{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2ZNN2M4TATN55P3WTAOHPRKWDR","short_pith_number":"pith:2ZNN2M4T","canonical_record":{"source":{"id":"2506.07343","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-06-09T01:34:30Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"fc3296734a30cb4a24451ecbc1a3e430e7e54e9d2f6da93cd760eb018447a9d8","abstract_canon_sha256":"7b73dde7ed9667fe71a683476ed01f064cc70f0db9bf922df909b22a7020388e"},"schema_version":"1.0"},"canonical_sha256":"d65add339304dbdebf76981c77c5561c56a863129c7bc5e11645e46ae2e33c18","source":{"kind":"arxiv","id":"2506.07343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07343","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07343v1","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07343","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"2ZNN2M4TATN5","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"2ZNN2M4TATN55P3W","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"2ZNN2M4T","created_at":"2026-07-05T11:18:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2ZNN2M4TATN55P3WTAOHPRKWDR","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07343","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-06-09T01:34:30Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"fc3296734a30cb4a24451ecbc1a3e430e7e54e9d2f6da93cd760eb018447a9d8","abstract_canon_sha256":"7b73dde7ed9667fe71a683476ed01f064cc70f0db9bf922df909b22a7020388e"},"schema_version":"1.0"},"canonical_sha256":"d65add339304dbdebf76981c77c5561c56a863129c7bc5e11645e46ae2e33c18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:25.389472Z","signature_b64":"hxOUOMmOIOf59XsI1bVyxk3CBDEhNcTPQ9UafksXbG81cYKC5f970DvCGph1p9ky7sVelJgoJpzqCUSjg7OIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d65add339304dbdebf76981c77c5561c56a863129c7bc5e11645e46ae2e33c18","last_reissued_at":"2026-07-05T11:18:25.388951Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:25.388951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07343","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":"2026-07-05T11:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61kL1PDR5II4bLh0bhOWtz74YGGFUM0oG0ioplAFvgurwDdCBYTfYy85UXYukYR+t9vvm8GLYhZxH8SHjkUsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:08:41.663901Z"},"content_sha256":"b3d47d70580bd9ee04898d51a5db0ca87701fc883d31ef92faa13a48f039cb51","schema_version":"1.0","event_id":"sha256:b3d47d70580bd9ee04898d51a5db0ca87701fc883d31ef92faa13a48f039cb51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2ZNN2M4TATN55P3WTAOHPRKWDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Powers of Magnetic Graph Matrix: Fourier Spectrum, Walk Compression, and Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"David F. Gleich, Pan Li, Yinan Huang","submitted_at":"2025-06-09T01:34:30Z","abstract_excerpt":"Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, non-equilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a novel combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles -- counts of graph walks indexed by the numb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07343","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/2506.07343/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":"2026-07-05T11:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ts54oxTsRHvx02/wehva9+28PPHIyumZJtCkz8K0dve1wS8NLpX0WD4j9jDJvwqGpiMoxL+v/Yoz5KcaWyoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:08:41.664460Z"},"content_sha256":"f79b26dfcfee25af52aacf73e7d5008dda5451c6c94bb0eba7280a465205bf06","schema_version":"1.0","event_id":"sha256:f79b26dfcfee25af52aacf73e7d5008dda5451c6c94bb0eba7280a465205bf06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZNN2M4TATN55P3WTAOHPRKWDR/bundle.json","state_url":"https://pith.science/pith/2ZNN2M4TATN55P3WTAOHPRKWDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZNN2M4TATN55P3WTAOHPRKWDR/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":"2026-08-08T04:08:41Z","links":{"resolver":"https://pith.science/pith/2ZNN2M4TATN55P3WTAOHPRKWDR","bundle":"https://pith.science/pith/2ZNN2M4TATN55P3WTAOHPRKWDR/bundle.json","state":"https://pith.science/pith/2ZNN2M4TATN55P3WTAOHPRKWDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZNN2M4TATN55P3WTAOHPRKWDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2ZNN2M4TATN55P3WTAOHPRKWDR","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":"7b73dde7ed9667fe71a683476ed01f064cc70f0db9bf922df909b22a7020388e","cross_cats_sorted":["cs.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-06-09T01:34:30Z","title_canon_sha256":"fc3296734a30cb4a24451ecbc1a3e430e7e54e9d2f6da93cd760eb018447a9d8"},"schema_version":"1.0","source":{"id":"2506.07343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07343","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07343v1","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07343","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"2ZNN2M4TATN5","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"2ZNN2M4TATN55P3W","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"2ZNN2M4T","created_at":"2026-07-05T11:18:25Z"}],"graph_snapshots":[{"event_id":"sha256:f79b26dfcfee25af52aacf73e7d5008dda5451c6c94bb0eba7280a465205bf06","target":"graph","created_at":"2026-07-05T11:18:25Z","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/2506.07343/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, non-equilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a novel combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles -- counts of graph walks indexed by the numb","authors_text":"David F. Gleich, Pan Li, Yinan Huang","cross_cats":["cs.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-06-09T01:34:30Z","title":"Powers of Magnetic Graph Matrix: Fourier Spectrum, Walk Compression, and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07343","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:b3d47d70580bd9ee04898d51a5db0ca87701fc883d31ef92faa13a48f039cb51","target":"record","created_at":"2026-07-05T11:18:25Z","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":"7b73dde7ed9667fe71a683476ed01f064cc70f0db9bf922df909b22a7020388e","cross_cats_sorted":["cs.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-06-09T01:34:30Z","title_canon_sha256":"fc3296734a30cb4a24451ecbc1a3e430e7e54e9d2f6da93cd760eb018447a9d8"},"schema_version":"1.0","source":{"id":"2506.07343","kind":"arxiv","version":1}},"canonical_sha256":"d65add339304dbdebf76981c77c5561c56a863129c7bc5e11645e46ae2e33c18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d65add339304dbdebf76981c77c5561c56a863129c7bc5e11645e46ae2e33c18","first_computed_at":"2026-07-05T11:18:25.388951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:25.388951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hxOUOMmOIOf59XsI1bVyxk3CBDEhNcTPQ9UafksXbG81cYKC5f970DvCGph1p9ky7sVelJgoJpzqCUSjg7OIDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:25.389472Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3d47d70580bd9ee04898d51a5db0ca87701fc883d31ef92faa13a48f039cb51","sha256:f79b26dfcfee25af52aacf73e7d5008dda5451c6c94bb0eba7280a465205bf06"],"state_sha256":"472b7d1940b23ac40fb24173d32d0d6fc3e994df0da713f8478874fb8a10597e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFApSy+7e5aZo7aQPrfBdgnvxmw0TG6w0SAhPu0JzIyH2KDssyfOmFkwVIwkxqRIJ5pBK/Qn1glbB+h9qZCvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:08:41.669367Z","bundle_sha256":"b280fa4e2e7334a8d6c67dd2427e448fb42f908a7afc904f06998b2c6aa361c4"}}