{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VV7G4AZXUD6K7OJYDFYFEYDBKH","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":"6798030ae684f0b4fb23d7c1a504133a045aadb68435a4117e37cc4801fc0b45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-07T11:38:50Z","title_canon_sha256":"cf70dcce217b603c4409ac5a181a150a3bafb0a3340edc09c3818ff9aacd4622"},"schema_version":"1.0","source":{"id":"1205.1348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1348","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1348v1","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1348","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"VV7G4AZXUD6K","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VV7G4AZXUD6K7OJY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VV7G4AZX","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:9743d38363cc00e745b034b63b3f63ab79ea25f8fb9b73693f128089509a9c97","target":"graph","created_at":"2026-05-18T01:57:37Z","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"},"paper":{"abstract_excerpt":"We construct monomial ideals with the property that their depth function has any given number of strict local maxima.","authors_text":"J\\\"urgen Herzog, Somayeh Bandari, Takayuki Hibi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-07T11:38:50Z","title":"Monomial ideals whose depth function has any given number of strict local maxima"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1348","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":"sha256:45ca227c3be9986c18bd586cb66970ea964990706680baa3d1007e6078d191f8","target":"record","created_at":"2026-05-18T01:57:37Z","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":"6798030ae684f0b4fb23d7c1a504133a045aadb68435a4117e37cc4801fc0b45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-07T11:38:50Z","title_canon_sha256":"cf70dcce217b603c4409ac5a181a150a3bafb0a3340edc09c3818ff9aacd4622"},"schema_version":"1.0","source":{"id":"1205.1348","kind":"arxiv","version":1}},"canonical_sha256":"ad7e6e0337a0fcafb938197052606151e2a718dbb408d04c55142927a7627bdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad7e6e0337a0fcafb938197052606151e2a718dbb408d04c55142927a7627bdc","first_computed_at":"2026-05-18T01:57:37.422562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:37.422562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zjVHsdiRjEK+9vYDXnolNbpaiuM9VlKgLZrDqE4dufW9Jdpbg9RwrTskyLiGW2xtnxH93lWkgzp5bL4OESFEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:37.423196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45ca227c3be9986c18bd586cb66970ea964990706680baa3d1007e6078d191f8","sha256:9743d38363cc00e745b034b63b3f63ab79ea25f8fb9b73693f128089509a9c97"],"state_sha256":"4b3f6b7c760f344f3ec8f788702296c0c602fd1fad6a78edacdd0f0b921ad195"}