{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:RM2XISV6OHMJ3ULEZYTZWJASVO","short_pith_number":"pith:RM2XISV6","canonical_record":{"source":{"id":"math/9808104","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1998-08-25T11:56:31Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e70aa3a088451835c9691706223e9426e401c436686784f23553ac705bd6ee1d","abstract_canon_sha256":"0a3feab35dc689071dec88760505d596e6a7ff12a19e251ea2d78e8684b6d274"},"schema_version":"1.0"},"canonical_sha256":"8b35744abe71d89dd164ce279b2412ab869c6706ea1e32bb2456c44b5a48d1b3","source":{"kind":"arxiv","id":"math/9808104","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9808104","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/9808104v2","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9808104","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"RM2XISV6OHMJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"RM2XISV6OHMJ3ULE","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"RM2XISV6","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:RM2XISV6OHMJ3ULEZYTZWJASVO","target":"record","payload":{"canonical_record":{"source":{"id":"math/9808104","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1998-08-25T11:56:31Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e70aa3a088451835c9691706223e9426e401c436686784f23553ac705bd6ee1d","abstract_canon_sha256":"0a3feab35dc689071dec88760505d596e6a7ff12a19e251ea2d78e8684b6d274"},"schema_version":"1.0"},"canonical_sha256":"8b35744abe71d89dd164ce279b2412ab869c6706ea1e32bb2456c44b5a48d1b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:19.344398Z","signature_b64":"4QMGRoPJek9LA6FAxht9qc7baBOtbpYHtmORYGKI974j6CD5PhelzxLCRO+6rTMiHwO2/dNcwIP1/d6GaIL6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b35744abe71d89dd164ce279b2412ab869c6706ea1e32bb2456c44b5a48d1b3","last_reissued_at":"2026-05-18T03:37:19.344020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:19.344020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9808104","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":"2026-05-18T03:37:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aPHt6tuNBS0NShp5w1mEmz4ebobU1vZmWHLKni7jSz1olEd+5w/SgoDIYemEoItFuv5wfQ72oGjXy3hwcFn/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:15:39.922871Z"},"content_sha256":"7e997c71c6362034c0f1a38329ae3a3bf6e7ce7f8f4b93425c753e171e04b631","schema_version":"1.0","event_id":"sha256:7e997c71c6362034c0f1a38329ae3a3bf6e7ce7f8f4b93425c753e171e04b631"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:RM2XISV6OHMJ3ULEZYTZWJASVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Forcing for hL and hd","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.LO","authors_text":"Andrzej Roslanowski, Saharon Shelah","submitted_at":"1998-08-25T11:56:31Z","abstract_excerpt":"The present paper addresses the problem of attainment of the supremums in various equivalent definitions of hereditary density hd and hereditary Lindelof degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk (Problems 50 and 54 in his book \"Cardinal Invariants on Boolean Algebras), showing consistency of different attainment behaviour and proving that (for the considered variants) this is the best result we can expect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9808104","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":"2026-05-18T03:37:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jEhg8GwO8M+ourKsc0BvQOEGVQmKVapV3qBwPmIMAfkOALEMDUF8mTMwuwUhYs7mEM4mJV1kH8Qjga+AtcNpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:15:39.923212Z"},"content_sha256":"926592667285002cd11004a579493bcff1d4ed39f9f1fccaa86a02520c91ec00","schema_version":"1.0","event_id":"sha256:926592667285002cd11004a579493bcff1d4ed39f9f1fccaa86a02520c91ec00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RM2XISV6OHMJ3ULEZYTZWJASVO/bundle.json","state_url":"https://pith.science/pith/RM2XISV6OHMJ3ULEZYTZWJASVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RM2XISV6OHMJ3ULEZYTZWJASVO/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":"2026-06-23T15:15:39Z","links":{"resolver":"https://pith.science/pith/RM2XISV6OHMJ3ULEZYTZWJASVO","bundle":"https://pith.science/pith/RM2XISV6OHMJ3ULEZYTZWJASVO/bundle.json","state":"https://pith.science/pith/RM2XISV6OHMJ3ULEZYTZWJASVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RM2XISV6OHMJ3ULEZYTZWJASVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:RM2XISV6OHMJ3ULEZYTZWJASVO","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":"0a3feab35dc689071dec88760505d596e6a7ff12a19e251ea2d78e8684b6d274","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.LO","submitted_at":"1998-08-25T11:56:31Z","title_canon_sha256":"e70aa3a088451835c9691706223e9426e401c436686784f23553ac705bd6ee1d"},"schema_version":"1.0","source":{"id":"math/9808104","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9808104","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/9808104v2","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9808104","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"RM2XISV6OHMJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"RM2XISV6OHMJ3ULE","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"RM2XISV6","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:926592667285002cd11004a579493bcff1d4ed39f9f1fccaa86a02520c91ec00","target":"graph","created_at":"2026-05-18T03:37:19Z","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":"The present paper addresses the problem of attainment of the supremums in various equivalent definitions of hereditary density hd and hereditary Lindelof degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk (Problems 50 and 54 in his book \"Cardinal Invariants on Boolean Algebras), showing consistency of different attainment behaviour and proving that (for the considered variants) this is the best result we can expect.","authors_text":"Andrzej Roslanowski, Saharon Shelah","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1998-08-25T11:56:31Z","title":"Forcing for hL and hd"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9808104","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":"sha256:7e997c71c6362034c0f1a38329ae3a3bf6e7ce7f8f4b93425c753e171e04b631","target":"record","created_at":"2026-05-18T03:37:19Z","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":"0a3feab35dc689071dec88760505d596e6a7ff12a19e251ea2d78e8684b6d274","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.LO","submitted_at":"1998-08-25T11:56:31Z","title_canon_sha256":"e70aa3a088451835c9691706223e9426e401c436686784f23553ac705bd6ee1d"},"schema_version":"1.0","source":{"id":"math/9808104","kind":"arxiv","version":2}},"canonical_sha256":"8b35744abe71d89dd164ce279b2412ab869c6706ea1e32bb2456c44b5a48d1b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b35744abe71d89dd164ce279b2412ab869c6706ea1e32bb2456c44b5a48d1b3","first_computed_at":"2026-05-18T03:37:19.344020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:19.344020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QMGRoPJek9LA6FAxht9qc7baBOtbpYHtmORYGKI974j6CD5PhelzxLCRO+6rTMiHwO2/dNcwIP1/d6GaIL6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:19.344398Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9808104","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e997c71c6362034c0f1a38329ae3a3bf6e7ce7f8f4b93425c753e171e04b631","sha256:926592667285002cd11004a579493bcff1d4ed39f9f1fccaa86a02520c91ec00"],"state_sha256":"91f3bd048352e38cdab313c53d8023d0a5e9e0bd214613ef37bf49e1c4fb7184"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+tdcY7i58wCbgepb+ocFgWopcP+rHWpuOjy8CPji38/FqYY76zRDAoJJDgXRGx6gSIQX6DpaYUv5XIq+QmsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:15:39.925329Z","bundle_sha256":"1f040f8c25a2903ce800c0eae86bfa7f98c8bd1ee315719cfa910f651ddd2354"}}