{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B643ITDLLHCH6GOSEHDN62BAJO","short_pith_number":"pith:B643ITDL","canonical_record":{"source":{"id":"1406.5275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T03:58:19Z","cross_cats_sorted":[],"title_canon_sha256":"e81f141db8bf0fe7f6221c7bdd05e251b410dd56e6f9dbda0b050d6812574dfc","abstract_canon_sha256":"5314245d7cb27dfdba38b11295d4704c0e03e3addf433915dfff24040021c86f"},"schema_version":"1.0"},"canonical_sha256":"0fb9b44c6b59c47f19d221c6df68204b91dcca3cd73eb6cb797f5e1b99434dbe","source":{"kind":"arxiv","id":"1406.5275","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5275","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5275v2","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5275","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"B643ITDLLHCH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B643ITDLLHCH6GOS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B643ITDL","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B643ITDLLHCH6GOSEHDN62BAJO","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T03:58:19Z","cross_cats_sorted":[],"title_canon_sha256":"e81f141db8bf0fe7f6221c7bdd05e251b410dd56e6f9dbda0b050d6812574dfc","abstract_canon_sha256":"5314245d7cb27dfdba38b11295d4704c0e03e3addf433915dfff24040021c86f"},"schema_version":"1.0"},"canonical_sha256":"0fb9b44c6b59c47f19d221c6df68204b91dcca3cd73eb6cb797f5e1b99434dbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:08.696512Z","signature_b64":"zbxuHIRJI4NEGtb2ggED7I6xw54pI4YY+XZnJZncjCaopvCzNZHolXoIpS5xZJdaP0aeYxZKgUTE6uhqtkv/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fb9b44c6b59c47f19d221c6df68204b91dcca3cd73eb6cb797f5e1b99434dbe","last_reissued_at":"2026-05-18T00:52:08.695908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:08.695908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5275","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"geFMx18EgUoMuMnNxLnbP8WrNRFZXOrlT3rpPTJfPkYCcAPKHUKGW/tyPbR9NzzorLyDGG/Zmpxw2En4/F6kCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:32:44.273038Z"},"content_sha256":"a15c879e132633e4e403197c11f86305b2f044417e5f92c26e0b25588e3edbde","schema_version":"1.0","event_id":"sha256:a15c879e132633e4e403197c11f86305b2f044417e5f92c26e0b25588e3edbde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B643ITDLLHCH6GOSEHDN62BAJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal existence domains of positive solutions for two-parametric systems of elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vladimir Bobkov, Yavdat Il'yasov","submitted_at":"2014-06-20T03:58:19Z","abstract_excerpt":"The paper is devoted to the study of two-parametric families of Dirichlet problems for systems of equations with $p, q$-Laplacians and indefinite nonlinearities. Continuous and monotone curves $\\Gamma_f$ and $\\Gamma_e$ on the parametric plane $\\lambda \\times \\mu$, which are the lower and upper bounds for a maximal domain of existence of weak positive solutions are introduced. The curve $\\Gamma_f$ is obtained by developing our previous work \\cite{BobkovIlyasov} and it determines a maximal domain of the applicability of the Nehari manifold and fibering methods. The curve $\\Gamma_e$ is derived ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5275","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":""},"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":"2026-05-18T00:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8mhz+xm8aC69cAarloiQsCseZ8SYp/8qtIJ8lTFqijuGG4Trb12MM+McZXfCKcTZr6UOfAJvDnKw2eVvxwpcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:32:44.273535Z"},"content_sha256":"8b830d38673d3fcd08a18e4f818d746266f1a8c416331eecef60151d5234625f","schema_version":"1.0","event_id":"sha256:8b830d38673d3fcd08a18e4f818d746266f1a8c416331eecef60151d5234625f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B643ITDLLHCH6GOSEHDN62BAJO/bundle.json","state_url":"https://pith.science/pith/B643ITDLLHCH6GOSEHDN62BAJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B643ITDLLHCH6GOSEHDN62BAJO/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":"2026-06-03T02:32:44Z","links":{"resolver":"https://pith.science/pith/B643ITDLLHCH6GOSEHDN62BAJO","bundle":"https://pith.science/pith/B643ITDLLHCH6GOSEHDN62BAJO/bundle.json","state":"https://pith.science/pith/B643ITDLLHCH6GOSEHDN62BAJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B643ITDLLHCH6GOSEHDN62BAJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B643ITDLLHCH6GOSEHDN62BAJO","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":"5314245d7cb27dfdba38b11295d4704c0e03e3addf433915dfff24040021c86f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T03:58:19Z","title_canon_sha256":"e81f141db8bf0fe7f6221c7bdd05e251b410dd56e6f9dbda0b050d6812574dfc"},"schema_version":"1.0","source":{"id":"1406.5275","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5275","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5275v2","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5275","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"B643ITDLLHCH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B643ITDLLHCH6GOS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B643ITDL","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:8b830d38673d3fcd08a18e4f818d746266f1a8c416331eecef60151d5234625f","target":"graph","created_at":"2026-05-18T00:52:08Z","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":"The paper is devoted to the study of two-parametric families of Dirichlet problems for systems of equations with $p, q$-Laplacians and indefinite nonlinearities. Continuous and monotone curves $\\Gamma_f$ and $\\Gamma_e$ on the parametric plane $\\lambda \\times \\mu$, which are the lower and upper bounds for a maximal domain of existence of weak positive solutions are introduced. The curve $\\Gamma_f$ is obtained by developing our previous work \\cite{BobkovIlyasov} and it determines a maximal domain of the applicability of the Nehari manifold and fibering methods. The curve $\\Gamma_e$ is derived ex","authors_text":"Vladimir Bobkov, Yavdat Il'yasov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T03:58:19Z","title":"Maximal existence domains of positive solutions for two-parametric systems of elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5275","kind":"arxiv","version":2},"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:a15c879e132633e4e403197c11f86305b2f044417e5f92c26e0b25588e3edbde","target":"record","created_at":"2026-05-18T00:52:08Z","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":"5314245d7cb27dfdba38b11295d4704c0e03e3addf433915dfff24040021c86f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T03:58:19Z","title_canon_sha256":"e81f141db8bf0fe7f6221c7bdd05e251b410dd56e6f9dbda0b050d6812574dfc"},"schema_version":"1.0","source":{"id":"1406.5275","kind":"arxiv","version":2}},"canonical_sha256":"0fb9b44c6b59c47f19d221c6df68204b91dcca3cd73eb6cb797f5e1b99434dbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fb9b44c6b59c47f19d221c6df68204b91dcca3cd73eb6cb797f5e1b99434dbe","first_computed_at":"2026-05-18T00:52:08.695908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:08.695908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zbxuHIRJI4NEGtb2ggED7I6xw54pI4YY+XZnJZncjCaopvCzNZHolXoIpS5xZJdaP0aeYxZKgUTE6uhqtkv/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:08.696512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5275","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a15c879e132633e4e403197c11f86305b2f044417e5f92c26e0b25588e3edbde","sha256:8b830d38673d3fcd08a18e4f818d746266f1a8c416331eecef60151d5234625f"],"state_sha256":"73199d0ffa87aa61a07d98355f0d2625ef68a4c131c2d2e57505d3baafe46372"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7aDb4F67zDnUYisU/pLK959ooLp6Kozw7ObUHfXWayGqYAbu9xTvY+x3+BLJHh17ttW7UwCqSUhtzKL5llEAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:32:44.275830Z","bundle_sha256":"699be18c3ae63e633fb361dcd03f3c2f072c85f147b4c950878cd67bd6d03402"}}