{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NG2EO7VQBASRFSCDUMYMZDJGMN","short_pith_number":"pith:NG2EO7VQ","canonical_record":{"source":{"id":"1704.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-25T11:05:18Z","cross_cats_sorted":[],"title_canon_sha256":"bb079e930117847984d5dbd23992692ec70da53b1cf346a6ff2b8c5814b1ee9c","abstract_canon_sha256":"c164217921571ce9c98a9bdd67316f1b659d850773c13c443b293fe4301221f0"},"schema_version":"1.0"},"canonical_sha256":"69b4477eb0082512c843a330cc8d2663681a69cda9890a90b83c0f76a6ea8973","source":{"kind":"arxiv","id":"1704.07631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07631","created_at":"2026-05-18T00:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07631v2","created_at":"2026-05-18T00:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07631","created_at":"2026-05-18T00:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"NG2EO7VQBASR","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NG2EO7VQBASRFSCD","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NG2EO7VQ","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NG2EO7VQBASRFSCDUMYMZDJGMN","target":"record","payload":{"canonical_record":{"source":{"id":"1704.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-25T11:05:18Z","cross_cats_sorted":[],"title_canon_sha256":"bb079e930117847984d5dbd23992692ec70da53b1cf346a6ff2b8c5814b1ee9c","abstract_canon_sha256":"c164217921571ce9c98a9bdd67316f1b659d850773c13c443b293fe4301221f0"},"schema_version":"1.0"},"canonical_sha256":"69b4477eb0082512c843a330cc8d2663681a69cda9890a90b83c0f76a6ea8973","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:52.623731Z","signature_b64":"GEapHUYtc3sCpdijhwLeNgF7tyrQFHl7jVygUZ4DQdT0+6WWOd9MySoZHcQNoKDsnUh5vnTbVdAeIElstBIIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69b4477eb0082512c843a330cc8d2663681a69cda9890a90b83c0f76a6ea8973","last_reissued_at":"2026-05-18T00:27:52.623212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:52.623212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.07631","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":"2026-05-18T00:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5sNcyj6ZDc+rgmbVx1kMpKCle8hPGQVIzJS715tdYcuX1ANapajeQ+mbwfB8l5pe/eKcGD6qVm4SiWnlPqeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:15:20.608388Z"},"content_sha256":"6c320d9b179e734afe2e6323c72dc878664877aeca9f4b6831482956ed9364c1","schema_version":"1.0","event_id":"sha256:6c320d9b179e734afe2e6323c72dc878664877aeca9f4b6831482956ed9364c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NG2EO7VQBASRFSCDUMYMZDJGMN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic orthogonality and commuting projections in operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anil Kumar Karn","submitted_at":"2017-04-25T11:05:18Z","abstract_excerpt":"We describe absolutely ordered $p$-normed spaces, for $1 \\le p \\le \\infty$ which presents a model for \"non-commutative\" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of {\\it absolute compatibility} among positive elements in absolute order unit spaces and relate it to symmetrized product in the case of a C$^{\\ast}$-algebra. In the latter case, whenever one of the elements is a projection, the elements are absolutely compatible if and only if they commute. We develop an order theoretic prototype of the results. For this purpose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07631","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":"2026-05-18T00:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VwOBQRiHTqaMVvLTDx/PFyx8wJVJT7w5xjBxh8dK2DSZhDMAd3Q82I/yH7Jdr0HT4sBYzSIpiXg8s/ol6TZ6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:15:20.608741Z"},"content_sha256":"d09783e60a7fe3192f79f4d846ca451584b1b6a872b14cbbbc0d25aba3d61322","schema_version":"1.0","event_id":"sha256:d09783e60a7fe3192f79f4d846ca451584b1b6a872b14cbbbc0d25aba3d61322"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NG2EO7VQBASRFSCDUMYMZDJGMN/bundle.json","state_url":"https://pith.science/pith/NG2EO7VQBASRFSCDUMYMZDJGMN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NG2EO7VQBASRFSCDUMYMZDJGMN/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":"2026-06-03T17:15:20Z","links":{"resolver":"https://pith.science/pith/NG2EO7VQBASRFSCDUMYMZDJGMN","bundle":"https://pith.science/pith/NG2EO7VQBASRFSCDUMYMZDJGMN/bundle.json","state":"https://pith.science/pith/NG2EO7VQBASRFSCDUMYMZDJGMN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NG2EO7VQBASRFSCDUMYMZDJGMN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NG2EO7VQBASRFSCDUMYMZDJGMN","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":"c164217921571ce9c98a9bdd67316f1b659d850773c13c443b293fe4301221f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-25T11:05:18Z","title_canon_sha256":"bb079e930117847984d5dbd23992692ec70da53b1cf346a6ff2b8c5814b1ee9c"},"schema_version":"1.0","source":{"id":"1704.07631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07631","created_at":"2026-05-18T00:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07631v2","created_at":"2026-05-18T00:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07631","created_at":"2026-05-18T00:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"NG2EO7VQBASR","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NG2EO7VQBASRFSCD","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NG2EO7VQ","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:d09783e60a7fe3192f79f4d846ca451584b1b6a872b14cbbbc0d25aba3d61322","target":"graph","created_at":"2026-05-18T00:27:52Z","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 describe absolutely ordered $p$-normed spaces, for $1 \\le p \\le \\infty$ which presents a model for \"non-commutative\" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of {\\it absolute compatibility} among positive elements in absolute order unit spaces and relate it to symmetrized product in the case of a C$^{\\ast}$-algebra. In the latter case, whenever one of the elements is a projection, the elements are absolutely compatible if and only if they commute. We develop an order theoretic prototype of the results. For this purpose","authors_text":"Anil Kumar Karn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-25T11:05:18Z","title":"Algebraic orthogonality and commuting projections in operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07631","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":"sha256:6c320d9b179e734afe2e6323c72dc878664877aeca9f4b6831482956ed9364c1","target":"record","created_at":"2026-05-18T00:27:52Z","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":"c164217921571ce9c98a9bdd67316f1b659d850773c13c443b293fe4301221f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-25T11:05:18Z","title_canon_sha256":"bb079e930117847984d5dbd23992692ec70da53b1cf346a6ff2b8c5814b1ee9c"},"schema_version":"1.0","source":{"id":"1704.07631","kind":"arxiv","version":2}},"canonical_sha256":"69b4477eb0082512c843a330cc8d2663681a69cda9890a90b83c0f76a6ea8973","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69b4477eb0082512c843a330cc8d2663681a69cda9890a90b83c0f76a6ea8973","first_computed_at":"2026-05-18T00:27:52.623212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:52.623212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GEapHUYtc3sCpdijhwLeNgF7tyrQFHl7jVygUZ4DQdT0+6WWOd9MySoZHcQNoKDsnUh5vnTbVdAeIElstBIIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:52.623731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c320d9b179e734afe2e6323c72dc878664877aeca9f4b6831482956ed9364c1","sha256:d09783e60a7fe3192f79f4d846ca451584b1b6a872b14cbbbc0d25aba3d61322"],"state_sha256":"5d748d5dfe143b02f9a04f770611de05b64119a845e2bd2fd0fbe3066f07f2ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S43TsCJ3zuc0/Qj48yIzzBeqlFWADUCknQGx9wdwGtGvqQ3MTYl3KQvF4RA/f41Odww12y2dj4zuBqrBsLb1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:15:20.611113Z","bundle_sha256":"28381360e04ea8b0dccd83bf9f772daf1232c0e77adbe17b0c8d4c1d0c40f491"}}