{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OJW27AA5OPFP4YTT4RWLGMHJ6Z","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":"c62ba5986569124daf529f2314f68015a258d6324883a9e11bf78064e8f51f87","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2021-12-13T09:41:32Z","title_canon_sha256":"407e7e8612e997ff7cab9d738cd3ea06d198c93ecfe10e65b04c9f8a4b9ec403"},"schema_version":"1.0","source":{"id":"2112.06509","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.06509","created_at":"2026-07-05T11:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"2112.06509v4","created_at":"2026-07-05T11:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06509","created_at":"2026-07-05T11:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"OJW27AA5OPFP","created_at":"2026-07-05T11:08:53Z"},{"alias_kind":"pith_short_16","alias_value":"OJW27AA5OPFP4YTT","created_at":"2026-07-05T11:08:53Z"},{"alias_kind":"pith_short_8","alias_value":"OJW27AA5","created_at":"2026-07-05T11:08:53Z"}],"graph_snapshots":[{"event_id":"sha256:a9fb40a37a299f717e6fd0d60b6600323b68d9b0541caf177394293f4422217b","target":"graph","created_at":"2026-07-05T11:08:53Z","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/2112.06509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization of the zeroth total multigraded Betti number. We give a fast algorithm for the computation of the shift-dimension of interval modules in the bivariate case. We construct multipersistence contours that are parameterized by multivariate functions and hence provide a large class of feature maps for machine learning tasks.","authors_text":"Anna-Laura Sattelberger, Ren\\'e Corbet, Wojciech Chach\\'olski","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2021-12-13T09:41:32Z","title":"The Shift-Dimension of Multipersistence Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06509","kind":"arxiv","version":4},"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:fce5a5f514d08828858399d6231d42506195a1a3f6ec55b7f1451b526b3d2d76","target":"record","created_at":"2026-07-05T11:08:53Z","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":"c62ba5986569124daf529f2314f68015a258d6324883a9e11bf78064e8f51f87","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2021-12-13T09:41:32Z","title_canon_sha256":"407e7e8612e997ff7cab9d738cd3ea06d198c93ecfe10e65b04c9f8a4b9ec403"},"schema_version":"1.0","source":{"id":"2112.06509","kind":"arxiv","version":4}},"canonical_sha256":"726daf801d73cafe6273e46cb330e9f65c336a7b86ca2a3adfe6132d5bb33fdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"726daf801d73cafe6273e46cb330e9f65c336a7b86ca2a3adfe6132d5bb33fdd","first_computed_at":"2026-07-05T11:08:53.479740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:08:53.479740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XXZ71OeOXRwVxQSitHYcpjdNd3TC+fhmmcNEYa7yHPHOHwLUg6mCod4PMOBq//2S0y3CucKBUNfk8LwhalI7AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:08:53.480206Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.06509","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fce5a5f514d08828858399d6231d42506195a1a3f6ec55b7f1451b526b3d2d76","sha256:a9fb40a37a299f717e6fd0d60b6600323b68d9b0541caf177394293f4422217b"],"state_sha256":"9d7fb12cef605f81e4b046422974443659b0a4a25f6caa71110478850f2c088d"}