHAGNUTUEAH4IPMWJ4","short_pith_number":"pith:DF22FYTO","schema_version":"1.0","canonical_sha256":"1975a2e26e31c066d274200fc43d964f20dee2cb5542cb577563f12f295a5a57","source":{"kind":"arxiv","id":"2602.12940","version":2},"attestation_state":"computed","paper":{"title":"Bifurcation curve detection with deflation for multiparametric PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Federico Pichi, Gianluigi Rozza, Nitin Kumar","submitted_at":"2026-02-13T13:54:00Z","abstract_excerpt":"This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given values of the parameters. Traditional continuation methods for one-dimensional parameterizations employ the previously computed solution as the initial guess for the next parameter value. These are usually very inefficient, since small step sizes increase computational cost, while larger steps could jeopardize the method convergence jumping to a different s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2602.12940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-02-13T13:54:00Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"3c76feaec87df5553582a92191bbbbe9b338671bce0164068b13c725a72120b1","abstract_canon_sha256":"73715bdc92ae0409b14450f7e9007dfe674ab9c5305eefbc38b062373431871d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T03:18:53.357681Z","signature_b64":"UKUFj/m3XwPRyuPPK6Ls8rJ2Cbhd9o38gAUZiIC1vQQCyWTBndTp0Xz2fwVXQ/qR8lcjG1+71t1iVDPoJLEzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1975a2e26e31c066d274200fc43d964f20dee2cb5542cb577563f12f295a5a57","last_reissued_at":"2026-07-07T03:18:53.357161Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T03:18:53.357161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bifurcation curve detection with deflation for multiparametric PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Federico Pichi, Gianluigi Rozza, Nitin Kumar","submitted_at":"2026-02-13T13:54:00Z","abstract_excerpt":"This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given values of the parameters. Traditional continuation methods for one-dimensional parameterizations employ the previously computed solution as the initial guess for the next parameter value. These are usually very inefficient, since small step sizes increase computational cost, while larger steps could jeopardize the method convergence jumping to a different s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.12940","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.12940/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2602.12940","created_at":"2026-07-07T03:18:53.357231+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.12940v2","created_at":"2026-07-07T03:18:53.357231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.12940","created_at":"2026-07-07T03:18:53.357231+00:00"},{"alias_kind":"pith_short_12","alias_value":"DF22FYTOGHAG","created_at":"2026-07-07T03:18:53.357231+00:00"},{"alias_kind":"pith_short_16","alias_value":"DF22FYTOGHAGNUTU","created_at":"2026-07-07T03:18:53.357231+00:00"},{"alias_kind":"pith_short_8","alias_value":"DF22FYTO","created_at":"2026-07-07T03:18:53.357231+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.31288","citing_title":"Stochastic bifurcation analysis via polynomial chaos: consistency and convergence of branch-approximating solutions","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4","json":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4.json","graph_json":"https://pith.science/api/pith-number/DF22FYTOGHAGNUTUEAH4IPMWJ4/graph.json","events_json":"https://pith.science/api/pith-number/DF22FYTOGHAGNUTUEAH4IPMWJ4/events.json","paper":"https://pith.science/paper/DF22FYTO"},"agent_actions":{"view_html":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4","download_json":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4.json","view_paper":"https://pith.science/paper/DF22FYTO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.12940&json=true","fetch_graph":"https://pith.science/api/pith-number/DF22FYTOGHAGNUTUEAH4IPMWJ4/graph.json","fetch_events":"https://pith.science/api/pith-number/DF22FYTOGHAGNUTUEAH4IPMWJ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4/action/storage_attestation","attest_author":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4/action/author_attestation","sign_citation":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4/action/citation_signature","submit_replication":"https://pith.science/pith/DF22FYTOGHAGNUTUEAH4IPMWJ4/action/replication_record"}},"created_at":"2026-07-07T03:18:53.357231+00:00","updated_at":"2026-07-07T03:18:53.357231+00:00"}