{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NCQSUW6OKILKECSTQY3SWNV73Y","short_pith_number":"pith:NCQSUW6O","canonical_record":{"source":{"id":"1612.06560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-20T09:12:38Z","cross_cats_sorted":[],"title_canon_sha256":"9416a42d07912c0656153fa22a6adff260e06749158cb64005aa3946ec14926c","abstract_canon_sha256":"ffd1241905e50c100ea720e5bbdc865f5e261f577cab5b5e64b72420ab8003dd"},"schema_version":"1.0"},"canonical_sha256":"68a12a5bce5216a20a5386372b36bfde0248a6cab42695099ec454e28074a8ca","source":{"kind":"arxiv","id":"1612.06560","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06560","created_at":"2026-05-18T00:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06560v1","created_at":"2026-05-18T00:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06560","created_at":"2026-05-18T00:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"NCQSUW6OKILK","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NCQSUW6OKILKECST","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NCQSUW6O","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NCQSUW6OKILKECSTQY3SWNV73Y","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-20T09:12:38Z","cross_cats_sorted":[],"title_canon_sha256":"9416a42d07912c0656153fa22a6adff260e06749158cb64005aa3946ec14926c","abstract_canon_sha256":"ffd1241905e50c100ea720e5bbdc865f5e261f577cab5b5e64b72420ab8003dd"},"schema_version":"1.0"},"canonical_sha256":"68a12a5bce5216a20a5386372b36bfde0248a6cab42695099ec454e28074a8ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:25.434003Z","signature_b64":"FNiXt158tWKh6JcPFXgOpdWuRFcy+GxkWyO9t5X0ZZ9jm13FvYdXFUQoSlhNxIFH+7nhMyXAaMWTiE3Lg0nZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68a12a5bce5216a20a5386372b36bfde0248a6cab42695099ec454e28074a8ca","last_reissued_at":"2026-05-18T00:54:25.433295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:25.433295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06560","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":"2026-05-18T00:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfJkaOcs6I50UnKqEPUl95aIr3haJpxdLxUwi7OnNsi/aC9UAXkZehDLgfM/KauDx75GKkTatALkBwizvhqrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:10:11.976738Z"},"content_sha256":"c3ceed6926cfb91f0c4ab800825c7d11ac100b0009b61e6fd0a4336353686c09","schema_version":"1.0","event_id":"sha256:c3ceed6926cfb91f0c4ab800825c7d11ac100b0009b61e6fd0a4336353686c09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NCQSUW6OKILKECSTQY3SWNV73Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector-valued Eidelheit sequences and the non B-completeness of tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Debrouwere, Jasson Vindas","submitted_at":"2016-12-20T09:12:38Z","abstract_excerpt":"We introduce vector-valued Eidelheit sequences and obtain a characterization that generalizes Eidelheit's classical theorem (Studia Math. 6 (1936), 139-148). As an application, we discuss criteria for non $B$-completeness of completed tensor products."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06560","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":"2026-05-18T00:54:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lLNhMWU/I83QJdsvHclBm7XDUbwpphDnW79/oTPw1BBkraFgUIP7NXDXLfsolK/S25YelAZAV8x+l8mP7prhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:10:11.977232Z"},"content_sha256":"73cc4baf279b76f2aafe8d910a96ec8b42242246bffed6260dd27ec3456bb766","schema_version":"1.0","event_id":"sha256:73cc4baf279b76f2aafe8d910a96ec8b42242246bffed6260dd27ec3456bb766"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCQSUW6OKILKECSTQY3SWNV73Y/bundle.json","state_url":"https://pith.science/pith/NCQSUW6OKILKECSTQY3SWNV73Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCQSUW6OKILKECSTQY3SWNV73Y/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":"2026-05-27T07:10:11Z","links":{"resolver":"https://pith.science/pith/NCQSUW6OKILKECSTQY3SWNV73Y","bundle":"https://pith.science/pith/NCQSUW6OKILKECSTQY3SWNV73Y/bundle.json","state":"https://pith.science/pith/NCQSUW6OKILKECSTQY3SWNV73Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCQSUW6OKILKECSTQY3SWNV73Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NCQSUW6OKILKECSTQY3SWNV73Y","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":"ffd1241905e50c100ea720e5bbdc865f5e261f577cab5b5e64b72420ab8003dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-20T09:12:38Z","title_canon_sha256":"9416a42d07912c0656153fa22a6adff260e06749158cb64005aa3946ec14926c"},"schema_version":"1.0","source":{"id":"1612.06560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06560","created_at":"2026-05-18T00:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06560v1","created_at":"2026-05-18T00:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06560","created_at":"2026-05-18T00:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"NCQSUW6OKILK","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NCQSUW6OKILKECST","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NCQSUW6O","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:73cc4baf279b76f2aafe8d910a96ec8b42242246bffed6260dd27ec3456bb766","target":"graph","created_at":"2026-05-18T00:54:25Z","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 introduce vector-valued Eidelheit sequences and obtain a characterization that generalizes Eidelheit's classical theorem (Studia Math. 6 (1936), 139-148). As an application, we discuss criteria for non $B$-completeness of completed tensor products.","authors_text":"Andreas Debrouwere, Jasson Vindas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-20T09:12:38Z","title":"Vector-valued Eidelheit sequences and the non B-completeness of tensor products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06560","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:c3ceed6926cfb91f0c4ab800825c7d11ac100b0009b61e6fd0a4336353686c09","target":"record","created_at":"2026-05-18T00:54:25Z","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":"ffd1241905e50c100ea720e5bbdc865f5e261f577cab5b5e64b72420ab8003dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-20T09:12:38Z","title_canon_sha256":"9416a42d07912c0656153fa22a6adff260e06749158cb64005aa3946ec14926c"},"schema_version":"1.0","source":{"id":"1612.06560","kind":"arxiv","version":1}},"canonical_sha256":"68a12a5bce5216a20a5386372b36bfde0248a6cab42695099ec454e28074a8ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68a12a5bce5216a20a5386372b36bfde0248a6cab42695099ec454e28074a8ca","first_computed_at":"2026-05-18T00:54:25.433295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:25.433295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FNiXt158tWKh6JcPFXgOpdWuRFcy+GxkWyO9t5X0ZZ9jm13FvYdXFUQoSlhNxIFH+7nhMyXAaMWTiE3Lg0nZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:25.434003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3ceed6926cfb91f0c4ab800825c7d11ac100b0009b61e6fd0a4336353686c09","sha256:73cc4baf279b76f2aafe8d910a96ec8b42242246bffed6260dd27ec3456bb766"],"state_sha256":"0dab3e692ae610a26a0bb528d8e0306c2e151c79eac904691966485518a53480"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1VF+5lZlBDlWB1MTCTjZAbKYbMu/aNw3iaJlQs6Far/c0Po2YwMgeT7dIo5Po6lDLNi2GwMaSfGcGGlQAGkDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:10:11.980505Z","bundle_sha256":"55914235460bd3a67e5d9d41d80c038544e04728fab5a2043215247780883c6b"}}