{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:64MZQOVBIXRPZRXFLL34GAHTDV","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":"bbcbf043ffd6d9ebec6922da9e64e6115dc7fdc0461914ad73b00132fa0a6828","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-03-15T03:14:06Z","title_canon_sha256":"7527e39f3fe0de39664a460ab53fde58bddcdfa54f35c443dd209b85085753d7"},"schema_version":"1.0","source":{"id":"2503.11976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.11976","created_at":"2026-07-05T10:32:02Z"},{"alias_kind":"arxiv_version","alias_value":"2503.11976v1","created_at":"2026-07-05T10:32:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.11976","created_at":"2026-07-05T10:32:02Z"},{"alias_kind":"pith_short_12","alias_value":"64MZQOVBIXRP","created_at":"2026-07-05T10:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"64MZQOVBIXRPZRXF","created_at":"2026-07-05T10:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"64MZQOVB","created_at":"2026-07-05T10:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:6aef7743390a7b6c24017df3b80cde0fd6f02d3e86b297630e71f9795508f08f","target":"graph","created_at":"2026-07-05T10:32:02Z","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/2503.11976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we analyze the structure and relationships between magnitude homology and Eulerian magnitude homology of finite graphs. Building on the work of Kaneta and Yoshinaga, Sazdanovic and Summers, and Asao and Izumihara, we provide two proofs of the existence of torsion in Eulerian magnitude homology, offer insights into the types and orders of torsion, and present explicit computations for various classes of graphs.","authors_text":"Patrick Martin II, Radmila Sazdanovic","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-03-15T03:14:06Z","title":"Torsion in Magnitude homology theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.11976","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":"sha256:3709df6baccbc64956e7aa120071a7a804776124829d0a4ff6d2b9ba5c32c159","target":"record","created_at":"2026-07-05T10:32:02Z","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":"bbcbf043ffd6d9ebec6922da9e64e6115dc7fdc0461914ad73b00132fa0a6828","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-03-15T03:14:06Z","title_canon_sha256":"7527e39f3fe0de39664a460ab53fde58bddcdfa54f35c443dd209b85085753d7"},"schema_version":"1.0","source":{"id":"2503.11976","kind":"arxiv","version":1}},"canonical_sha256":"f719983aa145e2fcc6e55af7c300f31d517ff15d16d75a8077ebab81e5b058bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f719983aa145e2fcc6e55af7c300f31d517ff15d16d75a8077ebab81e5b058bc","first_computed_at":"2026-07-05T10:32:02.955931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:32:02.955931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5hQyTCXV3dQK3F54JMF+AcewK+MTwIyfO4a4eco0ytZErUPPBDh5h3Ndvn7enHrLs7NrCT6GJei1jBR9Uc5VDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:32:02.956777Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.11976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3709df6baccbc64956e7aa120071a7a804776124829d0a4ff6d2b9ba5c32c159","sha256:6aef7743390a7b6c24017df3b80cde0fd6f02d3e86b297630e71f9795508f08f"],"state_sha256":"40b799a4f6d2a4613e161f94c605bc14447b5eb297276be4e7845b743551266c"}