{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I3JWFS4UPVEYWFPN5W2RBCSP4G","short_pith_number":"pith:I3JWFS4U","canonical_record":{"source":{"id":"1604.04245","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-14T18:14:16Z","cross_cats_sorted":[],"title_canon_sha256":"e80bb3cd2eb01aa360dc50ad9134b5817dcafd2c6d2b7b5b647fb7b3ad312970","abstract_canon_sha256":"042b935fbd575bd77187589b0f2e9228de0795cf17129ffce6e27f188918f76e"},"schema_version":"1.0"},"canonical_sha256":"46d362cb947d498b15ededb5108a4fe1b5a1a530d15eda7aeaa4f38620bb7b21","source":{"kind":"arxiv","id":"1604.04245","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04245","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04245v2","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04245","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"I3JWFS4UPVEY","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I3JWFS4UPVEYWFPN","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I3JWFS4U","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I3JWFS4UPVEYWFPN5W2RBCSP4G","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04245","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-14T18:14:16Z","cross_cats_sorted":[],"title_canon_sha256":"e80bb3cd2eb01aa360dc50ad9134b5817dcafd2c6d2b7b5b647fb7b3ad312970","abstract_canon_sha256":"042b935fbd575bd77187589b0f2e9228de0795cf17129ffce6e27f188918f76e"},"schema_version":"1.0"},"canonical_sha256":"46d362cb947d498b15ededb5108a4fe1b5a1a530d15eda7aeaa4f38620bb7b21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:04.643754Z","signature_b64":"jQD6VwYhUrRzQTWqfGcH+jeMO7m6LIdqGtV9wr4Upp7lDoGbET9McAearRrF5z26vxDQpRJ38/2ws913xviCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46d362cb947d498b15ededb5108a4fe1b5a1a530d15eda7aeaa4f38620bb7b21","last_reissued_at":"2026-05-18T01:17:04.642977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:04.642977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04245","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qkn32nHRbQRs62/L1McjHgRrzSyUO/fI7pA4+we/C1Rz/qbW0dpTzz+hjjQVn9xbBuq9+Joqa0igz2G8IYGZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:35:58.833673Z"},"content_sha256":"5f4b57e87a2701fbac2c1b9f634adb593aa642bb7b1a1f814ecd0fea4b495bda","schema_version":"1.0","event_id":"sha256:5f4b57e87a2701fbac2c1b9f634adb593aa642bb7b1a1f814ecd0fea4b495bda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I3JWFS4UPVEYWFPN5W2RBCSP4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant sign Green's function for simply supported beam equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Cabada, Lorena Saavedra","submitted_at":"2016-04-14T18:14:16Z","abstract_excerpt":"The aim of this paper consists on the study of the following fourth-order operator: \\begin{equation}\\label{Ec::T4} T[M]\\,u(t)\\equiv u^{(4)}(t)+p_1(t)\\,u\"'(t)+p_2(t)\\,u\"(t)+M\\,u(t)\\,,\\ t\\in I \\equiv [a,b]\\,, \\end{equation} coupled with the two point boundary conditions: \\begin{equation}\\label{Ec::cf} u(a)=u(b)=u\"(a)=u\"(b)=0\\,. \\end{equation}\n  So, we define the following space:\n  \\begin{equation}\\label{Ec::esp}\n  X=\\left\\lbrace u\\in C^4(I)\\quad\\mid\\quad u(a)=u(b)=u\"(a)=u\"(b)=0 \\right\\rbrace \\,.\n  \\end{equation}\n  Here $p_1\\in C^3(I)$ and $p_2\\in C^2(I)$.\n  By assuming that the second order line"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04245","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vjE3GdaMAfrFiSEwpWw2464tR8/Jz8oC0yRv6OthUGppxK0oOj0YB1VcmM/FKmfZ52mKlEfM0A/WAOoK99ZkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:35:58.834440Z"},"content_sha256":"21c41296703f860ac0f9ceeaa82cfa2827164ad3c5e636bd2594bf2e29cf7433","schema_version":"1.0","event_id":"sha256:21c41296703f860ac0f9ceeaa82cfa2827164ad3c5e636bd2594bf2e29cf7433"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G/bundle.json","state_url":"https://pith.science/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