{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3GKAVNX7Q7DKWRF5GSNEOTAEPI","short_pith_number":"pith:3GKAVNX7","canonical_record":{"source":{"id":"2507.14458","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-19T03:05:48Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"fd26c4f60c3cc93b963776e79ba9c8d414ea2d6e812e3e933b0d9b8fa452b0f4","abstract_canon_sha256":"ba311f06bba87fbb996edb5ed6c2837b21ecf41c06dd44e7d9ddb0eef5da2795"},"schema_version":"1.0"},"canonical_sha256":"d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d","source":{"kind":"arxiv","id":"2507.14458","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14458","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14458v2","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14458","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"3GKAVNX7Q7DK","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_16","alias_value":"3GKAVNX7Q7DKWRF5","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_8","alias_value":"3GKAVNX7","created_at":"2026-06-19T16:12:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3GKAVNX7Q7DKWRF5GSNEOTAEPI","target":"record","payload":{"canonical_record":{"source":{"id":"2507.14458","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-19T03:05:48Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"fd26c4f60c3cc93b963776e79ba9c8d414ea2d6e812e3e933b0d9b8fa452b0f4","abstract_canon_sha256":"ba311f06bba87fbb996edb5ed6c2837b21ecf41c06dd44e7d9ddb0eef5da2795"},"schema_version":"1.0"},"canonical_sha256":"d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:14.256790Z","signature_b64":"EfkoiDjKuHXsdoRCf4hKNdgtkSFJrRUuBTWtgcAtDKoAoXF8fO9nVMcsq8v3Sa3w59Lt9JpqlByYclL7VhbuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d","last_reissued_at":"2026-06-19T16:12:14.256370Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:14.256370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.14458","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":"2026-06-19T16:12:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JrXn/Xq4/3aot52satsHwKdZK55TreLnHTqA5XOc4JL0wzGNnnt9HtZC5op5unjrZ4lFILotrSX+1u4IwMNzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:49:03.325221Z"},"content_sha256":"7f98b74d4bd1585883fc5ace3b917a1ddf5267925826933e94a2423ef39feff1","schema_version":"1.0","event_id":"sha256:7f98b74d4bd1585883fc5ace3b917a1ddf5267925826933e94a2423ef39feff1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3GKAVNX7Q7DKWRF5GSNEOTAEPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ching-Hao Chang, I-Hsun Tsai, Jih-Hsin Cheng","submitted_at":"2025-07-19T03:05:48Z","abstract_excerpt":"In this paper we study the spectral analysis of Bochner-Kodaira Laplacians on an Abelian variety, complex projective space $\\mathbb{P}^{n}$ and a Grassmannian with a holomorphic line bundle. By imitating the method of creation and annihilation operators in physics, we convert those eigensections (of the \\textquotedblleft higher energy\" level) into holomorphic sections (of the \\textquotedblleft lowest energy\" level). This enables us to endow these spectral bundles, which are defined over the dual Abelian variety, with natural holomorphic structure. Using this conversion expressed in a concrete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14458","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.14458/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":"2026-06-19T16:12:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qxPjwCrPLcEa7o2C3VQJ8RmDj8r86KHFHbm2fRAUsEhEu8pbua1Rrv5LGyGAWYuD5OxlXjF2+gLc+/bwXnOfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:49:03.325669Z"},"content_sha256":"d1a54dcaa6a7adc038e8bcb45f46b4fb1e106a47d7918e7a558ad20a158361ed","schema_version":"1.0","event_id":"sha256:d1a54dcaa6a7adc038e8bcb45f46b4fb1e106a47d7918e7a558ad20a158361ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI/bundle.json","state_url":"https://pith.science/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI/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":"2026-06-22T09:49:03Z","links":{"resolver":"https://pith.science/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI","bundle":"https://pith.science/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI/bundle.json","state":"https://pith.science/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GKAVNX7Q7DKWRF5GSNEOTAEPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3GKAVNX7Q7DKWRF5GSNEOTAEPI","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":"ba311f06bba87fbb996edb5ed6c2837b21ecf41c06dd44e7d9ddb0eef5da2795","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-19T03:05:48Z","title_canon_sha256":"fd26c4f60c3cc93b963776e79ba9c8d414ea2d6e812e3e933b0d9b8fa452b0f4"},"schema_version":"1.0","source":{"id":"2507.14458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14458","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14458v2","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14458","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"3GKAVNX7Q7DK","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_16","alias_value":"3GKAVNX7Q7DKWRF5","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_8","alias_value":"3GKAVNX7","created_at":"2026-06-19T16:12:14Z"}],"graph_snapshots":[{"event_id":"sha256:d1a54dcaa6a7adc038e8bcb45f46b4fb1e106a47d7918e7a558ad20a158361ed","target":"graph","created_at":"2026-06-19T16:12:14Z","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/2507.14458/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the spectral analysis of Bochner-Kodaira Laplacians on an Abelian variety, complex projective space $\\mathbb{P}^{n}$ and a Grassmannian with a holomorphic line bundle. By imitating the method of creation and annihilation operators in physics, we convert those eigensections (of the \\textquotedblleft higher energy\" level) into holomorphic sections (of the \\textquotedblleft lowest energy\" level). This enables us to endow these spectral bundles, which are defined over the dual Abelian variety, with natural holomorphic structure. Using this conversion expressed in a concrete ","authors_text":"Ching-Hao Chang, I-Hsun Tsai, Jih-Hsin Cheng","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-19T03:05:48Z","title":"Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14458","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":"sha256:7f98b74d4bd1585883fc5ace3b917a1ddf5267925826933e94a2423ef39feff1","target":"record","created_at":"2026-06-19T16:12:14Z","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":"ba311f06bba87fbb996edb5ed6c2837b21ecf41c06dd44e7d9ddb0eef5da2795","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-19T03:05:48Z","title_canon_sha256":"fd26c4f60c3cc93b963776e79ba9c8d414ea2d6e812e3e933b0d9b8fa452b0f4"},"schema_version":"1.0","source":{"id":"2507.14458","kind":"arxiv","version":2}},"canonical_sha256":"d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d","first_computed_at":"2026-06-19T16:12:14.256370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:14.256370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EfkoiDjKuHXsdoRCf4hKNdgtkSFJrRUuBTWtgcAtDKoAoXF8fO9nVMcsq8v3Sa3w59Lt9JpqlByYclL7VhbuCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:14.256790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.14458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f98b74d4bd1585883fc5ace3b917a1ddf5267925826933e94a2423ef39feff1","sha256:d1a54dcaa6a7adc038e8bcb45f46b4fb1e106a47d7918e7a558ad20a158361ed"],"state_sha256":"44347e4b3ab5b81c3475aa5e6c5606cb39e30b9dc14bbd095bdebd4c9eaee7a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"soHHXOTdOYvjOo76tFSRYc2jw6TEXqqT+wqy1MzelPyEv3jgNtNEyXLo/qRK+wokOexFa8Z5UXFjRuiTibdRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:49:03.327743Z","bundle_sha256":"cb87a15cb5bbaeea591f64d1a24e97504ffeee8b44e56ac99929b0f46aad7262"}}