{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:P5LKVGE3GXKZAU6SQDGBQZKXJS","short_pith_number":"pith:P5LKVGE3","canonical_record":{"source":{"id":"1407.6852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-25T11:16:41Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cc584dc52bffd464366edb6a3e52722cb951bf9484496d615395c306199c424a","abstract_canon_sha256":"ac4600582c55c2c0281078deef2fd90d50a612d233f28be30372c9305e7670cc"},"schema_version":"1.0"},"canonical_sha256":"7f56aa989b35d59053d280cc1865574c84286512ad547616ea595719be154873","source":{"kind":"arxiv","id":"1407.6852","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6852","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6852v2","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6852","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"P5LKVGE3GXKZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5LKVGE3GXKZAU6S","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5LKVGE3","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:P5LKVGE3GXKZAU6SQDGBQZKXJS","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-25T11:16:41Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cc584dc52bffd464366edb6a3e52722cb951bf9484496d615395c306199c424a","abstract_canon_sha256":"ac4600582c55c2c0281078deef2fd90d50a612d233f28be30372c9305e7670cc"},"schema_version":"1.0"},"canonical_sha256":"7f56aa989b35d59053d280cc1865574c84286512ad547616ea595719be154873","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:10.058821Z","signature_b64":"skihKAKrhekigC4PtFCbLhRTRvaQNVf+nS36VT41W32LCaekBiKDo4NDqm70A1GJpZQROPzFVKlc4RWyq8l2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f56aa989b35d59053d280cc1865574c84286512ad547616ea595719be154873","last_reissued_at":"2026-05-18T02:40:10.058287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:10.058287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6852","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":"2026-05-18T02:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9LsyrU4zO8BKlsbkGi89INqLDCU2ZcTJEXhq9qrf2SbBuTWdwH0B2OvGH4aMRTVE9JL5PCmzfO16K8kkmu7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T21:05:57.852239Z"},"content_sha256":"e7e04d15e25d6b3d0e394160ee5310ee5ee395f5f706f0342fa2b1d26d6cb6c0","schema_version":"1.0","event_id":"sha256:e7e04d15e25d6b3d0e394160ee5310ee5ee395f5f706f0342fa2b1d26d6cb6c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:P5LKVGE3GXKZAU6SQDGBQZKXJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative position of three subspaces in a Hilbert space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Masatoshi Enomoto, Yasuo Watatani","submitted_at":"2014-07-25T11:16:41Z","abstract_excerpt":"We study the relative position of three subspaces in a separable infinite-dimensional Hilbert space. In the finite-dimensional case, Brenner described the general position of three subspaces completely. We extend it to a certain class of three subspaces in an infinite-dimensional Hilbert space. We also give a partial result which gives a condition on a system to have a (dense) decomposition containing a pentagon."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6852","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":"2026-05-18T02:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4DnZrNUc/28IQLTOFRi/I2TtAv4xOgNt4jmNAZ4Ec+M/IenC9XBzFe5Qf3HZ+oH/pkAsMdw4+V+yUBAo97SBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T21:05:57.852582Z"},"content_sha256":"25d4ca2c5c1c1cdd6e4a06736863af8965797f0ce01fa88f3da0dcafa426b60b","schema_version":"1.0","event_id":"sha256:25d4ca2c5c1c1cdd6e4a06736863af8965797f0ce01fa88f3da0dcafa426b60b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS/bundle.json","state_url":"https://pith.science/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS/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":"2026-07-04T21:05:57Z","links":{"resolver":"https://pith.science/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS","bundle":"https://pith.science/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS/bundle.json","state":"https://pith.science/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5LKVGE3GXKZAU6SQDGBQZKXJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P5LKVGE3GXKZAU6SQDGBQZKXJS","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":"ac4600582c55c2c0281078deef2fd90d50a612d233f28be30372c9305e7670cc","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-25T11:16:41Z","title_canon_sha256":"cc584dc52bffd464366edb6a3e52722cb951bf9484496d615395c306199c424a"},"schema_version":"1.0","source":{"id":"1407.6852","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6852","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6852v2","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6852","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"P5LKVGE3GXKZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5LKVGE3GXKZAU6S","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5LKVGE3","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:25d4ca2c5c1c1cdd6e4a06736863af8965797f0ce01fa88f3da0dcafa426b60b","target":"graph","created_at":"2026-05-18T02:40:10Z","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 study the relative position of three subspaces in a separable infinite-dimensional Hilbert space. In the finite-dimensional case, Brenner described the general position of three subspaces completely. We extend it to a certain class of three subspaces in an infinite-dimensional Hilbert space. We also give a partial result which gives a condition on a system to have a (dense) decomposition containing a pentagon.","authors_text":"Masatoshi Enomoto, Yasuo Watatani","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-25T11:16:41Z","title":"Relative position of three subspaces in a Hilbert space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6852","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:e7e04d15e25d6b3d0e394160ee5310ee5ee395f5f706f0342fa2b1d26d6cb6c0","target":"record","created_at":"2026-05-18T02:40:10Z","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":"ac4600582c55c2c0281078deef2fd90d50a612d233f28be30372c9305e7670cc","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-25T11:16:41Z","title_canon_sha256":"cc584dc52bffd464366edb6a3e52722cb951bf9484496d615395c306199c424a"},"schema_version":"1.0","source":{"id":"1407.6852","kind":"arxiv","version":2}},"canonical_sha256":"7f56aa989b35d59053d280cc1865574c84286512ad547616ea595719be154873","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f56aa989b35d59053d280cc1865574c84286512ad547616ea595719be154873","first_computed_at":"2026-05-18T02:40:10.058287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:10.058287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"skihKAKrhekigC4PtFCbLhRTRvaQNVf+nS36VT41W32LCaekBiKDo4NDqm70A1GJpZQROPzFVKlc4RWyq8l2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:10.058821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6852","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7e04d15e25d6b3d0e394160ee5310ee5ee395f5f706f0342fa2b1d26d6cb6c0","sha256:25d4ca2c5c1c1cdd6e4a06736863af8965797f0ce01fa88f3da0dcafa426b60b"],"state_sha256":"58f247bc71f6d04e2cd2d258f854073adc9a26d801f0dbee888ed6685cfdfcbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NKo3XYqZr2ZYPJY7+mYnTqgAupo18V/h2jH0gHjedYns8Dr8GO/qZcMN0jHiMObVF/DJljKmFzPq8fmP9GduCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T21:05:57.854422Z","bundle_sha256":"93bcd41a42281f546b6340f969876db6635f995cb03af4c6b2471042155c8baa"}}