{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KNT7MUNFL4AOKFCOMWLYY2V35Z","short_pith_number":"pith:KNT7MUNF","canonical_record":{"source":{"id":"1606.00900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-02T21:16:46Z","cross_cats_sorted":[],"title_canon_sha256":"d7d8ba79290731941fb1ac8ea3373100f4fc3cddc7c218a825357d2e970d9ee4","abstract_canon_sha256":"47f2a8d0b6a53c1c124636cff544d0ee721eec1ce4412c75daaf9c07bf699123"},"schema_version":"1.0"},"canonical_sha256":"5367f651a55f00e5144e65978c6abbee708a6221a3c83aa759f849a3f091b09d","source":{"kind":"arxiv","id":"1606.00900","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00900","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00900v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00900","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"KNT7MUNFL4AO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KNT7MUNFL4AOKFCO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KNT7MUNF","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KNT7MUNFL4AOKFCOMWLYY2V35Z","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-02T21:16:46Z","cross_cats_sorted":[],"title_canon_sha256":"d7d8ba79290731941fb1ac8ea3373100f4fc3cddc7c218a825357d2e970d9ee4","abstract_canon_sha256":"47f2a8d0b6a53c1c124636cff544d0ee721eec1ce4412c75daaf9c07bf699123"},"schema_version":"1.0"},"canonical_sha256":"5367f651a55f00e5144e65978c6abbee708a6221a3c83aa759f849a3f091b09d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:00.093885Z","signature_b64":"jGT5og1fYkSmK8NXoB8KYow1fGWawukm/Qqd1G+86NKIuH1/enIDGn6Igo3s4a+v+3yh6+3yqc94oEzGIA6TBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5367f651a55f00e5144e65978c6abbee708a6221a3c83aa759f849a3f091b09d","last_reissued_at":"2026-05-18T01:13:00.093479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:00.093479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00900","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":"2026-05-18T01:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JslYFeU9sgKAg6XQTN5JajVmGyCXH7zOUucSjrNzSB20jBdDhNEne351M9oDPKh/hr09DEDtfni7C/Cb99zPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:00:49.898489Z"},"content_sha256":"39546b20cb31a397605072c555f608f12abec8f0c8a49caf7857e9531c271c92","schema_version":"1.0","event_id":"sha256:39546b20cb31a397605072c555f608f12abec8f0c8a49caf7857e9531c271c92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KNT7MUNFL4AOKFCOMWLYY2V35Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some new computable structures of high rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gregory Igusa, Julia F. Knight, Matthew Harrison-Trainor","submitted_at":"2016-06-02T21:16:46Z","abstract_excerpt":"We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank $\\omega_1^{CK}$, the computable infinitary theory is $\\aleph_0$-categorical. Millar and Sacks asked whether this was always the case. We answer this question by constructing an example whose computable infinitary theory has non-isomorphic countable models.\n  The standard known computable structures of Scott rank $\\omega_1^{CK}+1$ have infinite indiscernible sequences. We give two constructions with no indiscernible ordered triple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00900","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":"2026-05-18T01:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+NkNNdKJdNG1gu3EbcXAq0xTXVsGDKy/LC0m4qrbJmhrSaB2/leNvlA/+id5DqiRDCzjOAcC/hvQq09HmOlQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:00:49.898831Z"},"content_sha256":"0272598e18410ad20eca0e929fbb97122fe9d54766f2bcbe1042bf206d802d68","schema_version":"1.0","event_id":"sha256:0272598e18410ad20eca0e929fbb97122fe9d54766f2bcbe1042bf206d802d68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z/bundle.json","state_url":"https://pith.science/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z/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":"2026-06-22T10:00:49Z","links":{"resolver":"https://pith.science/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z","bundle":"https://pith.science/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z/bundle.json","state":"https://pith.science/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNT7MUNFL4AOKFCOMWLYY2V35Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KNT7MUNFL4AOKFCOMWLYY2V35Z","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":"47f2a8d0b6a53c1c124636cff544d0ee721eec1ce4412c75daaf9c07bf699123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-02T21:16:46Z","title_canon_sha256":"d7d8ba79290731941fb1ac8ea3373100f4fc3cddc7c218a825357d2e970d9ee4"},"schema_version":"1.0","source":{"id":"1606.00900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00900","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00900v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00900","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"KNT7MUNFL4AO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KNT7MUNFL4AOKFCO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KNT7MUNF","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:0272598e18410ad20eca0e929fbb97122fe9d54766f2bcbe1042bf206d802d68","target":"graph","created_at":"2026-05-18T01:13:00Z","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":"We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank $\\omega_1^{CK}$, the computable infinitary theory is $\\aleph_0$-categorical. Millar and Sacks asked whether this was always the case. We answer this question by constructing an example whose computable infinitary theory has non-isomorphic countable models.\n  The standard known computable structures of Scott rank $\\omega_1^{CK}+1$ have infinite indiscernible sequences. We give two constructions with no indiscernible ordered triple.","authors_text":"Gregory Igusa, Julia F. Knight, Matthew Harrison-Trainor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-02T21:16:46Z","title":"Some new computable structures of high rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00900","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":"sha256:39546b20cb31a397605072c555f608f12abec8f0c8a49caf7857e9531c271c92","target":"record","created_at":"2026-05-18T01:13:00Z","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":"47f2a8d0b6a53c1c124636cff544d0ee721eec1ce4412c75daaf9c07bf699123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-02T21:16:46Z","title_canon_sha256":"d7d8ba79290731941fb1ac8ea3373100f4fc3cddc7c218a825357d2e970d9ee4"},"schema_version":"1.0","source":{"id":"1606.00900","kind":"arxiv","version":1}},"canonical_sha256":"5367f651a55f00e5144e65978c6abbee708a6221a3c83aa759f849a3f091b09d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5367f651a55f00e5144e65978c6abbee708a6221a3c83aa759f849a3f091b09d","first_computed_at":"2026-05-18T01:13:00.093479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.093479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jGT5og1fYkSmK8NXoB8KYow1fGWawukm/Qqd1G+86NKIuH1/enIDGn6Igo3s4a+v+3yh6+3yqc94oEzGIA6TBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.093885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39546b20cb31a397605072c555f608f12abec8f0c8a49caf7857e9531c271c92","sha256:0272598e18410ad20eca0e929fbb97122fe9d54766f2bcbe1042bf206d802d68"],"state_sha256":"9bad05e4bd1a8f1020224dc323b5d076e262f355287c0e428215ad79da740c28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4heZrVKSPcZHH/at8vYpqpOa+b41Cy0ASHUjg5ZflmzPETRZG7nbbRUiDoSGRTS0u23t72DfKzW/WcGoEPzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:00:49.901045Z","bundle_sha256":"b308952e6701fdcf089e3bb54d20f940e484df1853830d98e7a880f1a3d2b1b4"}}