{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NZHT6NRTDUYEXZEUHBSCZ5YHKM","short_pith_number":"pith:NZHT6NRT","canonical_record":{"source":{"id":"1506.07817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-17T01:00:05Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"6a970d0d22402d442423d3e23c6ec70d4a603396ac47f23477e95c37a837f174","abstract_canon_sha256":"6566e6cd2695b1f5d8c249f0347e8a436bdc3588e0e36fe7362fe415b52f44c3"},"schema_version":"1.0"},"canonical_sha256":"6e4f3f36331d304be49438642cf7075326198a990e53fad6a6f5e87bd6168541","source":{"kind":"arxiv","id":"1506.07817","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07817","created_at":"2026-05-18T01:38:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07817v1","created_at":"2026-05-18T01:38:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07817","created_at":"2026-05-18T01:38:50Z"},{"alias_kind":"pith_short_12","alias_value":"NZHT6NRTDUYE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZHT6NRTDUYEXZEU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZHT6NRT","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NZHT6NRTDUYEXZEUHBSCZ5YHKM","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-17T01:00:05Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"6a970d0d22402d442423d3e23c6ec70d4a603396ac47f23477e95c37a837f174","abstract_canon_sha256":"6566e6cd2695b1f5d8c249f0347e8a436bdc3588e0e36fe7362fe415b52f44c3"},"schema_version":"1.0"},"canonical_sha256":"6e4f3f36331d304be49438642cf7075326198a990e53fad6a6f5e87bd6168541","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:50.730445Z","signature_b64":"u0sonDi7YmYyPB9HXpY6MfcQbTIT9IEundnhGR4PbgjkUkxypv2PCh0p6J1rLXnKcUEucugLsxJqDw3AtB5BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e4f3f36331d304be49438642cf7075326198a990e53fad6a6f5e87bd6168541","last_reissued_at":"2026-05-18T01:38:50.729771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:50.729771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07817","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":"2026-05-18T01:38:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9/VBcnU30GAiOlL/dqg5U4k0In+WF577v4H5GWK3EcqNfH0DhObUmr5EczKMGpI3DigJtZQ65syeGTc28WyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:04:10.858075Z"},"content_sha256":"fb9169717cef80eb8391fefbd7acfc5e3ced4a0530cde577692eae45c753e3d4","schema_version":"1.0","event_id":"sha256:fb9169717cef80eb8391fefbd7acfc5e3ced4a0530cde577692eae45c753e3d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NZHT6NRTDUYEXZEUHBSCZ5YHKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the spectra of strong power graphs of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CO","authors_text":"Xuanlong Ma","submitted_at":"2015-06-17T01:00:05Z","abstract_excerpt":"We give the characteristic polynomial of the distance or adjacency matrix of the strong power graph of a finite group, and compute its distance and adjacency spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07817","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":"2026-05-18T01:38:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8UpMo/ZF5MV2pt2Ov8XVEFWiSyHKPHBJ9whdoETubJutDXWWjAPcFl0gAEQLLoC9sYPe1rL43vomcIpHwA6kAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:04:10.858438Z"},"content_sha256":"aca0a0e97f134b433b247aa6b3630d2fc8f7a4fa7b294f8111b1903f9e4f6f15","schema_version":"1.0","event_id":"sha256:aca0a0e97f134b433b247aa6b3630d2fc8f7a4fa7b294f8111b1903f9e4f6f15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM/bundle.json","state_url":"https://pith.science/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM/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":"2026-06-04T19:04:10Z","links":{"resolver":"https://pith.science/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM","bundle":"https://pith.science/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM/bundle.json","state":"https://pith.science/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZHT6NRTDUYEXZEUHBSCZ5YHKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NZHT6NRTDUYEXZEUHBSCZ5YHKM","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":"6566e6cd2695b1f5d8c249f0347e8a436bdc3588e0e36fe7362fe415b52f44c3","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-17T01:00:05Z","title_canon_sha256":"6a970d0d22402d442423d3e23c6ec70d4a603396ac47f23477e95c37a837f174"},"schema_version":"1.0","source":{"id":"1506.07817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07817","created_at":"2026-05-18T01:38:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07817v1","created_at":"2026-05-18T01:38:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07817","created_at":"2026-05-18T01:38:50Z"},{"alias_kind":"pith_short_12","alias_value":"NZHT6NRTDUYE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZHT6NRTDUYEXZEU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZHT6NRT","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:aca0a0e97f134b433b247aa6b3630d2fc8f7a4fa7b294f8111b1903f9e4f6f15","target":"graph","created_at":"2026-05-18T01:38:50Z","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 give the characteristic polynomial of the distance or adjacency matrix of the strong power graph of a finite group, and compute its distance and adjacency spectrum.","authors_text":"Xuanlong Ma","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-17T01:00:05Z","title":"On the spectra of strong power graphs of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07817","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:fb9169717cef80eb8391fefbd7acfc5e3ced4a0530cde577692eae45c753e3d4","target":"record","created_at":"2026-05-18T01:38:50Z","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":"6566e6cd2695b1f5d8c249f0347e8a436bdc3588e0e36fe7362fe415b52f44c3","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-17T01:00:05Z","title_canon_sha256":"6a970d0d22402d442423d3e23c6ec70d4a603396ac47f23477e95c37a837f174"},"schema_version":"1.0","source":{"id":"1506.07817","kind":"arxiv","version":1}},"canonical_sha256":"6e4f3f36331d304be49438642cf7075326198a990e53fad6a6f5e87bd6168541","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e4f3f36331d304be49438642cf7075326198a990e53fad6a6f5e87bd6168541","first_computed_at":"2026-05-18T01:38:50.729771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:50.729771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0sonDi7YmYyPB9HXpY6MfcQbTIT9IEundnhGR4PbgjkUkxypv2PCh0p6J1rLXnKcUEucugLsxJqDw3AtB5BDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:50.730445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb9169717cef80eb8391fefbd7acfc5e3ced4a0530cde577692eae45c753e3d4","sha256:aca0a0e97f134b433b247aa6b3630d2fc8f7a4fa7b294f8111b1903f9e4f6f15"],"state_sha256":"05c54afbc498553e9bcec9c7d70b62d212027be3767f9935f62da06d96f16150"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZIkDAOjhRN5ERxjRCqGjhkMqjJwzFj6ERCgAzDeZ70sT6XV76DDs+0KPQnKIOudfczmXb/ENAImkb1t/HHJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:04:10.860401Z","bundle_sha256":"79704c9748d1f4829d8fe2b2f1b87613fdb530f9bbb573b3da331db3c3f49e77"}}