{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZJ5CAOCE5JJFZFYUBR34NO53RV","short_pith_number":"pith:ZJ5CAOCE","canonical_record":{"source":{"id":"1709.01948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-06T18:05:59Z","cross_cats_sorted":[],"title_canon_sha256":"b9bd14f6e5fea41b89acfde9e3226c5fd2446e507db2bcb29d0b0b180d2c3095","abstract_canon_sha256":"2d34f3c6bd8ac06200c3940989802e3a351851ebf91defad23e2c3feb698663c"},"schema_version":"1.0"},"canonical_sha256":"ca7a203844ea525c97140c77c6bbbb8d5f5998315a5b6c6f40019a57dd167b5b","source":{"kind":"arxiv","id":"1709.01948","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01948","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01948v1","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01948","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ5CAOCE5JJF","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ5CAOCE5JJFZFYU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ5CAOCE","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZJ5CAOCE5JJFZFYUBR34NO53RV","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-06T18:05:59Z","cross_cats_sorted":[],"title_canon_sha256":"b9bd14f6e5fea41b89acfde9e3226c5fd2446e507db2bcb29d0b0b180d2c3095","abstract_canon_sha256":"2d34f3c6bd8ac06200c3940989802e3a351851ebf91defad23e2c3feb698663c"},"schema_version":"1.0"},"canonical_sha256":"ca7a203844ea525c97140c77c6bbbb8d5f5998315a5b6c6f40019a57dd167b5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:50.751750Z","signature_b64":"QKwAYsy74BVSd3YWvOTCbnSsFEbUwIqtW/rS9C6j0pWQDIQMrD00gH9k/lYA/qa4jOaJ7dhsARwTnbT3cgTFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca7a203844ea525c97140c77c6bbbb8d5f5998315a5b6c6f40019a57dd167b5b","last_reissued_at":"2026-05-18T00:35:50.751125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:50.751125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01948","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":"2026-05-18T00:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGF+/rW6ewPy+4Y1MKW3+YJmeG25j/J0MB/o+pbODhH3559U25KSvs4BLbcTdVNKhsbEJOZ91aHhcM5bnkbLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:03:11.267535Z"},"content_sha256":"7b83174af3d2c432e1047fe9ba941b7643ab821738141d7a65756b8ce5fe27f1","schema_version":"1.0","event_id":"sha256:7b83174af3d2c432e1047fe9ba941b7643ab821738141d7a65756b8ce5fe27f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZJ5CAOCE5JJFZFYUBR34NO53RV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Novel Discriminant Approximation of Periodic Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Franco, Joaquin Collado","submitted_at":"2017-09-06T18:05:59Z","abstract_excerpt":"A new approximation of the discriminant of a second order periodic differential equation is presented as a recursive summation of the evaluation of its excitation function at different values of time. The new approximation is obtained, at first, by means of Walsh functions and then, by using some algebraic properties the dependence on the Walsh functions is eliminated. This new approximation is then used to calculate the boundaries of stability. We prove that by letting the summation elements number approach to infinite, the discriminant approximation can be rewritten as a summation of definit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01948","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":"2026-05-18T00:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7nFOaAaMsy7INKztsNxBRysz6ZX4uLCuAZSDtUfUtqyqw1euL8R3tsAMcU9BeOOmnmlIl7u+81iop/J77D7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:03:11.268263Z"},"content_sha256":"ac21fe919fabf31b4c799c2d80b2594e6d465a041b1f596e7d0250cd04654376","schema_version":"1.0","event_id":"sha256:ac21fe919fabf31b4c799c2d80b2594e6d465a041b1f596e7d0250cd04654376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV/bundle.json","state_url":"https://pith.science/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV/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":"2026-06-12T02:03:11Z","links":{"resolver":"https://pith.science/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV","bundle":"https://pith.science/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV/bundle.json","state":"https://pith.science/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJ5CAOCE5JJFZFYUBR34NO53RV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZJ5CAOCE5JJFZFYUBR34NO53RV","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":"2d34f3c6bd8ac06200c3940989802e3a351851ebf91defad23e2c3feb698663c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-06T18:05:59Z","title_canon_sha256":"b9bd14f6e5fea41b89acfde9e3226c5fd2446e507db2bcb29d0b0b180d2c3095"},"schema_version":"1.0","source":{"id":"1709.01948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01948","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01948v1","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01948","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ5CAOCE5JJF","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ5CAOCE5JJFZFYU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ5CAOCE","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:ac21fe919fabf31b4c799c2d80b2594e6d465a041b1f596e7d0250cd04654376","target":"graph","created_at":"2026-05-18T00:35:50Z","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":"A new approximation of the discriminant of a second order periodic differential equation is presented as a recursive summation of the evaluation of its excitation function at different values of time. The new approximation is obtained, at first, by means of Walsh functions and then, by using some algebraic properties the dependence on the Walsh functions is eliminated. This new approximation is then used to calculate the boundaries of stability. We prove that by letting the summation elements number approach to infinite, the discriminant approximation can be rewritten as a summation of definit","authors_text":"Carlos Franco, Joaquin Collado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-06T18:05:59Z","title":"A Novel Discriminant Approximation of Periodic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01948","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":"sha256:7b83174af3d2c432e1047fe9ba941b7643ab821738141d7a65756b8ce5fe27f1","target":"record","created_at":"2026-05-18T00:35:50Z","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":"2d34f3c6bd8ac06200c3940989802e3a351851ebf91defad23e2c3feb698663c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-06T18:05:59Z","title_canon_sha256":"b9bd14f6e5fea41b89acfde9e3226c5fd2446e507db2bcb29d0b0b180d2c3095"},"schema_version":"1.0","source":{"id":"1709.01948","kind":"arxiv","version":1}},"canonical_sha256":"ca7a203844ea525c97140c77c6bbbb8d5f5998315a5b6c6f40019a57dd167b5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7a203844ea525c97140c77c6bbbb8d5f5998315a5b6c6f40019a57dd167b5b","first_computed_at":"2026-05-18T00:35:50.751125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:50.751125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QKwAYsy74BVSd3YWvOTCbnSsFEbUwIqtW/rS9C6j0pWQDIQMrD00gH9k/lYA/qa4jOaJ7dhsARwTnbT3cgTFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:50.751750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b83174af3d2c432e1047fe9ba941b7643ab821738141d7a65756b8ce5fe27f1","sha256:ac21fe919fabf31b4c799c2d80b2594e6d465a041b1f596e7d0250cd04654376"],"state_sha256":"1939d14b518476043a4b7ff5ed953ea241aefe1f97cb053b25a481a2d2e1fce8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FNALLqotGGhFXQAZxP4gQhXdPrX4GCB/GcOAyDmjZsiPqr1OUXrGG2aEgl6y7pPoEk4zz5RfGG6m6IdNw/9NBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:03:11.272792Z","bundle_sha256":"61d8976e74e2791be75ae31e8b276ed660b88114d1bd887d8bae622f7f878fd4"}}