{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RZ36TC4XJUHEIRSVCUJEFDTCLR","short_pith_number":"pith:RZ36TC4X","canonical_record":{"source":{"id":"1902.08220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-21T19:14:04Z","cross_cats_sorted":[],"title_canon_sha256":"5d4a17a64bbe0990864232fe5ab88443e39f7086fd8d16d187bc024d064fa8fc","abstract_canon_sha256":"c423f704224055770492f1fb261c5753cdf78cf3973dd6d2ea16dbcf53fbd534"},"schema_version":"1.0"},"canonical_sha256":"8e77e98b974d0e4446551512428e625c528e36917cc6af955518b6a67fcc1bab","source":{"kind":"arxiv","id":"1902.08220","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08220","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08220v1","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08220","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"RZ36TC4XJUHE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RZ36TC4XJUHEIRSV","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RZ36TC4X","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RZ36TC4XJUHEIRSVCUJEFDTCLR","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-21T19:14:04Z","cross_cats_sorted":[],"title_canon_sha256":"5d4a17a64bbe0990864232fe5ab88443e39f7086fd8d16d187bc024d064fa8fc","abstract_canon_sha256":"c423f704224055770492f1fb261c5753cdf78cf3973dd6d2ea16dbcf53fbd534"},"schema_version":"1.0"},"canonical_sha256":"8e77e98b974d0e4446551512428e625c528e36917cc6af955518b6a67fcc1bab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:57.966331Z","signature_b64":"e93Yel5EuG4eEghsTGKcGPpMstAM1Rr27BUNNth6Naj7Acq0fEQlsSLEm3EfueHm5KBq9ocJk0S/X3ACODZvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e77e98b974d0e4446551512428e625c528e36917cc6af955518b6a67fcc1bab","last_reissued_at":"2026-05-17T23:52:57.965454Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:57.965454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08220","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":"2026-05-17T23:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQJPPY/x9hACOqQDRs5BU8nCllOJvsmUAybYiNp8LMAxU7ZMQ25Vz4Sziqy59EwNYxJPJhAVw2AwYz72pGyrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:41:25.257202Z"},"content_sha256":"6d8b29a7475efbb59cd96c5f22808e2b50034126cd9860fa77fd3ba81605e480","schema_version":"1.0","event_id":"sha256:6d8b29a7475efbb59cd96c5f22808e2b50034126cd9860fa77fd3ba81605e480"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RZ36TC4XJUHEIRSVCUJEFDTCLR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of Solutions to Nonlinear Legendre Boundary Value Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Benjamin Freedman, Jesus Rodriguez","submitted_at":"2019-02-21T19:14:04Z","abstract_excerpt":"In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a qualitative description of solutions depending on a parameter. The results presented depend on the size and limiting behavior of the nonlinearities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08220","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":"2026-05-17T23:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xiga3WqSPVIaUmNNwF2xdZ8Ni7IFCQ9EgsJfyTff4Qhr6EEhYNwirdgoXhtNhmKzpsb2CYiyR0o8D3kYDNeyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:41:25.257569Z"},"content_sha256":"a9c8c95d6c1b042374edaeafb8ad747c34236a9de86533473cdf94c37d8201aa","schema_version":"1.0","event_id":"sha256:a9c8c95d6c1b042374edaeafb8ad747c34236a9de86533473cdf94c37d8201aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR/bundle.json","state_url":"https://pith.science/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR/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":"2026-06-25T20:41:25Z","links":{"resolver":"https://pith.science/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR","bundle":"https://pith.science/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR/bundle.json","state":"https://pith.science/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZ36TC4XJUHEIRSVCUJEFDTCLR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RZ36TC4XJUHEIRSVCUJEFDTCLR","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":"c423f704224055770492f1fb261c5753cdf78cf3973dd6d2ea16dbcf53fbd534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-21T19:14:04Z","title_canon_sha256":"5d4a17a64bbe0990864232fe5ab88443e39f7086fd8d16d187bc024d064fa8fc"},"schema_version":"1.0","source":{"id":"1902.08220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08220","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08220v1","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08220","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"RZ36TC4XJUHE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RZ36TC4XJUHEIRSV","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RZ36TC4X","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:a9c8c95d6c1b042374edaeafb8ad747c34236a9de86533473cdf94c37d8201aa","target":"graph","created_at":"2026-05-17T23:52:57Z","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 paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a qualitative description of solutions depending on a parameter. The results presented depend on the size and limiting behavior of the nonlinearities.","authors_text":"Benjamin Freedman, Jesus Rodriguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-21T19:14:04Z","title":"Existence of Solutions to Nonlinear Legendre Boundary Value Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08220","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":"sha256:6d8b29a7475efbb59cd96c5f22808e2b50034126cd9860fa77fd3ba81605e480","target":"record","created_at":"2026-05-17T23:52:57Z","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":"c423f704224055770492f1fb261c5753cdf78cf3973dd6d2ea16dbcf53fbd534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-02-21T19:14:04Z","title_canon_sha256":"5d4a17a64bbe0990864232fe5ab88443e39f7086fd8d16d187bc024d064fa8fc"},"schema_version":"1.0","source":{"id":"1902.08220","kind":"arxiv","version":1}},"canonical_sha256":"8e77e98b974d0e4446551512428e625c528e36917cc6af955518b6a67fcc1bab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e77e98b974d0e4446551512428e625c528e36917cc6af955518b6a67fcc1bab","first_computed_at":"2026-05-17T23:52:57.965454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:57.965454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e93Yel5EuG4eEghsTGKcGPpMstAM1Rr27BUNNth6Naj7Acq0fEQlsSLEm3EfueHm5KBq9ocJk0S/X3ACODZvDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:57.966331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d8b29a7475efbb59cd96c5f22808e2b50034126cd9860fa77fd3ba81605e480","sha256:a9c8c95d6c1b042374edaeafb8ad747c34236a9de86533473cdf94c37d8201aa"],"state_sha256":"1d308849a4ecf31cf209bac7686289efd71ce00b7280f27f82864be0cedf3d40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7qg/k4rNGGKzLreu6u/Os/pTAZEKAbxI+tSCuXIHQ6S1PmjYRySBcm/fLs9jMLjo9Om2l64lu+GA3wftcW/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:41:25.259533Z","bundle_sha256":"ff2049d573cc832a583b0f89d2cdb52b313f6460ea0d6a031a105ecbbf3f0cde"}}