{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YJZQWUW6XLTKSK4Q4T72XA6XNA","short_pith_number":"pith:YJZQWUW6","canonical_record":{"source":{"id":"1205.5302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T22:23:40Z","cross_cats_sorted":[],"title_canon_sha256":"d70096952b92ecdf6175400fc3680b3af91df0dfe1f4a110c831e673f3b7f648","abstract_canon_sha256":"dc38d0a83552c07cf64d8898ff3d80e534b3d773ebff5bd35c0d3074966d9260"},"schema_version":"1.0"},"canonical_sha256":"c2730b52debae6a92b90e4ffab83d76832250ab242feea6cce5c242c20362f47","source":{"kind":"arxiv","id":"1205.5302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5302","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5302v1","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5302","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"YJZQWUW6XLTK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YJZQWUW6XLTKSK4Q","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YJZQWUW6","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YJZQWUW6XLTKSK4Q4T72XA6XNA","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T22:23:40Z","cross_cats_sorted":[],"title_canon_sha256":"d70096952b92ecdf6175400fc3680b3af91df0dfe1f4a110c831e673f3b7f648","abstract_canon_sha256":"dc38d0a83552c07cf64d8898ff3d80e534b3d773ebff5bd35c0d3074966d9260"},"schema_version":"1.0"},"canonical_sha256":"c2730b52debae6a92b90e4ffab83d76832250ab242feea6cce5c242c20362f47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:01.306181Z","signature_b64":"FgZAFSzZ99EGKNo9vWW+AseyUkXrQiqwhWuByhWIVomNSQaahes9ajxFCRB8xDC3zAnRPqVR3Wb9CU7Lnq6vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2730b52debae6a92b90e4ffab83d76832250ab242feea6cce5c242c20362f47","last_reissued_at":"2026-05-18T03:55:01.305656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:01.305656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5302","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":"2026-05-18T03:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W5Mxx6vAwwHI7RFD/eVSJHL2j79RB61LGGaKM7HZJ94t8o0Q8NJKhkpsrAZC+g+DGu/mpi1WIdMclOKVmrduCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:27:08.707147Z"},"content_sha256":"5d644f40fd75e9a1a127fe11070791b9476bfdaf67e793dc46e1c330ce551435","schema_version":"1.0","event_id":"sha256:5d644f40fd75e9a1a127fe11070791b9476bfdaf67e793dc46e1c330ce551435"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YJZQWUW6XLTKSK4Q4T72XA6XNA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Floquet theory for integral and integro-differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"S. A. Belbas","submitted_at":"2012-05-23T22:23:40Z","abstract_excerpt":"We study the extension of Hill's method of infinite determinants to the case of integro-differential equations with periodic coefficients and kernels. We develop the analytical theory of such methods, and we obtain certain qualitative properties of the equations that determine the boundaries between regions of dynamic stability and dynamic instability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5302","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":"2026-05-18T03:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/rozVLDHyQyrPhzMoo8A9xWxwu/7vv6Ih3vSQ4yBX1rJdz+fVOE9AQ2mgw8jSy5n9Rbm0FH5aQFUj5sQFIUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:27:08.707510Z"},"content_sha256":"82a92b4bb283fa6caea19e55c26e0589d1cbf382a4e6b40b421d5dd58ba60690","schema_version":"1.0","event_id":"sha256:82a92b4bb283fa6caea19e55c26e0589d1cbf382a4e6b40b421d5dd58ba60690"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA/bundle.json","state_url":"https://pith.science/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA/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":"2026-06-20T11:27:08Z","links":{"resolver":"https://pith.science/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA","bundle":"https://pith.science/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA/bundle.json","state":"https://pith.science/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJZQWUW6XLTKSK4Q4T72XA6XNA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YJZQWUW6XLTKSK4Q4T72XA6XNA","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":"dc38d0a83552c07cf64d8898ff3d80e534b3d773ebff5bd35c0d3074966d9260","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T22:23:40Z","title_canon_sha256":"d70096952b92ecdf6175400fc3680b3af91df0dfe1f4a110c831e673f3b7f648"},"schema_version":"1.0","source":{"id":"1205.5302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5302","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5302v1","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5302","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"YJZQWUW6XLTK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YJZQWUW6XLTKSK4Q","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YJZQWUW6","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:82a92b4bb283fa6caea19e55c26e0589d1cbf382a4e6b40b421d5dd58ba60690","target":"graph","created_at":"2026-05-18T03:55:01Z","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":"We study the extension of Hill's method of infinite determinants to the case of integro-differential equations with periodic coefficients and kernels. We develop the analytical theory of such methods, and we obtain certain qualitative properties of the equations that determine the boundaries between regions of dynamic stability and dynamic instability.","authors_text":"S. A. Belbas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T22:23:40Z","title":"Floquet theory for integral and integro-differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5302","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":"sha256:5d644f40fd75e9a1a127fe11070791b9476bfdaf67e793dc46e1c330ce551435","target":"record","created_at":"2026-05-18T03:55:01Z","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":"dc38d0a83552c07cf64d8898ff3d80e534b3d773ebff5bd35c0d3074966d9260","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-23T22:23:40Z","title_canon_sha256":"d70096952b92ecdf6175400fc3680b3af91df0dfe1f4a110c831e673f3b7f648"},"schema_version":"1.0","source":{"id":"1205.5302","kind":"arxiv","version":1}},"canonical_sha256":"c2730b52debae6a92b90e4ffab83d76832250ab242feea6cce5c242c20362f47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2730b52debae6a92b90e4ffab83d76832250ab242feea6cce5c242c20362f47","first_computed_at":"2026-05-18T03:55:01.305656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:01.305656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FgZAFSzZ99EGKNo9vWW+AseyUkXrQiqwhWuByhWIVomNSQaahes9ajxFCRB8xDC3zAnRPqVR3Wb9CU7Lnq6vAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:01.306181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d644f40fd75e9a1a127fe11070791b9476bfdaf67e793dc46e1c330ce551435","sha256:82a92b4bb283fa6caea19e55c26e0589d1cbf382a4e6b40b421d5dd58ba60690"],"state_sha256":"19f865bc9f80a833f10c16e18416cb74a1a9dc0b4901c7ffe0f63caca2f9db96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/juOgYFFd7qggDqPl3ZcikjwrHnqYDmIR3CFCsNnJnP6PvlfkuubvUVhAWlX9MTCep82yLvN53aeaiSapfmKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:27:08.709497Z","bundle_sha256":"e1c1c151ecf3a2200d69fbb7346f8a163a96a84f8a23537b7e46661dd7a9fe56"}}