{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:GU2MIRTKR3I7TA7ABFLGPX7PVJ","short_pith_number":"pith:GU2MIRTK","canonical_record":{"source":{"id":"0801.0172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-12-30T23:54:52Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3874a027e31f5de8000934da42b22e012f6d53a7f70a0c1846d00123f3718b8a","abstract_canon_sha256":"32a69b679f375115a58f52964dc9409ba733faa2b337fcedb966db2c9875d8e2"},"schema_version":"1.0"},"canonical_sha256":"3534c4466a8ed1f983e0095667dfefaa5ba67079e38bbcf883800af7b0f8094b","source":{"kind":"arxiv","id":"0801.0172","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.0172","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"0801.0172v2","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.0172","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"GU2MIRTKR3I7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GU2MIRTKR3I7TA7A","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GU2MIRTK","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:GU2MIRTKR3I7TA7ABFLGPX7PVJ","target":"record","payload":{"canonical_record":{"source":{"id":"0801.0172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-12-30T23:54:52Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3874a027e31f5de8000934da42b22e012f6d53a7f70a0c1846d00123f3718b8a","abstract_canon_sha256":"32a69b679f375115a58f52964dc9409ba733faa2b337fcedb966db2c9875d8e2"},"schema_version":"1.0"},"canonical_sha256":"3534c4466a8ed1f983e0095667dfefaa5ba67079e38bbcf883800af7b0f8094b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:15.141841Z","signature_b64":"cHwNPNHnRr3rPBQ6A2zUqrn7/tqa82nlccxLkXf3qIB6kBM2YGTJ8dOMl9EAHj7xgGHFTIhclGAuYX+/LhJoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3534c4466a8ed1f983e0095667dfefaa5ba67079e38bbcf883800af7b0f8094b","last_reissued_at":"2026-05-18T04:35:15.141406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:15.141406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.0172","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":"2026-05-18T04:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gs8+sOqRb0E3xb7Fo/p22cJeYkEicSR/QyuXvw4NhLRQfdEFxzAvt5rxe1L50+ym9QKutDCm2bekZA4nDuqsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T06:28:35.169974Z"},"content_sha256":"2d7007b056fb4fd89a15aa6e236fbe60555df0707420c19a88488dacf5c45a9c","schema_version":"1.0","event_id":"sha256:2d7007b056fb4fd89a15aa6e236fbe60555df0707420c19a88488dacf5c45a9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:GU2MIRTKR3I7TA7ABFLGPX7PVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Lyonell Boulton, Marco Marletta, Michael Levitin","submitted_at":"2007-12-30T23:54:52Z","abstract_excerpt":"We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0172","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":"2026-05-18T04:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BuYZAwxEhJf6GW+mg4bfHAafrAmycs2aWQ4fnsHO+3g0fWMaASCbAkmkmP7LDL0fSa91tOyq9r/00UGMP4RDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T06:28:35.170492Z"},"content_sha256":"4df6496f0079c00a433d6d9c3cdaeb3c103b8a06e1e28dd1e41ba4d470a79e16","schema_version":"1.0","event_id":"sha256:4df6496f0079c00a433d6d9c3cdaeb3c103b8a06e1e28dd1e41ba4d470a79e16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ/bundle.json","state_url":"https://pith.science/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ/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":"2026-05-22T06:28:35Z","links":{"resolver":"https://pith.science/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ","bundle":"https://pith.science/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ/bundle.json","state":"https://pith.science/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GU2MIRTKR3I7TA7ABFLGPX7PVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:GU2MIRTKR3I7TA7ABFLGPX7PVJ","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":"32a69b679f375115a58f52964dc9409ba733faa2b337fcedb966db2c9875d8e2","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-12-30T23:54:52Z","title_canon_sha256":"3874a027e31f5de8000934da42b22e012f6d53a7f70a0c1846d00123f3718b8a"},"schema_version":"1.0","source":{"id":"0801.0172","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.0172","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"0801.0172v2","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.0172","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"GU2MIRTKR3I7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GU2MIRTKR3I7TA7A","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GU2MIRTK","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:4df6496f0079c00a433d6d9c3cdaeb3c103b8a06e1e28dd1e41ba4d470a79e16","target":"graph","created_at":"2026-05-18T04:35:15Z","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 prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371].","authors_text":"Lyonell Boulton, Marco Marletta, Michael Levitin","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-12-30T23:54:52Z","title":"On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0172","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":"sha256:2d7007b056fb4fd89a15aa6e236fbe60555df0707420c19a88488dacf5c45a9c","target":"record","created_at":"2026-05-18T04:35:15Z","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":"32a69b679f375115a58f52964dc9409ba733faa2b337fcedb966db2c9875d8e2","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-12-30T23:54:52Z","title_canon_sha256":"3874a027e31f5de8000934da42b22e012f6d53a7f70a0c1846d00123f3718b8a"},"schema_version":"1.0","source":{"id":"0801.0172","kind":"arxiv","version":2}},"canonical_sha256":"3534c4466a8ed1f983e0095667dfefaa5ba67079e38bbcf883800af7b0f8094b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3534c4466a8ed1f983e0095667dfefaa5ba67079e38bbcf883800af7b0f8094b","first_computed_at":"2026-05-18T04:35:15.141406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:15.141406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHwNPNHnRr3rPBQ6A2zUqrn7/tqa82nlccxLkXf3qIB6kBM2YGTJ8dOMl9EAHj7xgGHFTIhclGAuYX+/LhJoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:15.141841Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.0172","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d7007b056fb4fd89a15aa6e236fbe60555df0707420c19a88488dacf5c45a9c","sha256:4df6496f0079c00a433d6d9c3cdaeb3c103b8a06e1e28dd1e41ba4d470a79e16"],"state_sha256":"26b398964a95644491b29df1a55ca4f69736bab98da0d3bcf198e4171d3be8db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMDiXzDaFgZPrPd2xcoeuQ4X9QJqAbU2JiRbMVzosszflkMF3H8Y4tg9lb0sMMSnB9c9a3SousrJ0HaBhHIwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T06:28:35.172879Z","bundle_sha256":"a3bc7cf379acfb827e7f3876d63e5b96e6719ae338bdf71b1c8b85243b941e60"}}