{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LCK5LB2VBQHS4JP2TLFPRASO77","short_pith_number":"pith:LCK5LB2V","canonical_record":{"source":{"id":"2506.21227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-26T13:18:43Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"bab43dc46b46b4a260f82d28b6c04ba4dd58ca5a3dc6ee69a8bb4fe912173f45","abstract_canon_sha256":"9c95b66b8e5f4237d35dd84969a9b9a096fe76dd8033f7d359ea711a3e8b14fd"},"schema_version":"1.0"},"canonical_sha256":"5895d587550c0f2e25fa9acaf8824effe8d1ef6cd1e2c2b58e142262673e4063","source":{"kind":"arxiv","id":"2506.21227","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LCK5LB2VBQHS4JP2TLFPRASO77","target":"record","payload":{"canonical_record":{"source":{"id":"2506.21227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-26T13:18:43Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"bab43dc46b46b4a260f82d28b6c04ba4dd58ca5a3dc6ee69a8bb4fe912173f45","abstract_canon_sha256":"9c95b66b8e5f4237d35dd84969a9b9a096fe76dd8033f7d359ea711a3e8b14fd"},"schema_version":"1.0"},"canonical_sha256":"5895d587550c0f2e25fa9acaf8824effe8d1ef6cd1e2c2b58e142262673e4063","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:27:41.868563Z","signature_b64":"PhVVgfz88yji36d5J2Xf2KORr87+y4iFJ33tz+dLPB59K31Oi1cze30RR2SrUNmuFDrRf06phMK/f32hYPPpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5895d587550c0f2e25fa9acaf8824effe8d1ef6cd1e2c2b58e142262673e4063","last_reissued_at":"2026-07-05T11:27:41.868014Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:27:41.868014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.21227","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":"2026-07-05T11:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+hL7PWsvVc70wTAuJnRT4GicmeD7DqRPJb6TC+u6oWiXKfSinE/gBgnFtYeNL5rAGkAnqJMQvO6xvHvvacRnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:30:17.629878Z"},"content_sha256":"310b175e4af2acd82ea81e2bc981026067cc88c36788a96666683ba70384f8ea","schema_version":"1.0","event_id":"sha256:310b175e4af2acd82ea81e2bc981026067cc88c36788a96666683ba70384f8ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LCK5LB2VBQHS4JP2TLFPRASO77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On preservation of relative resolutions for poset representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.RT","authors_text":"Shunsuke Tada, Toshitaka Aoki","submitted_at":"2025-06-26T13:18:43Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21227","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/2506.21227/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":"2026-07-05T11:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyb1ICXty2KKMbZPetLNDN1qXZKbvJf54UrYhVWqTtCXN5OrLogDPozRBjS7Hz7zjbNPPjuUy6vbH/Q7exLIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:30:17.630783Z"},"content_sha256":"1710fa8ba113e2756e4f3238bf10cf375f76669e6d891e3d81330ad1cd2fb86e","schema_version":"1.0","event_id":"sha256:1710fa8ba113e2756e4f3238bf10cf375f76669e6d891e3d81330ad1cd2fb86e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCK5LB2VBQHS4JP2TLFPRASO77/bundle.json","state_url":"https://pith.science/pith/LCK5LB2VBQHS4JP2TLFPRASO77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCK5LB2VBQHS4JP2TLFPRASO77/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":"2026-08-09T03:30:17Z","links":{"resolver":"https://pith.science/pith/LCK5LB2VBQHS4JP2TLFPRASO77","bundle":"https://pith.science/pith/LCK5LB2VBQHS4JP2TLFPRASO77/bundle.json","state":"https://pith.science/pith/LCK5LB2VBQHS4JP2TLFPRASO77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCK5LB2VBQHS4JP2TLFPRASO77/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OmS4JgnAhzMG4wePhumx5d74hCUk/60dF9wnFUzYWnqqh/WhY7btdQomYQWZMrEWcLgziBeoVxmUsoCVqCIDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:30:17.636021Z","bundle_sha256":"3a2f6f08d76fa0576812d774c5ea88028d60879f16de0b8c80964178e5d71d84"}}