{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IJAA2VFKT2K3NQYNF6JZROVPPL","short_pith_number":"pith:IJAA2VFK","canonical_record":{"source":{"id":"1906.00262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-01T18:14:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1887c5f91620be4b6305121124ee344b6012c615ccf379f8068c8e6074ea9b36","abstract_canon_sha256":"fc4271702f3d127b576b8c60ed13c901da704f06576037141975aaf7cec44719"},"schema_version":"1.0"},"canonical_sha256":"42400d54aa9e95b6c30d2f9398baaf7af05d4249b2c962952579c17cfab5d5f4","source":{"kind":"arxiv","id":"1906.00262","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00262","created_at":"2026-05-17T23:44:27Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00262v1","created_at":"2026-05-17T23:44:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00262","created_at":"2026-05-17T23:44:27Z"},{"alias_kind":"pith_short_12","alias_value":"IJAA2VFKT2K3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IJAA2VFKT2K3NQYN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IJAA2VFK","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IJAA2VFKT2K3NQYNF6JZROVPPL","target":"record","payload":{"canonical_record":{"source":{"id":"1906.00262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-01T18:14:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1887c5f91620be4b6305121124ee344b6012c615ccf379f8068c8e6074ea9b36","abstract_canon_sha256":"fc4271702f3d127b576b8c60ed13c901da704f06576037141975aaf7cec44719"},"schema_version":"1.0"},"canonical_sha256":"42400d54aa9e95b6c30d2f9398baaf7af05d4249b2c962952579c17cfab5d5f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:27.709001Z","signature_b64":"OQhbQ2WwFwwf//WuSpZjjCxDnBgpf0dMHymYvmf6H2QQutvxBsEDZdRPH3T8oyo+5whaYmoup4sYipzZf6qFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42400d54aa9e95b6c30d2f9398baaf7af05d4249b2c962952579c17cfab5d5f4","last_reissued_at":"2026-05-17T23:44:27.708481Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:27.708481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.00262","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MwLrO8pVw+6SboOEwSjxNqbrks8uOrGnqt4rnDowyLgKEspfQdVrntn1QUXk6KPNr8Y9Q4gGxJCc6xc+OVwCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:42:00.871094Z"},"content_sha256":"bced349d7544be95bab60714e46fbc3b42a0ca98de2ed15e87202cb00f55842e","schema_version":"1.0","event_id":"sha256:bced349d7544be95bab60714e46fbc3b42a0ca98de2ed15e87202cb00f55842e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IJAA2VFKT2K3NQYNF6JZROVPPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Stanley depth of powers of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2019-06-01T18:14:52Z","abstract_excerpt":"Let $\\mathbb{K}$ be a field and $S=\\mathbb{K}[x_1,\\dots,x_n]$ be the polynomial ring in $n$ variables over $\\mathbb{K}$. In 1982, R. Stanley associated a combinatorial invariant to any finitely generated $\\mathbb{Z}^n$-graded $S$-module which is now called Stanley depth. Stanley conjectured that this invariant is an upper bound for the depth of module. Stanley's conjecture has been disproved by Duval et al. \\cite{abcj}, and the counterexample is a quotient of squarefree monomial ideals. On the other hand, there are evidences showing that Stanley's inequality can be true for high powers of mono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00262","kind":"arxiv","version":1},"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":"2026-05-17T23:44:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7Stz7n7SGGl+UwnvWLIIC2ta+EF315solK4etJY+f7mZiKXefEJ/+YSydcx8M+p280qK8xAWI6Ivy78q5PABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:42:00.871460Z"},"content_sha256":"539bf3a9e843019fd1d00c493d46d6b0af1db4ab26049c963095f8176d643581","schema_version":"1.0","event_id":"sha256:539bf3a9e843019fd1d00c493d46d6b0af1db4ab26049c963095f8176d643581"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJAA2VFKT2K3NQYNF6JZROVPPL/bundle.json","state_url":"https://pith.science/pith/IJAA2VFKT2K3NQYNF6JZROVPPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJAA2VFKT2K3NQYNF6JZROVPPL/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":"2026-06-25T11:42:00Z","links":{"resolver":"https://pith.science/pith/IJAA2VFKT2K3NQYNF6JZROVPPL","bundle":"https://pith.science/pith/IJAA2VFKT2K3NQYNF6JZROVPPL/bundle.json","state":"https://pith.science/pith/IJAA2VFKT2K3NQYNF6JZROVPPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJAA2VFKT2K3NQYNF6JZROVPPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IJAA2VFKT2K3NQYNF6JZROVPPL","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":"fc4271702f3d127b576b8c60ed13c901da704f06576037141975aaf7cec44719","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-01T18:14:52Z","title_canon_sha256":"1887c5f91620be4b6305121124ee344b6012c615ccf379f8068c8e6074ea9b36"},"schema_version":"1.0","source":{"id":"1906.00262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00262","created_at":"2026-05-17T23:44:27Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00262v1","created_at":"2026-05-17T23:44:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00262","created_at":"2026-05-17T23:44:27Z"},{"alias_kind":"pith_short_12","alias_value":"IJAA2VFKT2K3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IJAA2VFKT2K3NQYN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IJAA2VFK","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:539bf3a9e843019fd1d00c493d46d6b0af1db4ab26049c963095f8176d643581","target":"graph","created_at":"2026-05-17T23:44:27Z","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 $\\mathbb{K}$ be a field and $S=\\mathbb{K}[x_1,\\dots,x_n]$ be the polynomial ring in $n$ variables over $\\mathbb{K}$. In 1982, R. Stanley associated a combinatorial invariant to any finitely generated $\\mathbb{Z}^n$-graded $S$-module which is now called Stanley depth. Stanley conjectured that this invariant is an upper bound for the depth of module. Stanley's conjecture has been disproved by Duval et al. \\cite{abcj}, and the counterexample is a quotient of squarefree monomial ideals. On the other hand, there are evidences showing that Stanley's inequality can be true for high powers of mono","authors_text":"S. A. Seyed Fakhari","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-01T18:14:52Z","title":"On the Stanley depth of powers of monomial ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00262","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:bced349d7544be95bab60714e46fbc3b42a0ca98de2ed15e87202cb00f55842e","target":"record","created_at":"2026-05-17T23:44:27Z","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":"fc4271702f3d127b576b8c60ed13c901da704f06576037141975aaf7cec44719","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-01T18:14:52Z","title_canon_sha256":"1887c5f91620be4b6305121124ee344b6012c615ccf379f8068c8e6074ea9b36"},"schema_version":"1.0","source":{"id":"1906.00262","kind":"arxiv","version":1}},"canonical_sha256":"42400d54aa9e95b6c30d2f9398baaf7af05d4249b2c962952579c17cfab5d5f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42400d54aa9e95b6c30d2f9398baaf7af05d4249b2c962952579c17cfab5d5f4","first_computed_at":"2026-05-17T23:44:27.708481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:27.708481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OQhbQ2WwFwwf//WuSpZjjCxDnBgpf0dMHymYvmf6H2QQutvxBsEDZdRPH3T8oyo+5whaYmoup4sYipzZf6qFBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:27.709001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.00262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bced349d7544be95bab60714e46fbc3b42a0ca98de2ed15e87202cb00f55842e","sha256:539bf3a9e843019fd1d00c493d46d6b0af1db4ab26049c963095f8176d643581"],"state_sha256":"b1a72844e5519428e6938822dbd1e79384cae7b6611b33e7c18d836184cedca8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgZgQDT0Ppq5VLJP8dChb2ePHgX5o2AjhkU//dVZg5ks2dJM+gI4mrYEglwZ64PL0FKoLk8VGJBJ1WHRlK2nDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:42:00.873457Z","bundle_sha256":"bb6e10a6ceb210e087529cc1c0471d114be990060010063fa51243fd38b38582"}}