G/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":"2026-05-31T12:35:58Z","links":{"resolver":"https://pith.science/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G","bundle":"https://pith.science/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G/bundle.json","state":"https://pith.science/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3JWFS4UPVEYWFPN5W2RBCSP4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I3JWFS4UPVEYWFPN5W2RBCSP4G","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":"042b935fbd575bd77187589b0f2e9228de0795cf17129ffce6e27f188918f76e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-14T18:14:16Z","title_canon_sha256":"e80bb3cd2eb01aa360dc50ad9134b5817dcafd2c6d2b7b5b647fb7b3ad312970"},"schema_version":"1.0","source":{"id":"1604.04245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04245","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04245v2","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04245","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"I3JWFS4UPVEY","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I3JWFS4UPVEYWFPN","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I3JWFS4U","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:21c41296703f860ac0f9ceeaa82cfa2827164ad3c5e636bd2594bf2e29cf7433","target":"graph","created_at":"2026-05-18T01:17:04Z","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 aim of this paper consists on the study of the following fourth-order operator: \\begin{equation}\\label{Ec::T4} T[M]\\,u(t)\\equiv u^{(4)}(t)+p_1(t)\\,u\"'(t)+p_2(t)\\,u\"(t)+M\\,u(t)\\,,\\ t\\in I \\equiv [a,b]\\,, \\end{equation} coupled with the two point boundary conditions: \\begin{equation}\\label{Ec::cf} u(a)=u(b)=u\"(a)=u\"(b)=0\\,. \\end{equation}\n  So, we define the following space:\n  \\begin{equation}\\label{Ec::esp}\n  X=\\left\\lbrace u\\in C^4(I)\\quad\\mid\\quad u(a)=u(b)=u\"(a)=u\"(b)=0 \\right\\rbrace \\,.\n  \\end{equation}\n  Here $p_1\\in C^3(I)$ and $p_2\\in C^2(I)$.\n  By assuming that the second order line","authors_text":"Alberto Cabada, Lorena Saavedra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-14T18:14:16Z","title":"Constant sign Green's function for simply supported beam equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04245","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":"sha256:5f4b57e87a2701fbac2c1b9f634adb593aa642bb7b1a1f814ecd0fea4b495bda","target":"record","created_at":"2026-05-18T01:17:04Z","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":"042b935fbd575bd77187589b0f2e9228de0795cf17129ffce6e27f188918f76e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-14T18:14:16Z","title_canon_sha256":"e80bb3cd2eb01aa360dc50ad9134b5817dcafd2c6d2b7b5b647fb7b3ad312970"},"schema_version":"1.0","source":{"id":"1604.04245","kind":"arxiv","version":2}},"canonical_sha256":"46d362cb947d498b15ededb5108a4fe1b5a1a530d15eda7aeaa4f38620bb7b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46d362cb947d498b15ededb5108a4fe1b5a1a530d15eda7aeaa4f38620bb7b21","first_computed_at":"2026-05-18T01:17:04.642977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:04.642977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQD6VwYhUrRzQTWqfGcH+jeMO7m6LIdqGtV9wr4Upp7lDoGbET9McAearRrF5z26vxDQpRJ38/2ws913xviCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:04.643754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f4b57e87a2701fbac2c1b9f634adb593aa642bb7b1a1f814ecd0fea4b495bda","sha256:21c41296703f860ac0f9ceeaa82cfa2827164ad3c5e636bd2594bf2e29cf7433"],"state_sha256":"82b0b94c5092d82c48a5499b1b9e3017cb37c5106208b67f985099cbeaf889cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zhJ6bm/nmI4YBf7Q3NucqydfZvDwLU2vP9wf6BPaB5EEHD+HSyLxQoJOgnZ/zs9ClbhIL1yEDKY4oeVQ6lC1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:35:58.838577Z","bundle_sha256":"379c6a0fec8c400f1f03671f3cccd0cad2ef847dca2ad5cc625314e9f9d33042"}}