{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4H6CVPUY3O4IXGSXIXXWYWCNFK","short_pith_number":"pith:4H6CVPUY","canonical_record":{"source":{"id":"1205.6258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-29T04:22:32Z","cross_cats_sorted":["math.AC","math.AG","math.CO"],"title_canon_sha256":"e67a05d1bf21790510ef1d9b514097f5c068d7f30be9e5b5e5aa7ef3e89ee2c6","abstract_canon_sha256":"3da03bada496bfe9d0fad56b467035c62de0f90dfc72f06e910bf6d41fe67b5c"},"schema_version":"1.0"},"canonical_sha256":"e1fc2abe98dbb88b9a5745ef6c584d2aae64733b43441eb702777bdb8a07e09c","source":{"kind":"arxiv","id":"1205.6258","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6258","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6258v1","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6258","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"4H6CVPUY3O4I","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4H6CVPUY3O4IXGSX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4H6CVPUY","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4H6CVPUY3O4IXGSXIXXWYWCNFK","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-29T04:22:32Z","cross_cats_sorted":["math.AC","math.AG","math.CO"],"title_canon_sha256":"e67a05d1bf21790510ef1d9b514097f5c068d7f30be9e5b5e5aa7ef3e89ee2c6","abstract_canon_sha256":"3da03bada496bfe9d0fad56b467035c62de0f90dfc72f06e910bf6d41fe67b5c"},"schema_version":"1.0"},"canonical_sha256":"e1fc2abe98dbb88b9a5745ef6c584d2aae64733b43441eb702777bdb8a07e09c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:38.808902Z","signature_b64":"CUh2LsWtBURWPllUe4CwVBjoBn2PjFTMoUcmCcRi4Rc6PUvrW7QdAVKmkJKS9T1fMprxHhUy0PG2+l3yNM1wCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1fc2abe98dbb88b9a5745ef6c584d2aae64733b43441eb702777bdb8a07e09c","last_reissued_at":"2026-05-18T03:54:38.808412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:38.808412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6258","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":"2026-05-18T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m/rjcmz+E1PSmBD5KcQFX5uUdZK2wL61zzdFLA4w9iBGuZHBQeJ1WrCcCNxHoSfV6xaCGvyhdm8LiZUtSgF4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:32:32.732825Z"},"content_sha256":"41eee510a48ed6072b5a38288e4862ca14a4601880420d1519f1e4fab20e4857","schema_version":"1.0","event_id":"sha256:41eee510a48ed6072b5a38288e4862ca14a4601880420d1519f1e4fab20e4857"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4H6CVPUY3O4IXGSXIXXWYWCNFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On monomial ideal rings and a theorem of Trevisan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.CO"],"primary_cat":"math.AT","authors_text":"A. Bahri, F. R. Cohen, M. Bendersky, S. Gitler","submitted_at":"2012-05-29T04:22:32Z","abstract_excerpt":"A direct proof is presented of a form of Alvise Trevisan's result, that every monomial ideal ring is represented by the cohomology of topological space. Certain of these rings are shown to be realized by polyhedral products indexed by simplicial complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6258","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":"2026-05-18T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90Oa+LvGa/8nn37COopDIX5HE1yGFMKTtYa4PJBm+VnPKYYGzA3oT209kS4noQe9zgmd2KvPCo7UVBG+qmunAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:32:32.733174Z"},"content_sha256":"83e55f8a4987a1ef5ca1fccbefdbfac8f577c81a93c3f5772bb08109ae744226","schema_version":"1.0","event_id":"sha256:83e55f8a4987a1ef5ca1fccbefdbfac8f577c81a93c3f5772bb08109ae744226"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK/bundle.json","state_url":"https://pith.science/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK/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":"2026-05-31T06:32:32Z","links":{"resolver":"https://pith.science/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK","bundle":"https://pith.science/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK/bundle.json","state":"https://pith.science/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4H6CVPUY3O4IXGSXIXXWYWCNFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4H6CVPUY3O4IXGSXIXXWYWCNFK","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":"3da03bada496bfe9d0fad56b467035c62de0f90dfc72f06e910bf6d41fe67b5c","cross_cats_sorted":["math.AC","math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-29T04:22:32Z","title_canon_sha256":"e67a05d1bf21790510ef1d9b514097f5c068d7f30be9e5b5e5aa7ef3e89ee2c6"},"schema_version":"1.0","source":{"id":"1205.6258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6258","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6258v1","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6258","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"4H6CVPUY3O4I","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4H6CVPUY3O4IXGSX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4H6CVPUY","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:83e55f8a4987a1ef5ca1fccbefdbfac8f577c81a93c3f5772bb08109ae744226","target":"graph","created_at":"2026-05-18T03:54:38Z","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":"A direct proof is presented of a form of Alvise Trevisan's result, that every monomial ideal ring is represented by the cohomology of topological space. Certain of these rings are shown to be realized by polyhedral products indexed by simplicial complexes.","authors_text":"A. Bahri, F. R. Cohen, M. Bendersky, S. Gitler","cross_cats":["math.AC","math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-29T04:22:32Z","title":"On monomial ideal rings and a theorem of Trevisan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6258","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":"sha256:41eee510a48ed6072b5a38288e4862ca14a4601880420d1519f1e4fab20e4857","target":"record","created_at":"2026-05-18T03:54:38Z","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":"3da03bada496bfe9d0fad56b467035c62de0f90dfc72f06e910bf6d41fe67b5c","cross_cats_sorted":["math.AC","math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-29T04:22:32Z","title_canon_sha256":"e67a05d1bf21790510ef1d9b514097f5c068d7f30be9e5b5e5aa7ef3e89ee2c6"},"schema_version":"1.0","source":{"id":"1205.6258","kind":"arxiv","version":1}},"canonical_sha256":"e1fc2abe98dbb88b9a5745ef6c584d2aae64733b43441eb702777bdb8a07e09c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1fc2abe98dbb88b9a5745ef6c584d2aae64733b43441eb702777bdb8a07e09c","first_computed_at":"2026-05-18T03:54:38.808412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:38.808412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUh2LsWtBURWPllUe4CwVBjoBn2PjFTMoUcmCcRi4Rc6PUvrW7QdAVKmkJKS9T1fMprxHhUy0PG2+l3yNM1wCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:38.808902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41eee510a48ed6072b5a38288e4862ca14a4601880420d1519f1e4fab20e4857","sha256:83e55f8a4987a1ef5ca1fccbefdbfac8f577c81a93c3f5772bb08109ae744226"],"state_sha256":"1b25bfad0aa5cfb3e123e60635cb6bf9f3f949921ab5d227d677304f58f253f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlHWVYhnA2HPfuZTFwlunCdVzS1Zo0XvYfxm6rF4jm1xhzWDlC+vq+9RxdvBLjRocxWSaaCI8CC+yfUOKurfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:32:32.735351Z","bundle_sha256":"7e6a70abf426b06d9fb9caaa80347c6628242424e073a3d7f08854b8cdb3ca0e"}}