{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NJXYTTUKYQ2A5VHQLC53ASPX5A","short_pith_number":"pith:NJXYTTUK","canonical_record":{"source":{"id":"1303.1025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-05T13:20:54Z","cross_cats_sorted":[],"title_canon_sha256":"7fac682a2da925761a41c9a5ff4b3191d5454193c047b6690aca5734112a3512","abstract_canon_sha256":"e45141de934ab0558d43c428331a4635e1b377dd415661627ee78f128067586e"},"schema_version":"1.0"},"canonical_sha256":"6a6f89ce8ac4340ed4f058bbb049f7e8241d72afeaeaf6c1f60bc169a0a7bd05","source":{"kind":"arxiv","id":"1303.1025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1025","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1025v1","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1025","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"NJXYTTUKYQ2A","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NJXYTTUKYQ2A5VHQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NJXYTTUK","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NJXYTTUKYQ2A5VHQLC53ASPX5A","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-05T13:20:54Z","cross_cats_sorted":[],"title_canon_sha256":"7fac682a2da925761a41c9a5ff4b3191d5454193c047b6690aca5734112a3512","abstract_canon_sha256":"e45141de934ab0558d43c428331a4635e1b377dd415661627ee78f128067586e"},"schema_version":"1.0"},"canonical_sha256":"6a6f89ce8ac4340ed4f058bbb049f7e8241d72afeaeaf6c1f60bc169a0a7bd05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:53.126310Z","signature_b64":"3816f/YixnJtq12JE74UuFIsxqZ1nh+ZuTWwvhVbQ9iHmioGbMCW0rajETsT3KIEIMOHQVkV7dli29Vnk6w4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a6f89ce8ac4340ed4f058bbb049f7e8241d72afeaeaf6c1f60bc169a0a7bd05","last_reissued_at":"2026-05-18T03:31:53.125855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:53.125855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1025","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":"2026-05-18T03:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHisefrOq4d9VZC69YUQQda809cwoYPA/LMDUc7y1FdUxPY96Yw9RAM9j2sORzuTtZ0ojsVInM89Bj85Z+avDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:39:47.121349Z"},"content_sha256":"8cd9056cc4957b3aa38ba6604029b918de9505d88862aaa854a3a8455c009ab5","schema_version":"1.0","event_id":"sha256:8cd9056cc4957b3aa38ba6604029b918de9505d88862aaa854a3a8455c009ab5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NJXYTTUKYQ2A5VHQLC53ASPX5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry breaking of solutions of non-cooperative elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Piotr Stefaniak","submitted_at":"2013-03-05T13:20:54Z","abstract_excerpt":"In this article we study the symmetry breaking phenomenon of solutions of noncooperative elliptic systems. We apply the degree for G-invariant strongly indefinite functionals to obtain simultaneously a symmetry breaking and a global bifurcation phenomenon."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1025","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":"2026-05-18T03:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQlW+nklpMRNW7h2ZiODq5gGAUrsyN49CCsIV/WReYlNcizIY7XhUXDbISGw0wHTknPsdaqA8XZPhQQw0FQFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:39:47.121705Z"},"content_sha256":"f97053e431bce6aa596a830e504b6c3bd832e27510150d494c34b8d6ad46871c","schema_version":"1.0","event_id":"sha256:f97053e431bce6aa596a830e504b6c3bd832e27510150d494c34b8d6ad46871c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A/bundle.json","state_url":"https://pith.science/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A/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":"2026-06-24T05:39:47Z","links":{"resolver":"https://pith.science/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A","bundle":"https://pith.science/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A/bundle.json","state":"https://pith.science/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJXYTTUKYQ2A5VHQLC53ASPX5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NJXYTTUKYQ2A5VHQLC53ASPX5A","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":"e45141de934ab0558d43c428331a4635e1b377dd415661627ee78f128067586e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-05T13:20:54Z","title_canon_sha256":"7fac682a2da925761a41c9a5ff4b3191d5454193c047b6690aca5734112a3512"},"schema_version":"1.0","source":{"id":"1303.1025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1025","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1025v1","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1025","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"NJXYTTUKYQ2A","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NJXYTTUKYQ2A5VHQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NJXYTTUK","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:f97053e431bce6aa596a830e504b6c3bd832e27510150d494c34b8d6ad46871c","target":"graph","created_at":"2026-05-18T03:31:53Z","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 article we study the symmetry breaking phenomenon of solutions of noncooperative elliptic systems. We apply the degree for G-invariant strongly indefinite functionals to obtain simultaneously a symmetry breaking and a global bifurcation phenomenon.","authors_text":"Piotr Stefaniak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-05T13:20:54Z","title":"Symmetry breaking of solutions of non-cooperative elliptic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1025","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":"sha256:8cd9056cc4957b3aa38ba6604029b918de9505d88862aaa854a3a8455c009ab5","target":"record","created_at":"2026-05-18T03:31:53Z","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":"e45141de934ab0558d43c428331a4635e1b377dd415661627ee78f128067586e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-05T13:20:54Z","title_canon_sha256":"7fac682a2da925761a41c9a5ff4b3191d5454193c047b6690aca5734112a3512"},"schema_version":"1.0","source":{"id":"1303.1025","kind":"arxiv","version":1}},"canonical_sha256":"6a6f89ce8ac4340ed4f058bbb049f7e8241d72afeaeaf6c1f60bc169a0a7bd05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a6f89ce8ac4340ed4f058bbb049f7e8241d72afeaeaf6c1f60bc169a0a7bd05","first_computed_at":"2026-05-18T03:31:53.125855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:53.125855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3816f/YixnJtq12JE74UuFIsxqZ1nh+ZuTWwvhVbQ9iHmioGbMCW0rajETsT3KIEIMOHQVkV7dli29Vnk6w4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:53.126310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd9056cc4957b3aa38ba6604029b918de9505d88862aaa854a3a8455c009ab5","sha256:f97053e431bce6aa596a830e504b6c3bd832e27510150d494c34b8d6ad46871c"],"state_sha256":"ef94f81467e82c0204aedf8f52b8d438d90d30542017a7d9a08a0e0d82781e21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUJQ7Zf1w3Shd++EBmN3zpuvQGWpijE22kaThLoGELiNk9n+UiKUYWLzjGQmvW9g5UH7xDVno0ikp4ZnmDR2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:39:47.123781Z","bundle_sha256":"02ead0dcdc1e17abe92b8a9592a960e9b0f0d0ec46b5dc69755428067d148140"}}