{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LHE24QBVQSNXMATV5FJWFXLMZG","short_pith_number":"pith:LHE24QBV","canonical_record":{"source":{"id":"1012.3235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-15T06:42:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d7184e6c0f30f09859618fa4234cb915fbd66a89b05b3324e211351dccf39ec","abstract_canon_sha256":"e84c4638c2cae9cdff80c27fb1e3394e85beba61232d60a91636dda0e69ee868"},"schema_version":"1.0"},"canonical_sha256":"59c9ae4035849b760275e95362dd6cc983aa913cffccf5d9d51789d092bce141","source":{"kind":"arxiv","id":"1012.3235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3235","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3235v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3235","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"LHE24QBVQSNX","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LHE24QBVQSNXMATV","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LHE24QBV","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LHE24QBVQSNXMATV5FJWFXLMZG","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-15T06:42:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d7184e6c0f30f09859618fa4234cb915fbd66a89b05b3324e211351dccf39ec","abstract_canon_sha256":"e84c4638c2cae9cdff80c27fb1e3394e85beba61232d60a91636dda0e69ee868"},"schema_version":"1.0"},"canonical_sha256":"59c9ae4035849b760275e95362dd6cc983aa913cffccf5d9d51789d092bce141","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:20.032941Z","signature_b64":"cdQjY9Mw3EOmLVqmUUnWLo6Hgmdz65KDrsmk8UsZTPxeI+ea+lDNSlkULKQ8KUmhBMoi6uQdG3hgAe3IZ1nMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59c9ae4035849b760275e95362dd6cc983aa913cffccf5d9d51789d092bce141","last_reissued_at":"2026-05-18T03:49:20.032372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:20.032372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3235","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1s+xuS3/ePmC2Rk/cbj9xuF7xFToyo6ynWmkF5XGAwAfoqlcw+kZI5LgtYQlLVuRJetUf08QcYJwxXDT6c1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:40:55.774476Z"},"content_sha256":"743b05e83315797eeed090c7a86c1718cbd64179513a040cadc01a5b038a93ab","schema_version":"1.0","event_id":"sha256:743b05e83315797eeed090c7a86c1718cbd64179513a040cadc01a5b038a93ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LHE24QBVQSNXMATV5FJWFXLMZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A triangulation of $\\CC P^3$ as symmetric cube of $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2010-12-15T06:42:31Z","abstract_excerpt":"The symmetric group $S_3$ acts on $S^2 \\times S^2 \\times S^2$ by coordinate permutation, and the quotient space $(S^2 \\times S^2 \\times S^2)/S_3$ is homeomorphic to the complex projective space $\\CC P^3$. In this paper, we construct an 124-vertex simplicial subdivision $(S^2 \\times S^2 \\times S^2)_{124}$ of the 64-vertex standard cellulation $S^2_4 \\times S^2_4 \\times S^2_4$ of $S^2 \\times S^2 \\times S^2$, such that the $S_3$-action on this cellulation naturally extends to an action on $(S^2 \\times S^2 \\times S^2)_{124}$. Further, the $S_3$-action on $(S^2 \\times S^2 \\times S^2)_{124}$ is \"goo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3235","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ugTb9dP3BDy3RxUY+sbw7X28JH3BJcJYdhsiKtkW426PYRFuxJ3oADV1sgqQNpfMKP9/O1zftVgziOT3iKahBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:40:55.774893Z"},"content_sha256":"ce1ee93101cdbe4c458ed96b1fbe7bdd4dc678516511d283be4998b77c847972","schema_version":"1.0","event_id":"sha256:ce1ee93101cdbe4c458ed96b1fbe7bdd4dc678516511d283be4998b77c847972"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHE24QBVQSNXMATV5FJWFXLMZG/bundle.json","state_url":"https://pith.science/pith/LHE24QBVQSNXMATV5FJWFXLMZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHE24QBVQSNXMATV5FJWFXLMZG/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":"2026-05-26T03:40:55Z","links":{"resolver":"https://pith.science/pith/LHE24QBVQSNXMATV5FJWFXLMZG","bundle":"https://pith.science/pith/LHE24QBVQSNXMATV5FJWFXLMZG/bundle.json","state":"https://pith.science/pith/LHE24QBVQSNXMATV5FJWFXLMZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHE24QBVQSNXMATV5FJWFXLMZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LHE24QBVQSNXMATV5FJWFXLMZG","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":"e84c4638c2cae9cdff80c27fb1e3394e85beba61232d60a91636dda0e69ee868","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-15T06:42:31Z","title_canon_sha256":"9d7184e6c0f30f09859618fa4234cb915fbd66a89b05b3324e211351dccf39ec"},"schema_version":"1.0","source":{"id":"1012.3235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3235","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3235v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3235","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"LHE24QBVQSNX","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LHE24QBVQSNXMATV","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LHE24QBV","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:ce1ee93101cdbe4c458ed96b1fbe7bdd4dc678516511d283be4998b77c847972","target":"graph","created_at":"2026-05-18T03:49:20Z","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":"The symmetric group $S_3$ acts on $S^2 \\times S^2 \\times S^2$ by coordinate permutation, and the quotient space $(S^2 \\times S^2 \\times S^2)/S_3$ is homeomorphic to the complex projective space $\\CC P^3$. In this paper, we construct an 124-vertex simplicial subdivision $(S^2 \\times S^2 \\times S^2)_{124}$ of the 64-vertex standard cellulation $S^2_4 \\times S^2_4 \\times S^2_4$ of $S^2 \\times S^2 \\times S^2$, such that the $S_3$-action on this cellulation naturally extends to an action on $(S^2 \\times S^2 \\times S^2)_{124}$. Further, the $S_3$-action on $(S^2 \\times S^2 \\times S^2)_{124}$ is \"goo","authors_text":"Basudeb Datta, Bhaskar Bagchi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-15T06:42:31Z","title":"A triangulation of $\\CC P^3$ as symmetric cube of $S^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3235","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":"sha256:743b05e83315797eeed090c7a86c1718cbd64179513a040cadc01a5b038a93ab","target":"record","created_at":"2026-05-18T03:49:20Z","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":"e84c4638c2cae9cdff80c27fb1e3394e85beba61232d60a91636dda0e69ee868","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-15T06:42:31Z","title_canon_sha256":"9d7184e6c0f30f09859618fa4234cb915fbd66a89b05b3324e211351dccf39ec"},"schema_version":"1.0","source":{"id":"1012.3235","kind":"arxiv","version":1}},"canonical_sha256":"59c9ae4035849b760275e95362dd6cc983aa913cffccf5d9d51789d092bce141","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59c9ae4035849b760275e95362dd6cc983aa913cffccf5d9d51789d092bce141","first_computed_at":"2026-05-18T03:49:20.032372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:20.032372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cdQjY9Mw3EOmLVqmUUnWLo6Hgmdz65KDrsmk8UsZTPxeI+ea+lDNSlkULKQ8KUmhBMoi6uQdG3hgAe3IZ1nMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:20.032941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:743b05e83315797eeed090c7a86c1718cbd64179513a040cadc01a5b038a93ab","sha256:ce1ee93101cdbe4c458ed96b1fbe7bdd4dc678516511d283be4998b77c847972"],"state_sha256":"edea1cdce44b8c070d64fbfc7e16ef03a8a54f9fe7c15bf9ce4b67f1b9e823d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ih2t4slBDaTMOQDU0NONVKzSY+dWsTYExeYZY0NI6q0+Q9WMoDoBdc4+fQ2JDVPCW6noKXvPT06LNkjchB79DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:40:55.778405Z","bundle_sha256":"e462cb15f825613a1bbdfccd8d0080c3dd4812294d6c1c263970ff8d2f2978a7"}}