{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QHWRTQ2B5UUKTBQ62NEESAY6Z5","short_pith_number":"pith:QHWRTQ2B","canonical_record":{"source":{"id":"1810.01499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T20:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"dd7cd69b654bef0ebb46c9d600b662dfa1625daf269c356943919b0a296a9a78","abstract_canon_sha256":"8d44e6748c069f6d1781cf39fe7505ff2eecd20a549b03d07bdb249afd180e63"},"schema_version":"1.0"},"canonical_sha256":"81ed19c341ed28a9861ed34849031ecf539ec54eb6cf2e9abbe5e0661885a5ca","source":{"kind":"arxiv","id":"1810.01499","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01499","created_at":"2026-05-18T00:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01499v1","created_at":"2026-05-18T00:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01499","created_at":"2026-05-18T00:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"QHWRTQ2B5UUK","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHWRTQ2B5UUKTBQ6","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHWRTQ2B","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QHWRTQ2B5UUKTBQ62NEESAY6Z5","target":"record","payload":{"canonical_record":{"source":{"id":"1810.01499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T20:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"dd7cd69b654bef0ebb46c9d600b662dfa1625daf269c356943919b0a296a9a78","abstract_canon_sha256":"8d44e6748c069f6d1781cf39fe7505ff2eecd20a549b03d07bdb249afd180e63"},"schema_version":"1.0"},"canonical_sha256":"81ed19c341ed28a9861ed34849031ecf539ec54eb6cf2e9abbe5e0661885a5ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:11.959146Z","signature_b64":"V9URoGHXFWwGV3wXP2l2fICoR9/yWPaVLhdo519bTwRx6rjquyLE94Obt6nwzUZyLNLaDufOPQELS+oIF9QzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ed19c341ed28a9861ed34849031ecf539ec54eb6cf2e9abbe5e0661885a5ca","last_reissued_at":"2026-05-18T00:04:11.958494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:11.958494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.01499","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":"2026-05-18T00:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1DfFgZ6BgbfLorm1kS/BAWjNMdOv7m83O4I9vYV6scr5R77biTIFChibRJ7IpOno5RSImlKO1p910H5snVOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:36:32.181730Z"},"content_sha256":"bcdd0ae53805cdbfb9f52e7bacaf9898fbe0980f14ce2b7f591bc41622c5f915","schema_version":"1.0","event_id":"sha256:bcdd0ae53805cdbfb9f52e7bacaf9898fbe0980f14ce2b7f591bc41622c5f915"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QHWRTQ2B5UUKTBQ62NEESAY6Z5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing The Invariants of Intersection Algebras of Principal Monomial Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Florian Enescu, Sandra Spiroff","submitted_at":"2018-10-02T20:31:42Z","abstract_excerpt":"We continue the study of intersection algebras $\\mathcal B = \\mathcal B_R(I, J)$ of two ideals $I, J$ in a commutative Noetherian ring $R$. In particular, we exploit the semigroup ring and toric structures in order to calculate various invariants of the intersection algebra when $R$ is a polynomial ring over a field and $I,J$ are principal monomial ideals. Specifically, we calculate the $F$-signature, divisor class group, and Hilbert-Samuel and Hilbert-Kunz multiplicities, sometimes restricting to certain cases in order to obtain explicit formul{\\ae}. This provides a new class of rings where f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01499","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":"2026-05-18T00:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dqOy6E3dO5Fbuvn+BTm0jd3nB0UFMvB5gPWFJEaWgpR+XTYKO3xnCaPNF1CdRDtBE8TxCKqTzwJ+T+9NlG1CAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:36:32.182079Z"},"content_sha256":"636056de96b9d4a883bb0ea08909c183b5340f9e3a1489ce1742c84a9356ebfa","schema_version":"1.0","event_id":"sha256:636056de96b9d4a883bb0ea08909c183b5340f9e3a1489ce1742c84a9356ebfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5/bundle.json","state_url":"https://pith.science/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5/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":"2026-06-02T23:36:32Z","links":{"resolver":"https://pith.science/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5","bundle":"https://pith.science/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5/bundle.json","state":"https://pith.science/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHWRTQ2B5UUKTBQ62NEESAY6Z5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QHWRTQ2B5UUKTBQ62NEESAY6Z5","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":"8d44e6748c069f6d1781cf39fe7505ff2eecd20a549b03d07bdb249afd180e63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T20:31:42Z","title_canon_sha256":"dd7cd69b654bef0ebb46c9d600b662dfa1625daf269c356943919b0a296a9a78"},"schema_version":"1.0","source":{"id":"1810.01499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01499","created_at":"2026-05-18T00:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01499v1","created_at":"2026-05-18T00:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01499","created_at":"2026-05-18T00:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"QHWRTQ2B5UUK","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHWRTQ2B5UUKTBQ6","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHWRTQ2B","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:636056de96b9d4a883bb0ea08909c183b5340f9e3a1489ce1742c84a9356ebfa","target":"graph","created_at":"2026-05-18T00:04:11Z","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":"We continue the study of intersection algebras $\\mathcal B = \\mathcal B_R(I, J)$ of two ideals $I, J$ in a commutative Noetherian ring $R$. In particular, we exploit the semigroup ring and toric structures in order to calculate various invariants of the intersection algebra when $R$ is a polynomial ring over a field and $I,J$ are principal monomial ideals. Specifically, we calculate the $F$-signature, divisor class group, and Hilbert-Samuel and Hilbert-Kunz multiplicities, sometimes restricting to certain cases in order to obtain explicit formul{\\ae}. This provides a new class of rings where f","authors_text":"Florian Enescu, Sandra Spiroff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T20:31:42Z","title":"Computing The Invariants of Intersection Algebras of Principal Monomial Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01499","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:bcdd0ae53805cdbfb9f52e7bacaf9898fbe0980f14ce2b7f591bc41622c5f915","target":"record","created_at":"2026-05-18T00:04:11Z","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":"8d44e6748c069f6d1781cf39fe7505ff2eecd20a549b03d07bdb249afd180e63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T20:31:42Z","title_canon_sha256":"dd7cd69b654bef0ebb46c9d600b662dfa1625daf269c356943919b0a296a9a78"},"schema_version":"1.0","source":{"id":"1810.01499","kind":"arxiv","version":1}},"canonical_sha256":"81ed19c341ed28a9861ed34849031ecf539ec54eb6cf2e9abbe5e0661885a5ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81ed19c341ed28a9861ed34849031ecf539ec54eb6cf2e9abbe5e0661885a5ca","first_computed_at":"2026-05-18T00:04:11.958494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:11.958494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9URoGHXFWwGV3wXP2l2fICoR9/yWPaVLhdo519bTwRx6rjquyLE94Obt6nwzUZyLNLaDufOPQELS+oIF9QzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:11.959146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcdd0ae53805cdbfb9f52e7bacaf9898fbe0980f14ce2b7f591bc41622c5f915","sha256:636056de96b9d4a883bb0ea08909c183b5340f9e3a1489ce1742c84a9356ebfa"],"state_sha256":"fb6073bc35a9efe1f767533c1f5a5785dcc38a451f3b74bc29c94eecc902c0f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M+6r+gqfpP2fDta8Tkqu3C3C3XRVvA8tLdKZGT40QggFa4w0eC9uwUtVeyJEE9nx2MHFYg1IatMTNlK0w7aWAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:36:32.184137Z","bundle_sha256":"a71801d326be34e6a4207a295b60b5fe84a7247506d9ae3fa2be2e3d0fd96737"}}