{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PY3AVO4ZKUZBDGXILQZG3IOZ2I","short_pith_number":"pith:PY3AVO4Z","canonical_record":{"source":{"id":"1601.01308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T20:47:16Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"fed8cb2ad16330ad41d2e7dc1f8d8db79f12621b984a5c99ebc6721848ff9b21","abstract_canon_sha256":"d5923d9658b5f1847cb2933780afe16547c322c79bc218657d12ca0cb39a0e5f"},"schema_version":"1.0"},"canonical_sha256":"7e360abb995532119ae85c326da1d9d22d0e7bb7ce9a0dfc156eecd2bd53e30c","source":{"kind":"arxiv","id":"1601.01308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01308","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01308v1","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01308","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"PY3AVO4ZKUZB","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PY3AVO4ZKUZBDGXI","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PY3AVO4Z","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PY3AVO4ZKUZBDGXILQZG3IOZ2I","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T20:47:16Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"fed8cb2ad16330ad41d2e7dc1f8d8db79f12621b984a5c99ebc6721848ff9b21","abstract_canon_sha256":"d5923d9658b5f1847cb2933780afe16547c322c79bc218657d12ca0cb39a0e5f"},"schema_version":"1.0"},"canonical_sha256":"7e360abb995532119ae85c326da1d9d22d0e7bb7ce9a0dfc156eecd2bd53e30c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:44.948289Z","signature_b64":"lPmtPmQwPPYQCFoKdCurAJur1YEi2K/rwM8KMGVVUZe41XuvUYyV61lsfyqTaq708Chr6hr2D4OHZC1vZnXLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e360abb995532119ae85c326da1d9d22d0e7bb7ce9a0dfc156eecd2bd53e30c","last_reissued_at":"2026-05-18T00:20:44.947524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:44.947524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01308","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":"2026-05-18T00:20:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWnZjq9sqthP3aJDUdShAS/yN5cTquuqDCKyJ44d/aERWvW1H5LeNGYl22S9VitkGxIFDRvB2M73w+rbunsECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:01:18.495210Z"},"content_sha256":"08b0595432f687df7489141a5d3a398693f53a2994b266bb4de06cb0c9cfc77f","schema_version":"1.0","event_id":"sha256:08b0595432f687df7489141a5d3a398693f53a2994b266bb4de06cb0c9cfc77f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PY3AVO4ZKUZBDGXILQZG3IOZ2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the containment problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Justyna Szpond, Tomasz Szemberg","submitted_at":"2016-01-06T20:47:16Z","abstract_excerpt":"The purpose of this note is to provide an overview of the containment problem for symbolic and ordinary powers of homogeneous ideals, related conjectures and examples. We focus here on ideals with zero dimensional support. This is an area of ongoing active research. We conclude the note with a list of potential promising paths of further research."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01308","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":"2026-05-18T00:20:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N4kr7hk9CiKiYjeUiyYGAXCRJEfTmbscESMjgyRHRMcumq9hqX1jN+/g4o9LgAzXjWMRMoD/cresxLJFh08KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:01:18.495598Z"},"content_sha256":"5ff9cd7fa7414d47c1bdb7e34bc1d4bcf6c83a2187478d736e97f471072708a4","schema_version":"1.0","event_id":"sha256:5ff9cd7fa7414d47c1bdb7e34bc1d4bcf6c83a2187478d736e97f471072708a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I/bundle.json","state_url":"https://pith.science/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I/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":"2026-06-04T23:01:18Z","links":{"resolver":"https://pith.science/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I","bundle":"https://pith.science/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I/bundle.json","state":"https://pith.science/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PY3AVO4ZKUZBDGXILQZG3IOZ2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PY3AVO4ZKUZBDGXILQZG3IOZ2I","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":"d5923d9658b5f1847cb2933780afe16547c322c79bc218657d12ca0cb39a0e5f","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T20:47:16Z","title_canon_sha256":"fed8cb2ad16330ad41d2e7dc1f8d8db79f12621b984a5c99ebc6721848ff9b21"},"schema_version":"1.0","source":{"id":"1601.01308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01308","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01308v1","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01308","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"PY3AVO4ZKUZB","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PY3AVO4ZKUZBDGXI","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PY3AVO4Z","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:5ff9cd7fa7414d47c1bdb7e34bc1d4bcf6c83a2187478d736e97f471072708a4","target":"graph","created_at":"2026-05-18T00:20:44Z","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"},"paper":{"abstract_excerpt":"The purpose of this note is to provide an overview of the containment problem for symbolic and ordinary powers of homogeneous ideals, related conjectures and examples. We focus here on ideals with zero dimensional support. This is an area of ongoing active research. We conclude the note with a list of potential promising paths of further research.","authors_text":"Justyna Szpond, Tomasz Szemberg","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T20:47:16Z","title":"On the containment problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01308","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":"sha256:08b0595432f687df7489141a5d3a398693f53a2994b266bb4de06cb0c9cfc77f","target":"record","created_at":"2026-05-18T00:20:44Z","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":"d5923d9658b5f1847cb2933780afe16547c322c79bc218657d12ca0cb39a0e5f","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T20:47:16Z","title_canon_sha256":"fed8cb2ad16330ad41d2e7dc1f8d8db79f12621b984a5c99ebc6721848ff9b21"},"schema_version":"1.0","source":{"id":"1601.01308","kind":"arxiv","version":1}},"canonical_sha256":"7e360abb995532119ae85c326da1d9d22d0e7bb7ce9a0dfc156eecd2bd53e30c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e360abb995532119ae85c326da1d9d22d0e7bb7ce9a0dfc156eecd2bd53e30c","first_computed_at":"2026-05-18T00:20:44.947524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:44.947524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lPmtPmQwPPYQCFoKdCurAJur1YEi2K/rwM8KMGVVUZe41XuvUYyV61lsfyqTaq708Chr6hr2D4OHZC1vZnXLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:44.948289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08b0595432f687df7489141a5d3a398693f53a2994b266bb4de06cb0c9cfc77f","sha256:5ff9cd7fa7414d47c1bdb7e34bc1d4bcf6c83a2187478d736e97f471072708a4"],"state_sha256":"4c280d4e359fb7ef35d07f118c908f13c5122404bb01d86edb5f0e5ce524a069"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHrcqUO8KsU1ISZax7kCoHBqXa8smAalAzRiQPbvBBBwtRzdEXh5LRiW7gWV2Hh1Fgip0eXFwCLN1kCpz5eJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:01:18.498067Z","bundle_sha256":"e4cbd8062ea054ce62d4b64309f7765c69c9f8744c1c062f7ff4f26b243cbfe1"}}