{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZF25MRERIPO3P5FPOMC3BSMD6B","short_pith_number":"pith:ZF25MRER","canonical_record":{"source":{"id":"1702.07892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-25T13:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"4af7bcc832cd736cc690e9ec2f92e135dba7e06d643e7a464b3ef8d7c3dadbc2","abstract_canon_sha256":"111b2c571bfa9889a0b97874eb9d7c5f2c5ca6156cd6b171d5a11c71ea53bb7f"},"schema_version":"1.0"},"canonical_sha256":"c975d6449143ddb7f4af7305b0c983f07e0322c9a18cc0f17262088fb437a6ef","source":{"kind":"arxiv","id":"1702.07892","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07892","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07892v2","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07892","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZF25MRERIPO3","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZF25MRERIPO3P5FP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZF25MRER","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZF25MRERIPO3P5FPOMC3BSMD6B","target":"record","payload":{"canonical_record":{"source":{"id":"1702.07892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-25T13:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"4af7bcc832cd736cc690e9ec2f92e135dba7e06d643e7a464b3ef8d7c3dadbc2","abstract_canon_sha256":"111b2c571bfa9889a0b97874eb9d7c5f2c5ca6156cd6b171d5a11c71ea53bb7f"},"schema_version":"1.0"},"canonical_sha256":"c975d6449143ddb7f4af7305b0c983f07e0322c9a18cc0f17262088fb437a6ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:58.961577Z","signature_b64":"WjE8OZDVId6COogqW1Hhtof/EDTlXB9118sdsLHcWgKjwBBRZs4aD0aLvVEIRBVdrMwA57LwGgz3Ch+ZgJzGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c975d6449143ddb7f4af7305b0c983f07e0322c9a18cc0f17262088fb437a6ef","last_reissued_at":"2026-05-18T00:31:58.961149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:58.961149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.07892","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":"2026-05-18T00:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/ULZfg253spFqC+hrXNyGEFtNdqB682pL2OEjLzKKGJ32hCt2IvzbqztkzxRvS/1CzemKjoA9FiBwE+ec1bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:54:37.146457Z"},"content_sha256":"a485e18703948be5727f3dcb1aa4a98b4342d7f0cec6ac797ec7f5b547f914ad","schema_version":"1.0","event_id":"sha256:a485e18703948be5727f3dcb1aa4a98b4342d7f0cec6ac797ec7f5b547f914ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZF25MRERIPO3P5FPOMC3BSMD6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On dimensions supporting a rational projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Lee Kennard, Zhixu Su","submitted_at":"2017-02-25T13:53:33Z","abstract_excerpt":"A rational projective plane ($\\mathbb{QP}^2$) is a simply connected, smooth, closed manifold $M$ such that $H^*(M;\\mathbb{Q}) \\cong \\mathbb{Q}[\\alpha]/\\langle \\alpha^3 \\rangle$. An open problem is to classify the dimensions at which such a manifold exists. The Barge-Sullivan rational surgery realization theorem provides necessary and sufficient conditions that include the Hattori-Stong integrality conditions on the Pontryagin numbers. In this article, we simplify these conditions and combine them with the signature equation to give a single quadratic residue equation that determines whether a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07892","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":""},"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":"2026-05-18T00:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZC9ASwsECvFTp9EHdRV1IrxAF1F9kQkNy4hUKb8ATIJfteXiuUfvd59tA11ErCwfLD+o8tQBSG2arz4DQmPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:54:37.147063Z"},"content_sha256":"8a691cd7a023f18f44d51fa72b41d9ff54f5621e9035e2418d19dac6b7a64a0f","schema_version":"1.0","event_id":"sha256:8a691cd7a023f18f44d51fa72b41d9ff54f5621e9035e2418d19dac6b7a64a0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZF25MRERIPO3