{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:AZIKDZZXVQEAX3AAOYFMZWB5PO","short_pith_number":"pith:AZIKDZZX","schema_version":"1.0","canonical_sha256":"0650a1e737ac080bec00760accd83d7b936b423b5cc287af6842accb0041d9e5","source":{"kind":"arxiv","id":"2312.11088","version":3},"attestation_state":"computed","paper":{"title":"Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giorgio Poggesi, Lorenzo Cavallina","submitted_at":"2023-12-18T10:31:31Z","abstract_excerpt":"We provide a full characterization of multi-phase problems under a large class of overdetermined Serrin-type conditions. Our analysis includes both symmetry and asymmetry (including bifurcation) results. A broad range of techniques is needed to obtain a full characterization of all the cases, including applications of results obtained via the moving planes method, approaches via integral identities in the wake of Weinberger, applications of the Crandall-Rabinowitz theorem, and the Chauchy-Kovalevskaya theorem. The multi-phase setting entails intrinsic difficulties that make it difficult to pre"},"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":"2312.11088","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-18T10:31:31Z","cross_cats_sorted":[],"title_canon_sha256":"e5b3ae49094608eeec3dc2129935ffbc0168f4131e9b5779efdcba330e3673c4","abstract_canon_sha256":"0e74acf6e283f36d867e3734fcc2e7a0c9f161835a98698f47fdca79e40f2a24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:56.844617Z","signature_b64":"/pboi60JsV/MxS20ZOAX2AkKMtv78j1YjpU1Nquno6tCMnONOj0pncU7iao7wEmB5ruipUYcyQ5GozEl6FKuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0650a1e737ac080bec00760accd83d7b936b423b5cc287af6842accb0041d9e5","last_reissued_at":"2026-07-05T10:59:56.844195Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:56.844195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giorgio Poggesi, Lorenzo Cavallina","submitted_at":"2023-12-18T10:31:31Z","abstract_excerpt":"We provide a full characterization of multi-phase problems under a large class of overdetermined Serrin-type conditions. Our analysis includes both symmetry and asymmetry (including bifurcation) results. A broad range of techniques is needed to obtain a full characterization of all the cases, including applications of results obtained via the moving planes method, approaches via integral identities in the wake of Weinberger, applications of the Crandall-Rabinowitz theorem, and the Chauchy-Kovalevskaya theorem. The multi-phase setting entails intrinsic difficulties that make it difficult to pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.11088/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":"2312.11088","created_at":"2026-07-05T10:59:56.844250+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.11088v3","created_at":"2026-07-05T10:59:56.844250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11088","created_at":"2026-07-05T10:59:56.844250+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZIKDZZXVQEA","created_at":"2026-07-05T10:59:56.844250+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZIKDZZXVQEAX3AA","created_at":"2026-07-05T10:59:56.844250+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZIKDZZX","created_at":"2026-07-05T10:59:56.844250+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.09219","citing_title":"Stability results for nonlocal Serrin-type problems, antisymmetric Harnack inequalities, and geometric estimates","ref_index":1823,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO","json":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO.json","graph_json":"https://pith.science/api/pith-number/AZIKDZZXVQEAX3AAOYFMZWB5PO/graph.json","events_json":"https://pith.science/api/pith-number/AZIKDZZXVQEAX3AAOYFMZWB5PO/events.json","paper":"https://pith.science/paper/AZIKDZZX"},"agent_actions":{"view_html":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO","download_json":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO.json","view_paper":"https://pith.science/paper/AZIKDZZX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.11088&json=true","fetch_graph":"https://pith.science/api/pith-number/AZIKDZZXVQEAX3AAOYFMZWB5PO/graph.json","fetch_events":"https://pith.science/api/pith-number/AZIKDZZXVQEAX3AAOYFMZWB5PO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO/action/storage_attestation","attest_author":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO/action/author_attestation","sign_citation":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO/action/citation_signature","submit_replication":"https://pith.science/pith/AZIKDZZXVQEAX3AAOYFMZWB5PO/action/replication_record"}},"created_at":"2026-07-05T10:59:56.844250+00:00","updated_at":"2026-07-05T10:59:56.844250+00:00"}