{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BJOVIYKO5Q4XJO35HGGRILGF4Y","short_pith_number":"pith:BJOVIYKO","canonical_record":{"source":{"id":"1307.8292","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-07-31T11:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"3bf9e1f58aab63926ab7507023ff533777ab3818a5a7098edd932615b1791e14","abstract_canon_sha256":"f112e7ed26b99940296f855be9b2c084642090f60eb2c40fd4f3edc49db90564"},"schema_version":"1.0"},"canonical_sha256":"0a5d54614eec3974bb7d398d142cc5e6100961f15a1f4960c8e026ba7b05e852","source":{"kind":"arxiv","id":"1307.8292","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8292","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8292v6","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8292","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"BJOVIYKO5Q4X","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJOVIYKO5Q4XJO35","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJOVIYKO","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BJOVIYKO5Q4XJO35HGGRILGF4Y","target":"record","payload":{"canonical_record":{"source":{"id":"1307.8292","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-07-31T11:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"3bf9e1f58aab63926ab7507023ff533777ab3818a5a7098edd932615b1791e14","abstract_canon_sha256":"f112e7ed26b99940296f855be9b2c084642090f60eb2c40fd4f3edc49db90564"},"schema_version":"1.0"},"canonical_sha256":"0a5d54614eec3974bb7d398d142cc5e6100961f15a1f4960c8e026ba7b05e852","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:58.306040Z","signature_b64":"px9mBWwMys4od2Gu2cQdk5Ju2zdOriBWyW34XQsf5p1Ceo1iglFGjs7MRTVfV1xaAXM/gM3QlAsWI08VvMDSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a5d54614eec3974bb7d398d142cc5e6100961f15a1f4960c8e026ba7b05e852","last_reissued_at":"2026-05-18T02:45:58.305442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:58.305442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.8292","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRtTgNEmdPrw5VYu+txVmgHyxtdPpHv+I9pPNIOy5rstitDWdHgcupAQcOXtVrTXATJZBIc8BX5Epj6F9G2CBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:11:35.442577Z"},"content_sha256":"53b59aafe4ae193c88d909aa6cd3804fa3838a3675ac44db4c2219f3cb8a68c4","schema_version":"1.0","event_id":"sha256:53b59aafe4ae193c88d909aa6cd3804fa3838a3675ac44db4c2219f3cb8a68c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BJOVIYKO5Q4XJO35HGGRILGF4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three generated, squarefree, monomial ideals","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrei Zarojanu, Dorin Popescu","submitted_at":"2013-07-31T11:46:39Z","abstract_excerpt":"Let $I\\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\\geq d$, resp. $\\geq d+1$ . Suppose that $I$ is generated by three monomials of degrees $d$. If the Stanley depth of $I/J$ is $\\leq d+1$ then the usual depth of $I/J$ is $\\leq d+1$ too."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8292","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lSyHR5oMVugzIJeljlf4FifNfgnLgE9qLRKi8e5u3dU4BqIGzsLVRcXIDxowTv7PdYa2yh50tmO6fubfcxzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:11:35.442967Z"},"content_sha256":"47ef4bf0c5c5f7a9bb7de08167cfafadb5a98d076f4c2a1051bedf5e260dd69e","schema_version":"1.0","event_id":"sha256:47ef4bf0c5c5f7a9bb7de08167cfafadb5a98d076f4c2a1051bedf5e260dd69e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y/bundle.json","state_url":"https://pith.science/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y/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":"2026-06-09T01:11:35Z","links":{"resolver":"https://pith.science/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y","bundle":"https://pith.science/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y/bundle.json","state":"https://pith.science/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJOVIYKO5Q4XJO35HGGRILGF4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BJOVIYKO5Q4XJO35HGGRILGF4Y","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":"f112e7ed26b99940296f855be9b2c084642090f60eb2c40fd4f3edc49db90564","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-07-31T11:46:39Z","title_canon_sha256":"3bf9e1f58aab63926ab7507023ff533777ab3818a5a7098edd932615b1791e14"},"schema_version":"1.0","source":{"id":"1307.8292","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8292","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8292v6","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8292","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"BJOVIYKO5Q4X","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJOVIYKO5Q4XJO35","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJOVIYKO","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:47ef4bf0c5c5f7a9bb7de08167cfafadb5a98d076f4c2a1051bedf5e260dd69e","target":"graph","created_at":"2026-05-18T02:45:58Z","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":"Let $I\\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\\geq d$, resp. $\\geq d+1$ . Suppose that $I$ is generated by three monomials of degrees $d$. If the Stanley depth of $I/J$ is $\\leq d+1$ then the usual depth of $I/J$ is $\\leq d+1$ too.","authors_text":"Andrei Zarojanu, Dorin Popescu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-07-31T11:46:39Z","title":"Three generated, squarefree, monomial ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8292","kind":"arxiv","version":6},"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":"sha256:53b59aafe4ae193c88d909aa6cd3804fa3838a3675ac44db4c2219f3cb8a68c4","target":"record","created_at":"2026-05-18T02:45:58Z","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":"f112e7ed26b99940296f855be9b2c084642090f60eb2c40fd4f3edc49db90564","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-07-31T11:46:39Z","title_canon_sha256":"3bf9e1f58aab63926ab7507023ff533777ab3818a5a7098edd932615b1791e14"},"schema_version":"1.0","source":{"id":"1307.8292","kind":"arxiv","version":6}},"canonical_sha256":"0a5d54614eec3974bb7d398d142cc5e6100961f15a1f4960c8e026ba7b05e852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a5d54614eec3974bb7d398d142cc5e6100961f15a1f4960c8e026ba7b05e852","first_computed_at":"2026-05-18T02:45:58.305442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:58.305442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"px9mBWwMys4od2Gu2cQdk5Ju2zdOriBWyW34XQsf5p1Ceo1iglFGjs7MRTVfV1xaAXM/gM3QlAsWI08VvMDSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:58.306040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.8292","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53b59aafe4ae193c88d909aa6cd3804fa3838a3675ac44db4c2219f3cb8a68c4","sha256:47ef4bf0c5c5f7a9bb7de08167cfafadb5a98d076f4c2a1051bedf5e260dd69e"],"state_sha256":"e2f5bd158afa4fa3e736087235c56610a83f0e160d5a5e3b157cae2fe305a258"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJzIQ7pSNTMkad/SbkHcUPDKchaHVDZRksLIg4VgqaqUeFuplxcCB8FqhpDXvhxbH5xD4em5eE1+r68n7LNhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:11:35.444940Z","bundle_sha256":"2ed56d04114b52ff890f59948ba88310a5da390e1688ba7e2d30c258ca66ff9f"}}