{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:J73CVGAT4CJM7A2BTNITPCBPFG","short_pith_number":"pith:J73CVGAT","canonical_record":{"source":{"id":"math/0601083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-01-04T22:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"45fd2d78f8377b4c999aa6264e96698fcc8f9759ab0e82959047ac8e87e8953b","abstract_canon_sha256":"3abc2f94bd8677169f88f87cf05eac0d6422db2c5296f9e9a6fe3693ced25b97"},"schema_version":"1.0"},"canonical_sha256":"4ff62a9813e092cf83419b5137882f2994f28fa96bcca25281dddc7f28642430","source":{"kind":"arxiv","id":"math/0601083","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601083","created_at":"2026-05-18T04:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601083v2","created_at":"2026-05-18T04:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601083","created_at":"2026-05-18T04:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"J73CVGAT4CJM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"J73CVGAT4CJM7A2B","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"J73CVGAT","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:J73CVGAT4CJM7A2BTNITPCBPFG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0601083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-01-04T22:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"45fd2d78f8377b4c999aa6264e96698fcc8f9759ab0e82959047ac8e87e8953b","abstract_canon_sha256":"3abc2f94bd8677169f88f87cf05eac0d6422db2c5296f9e9a6fe3693ced25b97"},"schema_version":"1.0"},"canonical_sha256":"4ff62a9813e092cf83419b5137882f2994f28fa96bcca25281dddc7f28642430","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:00.307808Z","signature_b64":"yW39TaSO35+wdGUzXWn4KAIFmUFG5mZujIEuYzwyQQOvVaqsdr2JzDuCpV87a4M/at3aTIDKo57bJ4uDgCkrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ff62a9813e092cf83419b5137882f2994f28fa96bcca25281dddc7f28642430","last_reissued_at":"2026-05-18T04:31:00.306792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:00.306792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0601083","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":"2026-05-18T04:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2CBAxWYt8c1dJr7cklTfeW9T4EJvzpaIDJl9lbQGCZNhhjoMxrOcxL/JdSI5vGdpvumHqY/4V7R+VKnrlb9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:39:11.103863Z"},"content_sha256":"d6308e9f50ba2a29a8d10d0ec1182bad0c7a8dbd563ae9e713cc1e36b2dd5cfa","schema_version":"1.0","event_id":"sha256:d6308e9f50ba2a29a8d10d0ec1182bad0c7a8dbd563ae9e713cc1e36b2dd5cfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:J73CVGAT4CJM7A2BTNITPCBPFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decisive creatures and large continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jakob Kellner, Saharon Shelah","submitted_at":"2006-01-04T22:15:06Z","abstract_excerpt":"For $f,g\\in\\omega\\ho$ let $\\mycfa_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e. for every branch $\\nu$ of the $f$-tree, one of the $g$-trees contains $\\nu$. $\\myc_{f,g}$ is the dual notion: For every branch $\\nu$, one of the $g$-trees guesses $\\nu(m)$ infinitely often.\n  It is consistent that $\\myc_{f_\\epsilon,g_\\epsilon}=\\mycfa_{f_\\epsilon,g_\\epsilon}=\\kappa_\\epsilon$ for $\\al1$ many pairwise different cardinals $\\kappa_\\epsilon$ and suitable pairs $(f_\\epsilon,g_\\epsilon)$.\n  For the proof we use creatures with sufficient big"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601083","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":"2026-05-18T04:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FH4ceo9+BLZ0MTKpIr/BnhpBMHZT/7rrOqSVuMw6OTjvBIwBfxD+wQtCdPmwOsFvUKgrCkPMfi3v9WnRI0dMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:39:11.104626Z"},"content_sha256":"6407f405f7eab05d74c9a768f206b93d5a318501ea8ad760451d9c1025647e38","schema_version":"1.0","event_id":"sha256:6407f405f7eab05d74c9a768f206b93d5a318501ea8ad760451d9c1025647e38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J73CVGAT4CJM7A2BTNITPCBPFG/bundle.json","