{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SZI6GBAYQM3NCGZDUHDSZ7RUD3","short_pith_number":"pith:SZI6GBAY","canonical_record":{"source":{"id":"1410.0559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-10-02T14:21:07Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"28c0789520ceb2ad42ffc78d36ce00cce41f10c0fccaf56cb7ad6980d7eed503","abstract_canon_sha256":"97f64ada58c9c3cf4c26721d47630ef47d4ece396e33c3f410fa5a1435719bc0"},"schema_version":"1.0"},"canonical_sha256":"9651e304188336d11b23a1c72cfe341ecf42a641cdc7306a8c2eb09ff8088146","source":{"kind":"arxiv","id":"1410.0559","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0559","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0559v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0559","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"SZI6GBAYQM3N","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZI6GBAYQM3NCGZD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZI6GBAY","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SZI6GBAYQM3NCGZDUHDSZ7RUD3","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-10-02T14:21:07Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"28c0789520ceb2ad42ffc78d36ce00cce41f10c0fccaf56cb7ad6980d7eed503","abstract_canon_sha256":"97f64ada58c9c3cf4c26721d47630ef47d4ece396e33c3f410fa5a1435719bc0"},"schema_version":"1.0"},"canonical_sha256":"9651e304188336d11b23a1c72cfe341ecf42a641cdc7306a8c2eb09ff8088146","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:10.752694Z","signature_b64":"TtxpNtj6RqmDzmCOcS/xzui3oXTdMyJv4a0DutoBxbEG0/dfRIteI0+Dcd8BnaUmPEE/heegKGJvzJEPUPzuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9651e304188336d11b23a1c72cfe341ecf42a641cdc7306a8c2eb09ff8088146","last_reissued_at":"2026-05-18T02:41:10.752193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:10.752193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0559","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":"2026-05-18T02:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WG0nTN5vRKnpp5za+0fvIRZXFpUT9jNSNvvzKo4NWw7x8oXtU6fIyuRYRCKaEMx1w98PaCXK1oc6rSmsMO9zAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:13:06.744146Z"},"content_sha256":"5d564565c98172f90ad3bfa228a3de391f6d4b03cfcd8fe1ccfc6180cfb0c924","schema_version":"1.0","event_id":"sha256:5d564565c98172f90ad3bfa228a3de391f6d4b03cfcd8fe1ccfc6180cfb0c924"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SZI6GBAYQM3NCGZDUHDSZ7RUD3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A homogeneous space whose complement is rigid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Andrea Medini, Jan van Mill, Lyubomyr Zdomskyy","submitted_at":"2014-10-02T14:21:07Z","abstract_excerpt":"We construct a homogeneous subspace of $2^\\omega$ whose complement is dense in $2^\\omega$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homogeneous subspace of $2^\\omega$ whose complement is dense in $2^\\omega$ and rigid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0559","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":"2026-05-18T02:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iNYHgM6sGU/a9dbJ2CO7+dZiEYau1LvEcsZCzLpdfTNxTRwTKgY3w4NcOczLSZyWUijmoj8vmxQ6XWd5IvqTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:13:06.744835Z"},"content_sha256":"02bba3ee107af103068f640e87f96e6104688890f3f1920506768da9a8e15759","schema_version":"1.0","event_id":"sha256:02bba3ee107af103068f640e87f96e6104688890f3f1920506768da9a8e15759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3/bundle.json","state_url":"https://pith.science/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3/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":"2026-06-06T13:13:06Z","links":{"resolver":"https://pith.science/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3","bundle":"https://pith.science/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3/bundle.json","state":"https://pith.science/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZI6GBAYQM3NCGZDUHDSZ7RUD3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SZI6GBAYQM3NCGZDUHDSZ7RUD3","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":"97f64ada58c9c3cf4c26721d47630ef47d4ece396e33c3f410fa5a1435719bc0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-10-02T14:21:07Z","title_canon_sha256":"28c0789520ceb2ad42ffc78d36ce00cce41f10c0fccaf56cb7ad6980d7eed503"},"schema_version":"1.0","source":{"id":"1410.0559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0559","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0559v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0559","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"SZI6GBAYQM3N","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZI6GBAYQM3NCGZD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZI6GBAY","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:02bba3ee107af103068f640e87f96e6104688890f3f1920506768da9a8e15759","target":"graph","created_at":"2026-05-18T02:41:10Z","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 construct a homogeneous subspace of $2^\\omega$ whose complement is dense in $2^\\omega$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homogeneous subspace of $2^\\omega$ whose complement is dense in $2^\\omega$ and rigid.","authors_text":"Andrea Medini, Jan van Mill, Lyubomyr Zdomskyy","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-10-02T14:21:07Z","title":"A homogeneous space whose complement is rigid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0559","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":"sha256:5d564565c98172f90ad3bfa228a3de391f6d4b03cfcd8fe1ccfc6180cfb0c924","target":"record","created_at":"2026-05-18T02:41:10Z","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":"97f64ada58c9c3cf4c26721d47630ef47d4ece396e33c3f410fa5a1435719bc0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-10-02T14:21:07Z","title_canon_sha256":"28c0789520ceb2ad42ffc78d36ce00cce41f10c0fccaf56cb7ad6980d7eed503"},"schema_version":"1.0","source":{"id":"1410.0559","kind":"arxiv","version":1}},"canonical_sha256":"9651e304188336d11b23a1c72cfe341ecf42a641cdc7306a8c2eb09ff8088146","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9651e304188336d11b23a1c72cfe341ecf42a641cdc7306a8c2eb09ff8088146","first_computed_at":"2026-05-18T02:41:10.752193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:10.752193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TtxpNtj6RqmDzmCOcS/xzui3oXTdMyJv4a0DutoBxbEG0/dfRIteI0+Dcd8BnaUmPEE/heegKGJvzJEPUPzuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:10.752694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d564565c98172f90ad3bfa228a3de391f6d4b03cfcd8fe1ccfc6180cfb0c924","sha256:02bba3ee107af103068f640e87f96e6104688890f3f1920506768da9a8e15759"],"state_sha256":"2c1be6a0a7d2f23f68d3986871cc2df4a21132ae67a2827e3cb88d625cdc2e77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rd4QPWd6X9vWMY+B26Xuemc+jIJaPHE766RQMjCqmqzzWK/KOHDt4U1L7pe/guyoYSV+ubksjnY85OqIZ+NCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:13:06.748588Z","bundle_sha256":"ced7a7e31615445769120be8f6ad7bcd2f10228e6afb880b9ca1e1639155d520"}}