{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LCK5LB2VBQHS4JP2TLFPRASO77","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":"9c95b66b8e5f4237d35dd84969a9b9a096fe76dd8033f7d359ea711a3e8b14fd","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-26T13:18:43Z","title_canon_sha256":"bab43dc46b46b4a260f82d28b6c04ba4dd58ca5a3dc6ee69a8bb4fe912173f45"},"schema_version":"1.0","source":{"id":"2506.21227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21227","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21227v1","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21227","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"LCK5LB2VBQHS","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"pith_short_16","alias_value":"LCK5LB2VBQHS4JP2","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"pith_short_8","alias_value":"LCK5LB2V","created_at":"2026-07-05T11:27:41Z"}],"graph_snapshots":[{"event_id":"sha256:1710fa8ba113e2756e4f3238bf10cf375f76669e6d891e3d81330ad1cd2fb86e","target":"graph","created_at":"2026-07-05T11:27:41Z","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/2506.21227/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the adjoint quadruple between the categories of persistence modules (representations) of the posets via Kan extensions. One of central subjects in multiparameter persistent homology analysis is to understand structures of persistence modules. In this paper, we mainly study a class of Galois connections whose left adjoint is the canonical inclusion of a full subposet. We refer to such a subposet as an interior system, with ","authors_text":"Shunsuke Tada, Toshitaka Aoki","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-26T13:18:43Z","title":"On preservation of relative resolutions for poset representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21227","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":"sha256:310b175e4af2acd82ea81e2bc981026067cc88c36788a96666683ba70384f8ea","target":"record","created_at":"2026-07-05T11:27:41Z","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":"9c95b66b8e5f4237d35dd84969a9b9a096fe76dd8033f7d359ea711a3e8b14fd","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-26T13:18:43Z","title_canon_sha256":"bab43dc46b46b4a260f82d28b6c04ba4dd58ca5a3dc6ee69a8bb4fe912173f45"},"schema_version":"1.0","source":{"id":"2506.21227","kind":"arxiv","version":1}},"canonical_sha256":"5895d587550c0f2e25fa9acaf8824effe8d1ef6cd1e2c2b58e142262673e4063","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5895d587550c0f2e25fa9acaf8824effe8d1ef6cd1e2c2b58e142262673e4063","first_computed_at":"2026-07-05T11:27:41.868014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:41.868014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PhVVgfz88yji36d5J2Xf2KORr87+y4iFJ33tz+dLPB59K31Oi1cze30RR2SrUNmuFDrRf06phMK/f32hYPPpCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:41.868563Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.21227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:310b175e4af2acd82ea81e2bc981026067cc88c36788a96666683ba70384f8ea","sha256:1710fa8ba113e2756e4f3238bf10cf375f76669e6d891e3d81330ad1cd2fb86e"],"state_sha256":"a8c0d9b7b3f11d44f843c3e8f78b65549b898c6f82c6a62462c62537dcbcc7bf"}