{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:N25NGLZTFKLEK2MIGHSL53SMQB","short_pith_number":"pith:N25NGLZT","canonical_record":{"source":{"id":"1011.6462","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2010-11-30T05:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"dd70e6653d6ff4a65493f82ddc31f17b93c615dc50945d2304f5bd27e43cef4b","abstract_canon_sha256":"8278d002d4f9ddd7dff2e3c771bc4855f38077e1630cb716bf9904e1196c0526"},"schema_version":"1.0"},"canonical_sha256":"6ebad32f332a9645698831e4beee4c8079e484c2db22e5143b5a9ab866df9dc1","source":{"kind":"arxiv","id":"1011.6462","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6462","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6462v1","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6462","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"N25NGLZTFKLE","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N25NGLZTFKLEK2MI","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N25NGLZT","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:N25NGLZTFKLEK2MIGHSL53SMQB","target":"record","payload":{"canonical_record":{"source":{"id":"1011.6462","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2010-11-30T05:41:12Z","cross_cats_sorted":[],"title_canon_sha256":"dd70e6653d6ff4a65493f82ddc31f17b93c615dc50945d2304f5bd27e43cef4b","abstract_canon_sha256":"8278d002d4f9ddd7dff2e3c771bc4855f38077e1630cb716bf9904e1196c0526"},"schema_version":"1.0"},"canonical_sha256":"6ebad32f332a9645698831e4beee4c8079e484c2db22e5143b5a9ab866df9dc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:26.883400Z","signature_b64":"yAftxhvODZupGVklwyzo01O6nDmjYcM+siV1GbgKnGXf/0EK50FAjtyRF2qVxA6NSdlAZF5Y+AsW6CWqG28bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ebad32f332a9645698831e4beee4c8079e484c2db22e5143b5a9ab866df9dc1","last_reissued_at":"2026-05-18T04:34:26.882428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:26.882428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.6462","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":"2026-05-18T04:34:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixWhTsRiEQ6C2HpetNF9bJW7oVo8EPDSGg8fCv73nldKRdRwzcNK3pieAfi0XFUEUyn1x3u6cgkDlM62Pj9tCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:39:42.441506Z"},"content_sha256":"7a0f4f5f2630bfbd70c726ceba2a21db3ad6b86115617096e924e8b3beb47956","schema_version":"1.0","event_id":"sha256:7a0f4f5f2630bfbd70c726ceba2a21db3ad6b86115617096e924e8b3beb47956"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:N25NGLZTFKLEK2MIGHSL53SMQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stanley depth and size of a monomial ideal","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Dorin Popescu, J\\\"urgen Herzog, Marius Vladoiu","submitted_at":"2010-11-30T05:41:12Z","abstract_excerpt":"Lyubeznik introduced the concept of size of a monomial ideal and showed that the size of a monomial ideal increased by $1$ is a lower bound for its depth. We show that the size is also a lower bound for its Stanley depth. Applying Alexander duality we obtain upper bounds for the regularity and Stanley regularity of squarefree monomial ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6462","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":"2026-05-18T04:34:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4lyNg/n+wr8ZtTmFSZkVr1HcjKRorQ7BZhuWoXvxzXHHyhM1RAjLCevUFoVzJFPJiSxNovjvl5jjpyVXTRQWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:39:42.442046Z"},"content_sha256":"e72121a7e1744c10a48f326611f26ff01178423203423c47f8f5c8606c347c77","schema_version":"1.0","event_id":"sha256:e72121a7e1744c10a48f326611f26ff01178423203423c47f8f5c8606c347c77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N25NGLZTFKLEK2MIGHSL53SMQB/bundle.json","state_url":"https://pith.science/pith/N25NGLZTFKLEK2MIGHSL53SMQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N25NGLZTFKLEK2MIGHSL53SMQB/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":"2026-06-07T02:39:42Z","links":{"resolver":"https://pith.science/pith/N25NGLZTFKLEK2MIGHSL53SMQB","bundle":"https://pith.science/pith/N25NGLZTFKLEK2MIGHSL53SMQB/bundle.json","state":"https://pith.science/pith/N25NGLZTFKLEK2MIGHSL53SMQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N25NGLZTFKLEK2MIGHSL53SMQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:N25NGLZTFKLEK2MIGHSL53SMQB","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":"8278d002d4f9ddd7dff2e3c771bc4855f38077e1630cb716bf9904e1196c0526","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2010-11-30T05:41:12Z","title_canon_sha256":"dd70e6653d6ff4a65493f82ddc31f17b93c615dc50945d2304f5bd27e43cef4b"},"schema_version":"1.0","source":{"id":"1011.6462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6462","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6462v1","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6462","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"N25NGLZTFKLE","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N25NGLZTFKLEK2MI","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N25NGLZT","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:e72121a7e1744c10a48f326611f26ff01178423203423c47f8f5c8606c347c77","target":"graph","created_at":"2026-05-18T04:34:26Z","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":"Lyubeznik introduced the concept of size of a monomial ideal and showed that the size of a monomial ideal increased by $1$ is a lower bound for its depth. We show that the size is also a lower bound for its Stanley depth. Applying Alexander duality we obtain upper bounds for the regularity and Stanley regularity of squarefree monomial ideals.","authors_text":"Dorin Popescu, J\\\"urgen Herzog, Marius Vladoiu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2010-11-30T05:41:12Z","title":"Stanley depth and size of a monomial ideal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6462","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":"sha256:7a0f4f5f2630bfbd70c726ceba2a21db3ad6b86115617096e924e8b3beb47956","target":"record","created_at":"2026-05-18T04:34:26Z","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":"8278d002d4f9ddd7dff2e3c771bc4855f38077e1630cb716bf9904e1196c0526","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2010-11-30T05:41:12Z","title_canon_sha256":"dd70e6653d6ff4a65493f82ddc31f17b93c615dc50945d2304f5bd27e43cef4b"},"schema_version":"1.0","source":{"id":"1011.6462","kind":"arxiv","version":1}},"canonical_sha256":"6ebad32f332a9645698831e4beee4c8079e484c2db22e5143b5a9ab866df9dc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ebad32f332a9645698831e4beee4c8079e484c2db22e5143b5a9ab866df9dc1","first_computed_at":"2026-05-18T04:34:26.882428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:26.882428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yAftxhvODZupGVklwyzo01O6nDmjYcM+siV1GbgKnGXf/0EK50FAjtyRF2qVxA6NSdlAZF5Y+AsW6CWqG28bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:26.883400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a0f4f5f2630bfbd70c726ceba2a21db3ad6b86115617096e924e8b3beb47956","sha256:e72121a7e1744c10a48f326611f26ff01178423203423c47f8f5c8606c347c77"],"state_sha256":"d03adef2b17f6f10a24c002e289539941e98e90b121b7b0e4611390b272dfc02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30cw465OP52pImyOZSe2dXCKIjIb7nZixZWu80CyeM+khJp1uujGhJ6vJ5gzuWYTpH8mUcDtIEbFOCUE+eG+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:39:42.444959Z","bundle_sha256":"ab8568830324a57304db501f0fa20fce46cf396ac32b263e1600aa4e65ee6420"}}