{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:R3AT63EZF5OCW2YAV4ZJAMKYI2","short_pith_number":"pith:R3AT63EZ","canonical_record":{"source":{"id":"math/0105045","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"2001-05-06T17:16:24Z","cross_cats_sorted":["math.CO","math.GN"],"title_canon_sha256":"ce77f5332f511ef5e0e5dfd66db276829b392c84611df6698bb403c3d4cc29cd","abstract_canon_sha256":"2802aa5820a74952746f0b82072b2fb75f76b40cf1f8bdb9bd92059897252178"},"schema_version":"1.0"},"canonical_sha256":"8ec13f6c992f5c2b6b00af3290315846bdac5d8b64259f0dbcdeef567cd5c684","source":{"kind":"arxiv","id":"math/0105045","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0105045","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0105045v6","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0105045","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"R3AT63EZF5OC","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"R3AT63EZF5OCW2YA","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"R3AT63EZ","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:R3AT63EZF5OCW2YAV4ZJAMKYI2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0105045","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"2001-05-06T17:16:24Z","cross_cats_sorted":["math.CO","math.GN"],"title_canon_sha256":"ce77f5332f511ef5e0e5dfd66db276829b392c84611df6698bb403c3d4cc29cd","abstract_canon_sha256":"2802aa5820a74952746f0b82072b2fb75f76b40cf1f8bdb9bd92059897252178"},"schema_version":"1.0"},"canonical_sha256":"8ec13f6c992f5c2b6b00af3290315846bdac5d8b64259f0dbcdeef567cd5c684","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:45.019748Z","signature_b64":"Mwm812pWkZpP8YvvQnvJM7DRKZqAtjapfMp9jw+78Tuk3pVcctQgBKsSrtKUoXnpE37JouaaP8rNNjj5lpKLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ec13f6c992f5c2b6b00af3290315846bdac5d8b64259f0dbcdeef567cd5c684","last_reissued_at":"2026-05-18T04:42:45.019096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:45.019096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0105045","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0XAwo5PFYlmuC2G98M+0bZ63UaDPVy+CNob3ct9jCqV9q3r7pn6b4TaO6EmLQadfHDjNkmbdE0K6AGDRaTPGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:25:07.358898Z"},"content_sha256":"f1e20d72a27da003798b22cf8ec03e918e6f5bb57cb1f57a082956f8bebad17e","schema_version":"1.0","event_id":"sha256:f1e20d72a27da003798b22cf8ec03e918e6f5bb57cb1f57a082956f8bebad17e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:R3AT63EZF5OCW2YAV4ZJAMKYI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Selection principles and the minimal tower problem","license":"","headline":"","cross_cats":["math.CO","math.GN"],"primary_cat":"math.LO","authors_text":"Boaz Tsaban","submitted_at":"2001-05-06T17:16:24Z","abstract_excerpt":"We study diagonalizations of covers using various selection principles, where the covers are related to linear quasiorderings (tau-covers). This includes: equivalences and nonequivalences, combinatorial characterizations, critical cardinalities and constructions of special sets of reals. This study leads to a solution of a topological problem which was suggested to the author by Scheepers (and stated in an earlier work) and is related to the Minimal Tower problem.\n  We also introduce a variant of the notion of tau-cover, called tau^*-cover, and settle some problems for this variant which are s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105045","kind":"arxiv","version":6},"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":"2026-05-18T04:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KKw28BXIt8ys7TPghSJ7oOa+Lo+H0j5m1/9EC5eh9rdYWZeywGzHfmacjmqpRGYMYf7moicM/JnSHgzQKiC6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:25:07.359537Z"},"content_sha256":"df6f353538646681ea385e92d634dde1bb494dc26205d533d6f15c30976dae7e","schema_version":"1.0","event_id":"sha256:df6f353538646681ea385e92d634dde1bb494dc26205d533d6f15c30976dae7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2/bundle.json","state_url":"https://pith.science/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2/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":"2026-06-02T11:25:07Z","links":{"resolver":"https://pith.science/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2","bundle":"https://pith.science/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2/bundle.json","state":"https://pith.science/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R3AT63EZF5OCW2YAV4ZJAMKYI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:R3AT63EZF5OCW2YAV4ZJAMKYI2","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":"2802aa5820a74952746f0b82072b2fb75f76b40cf1f8bdb9bd92059897252178","cross_cats_sorted":["math.CO","math.GN"],"license":"","primary_cat":"math.LO","submitted_at":"2001-05-06T17:16:24Z","title_canon_sha256":"ce77f5332f511ef5e0e5dfd66db276829b392c84611df6698bb403c3d4cc29cd"},"schema_version":"1.0","source":{"id":"math/0105045","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0105045","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0105045v6","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0105045","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"R3AT63EZF5OC","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"R3AT63EZF5OCW2YA","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"R3AT63EZ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:df6f353538646681ea385e92d634dde1bb494dc26205d533d6f15c30976dae7e","target":"graph","created_at":"2026-05-18T04:42:45Z","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 diagonalizations of covers using various selection principles, where the covers are related to linear quasiorderings (tau-covers). This includes: equivalences and nonequivalences, combinatorial characterizations, critical cardinalities and constructions of special sets of reals. This study leads to a solution of a topological problem which was suggested to the author by Scheepers (and stated in an earlier work) and is related to the Minimal Tower problem.\n  We also introduce a variant of the notion of tau-cover, called tau^*-cover, and settle some problems for this variant which are s","authors_text":"Boaz Tsaban","cross_cats":["math.CO","math.GN"],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"2001-05-06T17:16:24Z","title":"Selection principles and the minimal tower problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105045","kind":"arxiv","version":6},"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:f1e20d72a27da003798b22cf8ec03e918e6f5bb57cb1f57a082956f8bebad17e","target":"record","created_at":"2026-05-18T04:42:45Z","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":"2802aa5820a74952746f0b82072b2fb75f76b40cf1f8bdb9bd92059897252178","cross_cats_sorted":["math.CO","math.GN"],"license":"","primary_cat":"math.LO","submitted_at":"2001-05-06T17:16:24Z","title_canon_sha256":"ce77f5332f511ef5e0e5dfd66db276829b392c84611df6698bb403c3d4cc29cd"},"schema_version":"1.0","source":{"id":"math/0105045","kind":"arxiv","version":6}},"canonical_sha256":"8ec13f6c992f5c2b6b00af3290315846bdac5d8b64259f0dbcdeef567cd5c684","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ec13f6c992f5c2b6b00af3290315846bdac5d8b64259f0dbcdeef567cd5c684","first_computed_at":"2026-05-18T04:42:45.019096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:45.019096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mwm812pWkZpP8YvvQnvJM7DRKZqAtjapfMp9jw+78Tuk3pVcctQgBKsSrtKUoXnpE37JouaaP8rNNjj5lpKLDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:45.019748Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0105045","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1e20d72a27da003798b22cf8ec03e918e6f5bb57cb1f57a082956f8bebad17e","sha256:df6f353538646681ea385e92d634dde1bb494dc26205d533d6f15c30976dae7e"],"state_sha256":"aa992ce1004c813d89ce0c2e3b2ccaefe70c80d55188293d5e5a0613a9091a5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYDA+49ykWIO0H0xvEFUm0MhKIiWpdFgU3/gYHMvJ309FQcAPYhEigK09DlxGwkRKWv2AnTGG01qHssOKeC1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:25:07.362754Z","bundle_sha256":"5dc7d03934e462ac2d8912e1dd604ab79d2f6034bd318649fb5d9a75ab88102f"}}