{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:66B4N6TAHRLTIYRJYDXHVA7PMD","short_pith_number":"pith:66B4N6TA","canonical_record":{"source":{"id":"1906.09723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-24T04:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"78bd7f3d0116b6e46207be1c36e34122998c65e0f29e01c04e90a7041a79f298","abstract_canon_sha256":"7a199347f9e905817c42f2f66fb32b9767811c0d130ccd878adba78ab511ec86"},"schema_version":"1.0"},"canonical_sha256":"f783c6fa603c57346229c0ee7a83ef60f43068ac9a1fa9909789a5c6e64a3178","source":{"kind":"arxiv","id":"1906.09723","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09723","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09723v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09723","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"66B4N6TAHRLT","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"66B4N6TAHRLTIYRJ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"66B4N6TA","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:66B4N6TAHRLTIYRJYDXHVA7PMD","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-24T04:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"78bd7f3d0116b6e46207be1c36e34122998c65e0f29e01c04e90a7041a79f298","abstract_canon_sha256":"7a199347f9e905817c42f2f66fb32b9767811c0d130ccd878adba78ab511ec86"},"schema_version":"1.0"},"canonical_sha256":"f783c6fa603c57346229c0ee7a83ef60f43068ac9a1fa9909789a5c6e64a3178","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:36.970468Z","signature_b64":"KSkyMLbIW+EWIx0OKmuaWgTOMKCGvr6H2pkWZT0pZ9QCr+x+/ixwiiMqFrO1MPKq0bpdZog01kEI+w7Jfj0+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f783c6fa603c57346229c0ee7a83ef60f43068ac9a1fa9909789a5c6e64a3178","last_reissued_at":"2026-05-17T23:42:36.969684Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:36.969684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09723","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":"2026-05-17T23:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oH64qVlWPsPDkmZEpWU7/yMxttN9uBh8H6hny0Obvc/HeEkJjDDBOffCUAd2zHl0l2+M/vNp5CVQhYAFODb0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:24:35.703764Z"},"content_sha256":"3af4b8760ba59498c79da7f2746da80087edc0e6dd0d6799ca5925e1bbc4b8a3","schema_version":"1.0","event_id":"sha256:3af4b8760ba59498c79da7f2746da80087edc0e6dd0d6799ca5925e1bbc4b8a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:66B4N6TAHRLTIYRJYDXHVA7PMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolutely compatible pair of elements in a von Neumann algebra-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Anil Kumar Karn","submitted_at":"2019-06-24T04:54:34Z","abstract_excerpt":"Let $A$ be a unital C$^*$-algebra with unity $1_A$. A pair of elements $0 \\le a, b \\le 1_A$ in $A$ is said to be \\emph{absolutely compatible} if, $\\vert a - b \\vert + \\vert 1_A - a - b \\vert = 1_A.$ In this paper we provide a complete description of absolutely compatible pair of strict elements in a von Neumann algebra. The end form of such a pair has a striking resemblance with that of a `generic pair' of projections on a complex Hilbert space introduced by Halmos."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09723","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":"2026-05-17T23:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oka42++wJ4+kgwjAYHcRx3ygGoppJtiUyz1tCkCv9FQCd2F+ToRhaGQlgrYEdg7nBVyC2jjHCLJpUMaVhTNHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:24:35.704108Z"},"content_sha256":"9233ecff957ce613fd3abbb19b7556adb11b466941feb9c751b679b6341d92e5","schema_version":"1.0","event_id":"sha256:9233ecff957ce613fd3abbb19b7556adb11b466941feb9c751b679b6341d92e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66B4N6TAHRLTIYRJYDXHVA7PMD/bundle.json","state_url":"https://pith.science/pith/66B4N6TAHRLTIYRJYDXHVA7PMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66B4N6TAHRLTIYRJYDXHVA7PMD/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":"2026-06-03T20:24:35Z","links":{"resolver":"https://pith.science/pith/66B4N6TAHRLTIYRJYDXHVA7PMD","bundle":"https://pith.science/pith/66B4N6TAHRLTIYRJYDXHVA7PMD/bundle.json","state":"https://pith.science/pith/66B4N6TAHRLTIYRJYDXHVA7PMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66B4N6TAHRLTIYRJYDXHVA7PMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:66B4N6TAHRLTIYRJYDXHVA7PMD","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":"7a199347f9e905817c42f2f66fb32b9767811c0d130ccd878adba78ab511ec86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-24T04:54:34Z","title_canon_sha256":"78bd7f3d0116b6e46207be1c36e34122998c65e0f29e01c04e90a7041a79f298"},"schema_version":"1.0","source":{"id":"1906.09723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09723","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09723v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09723","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"66B4N6TAHRLT","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"66B4N6TAHRLTIYRJ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"66B4N6TA","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:9233ecff957ce613fd3abbb19b7556adb11b466941feb9c751b679b6341d92e5","target":"graph","created_at":"2026-05-17T23:42:36Z","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":"Let $A$ be a unital C$^*$-algebra with unity $1_A$. A pair of elements $0 \\le a, b \\le 1_A$ in $A$ is said to be \\emph{absolutely compatible} if, $\\vert a - b \\vert + \\vert 1_A - a - b \\vert = 1_A.$ In this paper we provide a complete description of absolutely compatible pair of strict elements in a von Neumann algebra. The end form of such a pair has a striking resemblance with that of a `generic pair' of projections on a complex Hilbert space introduced by Halmos.","authors_text":"Anil Kumar Karn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-24T04:54:34Z","title":"Absolutely compatible pair of elements in a von Neumann algebra-II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09723","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":"sha256:3af4b8760ba59498c79da7f2746da80087edc0e6dd0d6799ca5925e1bbc4b8a3","target":"record","created_at":"2026-05-17T23:42:36Z","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":"7a199347f9e905817c42f2f66fb32b9767811c0d130ccd878adba78ab511ec86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-24T04:54:34Z","title_canon_sha256":"78bd7f3d0116b6e46207be1c36e34122998c65e0f29e01c04e90a7041a79f298"},"schema_version":"1.0","source":{"id":"1906.09723","kind":"arxiv","version":1}},"canonical_sha256":"f783c6fa603c57346229c0ee7a83ef60f43068ac9a1fa9909789a5c6e64a3178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f783c6fa603c57346229c0ee7a83ef60f43068ac9a1fa9909789a5c6e64a3178","first_computed_at":"2026-05-17T23:42:36.969684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:36.969684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KSkyMLbIW+EWIx0OKmuaWgTOMKCGvr6H2pkWZT0pZ9QCr+x+/ixwiiMqFrO1MPKq0bpdZog01kEI+w7Jfj0+Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:36.970468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3af4b8760ba59498c79da7f2746da80087edc0e6dd0d6799ca5925e1bbc4b8a3","sha256:9233ecff957ce613fd3abbb19b7556adb11b466941feb9c751b679b6341d92e5"],"state_sha256":"0f754c6dbbecba68e077d2b8845d43e18785c1f28e7ae6465e8fb8fe86e644b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mPoA92w/u5BXuTgydtaZqrI4FK5z1LuhtjyxF2ZUtN71rhIsI0jnjTdwIBPZks90wm/opA+r5DpvUdPhBYqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:24:35.706035Z","bundle_sha256":"6dc3e05e299133b28c51f614c84cad0db5d00c6bc873d68251ae0bddd959b213"}}