{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KTEMQ3D5UYBAOXDGXWOSHVEFR7","short_pith_number":"pith:KTEMQ3D5","canonical_record":{"source":{"id":"2607.29146","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-31T08:24:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fda33c5512a77f662b86150e2275a9778869c922366ebe4ff31fc034f5222de2","abstract_canon_sha256":"ac8457d6827cbd970175a32707909e28dc14a7700968610846e1643bdb19f481"},"schema_version":"1.0"},"canonical_sha256":"54c8c86c7da602075c66bd9d23d4858fc74e611a4f66b8a851610d122f2cf0dc","source":{"kind":"arxiv","id":"2607.29146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29146","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29146v1","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29146","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"KTEMQ3D5UYBA","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"pith_short_16","alias_value":"KTEMQ3D5UYBAOXDG","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"pith_short_8","alias_value":"KTEMQ3D5","created_at":"2026-08-03T01:20:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KTEMQ3D5UYBAOXDGXWOSHVEFR7","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29146","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-31T08:24:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fda33c5512a77f662b86150e2275a9778869c922366ebe4ff31fc034f5222de2","abstract_canon_sha256":"ac8457d6827cbd970175a32707909e28dc14a7700968610846e1643bdb19f481"},"schema_version":"1.0"},"canonical_sha256":"54c8c86c7da602075c66bd9d23d4858fc74e611a4f66b8a851610d122f2cf0dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:20:07.681095Z","signature_b64":"q3+eQWdDLyiI7B4MAmctnvjf24VsZ6QlsZCIkmdIayvFrDhdQNdFu08M5OQn+1+KF0wCGOcyGHbgc4cVRTQcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54c8c86c7da602075c66bd9d23d4858fc74e611a4f66b8a851610d122f2cf0dc","last_reissued_at":"2026-08-03T01:20:07.679606Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:20:07.679606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29146","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":"2026-08-03T01:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0X5VGnXc/WhVCScgFYP2Yvu2z5AfCfqW7UYYSkZjvZVdpjwMbTxAClwzFrsbJ+oDNCXKak2Q9NhHw8bExNnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:26:48.358843Z"},"content_sha256":"3078bfd42b6db9ef9d359260e6096b9b96fbc9aa115fc5ae64b88e36d29fa1bd","schema_version":"1.0","event_id":"sha256:3078bfd42b6db9ef9d359260e6096b9b96fbc9aa115fc5ae64b88e36d29fa1bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KTEMQ3D5UYBAOXDGXWOSHVEFR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology in One Point Interaction Problem on Extended Non-Local Star Graphs and its Eigenvalues","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Lung-Hui Chen","submitted_at":"2026-07-31T08:24:46Z","abstract_excerpt":"The author studies the inverse spectral problem of Sturm-Liouville operator on a star-like metric graph. At the vertex of this star-like graph, there are attached $m$ edges that imposed with non-local Sturm-Liouville operator satisfying some suitable non-local boundary conditions. At the vertex, we consider one point interaction condition to model a metric graph that fixed on the end of edges of the graph. This models the vibration or flux that changes over time that monitored at the vertex which serves as certain control/regulation center. The author shows that the system is solvable under ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29146","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29146/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-03T01:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4lkFEAPF2E/htg4WzvYRTdTI0zjTtUJQ+Wfky6cfQb5VpKu0CyenrvcfA58wE7/gUwNjQ1rW72BZs7YKHlFDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:26:48.359403Z"},"content_sha256":"8d91b586e22f01c91b0a111ced63b8aa860ebb537b8d67859ba4490c0eee0cc4","schema_version":"1.0","event_id":"sha256:8d91b586e22f01c91b0a111ced63b8aa860ebb537b8d67859ba4490c0eee0cc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7/bundle.json","state_url":"https://pith.science/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7/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":"2026-08-12T20:26:48Z","links":{"resolver":"https://pith.science/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7","bundle":"https://pith.science/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7/bundle.json","state":"https://pith.science/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTEMQ3D5UYBAOXDGXWOSHVEFR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KTEMQ3D5UYBAOXDGXWOSHVEFR7","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":"ac8457d6827cbd970175a32707909e28dc14a7700968610846e1643bdb19f481","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-31T08:24:46Z","title_canon_sha256":"fda33c5512a77f662b86150e2275a9778869c922366ebe4ff31fc034f5222de2"},"schema_version":"1.0","source":{"id":"2607.29146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29146","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29146v1","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29146","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"KTEMQ3D5UYBA","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"pith_short_16","alias_value":"KTEMQ3D5UYBAOXDG","created_at":"2026-08-03T01:20:07Z"},{"alias_kind":"pith_short_8","alias_value":"KTEMQ3D5","created_at":"2026-08-03T01:20:07Z"}],"graph_snapshots":[{"event_id":"sha256:8d91b586e22f01c91b0a111ced63b8aa860ebb537b8d67859ba4490c0eee0cc4","target":"graph","created_at":"2026-08-03T01:20:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.29146/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The author studies the inverse spectral problem of Sturm-Liouville operator on a star-like metric graph. At the vertex of this star-like graph, there are attached $m$ edges that imposed with non-local Sturm-Liouville operator satisfying some suitable non-local boundary conditions. At the vertex, we consider one point interaction condition to model a metric graph that fixed on the end of edges of the graph. This models the vibration or flux that changes over time that monitored at the vertex which serves as certain control/regulation center. The author shows that the system is solvable under ve","authors_text":"Lung-Hui Chen","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-31T08:24:46Z","title":"Topology in One Point Interaction Problem on Extended Non-Local Star Graphs and its Eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29146","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":"sha256:3078bfd42b6db9ef9d359260e6096b9b96fbc9aa115fc5ae64b88e36d29fa1bd","target":"record","created_at":"2026-08-03T01:20:07Z","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":"ac8457d6827cbd970175a32707909e28dc14a7700968610846e1643bdb19f481","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-31T08:24:46Z","title_canon_sha256":"fda33c5512a77f662b86150e2275a9778869c922366ebe4ff31fc034f5222de2"},"schema_version":"1.0","source":{"id":"2607.29146","kind":"arxiv","version":1}},"canonical_sha256":"54c8c86c7da602075c66bd9d23d4858fc74e611a4f66b8a851610d122f2cf0dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54c8c86c7da602075c66bd9d23d4858fc74e611a4f66b8a851610d122f2cf0dc","first_computed_at":"2026-08-03T01:20:07.679606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:20:07.679606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3+eQWdDLyiI7B4MAmctnvjf24VsZ6QlsZCIkmdIayvFrDhdQNdFu08M5OQn+1+KF0wCGOcyGHbgc4cVRTQcBA==","signature_status":"signed_v1","signed_at":"2026-08-03T01:20:07.681095Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3078bfd42b6db9ef9d359260e6096b9b96fbc9aa115fc5ae64b88e36d29fa1bd","sha256:8d91b586e22f01c91b0a111ced63b8aa860ebb537b8d67859ba4490c0eee0cc4"],"state_sha256":"ad1e5c9a3321e0c36a1b7d8861d51b17086a9a86f2588a9053e5d90bac3e10b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"58AiUyArfHWW6Lbyu8mOBgQ35wE+cvbsgdlISrYDFSge7450cOV/CkBOEFtOE87+dCxjZDSzMBXdeYbvjLHCAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T20:26:48.364554Z","bundle_sha256":"d559e93cf1d51bcf5c022d04ec9d5c1f7ddef065834c3bc4cb38c3e0f9376fba"}}