{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LX3H7OZNXOQGUYUV3GROEXN5TQ","short_pith_number":"pith:LX3H7OZN","canonical_record":{"source":{"id":"2505.12446","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-18T14:37:28Z","cross_cats_sorted":[],"title_canon_sha256":"fc62aafe5fffe4c6be257bd52a7e37f2b2b971f5f0021f79d0e0af2428a4a94d","abstract_canon_sha256":"e5240da21dd6eb3cbf0dcfa0ed9e63fb3bfa05b59321a4547ebc33bda42c0072"},"schema_version":"1.0"},"canonical_sha256":"5df67fbb2dbba06a6295d9a2e25dbd9c0e4373ccd131c519360711461cce44bd","source":{"kind":"arxiv","id":"2505.12446","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12446","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12446v1","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12446","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"LX3H7OZNXOQG","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"LX3H7OZNXOQGUYUV","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"LX3H7OZN","created_at":"2026-07-05T11:05:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LX3H7OZNXOQGUYUV3GROEXN5TQ","target":"record","payload":{"canonical_record":{"source":{"id":"2505.12446","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-18T14:37:28Z","cross_cats_sorted":[],"title_canon_sha256":"fc62aafe5fffe4c6be257bd52a7e37f2b2b971f5f0021f79d0e0af2428a4a94d","abstract_canon_sha256":"e5240da21dd6eb3cbf0dcfa0ed9e63fb3bfa05b59321a4547ebc33bda42c0072"},"schema_version":"1.0"},"canonical_sha256":"5df67fbb2dbba06a6295d9a2e25dbd9c0e4373ccd131c519360711461cce44bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:04.445824Z","signature_b64":"21wRclKxdrgLmwdKqPN5Ttff72YQov14Gp4CR1CXEfvRSmjXM6F7mNBwiWW+wAo0EQJVv/iEuh7juerx7OvRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5df67fbb2dbba06a6295d9a2e25dbd9c0e4373ccd131c519360711461cce44bd","last_reissued_at":"2026-07-05T11:05:04.445330Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:04.445330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.12446","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":"2026-07-05T11:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xpl9h+0kPunb1rlaz5NYFNXMRbbNLELsWDVnLyVAmZ6O2FaDbu/lQUxFcpzOMsjNcRObe4xjk0qjSoNyziIPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T13:28:35.610194Z"},"content_sha256":"633af4327fe00656951085933fee9950daec81837ff8513561caeadd348131fe","schema_version":"1.0","event_id":"sha256:633af4327fe00656951085933fee9950daec81837ff8513561caeadd348131fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LX3H7OZNXOQGUYUV3GROEXN5TQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized spectral characterization of signed bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lele Li, Songlin Guo, Wei Wang","submitted_at":"2025-05-18T14:37:28Z","abstract_excerpt":"Let $\\Sigma$ be an $n$-vertex controllable or almost controllable signed bipartite graph, and let $\\Delta_\\Sigma$ denote the discriminant of its characteristic polynomial $\\chi(\\Sigma; x)$. We prove that if (\\rmnum{1}) the integer $2^{ -\\lfloor n/2 \\rfloor }\\sqrt{\\Delta _{\\Sigma}}$ is squarefree, and (\\rmnum{2}) the constant term (even $n$) or linear coefficient (odd $n$) of $\\chi(\\Sigma; x)$ is $\\pm 1$, then $\\Sigma$ is determined by its generalized spectrum. This result extends a recent theorem of Ji, Wang, and Zhang [Electron. J. Combin. 32 (2025), \\#P2.18], which established a similar crit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12446","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/2505.12446/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":"2026-07-05T11:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPBWidACMwfq5j6K6r/VYfxOCWQPv4szYm7DxZCrNeuge/XsQAciJl4HqSjJb8ylxLaqePx54BPwAF5Hq+oyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T13:28:35.611088Z"},"content_sha256":"c5978a1e1b772b0fb461081153a32dacd1298754443337ea697abbc7b1874ce2","schema_version":"1.0","event_id":"sha256:c5978a1e1b772b0fb461081153a32dacd1298754443337ea697abbc7b1874ce2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ/bundle.json","state_url":"https://pith.science/