{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4XUJBF4EVED4D7KVXR4NNFK6RY","short_pith_number":"pith:4XUJBF4E","canonical_record":{"source":{"id":"1603.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-04T02:07:50Z","cross_cats_sorted":[],"title_canon_sha256":"c4fb5efb57a9f2739832b9a4612c53a4c7cd4217d5fd2311695926cf4ac74832","abstract_canon_sha256":"1c1e0ad0a6bc45dcd9af5cfd704e3f619c8be6bf5316c8c91c54f5c16d9b3253"},"schema_version":"1.0"},"canonical_sha256":"e5e8909784a907c1fd55bc78d6955e8e1deee5fb308ead094930d935eb3923f7","source":{"kind":"arxiv","id":"1603.01331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01331","created_at":"2026-05-18T01:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01331v1","created_at":"2026-05-18T01:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01331","created_at":"2026-05-18T01:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"4XUJBF4EVED4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4XUJBF4EVED4D7KV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4XUJBF4E","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4XUJBF4EVED4D7KVXR4NNFK6RY","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-04T02:07:50Z","cross_cats_sorted":[],"title_canon_sha256":"c4fb5efb57a9f2739832b9a4612c53a4c7cd4217d5fd2311695926cf4ac74832","abstract_canon_sha256":"1c1e0ad0a6bc45dcd9af5cfd704e3f619c8be6bf5316c8c91c54f5c16d9b3253"},"schema_version":"1.0"},"canonical_sha256":"e5e8909784a907c1fd55bc78d6955e8e1deee5fb308ead094930d935eb3923f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:37.910873Z","signature_b64":"pGUJkywQ732ebGe6KHBAbq/ftXi2CQOF54dN1hInD1JG4QCZQP8yjzknz1zuOlp7oArCaftaPIOPuA9M2CQlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5e8909784a907c1fd55bc78d6955e8e1deee5fb308ead094930d935eb3923f7","last_reissued_at":"2026-05-18T01:19:37.910194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:37.910194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01331","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":"2026-05-18T01:19:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3qCVfGZWHOhelpJ/6o59FpWMcoHQV6hqDjphZfQrMn3MORFxZvE/iAZWSI0x4GlkGvpOQrsx2cg4Ad9AzxFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:15:38.516643Z"},"content_sha256":"928ebe6dcabed08c288a029c5379f0471c93d03da0ba4e63f467322e5716b8f1","schema_version":"1.0","event_id":"sha256:928ebe6dcabed08c288a029c5379f0471c93d03da0ba4e63f467322e5716b8f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4XUJBF4EVED4D7KVXR4NNFK6RY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypergraphs with high projective dimension and 1-dimensional Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kuei-Nuan Lin, Paolo Mantero","submitted_at":"2016-03-04T02:07:50Z","abstract_excerpt":"We prove a sufficient and a necessary condition for a square-free monomial ideal $J$ associated to a (dual) hypergraph to have projective dimension equal to the minimal number of generators of $J$ minus 2. We also provide an effective explicit procedure to compute the projective dimension of 1-dimensional hypergraphs $\\mathcal{H}$ when each connected component contains at most one cycle. An algorithm to compute the projective dimension is also included. Applications of these results are given; they include, for instance, computing the projective dimension of monomial ideals whose associated hy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01331","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":"2026-05-18T01:19:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8hy/3ULp/UxxVy8rDM8u8bNxUzeX/tx/G65NE96QhZlp1Fyut/PIRb9p3rC0LjeDcS/iiUvHJSp141nolHDrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:15:38.517034Z"},"content_sha256":"df7e3e51a0b19613e08b97367f6ffcfa63ca295e11925ee8242ac6781f5c5645","schema_version":"1.0","event_id":"sha256:df7e3e51a0b19613e08b97367f6ffcfa63ca295e11925ee8242ac6781f5c5645"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XUJBF4EVED4D7KVXR4NNFK6RY/bundle.json","state_url":"https://pith.science/pith/4XUJBF4EVED4D7KVXR4NNFK6RY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XUJBF4EVED4D7KVXR4NNFK6RY/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":"2026-06-02T13:15:38Z","links":{"resolver":"https://pith.science/pith/4XUJBF4EVED4D7KVXR4NNFK6RY","bundle":"https://pith.science/pith/4XUJBF4EVED4D7KVXR4NNFK6RY/bundle.json","state":"https://pith.science/pith/4XUJBF4EVED4D7KVXR4NNFK6RY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XUJBF4EVED4D7KVXR4NNFK6RY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4XUJBF4EVED4D7KVXR4NNFK6RY","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":"1c1e0ad0a6bc45dcd9af5cfd704e3f619c8be6bf5316c8c91c54f5c16d9b3253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-04T02:07:50Z","title_canon_sha256":"c4fb5efb57a9f2739832b9a4612c53a4c7cd4217d5fd2311695926cf4ac74832"},"schema_version":"1.0","source":{"id":"1603.01331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01331","created_at":"2026-05-18T01:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01331v1","created_at":"2026-05-18T01:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01331","created_at":"2026-05-18T01:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"4XUJBF4EVED4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4XUJBF4EVED4D7KV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4XUJBF4E","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:df7e3e51a0b19613e08b97367f6ffcfa63ca295e11925ee8242ac6781f5c5645","target":"graph","created_at":"2026-05-18T01:19:37Z","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 prove a sufficient and a necessary condition for a square-free monomial ideal $J$ associated to a (dual) hypergraph to have projective dimension equal to the minimal number of generators of $J$ minus 2. We also provide an effective explicit procedure to compute the projective dimension of 1-dimensional hypergraphs $\\mathcal{H}$ when each connected component contains at most one cycle. An algorithm to compute the projective dimension is also included. Applications of these results are given; they include, for instance, computing the projective dimension of monomial ideals whose associated hy","authors_text":"Kuei-Nuan Lin, Paolo Mantero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-04T02:07:50Z","title":"Hypergraphs with high projective dimension and 1-dimensional Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01331","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":"sha256:928ebe6dcabed08c288a029c5379f0471c93d03da0ba4e63f467322e5716b8f1","target":"record","created_at":"2026-05-18T01:19:37Z","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":"1c1e0ad0a6bc45dcd9af5cfd704e3f619c8be6bf5316c8c91c54f5c16d9b3253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-04T02:07:50Z","title_canon_sha256":"c4fb5efb57a9f2739832b9a4612c53a4c7cd4217d5fd2311695926cf4ac74832"},"schema_version":"1.0","source":{"id":"1603.01331","kind":"arxiv","version":1}},"canonical_sha256":"e5e8909784a907c1fd55bc78d6955e8e1deee5fb308ead094930d935eb3923f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5e8909784a907c1fd55bc78d6955e8e1deee5fb308ead094930d935eb3923f7","first_computed_at":"2026-05-18T01:19:37.910194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:37.910194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pGUJkywQ732ebGe6KHBAbq/ftXi2CQOF54dN1hInD1JG4QCZQP8yjzknz1zuOlp7oArCaftaPIOPuA9M2CQlDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:37.910873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928ebe6dcabed08c288a029c5379f0471c93d03da0ba4e63f467322e5716b8f1","sha256:df7e3e51a0b19613e08b97367f6ffcfa63ca295e11925ee8242ac6781f5c5645"],"state_sha256":"68343ef6c3a9e07887caebf3bdc0ac61440eab7d459159345eb247bd1a8ef80f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0i9H9a3LjYFgUXaNFOZmQEVolR/i5atEWE1proPn9/918oo5ZgLxDWYPNc5Ha9+wIxochoQW6Kwjt0dQDNEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:15:38.519074Z","bundle_sha256":"4e4f59ca14d7bde8455b84a3186a56aec57c0f6ebe31eceb33335ce5bf140607"}}