{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ASKZPSGWRV23NPFV7GQX2AI2MK","short_pith_number":"pith:ASKZPSGW","canonical_record":{"source":{"id":"1207.4435","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-18T18:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"726ba0997f947f1137d9cfe99754f225616a14936646f6130fe49eb93dc5cd99","abstract_canon_sha256":"c871008fe5bc7988963e11412f9f6fc066e3753e09befa892672690c142e88eb"},"schema_version":"1.0"},"canonical_sha256":"049597c8d68d75b6bcb5f9a17d011a62a7d366e868cce238ec9726f2387405c5","source":{"kind":"arxiv","id":"1207.4435","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4435","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4435v3","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4435","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"ASKZPSGWRV23","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASKZPSGWRV23NPFV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASKZPSGW","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ASKZPSGWRV23NPFV7GQX2AI2MK","target":"record","payload":{"canonical_record":{"source":{"id":"1207.4435","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-18T18:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"726ba0997f947f1137d9cfe99754f225616a14936646f6130fe49eb93dc5cd99","abstract_canon_sha256":"c871008fe5bc7988963e11412f9f6fc066e3753e09befa892672690c142e88eb"},"schema_version":"1.0"},"canonical_sha256":"049597c8d68d75b6bcb5f9a17d011a62a7d366e868cce238ec9726f2387405c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:10.638985Z","signature_b64":"5KuxkvgU8HVSSp+miTFHIsmjErikP+eVlT8ICBWIFQORZofgYYxzfArEUBdgCfOQeXTHzpu11WQ2/uEZqg1MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"049597c8d68d75b6bcb5f9a17d011a62a7d366e868cce238ec9726f2387405c5","last_reissued_at":"2026-05-18T02:25:10.638590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:10.638590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.4435","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":"2026-05-18T02:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTEhpBlXS3ewh/aDBz3uwQx9IL2/pZdlvJ23Dk0Qkvzfv+8XdInPS8X0tb0cP3YtKb+VtIgf7MdYLPa+RX7NBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:44:02.907787Z"},"content_sha256":"fb30fd84804b3bea541210a4330f39092843d5bab9833ec5bce52105681d4b22","schema_version":"1.0","event_id":"sha256:fb30fd84804b3bea541210a4330f39092843d5bab9833ec5bce52105681d4b22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ASKZPSGWRV23NPFV7GQX2AI2MK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric inequalities and symmetry results for elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Serena Dipierro","submitted_at":"2012-07-18T18:32:22Z","abstract_excerpt":"We obtain some Poincar\\'{e} type formulas, that we use, together with the level set analysis, to detect the one-dimensional symmetry of monotone and stable solutions of possibly degenerate elliptic systems of the form {eqnarray*} {{array}{ll} div(a(|\\nabla u|) \\nabla u) = F_1(u, v), div(b(|\\nabla v|) \\nabla v) = F_2(u, v), {array}. {eqnarray*} where $F\\in C^{1,1}_{loc}(\\R^2)$. Our setting is very general, and it comprises, as a particular case, a conjecture of De Giorgi for phase separations in $\\R^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4435","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":"2026-05-18T02:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDss32UaCHpkO/36kApNbRaSTYS6remP25IBehsdc4fv70E9cCl8m3bwUln/jMPST/u7jkpKvm5YAKb3/lxKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:44:02.908128Z"},"content_sha256":"4da4bd16d5155cd29059c2cab48732689b44e0d1037b4991496bce0b10d677bd","schema_version":"1.0","event_id":"sha256:4da4bd16d5155cd29059c2cab48732689b44e0d1037b4991496bce0b10d677bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASKZPSGWRV23NPFV7GQX2AI2MK/bundle.json","state_url":"https://pith.science/pith/ASKZPSGWRV23NPFV7GQX2AI2MK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASKZPSGWRV23NPFV7GQX2AI2MK/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":"2026-06-05T15:44:02Z","links":{"resolver":"https://pith.science/pith/ASKZPSGWRV23NPFV7GQX2AI2MK","bundle":"https://pith.science/pith/ASKZPSGWRV23NPFV7GQX2AI2MK/bundle.json","state":"https://pith.science/pith/ASKZPSGWRV23NPFV7GQX2AI2MK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASKZPSGWRV23NPFV7GQX2AI2MK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ASKZPSGWRV23NPFV7GQX2AI2MK","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":"c871008fe5bc7988963e11412f9f6fc066e3753e09befa892672690c142e88eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-18T18:32:22Z","title_canon_sha256":"726ba0997f947f1137d9cfe99754f225616a14936646f6130fe49eb93dc5cd99"},"schema_version":"1.0","source":{"id":"1207.4435","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4435","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4435v3","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4435","created_at":"2026-05-18T02:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"ASKZPSGWRV23","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASKZPSGWRV23NPFV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASKZPSGW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:4da4bd16d5155cd29059c2cab48732689b44e0d1037b4991496bce0b10d677bd","target":"graph","created_at":"2026-05-18T02:25:10Z","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 obtain some Poincar\\'{e} type formulas, that we use, together with the level set analysis, to detect the one-dimensional symmetry of monotone and stable solutions of possibly degenerate elliptic systems of the form {eqnarray*} {{array}{ll} div(a(|\\nabla u|) \\nabla u) = F_1(u, v), div(b(|\\nabla v|) \\nabla v) = F_2(u, v), {array}. {eqnarray*} where $F\\in C^{1,1}_{loc}(\\R^2)$. Our setting is very general, and it comprises, as a particular case, a conjecture of De Giorgi for phase separations in $\\R^2$.","authors_text":"Serena Dipierro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-18T18:32:22Z","title":"Geometric inequalities and symmetry results for elliptic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4435","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:fb30fd84804b3bea541210a4330f39092843d5bab9833ec5bce52105681d4b22","target":"record","created_at":"2026-05-18T02:25:10Z","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":"c871008fe5bc7988963e11412f9f6fc066e3753e09befa892672690c142e88eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-18T18:32:22Z","title_canon_sha256":"726ba0997f947f1137d9cfe99754f225616a14936646f6130fe49eb93dc5cd99"},"schema_version":"1.0","source":{"id":"1207.4435","kind":"arxiv","version":3}},"canonical_sha256":"049597c8d68d75b6bcb5f9a17d011a62a7d366e868cce238ec9726f2387405c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"049597c8d68d75b6bcb5f9a17d011a62a7d366e868cce238ec9726f2387405c5","first_computed_at":"2026-05-18T02:25:10.638590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:10.638590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5KuxkvgU8HVSSp+miTFHIsmjErikP+eVlT8ICBWIFQORZofgYYxzfArEUBdgCfOQeXTHzpu11WQ2/uEZqg1MDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:10.638985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4435","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb30fd84804b3bea541210a4330f39092843d5bab9833ec5bce52105681d4b22","sha256:4da4bd16d5155cd29059c2cab48732689b44e0d1037b4991496bce0b10d677bd"],"state_sha256":"8b099721e715a1dcb94b635f9e0b24699ef0d080a6f9c80f614bb01409f03fde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHkiEiLtippozI6jJ2EmwaDh/wPlEycSByiHoc52pGzpu4tQqfAXbtY962VD6wR2kgqs2DTvACzO6susR20JBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:44:02.910221Z","bundle_sha256":"c4c9ffaf6339ccda07c0505e6f2c8bbc24f8ef4d765473f7d078c6da45b5b3d6"}}