{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EHPA3MP2B5ORRUY4I26REU6TOM","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"78fe9bfe4464df5d51d7404680b818ad328862d33e1c1740b9688e1f65e25879","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-07-11T18:58:45Z","title_canon_sha256":"b56d823942170eea3770d3d0524215da13653822b84719dba400bf283f7ac403"},"schema_version":"1.0","source":{"id":"2607.10442","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10442","created_at":"2026-07-14T01:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10442v1","created_at":"2026-07-14T01:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10442","created_at":"2026-07-14T01:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"EHPA3MP2B5OR","created_at":"2026-07-14T01:21:16Z"},{"alias_kind":"pith_short_16","alias_value":"EHPA3MP2B5ORRUY4","created_at":"2026-07-14T01:21:16Z"},{"alias_kind":"pith_short_8","alias_value":"EHPA3MP2","created_at":"2026-07-14T01:21:16Z"}],"graph_snapshots":[{"event_id":"sha256:c16f562d74980ebbd1720a543c1df0493f53d04eea5940f9415571c486b443ae","target":"graph","created_at":"2026-07-14T01:21:16Z","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/2607.10442/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graphs that change over time arise throughout applications, but there is no single standard way to decompose them into smaller pieces. In this paper, we propose a systematic categorical method for doing so. The main idea is to combine structured decompositions, which generalize graph decompositions, such as tree-decompositions, with persistent narratives, which model time-varying data as diagrams. We prove that, under suitable categorical hypotheses, any static theory of decompositions can be lifted to a corresponding temporal theory. As case studies, we apply this construction to time-varying","authors_text":"Benjamin Merlin Bumpus, Jana K. Nickel","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-07-11T18:58:45Z","title":"Decomposing time-varying data into simple pieces: structured decompositions of narratives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10442","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:f742ec30d68879252a5bfec6e7fd518cadc08a69ecfc293859adf9c3e3ff5886","target":"record","created_at":"2026-07-14T01:21:16Z","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":"78fe9bfe4464df5d51d7404680b818ad328862d33e1c1740b9688e1f65e25879","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-07-11T18:58:45Z","title_canon_sha256":"b56d823942170eea3770d3d0524215da13653822b84719dba400bf283f7ac403"},"schema_version":"1.0","source":{"id":"2607.10442","kind":"arxiv","version":1}},"canonical_sha256":"21de0db1fa0f5d18d31c46bd1253d3731b7fb6528952d9c052caaf2260f82ff3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21de0db1fa0f5d18d31c46bd1253d3731b7fb6528952d9c052caaf2260f82ff3","first_computed_at":"2026-07-14T01:21:16.142679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:21:16.142679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ld+XWutP0NYZwaNJ/2viuLclheoNRROHcpU7G+7Rl6wtteEFB18hl0kVgZDf7ohFtwBahKKM1yqPmGrzMUQDA==","signature_status":"signed_v1","signed_at":"2026-07-14T01:21:16.143482Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10442","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f742ec30d68879252a5bfec6e7fd518cadc08a69ecfc293859adf9c3e3ff5886","sha256:c16f562d74980ebbd1720a543c1df0493f53d04eea5940f9415571c486b443ae","sha256:b5ba164d0acac064b6de99948b1cd503fc1cab3c650f4428a0a7bf34bb410c9a"],"state_sha256":"3f5757305bcd8fcdcea534b7343d5d9c4416189e05bc2b7b7394c83980ae6765"}