{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:PB2T3ECCQC6B3LS5NC4UGZDWAX","short_pith_number":"pith:PB2T3ECC","canonical_record":{"source":{"id":"math/9807172","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1998-07-30T19:42:07Z","cross_cats_sorted":[],"title_canon_sha256":"e0ec146f735871ad0ee8e7bca753855aca5e416cf304a937dacbc056a9cad4f0","abstract_canon_sha256":"d1c6e2b85d4dec741ed98cae9da6d4c7abad16c9a6def1475d19b8c74b61f000"},"schema_version":"1.0"},"canonical_sha256":"78753d904280bc1dae5d68b943647605ca63811fd2ad5bce78de551d618dc4a6","source":{"kind":"arxiv","id":"math/9807172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9807172","created_at":"2026-05-18T03:37:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/9807172v1","created_at":"2026-05-18T03:37:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9807172","created_at":"2026-05-18T03:37:27Z"},{"alias_kind":"pith_short_12","alias_value":"PB2T3ECCQC6B","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"PB2T3ECCQC6B3LS5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"PB2T3ECC","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:PB2T3ECCQC6B3LS5NC4UGZDWAX","target":"record","payload":{"canonical_record":{"source":{"id":"math/9807172","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1998-07-30T19:42:07Z","cross_cats_sorted":[],"title_canon_sha256":"e0ec146f735871ad0ee8e7bca753855aca5e416cf304a937dacbc056a9cad4f0","abstract_canon_sha256":"d1c6e2b85d4dec741ed98cae9da6d4c7abad16c9a6def1475d19b8c74b61f000"},"schema_version":"1.0"},"canonical_sha256":"78753d904280bc1dae5d68b943647605ca63811fd2ad5bce78de551d618dc4a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:27.220572Z","signature_b64":"fV2dnLzuo5kTUO+cH9ZMIGnl708C2xunaUaLfMFfwv/Tdk01wyV6Uey5yK9CLjORDd8/POpBF1bEju0ft+stBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78753d904280bc1dae5d68b943647605ca63811fd2ad5bce78de551d618dc4a6","last_reissued_at":"2026-05-18T03:37:27.220100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:27.220100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9807172","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":"2026-05-18T03:37:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HbfQIMm154O8XUgx0vifXhN9BQHXY1LQJ8w4Gb7168cGiIq5W829Rn3h3E7ZhdNJN/gZLbUu0lq+siuWqfqECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:00:50.312540Z"},"content_sha256":"3527a2d281aa3cea3c75fcd5d28d869b4055c957618fcee7f843644ddd356a48","schema_version":"1.0","event_id":"sha256:3527a2d281aa3cea3c75fcd5d28d869b4055c957618fcee7f843644ddd356a48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:PB2T3ECCQC6B3LS5NC4UGZDWAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norms on possibilities I: forcing with trees and creatures","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrzej Roslanowski, Saharon Shelah","submitted_at":"1998-07-30T19:42:07Z","abstract_excerpt":"We present a systematic study of the method of \"norms on possibilities\" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the solutions we develop various ideas interesting per se.These include a new iterable condition for ``not adding Cohen reals'' (which has a flavour of preserving special properties of p-points), new intriguing properties of ultrafilters (weaker than being Ramsey but stronger than p-point) and some new applications of variants of the PP--property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9807172","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":"2026-05-18T03:37:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxWy8ljKleBs6HSuAfm4SWK1N5ri0L+7dt7CA6uxLwiK+rUqEWVE95s7mbM1Y0Se5CT+oddAJmPjbaTepBTeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:00:50.312882Z"},"content_sha256":"d0865766557db1168bf47c2e526e4db37a4086a9f523d8ec2b452c57d2fcd1c2","schema_version":"1.0","event_id":"sha256:d0865766557db1168bf47c2e526e4db37a4086a9f523d8ec2b452c57d2fcd1c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX/bundle.json","state_url":"https://pith.science/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX/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":"2026-06-23T18:00:50Z","links":{"resolver":"https://pith.science/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX","bundle":"https://pith.science/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX/bundle.json","state":"https://pith.science/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PB2T3ECCQC6B3LS5NC4UGZDWAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:PB2T3ECCQC6B3LS5NC4UGZDWAX","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":"d1c6e2b85d4dec741ed98cae9da6d4c7abad16c9a6def1475d19b8c74b61f000","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1998-07-30T19:42:07Z","title_canon_sha256":"e0ec146f735871ad0ee8e7bca753855aca5e416cf304a937dacbc056a9cad4f0"},"schema_version":"1.0","source":{"id":"math/9807172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9807172","created_at":"2026-05-18T03:37:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/9807172v1","created_at":"2026-05-18T03:37:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9807172","created_at":"2026-05-18T03:37:27Z"},{"alias_kind":"pith_short_12","alias_value":"PB2T3ECCQC6B","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"PB2T3ECCQC6B3LS5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"PB2T3ECC","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:d0865766557db1168bf47c2e526e4db37a4086a9f523d8ec2b452c57d2fcd1c2","target":"graph","created_at":"2026-05-18T03:37:27Z","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 present a systematic study of the method of \"norms on possibilities\" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the solutions we develop various ideas interesting per se.These include a new iterable condition for ``not adding Cohen reals'' (which has a flavour of preserving special properties of p-points), new intriguing properties of ultrafilters (weaker than being Ramsey but stronger than p-point) and some new applications of variants of the PP--property.","authors_text":"Andrzej Roslanowski, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1998-07-30T19:42:07Z","title":"Norms on possibilities I: forcing with trees and creatures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9807172","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":"sha256:3527a2d281aa3cea3c75fcd5d28d869b4055c957618fcee7f843644ddd356a48","target":"record","created_at":"2026-05-18T03:37:27Z","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":"d1c6e2b85d4dec741ed98cae9da6d4c7abad16c9a6def1475d19b8c74b61f000","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1998-07-30T19:42:07Z","title_canon_sha256":"e0ec146f735871ad0ee8e7bca753855aca5e416cf304a937dacbc056a9cad4f0"},"schema_version":"1.0","source":{"id":"math/9807172","kind":"arxiv","version":1}},"canonical_sha256":"78753d904280bc1dae5d68b943647605ca63811fd2ad5bce78de551d618dc4a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78753d904280bc1dae5d68b943647605ca63811fd2ad5bce78de551d618dc4a6","first_computed_at":"2026-05-18T03:37:27.220100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:27.220100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fV2dnLzuo5kTUO+cH9ZMIGnl708C2xunaUaLfMFfwv/Tdk01wyV6Uey5yK9CLjORDd8/POpBF1bEju0ft+stBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:27.220572Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9807172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3527a2d281aa3cea3c75fcd5d28d869b4055c957618fcee7f843644ddd356a48","sha256:d0865766557db1168bf47c2e526e4db37a4086a9f523d8ec2b452c57d2fcd1c2"],"state_sha256":"914dc5c14ca3c124424ae10e6914a27880f8a2b96e212bf08ac700ba82fe69f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7vDRllJd07adhdTMmheiLbvdyEgZLnJnnWoTgMFmE9yPsZmPCZd6Ko28mqV0CBtyeMIudsEECbBtKnjSW94Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:00:50.314845Z","bundle_sha256":"7279430e2aa531c7c565d16aefb6cadc864dee7d8994efc34910cbcbbcdc02e7"}}