{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HI3TXTOZ3JKAFEEHY3FBO2XHG2","short_pith_number":"pith:HI3TXTOZ","canonical_record":{"source":{"id":"1204.2057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T06:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"8ce5ceccb9f231cd5312d31c4979ab69dc6a2a7272ac2d302e81d314cee3de92","abstract_canon_sha256":"6549d165c32a0343cc3dc010443ecbd8fdcb7c07b362badc28cdfbe027358791"},"schema_version":"1.0"},"canonical_sha256":"3a373bcdd9da54029087c6ca176ae736a80abc7e734397854d383388e876f8a7","source":{"kind":"arxiv","id":"1204.2057","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2057","created_at":"2026-05-18T03:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2057v2","created_at":"2026-05-18T03:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2057","created_at":"2026-05-18T03:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"HI3TXTOZ3JKA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HI3TXTOZ3JKAFEEH","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HI3TXTOZ","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HI3TXTOZ3JKAFEEHY3FBO2XHG2","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T06:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"8ce5ceccb9f231cd5312d31c4979ab69dc6a2a7272ac2d302e81d314cee3de92","abstract_canon_sha256":"6549d165c32a0343cc3dc010443ecbd8fdcb7c07b362badc28cdfbe027358791"},"schema_version":"1.0"},"canonical_sha256":"3a373bcdd9da54029087c6ca176ae736a80abc7e734397854d383388e876f8a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:59.991461Z","signature_b64":"4ZAUz76iFaEaMz957mbBXkXfelBEaJXBJU0DjZtXHamtnTHaHT6bhs4RdeN+n5lN+mtzIj18cJMet7Y36sZADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a373bcdd9da54029087c6ca176ae736a80abc7e734397854d383388e876f8a7","last_reissued_at":"2026-05-18T03:54:59.990745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:59.990745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2057","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":"2026-05-18T03:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"STiurgRKRPJjfi8LasFn7x/4lIQT/CdZZPA1S6pNL1Chvb0TztfNdOXQf3uzBo2WZ1GwLQJkeepd1HWHrdTtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T11:26:33.723977Z"},"content_sha256":"03f27744c8fbf77668304b9da5f15b41ab2aa0622da2a6a0c7cde066b49df1dd","schema_version":"1.0","event_id":"sha256:03f27744c8fbf77668304b9da5f15b41ab2aa0622da2a6a0c7cde066b49df1dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HI3TXTOZ3JKAFEEHY3FBO2XHG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Reflexivity of the set of n-Isometries on C(X,E)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. B. Abubaker","submitted_at":"2012-04-10T06:58:23Z","abstract_excerpt":"We prove that if the group of isometries of C(X,E) is algebraically reflexive, then the group of n-isometries is also algebraically reflexive. Here, X is a compact Hausdorff space and E is a Banach space. As a corollary to this, we establish the algebraic reflexivity of the set of generalized bi-circular projections on C(X,E)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2057","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":"2026-05-18T03:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5Bo+S3K2DQJcTeYOR0Y9H92i34e6TCF4VwAvhTFg9AtH/aq2o+AVmrgRpC81cLbyXOGMhaiAxIraudJ4ei1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T11:26:33.724391Z"},"content_sha256":"432328e8975492a9063cccdaf418bf72e4826334c49267e1d5b16fe5272256f6","schema_version":"1.0","event_id":"sha256:432328e8975492a9063cccdaf418bf72e4826334c49267e1d5b16fe5272256f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2/bundle.json","state_url":"https://pith.science/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2/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":"2026-07-02T11:26:33Z","links":{"resolver":"https://pith.science/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2","bundle":"https://pith.science/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2/bundle.json","state":"https://pith.science/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HI3TXTOZ3JKAFEEHY3FBO2XHG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HI3TXTOZ3JKAFEEHY3FBO2XHG2","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":"6549d165c32a0343cc3dc010443ecbd8fdcb7c07b362badc28cdfbe027358791","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T06:58:23Z","title_canon_sha256":"8ce5ceccb9f231cd5312d31c4979ab69dc6a2a7272ac2d302e81d314cee3de92"},"schema_version":"1.0","source":{"id":"1204.2057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2057","created_at":"2026-05-18T03:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2057v2","created_at":"2026-05-18T03:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2057","created_at":"2026-05-18T03:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"HI3TXTOZ3JKA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HI3TXTOZ3JKAFEEH","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HI3TXTOZ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:432328e8975492a9063cccdaf418bf72e4826334c49267e1d5b16fe5272256f6","target":"graph","created_at":"2026-05-18T03:54:59Z","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 prove that if the group of isometries of C(X,E) is algebraically reflexive, then the group of n-isometries is also algebraically reflexive. Here, X is a compact Hausdorff space and E is a Banach space. As a corollary to this, we establish the algebraic reflexivity of the set of generalized bi-circular projections on C(X,E).","authors_text":"A. B. Abubaker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T06:58:23Z","title":"Algebraic Reflexivity of the set of n-Isometries on C(X,E)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2057","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":"sha256:03f27744c8fbf77668304b9da5f15b41ab2aa0622da2a6a0c7cde066b49df1dd","target":"record","created_at":"2026-05-18T03:54:59Z","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":"6549d165c32a0343cc3dc010443ecbd8fdcb7c07b362badc28cdfbe027358791","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-10T06:58:23Z","title_canon_sha256":"8ce5ceccb9f231cd5312d31c4979ab69dc6a2a7272ac2d302e81d314cee3de92"},"schema_version":"1.0","source":{"id":"1204.2057","kind":"arxiv","version":2}},"canonical_sha256":"3a373bcdd9da54029087c6ca176ae736a80abc7e734397854d383388e876f8a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a373bcdd9da54029087c6ca176ae736a80abc7e734397854d383388e876f8a7","first_computed_at":"2026-05-18T03:54:59.990745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:59.990745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ZAUz76iFaEaMz957mbBXkXfelBEaJXBJU0DjZtXHamtnTHaHT6bhs4RdeN+n5lN+mtzIj18cJMet7Y36sZADA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:59.991461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03f27744c8fbf77668304b9da5f15b41ab2aa0622da2a6a0c7cde066b49df1dd","sha256:432328e8975492a9063cccdaf418bf72e4826334c49267e1d5b16fe5272256f6"],"state_sha256":"5221a7954a4901e2769aa027298c958dfd42efb489bbd4bb080253abecc19321"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWx3IZmaCzSwdyqNygs4RSPh4mOlCJDs8Mvlie4+TbVDudCSmNl9VCqH+LBH4Qo8tD+dl32FZ7FjawhDh+VaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T11:26:33.726695Z","bundle_sha256":"ba980d67cb24b6195b443cdf11d99bc87bdbcf7c1067a88cc6834c696a0b8093"}}