P5FPOMC3BSMD6B/bundle.json","state_url":"https://pith.science/pith/ZF25MRERIPO3P5FPOMC3BSMD6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZF25MRERIPO3P5FPOMC3BSMD6B/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":"2026-06-07T09:54:37Z","links":{"resolver":"https://pith.science/pith/ZF25MRERIPO3P5FPOMC3BSMD6B","bundle":"https://pith.science/pith/ZF25MRERIPO3P5FPOMC3BSMD6B/bundle.json","state":"https://pith.science/pith/ZF25MRERIPO3P5FPOMC3BSMD6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZF25MRERIPO3P5FPOMC3BSMD6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZF25MRERIPO3P5FPOMC3BSMD6B","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":"111b2c571bfa9889a0b97874eb9d7c5f2c5ca6156cd6b171d5a11c71ea53bb7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-25T13:53:33Z","title_canon_sha256":"4af7bcc832cd736cc690e9ec2f92e135dba7e06d643e7a464b3ef8d7c3dadbc2"},"schema_version":"1.0","source":{"id":"1702.07892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07892","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07892v2","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07892","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZF25MRERIPO3","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZF25MRERIPO3P5FP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZF25MRER","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:8a691cd7a023f18f44d51fa72b41d9ff54f5621e9035e2418d19dac6b7a64a0f","target":"graph","created_at":"2026-05-18T00:31:58Z","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 rational projective plane ($\\mathbb{QP}^2$) is a simply connected, smooth, closed manifold $M$ such that $H^*(M;\\mathbb{Q}) \\cong \\mathbb{Q}[\\alpha]/\\langle \\alpha^3 \\rangle$. An open problem is to classify the dimensions at which such a manifold exists. The Barge-Sullivan rational surgery realization theorem provides necessary and sufficient conditions that include the Hattori-Stong integrality conditions on the Pontryagin numbers. In this article, we simplify these conditions and combine them with the signature equation to give a single quadratic residue equation that determines whether a ","authors_text":"Lee Kennard, Zhixu Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-25T13:53:33Z","title":"On dimensions supporting a rational projective plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07892","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:a485e18703948be5727f3dcb1aa4a98b4342d7f0cec6ac797ec7f5b547f914ad","target":"record","created_at":"2026-05-18T00:31:58Z","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":"111b2c571bfa9889a0b97874eb9d7c5f2c5ca6156cd6b171d5a11c71ea53bb7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-25T13:53:33Z","title_canon_sha256":"4af7bcc832cd736cc690e9ec2f92e135dba7e06d643e7a464b3ef8d7c3dadbc2"},"schema_version":"1.0","source":{"id":"1702.07892","kind":"arxiv","version":2}},"canonical_sha256":"c975d6449143ddb7f4af7305b0c983f07e0322c9a18cc0f17262088fb437a6ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c975d6449143ddb7f4af7305b0c983f07e0322c9a18cc0f17262088fb437a6ef","first_computed_at":"2026-05-18T00:31:58.961149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:58.961149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WjE8OZDVId6COogqW1Hhtof/EDTlXB9118sdsLHcWgKjwBBRZs4aD0aLvVEIRBVdrMwA57LwGgz3Ch+ZgJzGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:58.961577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a485e18703948be5727f3dcb1aa4a98b4342d7f0cec6ac797ec7f5b547f914ad","sha256:8a691cd7a023f18f44d51fa72b41d9ff54f5621e9035e2418d19dac6b7a64a0f"],"state_sha256":"122ba2184cc73b377dfbcf448ab8feb607f7e4d3f34549aad6c4e38a157898fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oG/xmKZ4E8WK1JEifVVQeBcC/y/gqHSF0XrSyg26imUk1FE2XU0FldpG3MILw+TcmB5mxUYv0OGoNeMQVGerDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:54:37.150180Z","bundle_sha256":"f65a7163f4adc9595a593841b91d61549b590b9fb6982017acdaf7dee0ae5a2d"}}