{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7M5ZR7ZGSAYDZL5XG4FTL2GW6D","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":"31c7d7a2312dba6c8a50a9bd178a98c51c7d6c04ce3ec250c7f98ebebfb4cae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-06-05T17:09:06Z","title_canon_sha256":"c8da8c0f52abeab053a21f12116a75395d35c22414c48dcc703174bb376b40c2"},"schema_version":"1.0","source":{"id":"2506.05248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05248","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05248v1","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05248","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"7M5ZR7ZGSAYD","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_16","alias_value":"7M5ZR7ZGSAYDZL5X","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_8","alias_value":"7M5ZR7ZG","created_at":"2026-07-05T11:16:44Z"}],"graph_snapshots":[{"event_id":"sha256:8fb7c88aea529cd1ebe07ed84f6fd9ce313693372cf9b5b82320106747f80663","target":"graph","created_at":"2026-07-05T11:16:44Z","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/2506.05248/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We express multiplicities and degree functions of graded families of $\\mathfrak{m}_R$-primary ideals in an excellent normal local ring $(R,\\mathfrak{m}_R)$ as limits of intersection products. Moreover, in dimension 2, we show more refined results for divisorial filtrations. Finally, also in dimension 2, we give an example of a non-Noetherian divisorial filtration $\\{I_n\\}_{n\\geqslant 0}$ of $\\mathfrak{m}_R$-primary ideals such that the union of all the sets of Rees valuations of all the $I_n$ is a finite set, and another example of a (necessarily non-Noetherian) divisorial filtration of $\\math","authors_text":"Jonathan Monta\\~no, Steven Dale Cutkosky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-06-05T17:09:06Z","title":"Degree functions of graded families of ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05248","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":"sha256:650da94ff65865ed3508f564028aa5b62a3e56f3296207bbaf42eaf1fa3ec38d","target":"record","created_at":"2026-07-05T11:16:44Z","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":"31c7d7a2312dba6c8a50a9bd178a98c51c7d6c04ce3ec250c7f98ebebfb4cae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-06-05T17:09:06Z","title_canon_sha256":"c8da8c0f52abeab053a21f12116a75395d35c22414c48dcc703174bb376b40c2"},"schema_version":"1.0","source":{"id":"2506.05248","kind":"arxiv","version":1}},"canonical_sha256":"fb3b98ff2690303cafb7370b35e8d6f0d61192c6d654610bf43edb8c72a43c83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb3b98ff2690303cafb7370b35e8d6f0d61192c6d654610bf43edb8c72a43c83","first_computed_at":"2026-07-05T11:16:44.732806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:44.732806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Cj5P7c/X/4Xeosq9epxNCIQBDlDSEwfj+VtcIqfAID8jTHSI8StcNgoMlfr8vFD9jR8lXX6KjiZkEWay5VuAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:44.733356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:650da94ff65865ed3508f564028aa5b62a3e56f3296207bbaf42eaf1fa3ec38d","sha256:8fb7c88aea529cd1ebe07ed84f6fd9ce313693372cf9b5b82320106747f80663"],"state_sha256":"799354015a7514e324436a74b9c478748b1fcccb76e63248309b2d8dfbc8c9fc"}