{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EZQDRM6R5EW54OGCVT2YGKE662","short_pith_number":"pith:EZQDRM6R","canonical_record":{"source":{"id":"2510.16566","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-10-18T16:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"eaff7e22422090c3e460ec3576e8df29970305b6746ae79e1baaa9e53eee0589","abstract_canon_sha256":"462e26cd30699a8ae36b55a1e22be47eab3fbb48efae6ade4857ffdf4789b406"},"schema_version":"1.0"},"canonical_sha256":"266038b3d1e92dde38c2acf583289ef6bd806b6d8dd2d497f3a6c0df5727ad4a","source":{"kind":"arxiv","id":"2510.16566","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.16566","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"2510.16566v2","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.16566","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"EZQDRM6R5EW5","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"EZQDRM6R5EW54OGC","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"EZQDRM6R","created_at":"2026-05-25T02:01:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EZQDRM6R5EW54OGCVT2YGKE662","target":"record","payload":{"canonical_record":{"source":{"id":"2510.16566","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-10-18T16:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"eaff7e22422090c3e460ec3576e8df29970305b6746ae79e1baaa9e53eee0589","abstract_canon_sha256":"462e26cd30699a8ae36b55a1e22be47eab3fbb48efae6ade4857ffdf4789b406"},"schema_version":"1.0"},"canonical_sha256":"266038b3d1e92dde38c2acf583289ef6bd806b6d8dd2d497f3a6c0df5727ad4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:08.613842Z","signature_b64":"NK9K0bWmM68WuLqZi7xGPR+0T2hYWYXIScyHMGPmwtsNrT4E8yqTLtz8MNvDu+mOrP5vsKvUZg8JilCaJiyvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"266038b3d1e92dde38c2acf583289ef6bd806b6d8dd2d497f3a6c0df5727ad4a","last_reissued_at":"2026-05-25T02:01:08.613166Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:08.613166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.16566","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L30QXNqmY16k6J12IMkyGcHNaFgBA+pLkD8MUKcPQNtXHynIpqNqxQ/Ll1Oy6jd4nDgzl+gbMhyxnYKyHIrQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:56:29.964416Z"},"content_sha256":"0ebc28422dad29c78839500a3c2c6bb3dbcd897ce39809b9d7c35f53d91be416","schema_version":"1.0","event_id":"sha256:0ebc28422dad29c78839500a3c2c6bb3dbcd897ce39809b9d7c35f53d91be416"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EZQDRM6R5EW54OGCVT2YGKE662","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Criteria for the presence of the maximal ideal in the set of associated primes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jonathan Toledo, Mehrdad Nasernejad","submitted_at":"2025-10-18T16:21:07Z","abstract_excerpt":"In this paper, we establish some criteria to detect the presence of the maximal ideal $(x_1, \\ldots, x_n)$ in the set of associated primes of powers of monomial ideals in the polynomial ring $K[x_1, \\ldots, x_n]$. Furthermore, for each of these criteria, we illustrate its applicability with corresponding examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16566","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.16566/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-25T02:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hfWpF5vYlQg1UKnFVnWkGsGLGwi9LiTt+Vwo0DxBSybZ4iphzSVAGCEQKKcd7ielfxfpWwCnGO6HHCb3NToCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:56:29.965160Z"},"content_sha256":"74872798f6e862e7fce5036239b042ea1f163028c2ab32ab0ada5c15e14b5f97","schema_version":"1.0","event_id":"sha256:74872798f6e862e7fce5036239b042ea1f163028c2ab32ab0ada5c15e14b5f97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZQDRM6R5EW54OGCVT2YGKE662/bundle.json","state_url":"https://pith.science/pith/EZQDRM6R5EW54OGCVT2YGKE662/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZQDRM6R5EW54OGCVT2YGKE662/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":"2026-06-10T16:56:29Z","links":{"resolver":"https://pith.science/pith/EZQDRM6R5EW54OGCVT2YGKE662","bundle":"https://pith.science/pith/EZQDRM6R5EW54OGCVT2YGKE662/bundle.json","state":"https://pith.science/pith/EZQDRM6R5EW54OGCVT2YGKE662/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZQDRM6R5EW54OGCVT2YGKE662/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EZQDRM6R5EW54OGCVT2YGKE662","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":"462e26cd30699a8ae36b55a1e22be47eab3fbb48efae6ade4857ffdf4789b406","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-10-18T16:21:07Z","title_canon_sha256":"eaff7e22422090c3e460ec3576e8df29970305b6746ae79e1baaa9e53eee0589"},"schema_version":"1.0","source":{"id":"2510.16566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.16566","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"2510.16566v2","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.16566","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"EZQDRM6R5EW5","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"EZQDRM6R5EW54OGC","created_at":"2026-05-25T02:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"EZQDRM6R","created_at":"2026-05-25T02:01:08Z"}],"graph_snapshots":[{"event_id":"sha256:74872798f6e862e7fce5036239b042ea1f163028c2ab32ab0ada5c15e14b5f97","target":"graph","created_at":"2026-05-25T02:01:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2510.16566/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish some criteria to detect the presence of the maximal ideal $(x_1, \\ldots, x_n)$ in the set of associated primes of powers of monomial ideals in the polynomial ring $K[x_1, \\ldots, x_n]$. Furthermore, for each of these criteria, we illustrate its applicability with corresponding examples.","authors_text":"Jonathan Toledo, Mehrdad Nasernejad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-10-18T16:21:07Z","title":"Criteria for the presence of the maximal ideal in the set of associated primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16566","kind":"arxiv","version":2},"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":"sha256:0ebc28422dad29c78839500a3c2c6bb3dbcd897ce39809b9d7c35f53d91be416","target":"record","created_at":"2026-05-25T02:01:08Z","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":"462e26cd30699a8ae36b55a1e22be47eab3fbb48efae6ade4857ffdf4789b406","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-10-18T16:21:07Z","title_canon_sha256":"eaff7e22422090c3e460ec3576e8df29970305b6746ae79e1baaa9e53eee0589"},"schema_version":"1.0","source":{"id":"2510.16566","kind":"arxiv","version":2}},"canonical_sha256":"266038b3d1e92dde38c2acf583289ef6bd806b6d8dd2d497f3a6c0df5727ad4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"266038b3d1e92dde38c2acf583289ef6bd806b6d8dd2d497f3a6c0df5727ad4a","first_computed_at":"2026-05-25T02:01:08.613166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:08.613166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NK9K0bWmM68WuLqZi7xGPR+0T2hYWYXIScyHMGPmwtsNrT4E8yqTLtz8MNvDu+mOrP5vsKvUZg8JilCaJiyvDA==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:08.613842Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.16566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ebc28422dad29c78839500a3c2c6bb3dbcd897ce39809b9d7c35f53d91be416","sha256:74872798f6e862e7fce5036239b042ea1f163028c2ab32ab0ada5c15e14b5f97"],"state_sha256":"ae9433677f2e951ff924a6620c4088f67e82cd7ee1ba495984e4156c52851680"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHThkpqiVrQ4ZJGrV/8ssnzds2RL0p9YjHCVPB/Ujc+W7R7f8dqpMwCH7Np/uGK0yNY+QW/DTSatljRdCmcsCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:56:29.969130Z","bundle_sha256":"e054c122a58e0eb5bb09f9361046b0e9989af83a00310a382e5c406a477b62d1"}}