{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:33PGLYYVSCMRNBZ3RUC5NT7ETD","short_pith_number":"pith:33PGLYYV","canonical_record":{"source":{"id":"1905.05043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T14:00:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"1d2c4ee184b4942c670b5bfc19ca267cdbf5349da145691816f328fe9aaa2e0b","abstract_canon_sha256":"75e7ea14a60a2a0d8f89f09ca1c25e242f020d01a91b66e391279f47445c2e05"},"schema_version":"1.0"},"canonical_sha256":"dede65e315909916873b8d05d6cfe498e6b816241c39998bceef5b380baef4b0","source":{"kind":"arxiv","id":"1905.05043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05043","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05043v1","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05043","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"33PGLYYVSCMR","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"33PGLYYVSCMRNBZ3","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"33PGLYYV","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:33PGLYYVSCMRNBZ3RUC5NT7ETD","target":"record","payload":{"canonical_record":{"source":{"id":"1905.05043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T14:00:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"1d2c4ee184b4942c670b5bfc19ca267cdbf5349da145691816f328fe9aaa2e0b","abstract_canon_sha256":"75e7ea14a60a2a0d8f89f09ca1c25e242f020d01a91b66e391279f47445c2e05"},"schema_version":"1.0"},"canonical_sha256":"dede65e315909916873b8d05d6cfe498e6b816241c39998bceef5b380baef4b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:22.693786Z","signature_b64":"D6pG1Z0sKIuMa/UdjHFc21sNjhUHHM8Ud53voW6nTAaO1mTDG55aD9QWnkB2wZ11ea25CzL+KdoC85RhxoNRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dede65e315909916873b8d05d6cfe498e6b816241c39998bceef5b380baef4b0","last_reissued_at":"2026-05-17T23:46:22.693054Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:22.693054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.05043","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":"2026-05-17T23:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3yS9QXPkxD8keJmbvvLrfsuc1ktBfppbsSSiSsiYgZDbVT9Vqg0PbvSf4moNGzcC+5vOIDHZf87uQa/egfpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:00:28.713579Z"},"content_sha256":"3f6b5eb07fbd4e9daf7d3510081f4e208d1d5202dda5ee6d9ff167a9c6683df4","schema_version":"1.0","event_id":"sha256:3f6b5eb07fbd4e9daf7d3510081f4e208d1d5202dda5ee6d9ff167a9c6683df4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:33PGLYYVSCMRNBZ3RUC5NT7ETD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal Cohen-Macaulay Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Hailong Dao, Joseph Doolittle, Justin Lyle","submitted_at":"2019-05-13T14:00:28Z","abstract_excerpt":"We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal Cohen-Macaulay. We show that many interesting examples of Cohen-Macaulay complexes in combinatorics are minimal, including Rudin's ball, Ziegler's ball, the dunce hat, and recently discovered non-partitionable Cohen-Macaulay complexes. We further provide various ways to construct such complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05043","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":"2026-05-17T23:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sl1rlwm9J2q944jm5HPFYp6k3dIiVS8MkaE2F5thzw6/t1cMM8Qyu5GInUCUNR9sF1JH1EjgDccBoCq+vELAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:00:28.714294Z"},"content_sha256":"6057a51452c3a50655d7251d2d7d781b38f652b40049a747af89568847b6c1b5","schema_version":"1.0","event_id":"sha256:6057a51452c3a50655d7251d2d7d781b38f652b40049a747af89568847b6c1b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD/bundle.json","state_url":"https://pith.science/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD/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":"2026-06-08T08:00:28Z","links":{"resolver":"https://pith.science/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD","bundle":"https://pith.science/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD/bundle.json","state":"https://pith.science/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33PGLYYVSCMRNBZ3RUC5NT7ETD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:33PGLYYVSCMRNBZ3RUC5NT7ETD","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":"75e7ea14a60a2a0d8f89f09ca1c25e242f020d01a91b66e391279f47445c2e05","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T14:00:28Z","title_canon_sha256":"1d2c4ee184b4942c670b5bfc19ca267cdbf5349da145691816f328fe9aaa2e0b"},"schema_version":"1.0","source":{"id":"1905.05043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05043","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05043v1","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05043","created_at":"2026-05-17T23:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"33PGLYYVSCMR","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"33PGLYYVSCMRNBZ3","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"33PGLYYV","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:6057a51452c3a50655d7251d2d7d781b38f652b40049a747af89568847b6c1b5","target":"graph","created_at":"2026-05-17T23:46:22Z","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 define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal Cohen-Macaulay. We show that many interesting examples of Cohen-Macaulay complexes in combinatorics are minimal, including Rudin's ball, Ziegler's ball, the dunce hat, and recently discovered non-partitionable Cohen-Macaulay complexes. We further provide various ways to construct such complexes.","authors_text":"Hailong Dao, Joseph Doolittle, Justin Lyle","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T14:00:28Z","title":"Minimal Cohen-Macaulay Simplicial Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05043","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":"sha256:3f6b5eb07fbd4e9daf7d3510081f4e208d1d5202dda5ee6d9ff167a9c6683df4","target":"record","created_at":"2026-05-17T23:46:22Z","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":"75e7ea14a60a2a0d8f89f09ca1c25e242f020d01a91b66e391279f47445c2e05","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T14:00:28Z","title_canon_sha256":"1d2c4ee184b4942c670b5bfc19ca267cdbf5349da145691816f328fe9aaa2e0b"},"schema_version":"1.0","source":{"id":"1905.05043","kind":"arxiv","version":1}},"canonical_sha256":"dede65e315909916873b8d05d6cfe498e6b816241c39998bceef5b380baef4b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dede65e315909916873b8d05d6cfe498e6b816241c39998bceef5b380baef4b0","first_computed_at":"2026-05-17T23:46:22.693054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:22.693054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D6pG1Z0sKIuMa/UdjHFc21sNjhUHHM8Ud53voW6nTAaO1mTDG55aD9QWnkB2wZ11ea25CzL+KdoC85RhxoNRCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:22.693786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f6b5eb07fbd4e9daf7d3510081f4e208d1d5202dda5ee6d9ff167a9c6683df4","sha256:6057a51452c3a50655d7251d2d7d781b38f652b40049a747af89568847b6c1b5"],"state_sha256":"f807bc49f648f418ac79c767b027b3dca9c7e3ba41dcf5301a33d3a3798ee21f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"siCrbXy6wyWm76tgL7QOKjQhNMsoBsXzwbFR2MvOAbpXAKg3EFjnuJgjlubQOq6tFmc7pgiI3f4d22KMBf9nAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T08:00:28.718209Z","bundle_sha256":"94dfdd00f0c9e1c3c12fc9b3a5e10c01909b9e5437654fbc638c46526ab692a6"}}