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ/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":"2026-08-22T13:28:35Z","links":{"resolver":"https://pith.science/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ","bundle":"https://pith.science/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ/bundle.json","state":"https://pith.science/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LX3H7OZNXOQGUYUV3GROEXN5TQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LX3H7OZNXOQGUYUV3GROEXN5TQ","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":"e5240da21dd6eb3cbf0dcfa0ed9e63fb3bfa05b59321a4547ebc33bda42c0072","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-18T14:37:28Z","title_canon_sha256":"fc62aafe5fffe4c6be257bd52a7e37f2b2b971f5f0021f79d0e0af2428a4a94d"},"schema_version":"1.0","source":{"id":"2505.12446","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12446","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12446v1","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12446","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"LX3H7OZNXOQG","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"LX3H7OZNXOQGUYUV","created_at":"2026-07-05T11:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"LX3H7OZN","created_at":"2026-07-05T11:05:04Z"}],"graph_snapshots":[{"event_id":"sha256:c5978a1e1b772b0fb461081153a32dacd1298754443337ea697abbc7b1874ce2","target":"graph","created_at":"2026-07-05T11:05:04Z","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/2505.12446/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Sigma$ be an $n$-vertex controllable or almost controllable signed bipartite graph, and let $\\Delta_\\Sigma$ denote the discriminant of its characteristic polynomial $\\chi(\\Sigma; x)$. We prove that if (\\rmnum{1}) the integer $2^{ -\\lfloor n/2 \\rfloor }\\sqrt{\\Delta _{\\Sigma}}$ is squarefree, and (\\rmnum{2}) the constant term (even $n$) or linear coefficient (odd $n$) of $\\chi(\\Sigma; x)$ is $\\pm 1$, then $\\Sigma$ is determined by its generalized spectrum. This result extends a recent theorem of Ji, Wang, and Zhang [Electron. J. Combin. 32 (2025), \\#P2.18], which established a similar crit","authors_text":"Lele Li, Songlin Guo, Wei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-18T14:37:28Z","title":"Generalized spectral characterization of signed bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12446","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":"sha256:633af4327fe00656951085933fee9950daec81837ff8513561caeadd348131fe","target":"record","created_at":"2026-07-05T11:05:04Z","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":"e5240da21dd6eb3cbf0dcfa0ed9e63fb3bfa05b59321a4547ebc33bda42c0072","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-18T14:37:28Z","title_canon_sha256":"fc62aafe5fffe4c6be257bd52a7e37f2b2b971f5f0021f79d0e0af2428a4a94d"},"schema_version":"1.0","source":{"id":"2505.12446","kind":"arxiv","version":1}},"canonical_sha256":"5df67fbb2dbba06a6295d9a2e25dbd9c0e4373ccd131c519360711461cce44bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df67fbb2dbba06a6295d9a2e25dbd9c0e4373ccd131c519360711461cce44bd","first_computed_at":"2026-07-05T11:05:04.445330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:04.445330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"21wRclKxdrgLmwdKqPN5Ttff72YQov14Gp4CR1CXEfvRSmjXM6F7mNBwiWW+wAo0EQJVv/iEuh7juerx7OvRAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:04.445824Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.12446","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:633af4327fe00656951085933fee9950daec81837ff8513561caeadd348131fe","sha256:c5978a1e1b772b0fb461081153a32dacd1298754443337ea697abbc7b1874ce2"],"state_sha256":"a1f09100ad48c1c2046b90186e896291ea4086682baf0552d3b7e0d4fcbdb79d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TF9xiGnuocjRpyLHA2bpzPX6LXTPFF9PyEKCLssjRyhxmy2PxRhbE+vCYY1CCFGO1k55H/bHyQY42yaL3tG9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T13:28:35.617044Z","bundle_sha256":"4c1367403aefd60ad1e62be5c08cf72d6754e8a4dbdcc4f207874a610d121bf6"}}