state_url":"https://pith.science/pith/J73CVGAT4CJM7A2BTNITPCBPFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J73CVGAT4CJM7A2BTNITPCBPFG/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":"2026-06-09T03:39:11Z","links":{"resolver":"https://pith.science/pith/J73CVGAT4CJM7A2BTNITPCBPFG","bundle":"https://pith.science/pith/J73CVGAT4CJM7A2BTNITPCBPFG/bundle.json","state":"https://pith.science/pith/J73CVGAT4CJM7A2BTNITPCBPFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J73CVGAT4CJM7A2BTNITPCBPFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:J73CVGAT4CJM7A2BTNITPCBPFG","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":"3abc2f94bd8677169f88f87cf05eac0d6422db2c5296f9e9a6fe3693ced25b97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-01-04T22:15:06Z","title_canon_sha256":"45fd2d78f8377b4c999aa6264e96698fcc8f9759ab0e82959047ac8e87e8953b"},"schema_version":"1.0","source":{"id":"math/0601083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601083","created_at":"2026-05-18T04:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601083v2","created_at":"2026-05-18T04:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601083","created_at":"2026-05-18T04:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"J73CVGAT4CJM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"J73CVGAT4CJM7A2B","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"J73CVGAT","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:6407f405f7eab05d74c9a768f206b93d5a318501ea8ad760451d9c1025647e38","target":"graph","created_at":"2026-05-18T04:31:00Z","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":"For $f,g\\in\\omega\\ho$ let $\\mycfa_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e. for every branch $\\nu$ of the $f$-tree, one of the $g$-trees contains $\\nu$. $\\myc_{f,g}$ is the dual notion: For every branch $\\nu$, one of the $g$-trees guesses $\\nu(m)$ infinitely often.\n  It is consistent that $\\myc_{f_\\epsilon,g_\\epsilon}=\\mycfa_{f_\\epsilon,g_\\epsilon}=\\kappa_\\epsilon$ for $\\al1$ many pairwise different cardinals $\\kappa_\\epsilon$ and suitable pairs $(f_\\epsilon,g_\\epsilon)$.\n  For the proof we use creatures with sufficient big","authors_text":"Jakob Kellner, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-01-04T22:15:06Z","title":"Decisive creatures and large continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601083","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:d6308e9f50ba2a29a8d10d0ec1182bad0c7a8dbd563ae9e713cc1e36b2dd5cfa","target":"record","created_at":"2026-05-18T04:31:00Z","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":"3abc2f94bd8677169f88f87cf05eac0d6422db2c5296f9e9a6fe3693ced25b97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-01-04T22:15:06Z","title_canon_sha256":"45fd2d78f8377b4c999aa6264e96698fcc8f9759ab0e82959047ac8e87e8953b"},"schema_version":"1.0","source":{"id":"math/0601083","kind":"arxiv","version":2}},"canonical_sha256":"4ff62a9813e092cf83419b5137882f2994f28fa96bcca25281dddc7f28642430","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ff62a9813e092cf83419b5137882f2994f28fa96bcca25281dddc7f28642430","first_computed_at":"2026-05-18T04:31:00.306792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:00.306792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yW39TaSO35+wdGUzXWn4KAIFmUFG5mZujIEuYzwyQQOvVaqsdr2JzDuCpV87a4M/at3aTIDKo57bJ4uDgCkrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:00.307808Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6308e9f50ba2a29a8d10d0ec1182bad0c7a8dbd563ae9e713cc1e36b2dd5cfa","sha256:6407f405f7eab05d74c9a768f206b93d5a318501ea8ad760451d9c1025647e38"],"state_sha256":"34b18edf027cde6837c1d42f14f8602a1fd2018786d612ebc23597397b946745"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzyma/KZKJx5N67cAeP83AeNvLfHDV6wtATrG6te8XdP5+X8vpK+6GWW5AuxVO0miggSHZWzwHcgInmay/1yBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:39:11.108798Z","bundle_sha256":"2ab74e10c0130342912546611ee52cff3e509259589c72fd3c2215ec3276bddd"}}