{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UMABM3H7SNRQTI54DULWQI2GK4","short_pith_number":"pith:UMABM3H7","canonical_record":{"source":{"id":"1107.4699","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-23T17:29:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a517c44470501b1c14635bfea6d98fc2724d2665860a4c85976bf3e154c21943","abstract_canon_sha256":"6ac4ba39419662ab46ede611c86de539eff6c6fd017af7eb5ad28e8121a30aba"},"schema_version":"1.0"},"canonical_sha256":"a300166cff936309a3bc1d17682346572d4696ffa16613098960b3bdcebbf45b","source":{"kind":"arxiv","id":"1107.4699","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4699","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4699v5","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4699","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"UMABM3H7SNRQ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UMABM3H7SNRQTI54","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UMABM3H7","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UMABM3H7SNRQTI54DULWQI2GK4","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4699","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-23T17:29:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a517c44470501b1c14635bfea6d98fc2724d2665860a4c85976bf3e154c21943","abstract_canon_sha256":"6ac4ba39419662ab46ede611c86de539eff6c6fd017af7eb5ad28e8121a30aba"},"schema_version":"1.0"},"canonical_sha256":"a300166cff936309a3bc1d17682346572d4696ffa16613098960b3bdcebbf45b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:32.898284Z","signature_b64":"faVuGYWzvb3IZpNEsSSShjLcloQevmfldCGXUZ9bIqiOHAiekNHjOgRbPr0gPCbAhO86S05B2ZMTp3x04hNCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a300166cff936309a3bc1d17682346572d4696ffa16613098960b3bdcebbf45b","last_reissued_at":"2026-05-18T01:33:32.897613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:32.897613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4699","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmbAEfOHDI0h8h/yqkhsmnJ3pGolROI6HiPClY8QalsgZWnHV8dgQG+7IRVsrdswNGIrsXA1kuQinqizMMDaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:41:34.462972Z"},"content_sha256":"2d6e537759d70c4bb7c6bdc2f3ff9521dbe69122c35631e9482f09779e81b459","schema_version":"1.0","event_id":"sha256:2d6e537759d70c4bb7c6bdc2f3ff9521dbe69122c35631e9482f09779e81b459"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UMABM3H7SNRQTI54DULWQI2GK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decompositions of commutative monoid congruences and binomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ezra Miller, Thomas Kahle","submitted_at":"2011-07-23T17:29:57Z","abstract_excerpt":"Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences, introduced here complete with witnesses and associated prime objects. The combinatorial theory of mesoprimary decomposition lifts to arbitrary binomial ideals in monoid algebras. The resulting binomial mesoprimary decomposition is a new type of intersection decomposition for binomial ideals that enjoys computational efficiency and independence from ground fiel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4699","kind":"arxiv","version":5},"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":"2026-05-18T01:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTVfNgQCXhKNObycwC3VnHqLWTBCp+yM7s0F70T1FJw+IK51mNPFYTp+9dyy6aeNmKFid53SWBWIRDKnjQGaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:41:34.463358Z"},"content_sha256":"54ea1ac9f18871bfa769d4350aa45cb76b07cf910c451f83bef36a51dcdc6938","schema_version":"1.0","event_id":"sha256:54ea1ac9f18871bfa769d4350aa45cb76b07cf910c451f83bef36a51dcdc6938"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMABM3H7SNRQTI54DULWQI2GK4/bundle.json","state_url":"https://pith.science/pith/UMABM3H7SNRQTI54DULWQI2GK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMABM3H7SNRQTI54DULWQI2GK4/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":"2026-05-30T11:41:34Z","links":{"resolver":"https://pith.science/pith/UMABM3H7SNRQTI54DULWQI2GK4","bundle":"https://pith.science/pith/UMABM3H7SNRQTI54DULWQI2GK4/bundle.json","state":"https://pith.science/pith/UMABM3H7SNRQTI54DULWQI2GK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMABM3H7SNRQTI54DULWQI2GK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UMABM3H7SNRQTI54DULWQI2GK4","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":"6ac4ba39419662ab46ede611c86de539eff6c6fd017af7eb5ad28e8121a30aba","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-23T17:29:57Z","title_canon_sha256":"a517c44470501b1c14635bfea6d98fc2724d2665860a4c85976bf3e154c21943"},"schema_version":"1.0","source":{"id":"1107.4699","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4699","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4699v5","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4699","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"UMABM3H7SNRQ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UMABM3H7SNRQTI54","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UMABM3H7","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:54ea1ac9f18871bfa769d4350aa45cb76b07cf910c451f83bef36a51dcdc6938","target":"graph","created_at":"2026-05-18T01:33:32Z","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":"Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences, introduced here complete with witnesses and associated prime objects. The combinatorial theory of mesoprimary decomposition lifts to arbitrary binomial ideals in monoid algebras. The resulting binomial mesoprimary decomposition is a new type of intersection decomposition for binomial ideals that enjoys computational efficiency and independence from ground fiel","authors_text":"Ezra Miller, Thomas Kahle","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-23T17:29:57Z","title":"Decompositions of commutative monoid congruences and binomial ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4699","kind":"arxiv","version":5},"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":"sha256:2d6e537759d70c4bb7c6bdc2f3ff9521dbe69122c35631e9482f09779e81b459","target":"record","created_at":"2026-05-18T01:33:32Z","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":"6ac4ba39419662ab46ede611c86de539eff6c6fd017af7eb5ad28e8121a30aba","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-23T17:29:57Z","title_canon_sha256":"a517c44470501b1c14635bfea6d98fc2724d2665860a4c85976bf3e154c21943"},"schema_version":"1.0","source":{"id":"1107.4699","kind":"arxiv","version":5}},"canonical_sha256":"a300166cff936309a3bc1d17682346572d4696ffa16613098960b3bdcebbf45b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a300166cff936309a3bc1d17682346572d4696ffa16613098960b3bdcebbf45b","first_computed_at":"2026-05-18T01:33:32.897613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:32.897613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"faVuGYWzvb3IZpNEsSSShjLcloQevmfldCGXUZ9bIqiOHAiekNHjOgRbPr0gPCbAhO86S05B2ZMTp3x04hNCCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:32.898284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4699","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d6e537759d70c4bb7c6bdc2f3ff9521dbe69122c35631e9482f09779e81b459","sha256:54ea1ac9f18871bfa769d4350aa45cb76b07cf910c451f83bef36a51dcdc6938"],"state_sha256":"8f0d82141b217474c66c5287ef4acd0dcdc036a97acee4592a778f6e6c8edd58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xh9/q6r3IC13O0BP0aKVLSwnjSLsjnyT+s+Dvf0dPbzhVARBPVD1koYA2UuLqj5o/qwkqFTjaArDJWPV2ai4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:41:34.468286Z","bundle_sha256":"db1cc3a137c9a8bf2288fc9aa5bf51a1a62ace52cc02d5f2759e06b34033a74e"}}