{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TPEPUUTRETZWO26ZHG2DBBILUP","short_pith_number":"pith:TPEPUUTR","canonical_record":{"source":{"id":"1011.5695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-26T02:39:48Z","cross_cats_sorted":[],"title_canon_sha256":"476d8017bbf6d26eadd012d41508faa023bdac7cb3243ee6c21f4809107cd6f3","abstract_canon_sha256":"cee822679819061913dd2b6db066ffedfd336af413ff753352ef12fe0fa044f2"},"schema_version":"1.0"},"canonical_sha256":"9bc8fa527124f3676bd939b430850ba3c282dc608ede70f6f1b83f40cd8db243","source":{"kind":"arxiv","id":"1011.5695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5695","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5695v1","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5695","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"TPEPUUTRETZW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TPEPUUTRETZWO26Z","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TPEPUUTR","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TPEPUUTRETZWO26ZHG2DBBILUP","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-26T02:39:48Z","cross_cats_sorted":[],"title_canon_sha256":"476d8017bbf6d26eadd012d41508faa023bdac7cb3243ee6c21f4809107cd6f3","abstract_canon_sha256":"cee822679819061913dd2b6db066ffedfd336af413ff753352ef12fe0fa044f2"},"schema_version":"1.0"},"canonical_sha256":"9bc8fa527124f3676bd939b430850ba3c282dc608ede70f6f1b83f40cd8db243","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:38.647571Z","signature_b64":"Msfb0oE9Md0sRz7zQ1SWYpd+J/kIybfr0QPk8LHarLGXY2Gb5fzyqHidHh+zPvGiuiKaPi11vMAGSXEbVAWvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bc8fa527124f3676bd939b430850ba3c282dc608ede70f6f1b83f40cd8db243","last_reissued_at":"2026-05-18T04:34:38.647130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:38.647130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5695","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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8PL1oifkXoIXvdm/KoxSOErfLoGs+8SB10EFkvp6sI7ZSsG3LInGVdGYNmt1o0uzcjtcwr9GSRVQKZM/kFg+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:27:28.897681Z"},"content_sha256":"3ebbd312566a4ee381f09766fd571db8c5061a9981f5a609100a0418d26be222","schema_version":"1.0","event_id":"sha256:3ebbd312566a4ee381f09766fd571db8c5061a9981f5a609100a0418d26be222"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TPEPUUTRETZWO26ZHG2DBBILUP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$2$-modified characteristic Fredholm determinants, Hill's method, and the periodic Evans function of Gardne","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Kevin Zumbrun","submitted_at":"2010-11-26T02:39:48Z","abstract_excerpt":"Using the relation established by Johnson--Zumbrun between Hill's method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the $2$-modified characteristic Fredholm determinant of an associated Birman--Schwinger system, together with a Volterra integral computation introduced by Gesztesy--Makarov, we give an explicit connection between the generalized Birman--Schwinger-type periodic Evans function and the standard Jost function-type periodic Evans function defined by Gardner in terms of the fundamental solution of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5695","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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H59TrBA/4wcAsHwREpFTQf1YP3/zj9zp+f1Bo3YB2iCpbP6RTR31NlHRMSmtMmCqAFUvrbz0upWcuI29PIoaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:27:28.898077Z"},"content_sha256":"54bc1b31f56d64a1961ac9ea56d1e4c90d107e7dd9b2c34cb5b1357d4dc6c19b","schema_version":"1.0","event_id":"sha256:54bc1b31f56d64a1961ac9ea56d1e4c90d107e7dd9b2c34cb5b1357d4dc6c19b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPEPUUTRETZWO26ZHG2DBBILUP/bundle.json","state_url":"https://pith.science/pith/TPEPUUTRETZWO26ZHG2DBBILUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPEPUUTRETZWO26ZHG2DBBILUP/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":"2026-05-28T00:27:28Z","links":{"resolver":"https://pith.science/pith/TPEPUUTRETZWO26ZHG2DBBILUP","bundle":"https://pith.science/pith/TPEPUUTRETZWO26ZHG2DBBILUP/bundle.json","state":"https://pith.science/pith/TPEPUUTRETZWO26ZHG2DBBILUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPEPUUTRETZWO26ZHG2DBBILUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TPEPUUTRETZWO26ZHG2DBBILUP","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":"cee822679819061913dd2b6db066ffedfd336af413ff753352ef12fe0fa044f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-26T02:39:48Z","title_canon_sha256":"476d8017bbf6d26eadd012d41508faa023bdac7cb3243ee6c21f4809107cd6f3"},"schema_version":"1.0","source":{"id":"1011.5695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5695","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5695v1","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5695","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"TPEPUUTRETZW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TPEPUUTRETZWO26Z","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TPEPUUTR","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:54bc1b31f56d64a1961ac9ea56d1e4c90d107e7dd9b2c34cb5b1357d4dc6c19b","target":"graph","created_at":"2026-05-18T04:34:38Z","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":"Using the relation established by Johnson--Zumbrun between Hill's method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the $2$-modified characteristic Fredholm determinant of an associated Birman--Schwinger system, together with a Volterra integral computation introduced by Gesztesy--Makarov, we give an explicit connection between the generalized Birman--Schwinger-type periodic Evans function and the standard Jost function-type periodic Evans function defined by Gardner in terms of the fundamental solution of ","authors_text":"Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-26T02:39:48Z","title":"$2$-modified characteristic Fredholm determinants, Hill's method, and the periodic Evans function of Gardne"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5695","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":"sha256:3ebbd312566a4ee381f09766fd571db8c5061a9981f5a609100a0418d26be222","target":"record","created_at":"2026-05-18T04:34:38Z","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":"cee822679819061913dd2b6db066ffedfd336af413ff753352ef12fe0fa044f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-26T02:39:48Z","title_canon_sha256":"476d8017bbf6d26eadd012d41508faa023bdac7cb3243ee6c21f4809107cd6f3"},"schema_version":"1.0","source":{"id":"1011.5695","kind":"arxiv","version":1}},"canonical_sha256":"9bc8fa527124f3676bd939b430850ba3c282dc608ede70f6f1b83f40cd8db243","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bc8fa527124f3676bd939b430850ba3c282dc608ede70f6f1b83f40cd8db243","first_computed_at":"2026-05-18T04:34:38.647130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:38.647130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Msfb0oE9Md0sRz7zQ1SWYpd+J/kIybfr0QPk8LHarLGXY2Gb5fzyqHidHh+zPvGiuiKaPi11vMAGSXEbVAWvCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:38.647571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ebbd312566a4ee381f09766fd571db8c5061a9981f5a609100a0418d26be222","sha256:54bc1b31f56d64a1961ac9ea56d1e4c90d107e7dd9b2c34cb5b1357d4dc6c19b"],"state_sha256":"72f7a5fed9a8e2b88a1a5f88fa121963f113657b4f37f48146ff9495242e7441"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyzno4D0yzMXtbRgkw4fRSlZ6CfGQfyOXa3vkIfNxMNS7z8j6a0ZnYQ4AwZKm6UoF2p27q578pr+KrON8ORFDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:27:28.900988Z","bundle_sha256":"1fedf6e5638e5cadac51760e647c3843c2d5de0fca3829b1f6c6437307d4e4b2"}}