{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FXSW6BJVU6LXWWBJWRTDCFHFXI","short_pith_number":"pith:FXSW6BJV","canonical_record":{"source":{"id":"1304.7215","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-26T16:15:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"21b484863a8352996ff5f425f2a64cc8c2130ea380ef88dc2a863c7d1bd1481e","abstract_canon_sha256":"10c81cbf87d44ff4f710ea934f31c425ad14f59e3914d9d722aa3ab90b14ffa7"},"schema_version":"1.0"},"canonical_sha256":"2de56f0535a7977b5829b4663114e5ba32eda6af58a79f7faf8b4e922ceb206c","source":{"kind":"arxiv","id":"1304.7215","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7215","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7215v3","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7215","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"FXSW6BJVU6LX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FXSW6BJVU6LXWWBJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FXSW6BJV","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FXSW6BJVU6LXWWBJWRTDCFHFXI","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7215","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-26T16:15:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"21b484863a8352996ff5f425f2a64cc8c2130ea380ef88dc2a863c7d1bd1481e","abstract_canon_sha256":"10c81cbf87d44ff4f710ea934f31c425ad14f59e3914d9d722aa3ab90b14ffa7"},"schema_version":"1.0"},"canonical_sha256":"2de56f0535a7977b5829b4663114e5ba32eda6af58a79f7faf8b4e922ceb206c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:39.437762Z","signature_b64":"VLtEVMWKWhTOj6rZ4mQw4TGiq5eA8Yq6SOpL1nhYMqlyLXv75Dbhl6avhtBDXZdfZfegSKwNsmhk0IIumSzICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2de56f0535a7977b5829b4663114e5ba32eda6af58a79f7faf8b4e922ceb206c","last_reissued_at":"2026-05-18T02:46:39.437378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:39.437378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7215","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"31iHnMICM9CAGp5SBO67T28HwSAWJ2yByCar7vG0z/lCcofw3vSQ78OIazbneUu+Jpd9rL+6lD/r+p6Hs8cfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:38:01.271195Z"},"content_sha256":"8700e8db05823e040647574fbc64cf430343a84f0debc634fea32c37edf59e4c","schema_version":"1.0","event_id":"sha256:8700e8db05823e040647574fbc64cf430343a84f0debc634fea32c37edf59e4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FXSW6BJVU6LXWWBJWRTDCFHFXI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm for computing the multigraded Hilbert depth of a module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Andrei Zarojanu, Bogdan Ichim","submitted_at":"2013-04-26T16:15:08Z","abstract_excerpt":"A method for computing the multigraded Hilbert depth of a module was presented in [16]. In this paper we improve the method and we introduce an effective algorithm for performing the computations. In a particular case, the algorithm may also be easily adapted for computing the Stanley depth of the module. We further present interesting examples which were found with the help of an experimental implementation of the algorithm. Thus, we completely solve several open problems proposed by Herzog in [12]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7215","kind":"arxiv","version":3},"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":"2026-05-18T02:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LmS8xyjqXcezjGhn5T2MLLdZv7t299HbvaAz57/84lETUP3xV5NnDtqQ+yTirc28zANe8COTT/+INEwUgbKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:38:01.271556Z"},"content_sha256":"d9409783a70b8ec638b72b4529beeda50b7cf3c0237c80d3b4da8d642c691eea","schema_version":"1.0","event_id":"sha256:d9409783a70b8ec638b72b4529beeda50b7cf3c0237c80d3b4da8d642c691eea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI/bundle.json","state_url":"https://pith.science/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI/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":"2026-06-03T20:38:01Z","links":{"resolver":"https://pith.science/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI","bundle":"https://pith.science/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI/bundle.json","state":"https://pith.science/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXSW6BJVU6LXWWBJWRTDCFHFXI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FXSW6BJVU6LXWWBJWRTDCFHFXI","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":"10c81cbf87d44ff4f710ea934f31c425ad14f59e3914d9d722aa3ab90b14ffa7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-26T16:15:08Z","title_canon_sha256":"21b484863a8352996ff5f425f2a64cc8c2130ea380ef88dc2a863c7d1bd1481e"},"schema_version":"1.0","source":{"id":"1304.7215","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7215","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7215v3","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7215","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"FXSW6BJVU6LX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FXSW6BJVU6LXWWBJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FXSW6BJV","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:d9409783a70b8ec638b72b4529beeda50b7cf3c0237c80d3b4da8d642c691eea","target":"graph","created_at":"2026-05-18T02:46:39Z","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":"A method for computing the multigraded Hilbert depth of a module was presented in [16]. In this paper we improve the method and we introduce an effective algorithm for performing the computations. In a particular case, the algorithm may also be easily adapted for computing the Stanley depth of the module. We further present interesting examples which were found with the help of an experimental implementation of the algorithm. Thus, we completely solve several open problems proposed by Herzog in [12].","authors_text":"Andrei Zarojanu, Bogdan Ichim","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-26T16:15:08Z","title":"An algorithm for computing the multigraded Hilbert depth of a module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7215","kind":"arxiv","version":3},"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":"sha256:8700e8db05823e040647574fbc64cf430343a84f0debc634fea32c37edf59e4c","target":"record","created_at":"2026-05-18T02:46:39Z","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":"10c81cbf87d44ff4f710ea934f31c425ad14f59e3914d9d722aa3ab90b14ffa7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-26T16:15:08Z","title_canon_sha256":"21b484863a8352996ff5f425f2a64cc8c2130ea380ef88dc2a863c7d1bd1481e"},"schema_version":"1.0","source":{"id":"1304.7215","kind":"arxiv","version":3}},"canonical_sha256":"2de56f0535a7977b5829b4663114e5ba32eda6af58a79f7faf8b4e922ceb206c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2de56f0535a7977b5829b4663114e5ba32eda6af58a79f7faf8b4e922ceb206c","first_computed_at":"2026-05-18T02:46:39.437378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:39.437378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VLtEVMWKWhTOj6rZ4mQw4TGiq5eA8Yq6SOpL1nhYMqlyLXv75Dbhl6avhtBDXZdfZfegSKwNsmhk0IIumSzICw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:39.437762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7215","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8700e8db05823e040647574fbc64cf430343a84f0debc634fea32c37edf59e4c","sha256:d9409783a70b8ec638b72b4529beeda50b7cf3c0237c80d3b4da8d642c691eea"],"state_sha256":"afbb90b732d0874c741408c3d29e2641252da5f90be11e9c5b504dfd9d3547a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GGBM36yQIiX3x/kf0irAgVlA5p0gv/AszIIcCKgAg3NPYqfrTB6uBWaS778q5oW1DlB9shh2lpyfYeTon+ihAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:38:01.273496Z","bundle_sha256":"0a575adb1b4eff576246f29b6a2e2333d3e216b7012486a8d8c09068d354c3a7"}}