{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ICRXFWOQDZ7TCBWX7DO7YPMRXX","short_pith_number":"pith:ICRXFWOQ","canonical_record":{"source":{"id":"1609.02433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-08T14:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"89026bf36e5eaaa17e99434209fe6730e24b3a3d038c377f45f022d247950df2","abstract_canon_sha256":"568b4afe95375e8d8cea5757f6f7d9f52534e3d688bd5b2081aac34b24205f81"},"schema_version":"1.0"},"canonical_sha256":"40a372d9d01e7f3106d7f8ddfc3d91bdca4511b6929b067b1f514afcd65739ff","source":{"kind":"arxiv","id":"1609.02433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02433","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02433v1","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02433","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"ICRXFWOQDZ7T","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"ICRXFWOQDZ7TCBWX","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"ICRXFWOQ","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ICRXFWOQDZ7TCBWX7DO7YPMRXX","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-08T14:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"89026bf36e5eaaa17e99434209fe6730e24b3a3d038c377f45f022d247950df2","abstract_canon_sha256":"568b4afe95375e8d8cea5757f6f7d9f52534e3d688bd5b2081aac34b24205f81"},"schema_version":"1.0"},"canonical_sha256":"40a372d9d01e7f3106d7f8ddfc3d91bdca4511b6929b067b1f514afcd65739ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:54.673333Z","signature_b64":"r87aVlKtcUmvQCmlQenlW+nlXSHhclZwtqZ+kTNKhEYPdM7rxBKsfDnRNTWcQxsCCV1+2WcmXmNlGHL8U6GtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40a372d9d01e7f3106d7f8ddfc3d91bdca4511b6929b067b1f514afcd65739ff","last_reissued_at":"2026-05-18T01:04:54.672588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:54.672588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02433","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":"2026-05-18T01:04:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTe3tRiWOucW9KWQpSMOpFQ8Y5t2uosNonGHC3zcpevQrdQrPXpPPX8QR1la7SbLe7RpSv7CwMTiaCzqmX2WCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:18:42.144199Z"},"content_sha256":"55981434c2493c2feb2b8d031c3f1d4c875fe2cbf56df3f5e0e93ac01879778a","schema_version":"1.0","event_id":"sha256:55981434c2493c2feb2b8d031c3f1d4c875fe2cbf56df3f5e0e93ac01879778a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ICRXFWOQDZ7TCBWX7DO7YPMRXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Binary simple homogeneous structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vera Koponen","submitted_at":"2016-09-08T14:04:49Z","abstract_excerpt":"We describe all binary simple homogeneous structures M in terms of 0-definable equivalence relations on M, which \"coordinatize\" M and control dividing, and extension properties that respect these equivalence relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02433","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":"2026-05-18T01:04:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSowAwRnlZcgh+TlNrVhoxh7G6s4S7rr0xdSnPkLPFvWm5XeIOoPt0H0H5NMnpj2fhbIbLSy1dRTk15pjYWbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:18:42.144684Z"},"content_sha256":"dfb108f7d883d38475a94378069043741914f85f438864c337c7973fcd11a397","schema_version":"1.0","event_id":"sha256:dfb108f7d883d38475a94378069043741914f85f438864c337c7973fcd11a397"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX/bundle.json","state_url":"https://pith.science/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX/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":"2026-06-24T16:18:42Z","links":{"resolver":"https://pith.science/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX","bundle":"https://pith.science/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX/bundle.json","state":"https://pith.science/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ICRXFWOQDZ7TCBWX7DO7YPMRXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ICRXFWOQDZ7TCBWX7DO7YPMRXX","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":"568b4afe95375e8d8cea5757f6f7d9f52534e3d688bd5b2081aac34b24205f81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-08T14:04:49Z","title_canon_sha256":"89026bf36e5eaaa17e99434209fe6730e24b3a3d038c377f45f022d247950df2"},"schema_version":"1.0","source":{"id":"1609.02433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02433","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02433v1","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02433","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"ICRXFWOQDZ7T","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"ICRXFWOQDZ7TCBWX","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"ICRXFWOQ","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:dfb108f7d883d38475a94378069043741914f85f438864c337c7973fcd11a397","target":"graph","created_at":"2026-05-18T01:04:54Z","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 describe all binary simple homogeneous structures M in terms of 0-definable equivalence relations on M, which \"coordinatize\" M and control dividing, and extension properties that respect these equivalence relations.","authors_text":"Vera Koponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-08T14:04:49Z","title":"Binary simple homogeneous structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02433","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":"sha256:55981434c2493c2feb2b8d031c3f1d4c875fe2cbf56df3f5e0e93ac01879778a","target":"record","created_at":"2026-05-18T01:04:54Z","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":"568b4afe95375e8d8cea5757f6f7d9f52534e3d688bd5b2081aac34b24205f81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-08T14:04:49Z","title_canon_sha256":"89026bf36e5eaaa17e99434209fe6730e24b3a3d038c377f45f022d247950df2"},"schema_version":"1.0","source":{"id":"1609.02433","kind":"arxiv","version":1}},"canonical_sha256":"40a372d9d01e7f3106d7f8ddfc3d91bdca4511b6929b067b1f514afcd65739ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40a372d9d01e7f3106d7f8ddfc3d91bdca4511b6929b067b1f514afcd65739ff","first_computed_at":"2026-05-18T01:04:54.672588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:54.672588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r87aVlKtcUmvQCmlQenlW+nlXSHhclZwtqZ+kTNKhEYPdM7rxBKsfDnRNTWcQxsCCV1+2WcmXmNlGHL8U6GtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:54.673333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55981434c2493c2feb2b8d031c3f1d4c875fe2cbf56df3f5e0e93ac01879778a","sha256:dfb108f7d883d38475a94378069043741914f85f438864c337c7973fcd11a397"],"state_sha256":"b3a98d3dbeee00ce8d074dc5efe28d06a2eccb924ebafa2816200402bca317f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alL98Q/p0ZWV8TuwRMDV71UaxaVOI2OoaXLALORhxNoW1vPn/CH3h+jrBAjzaEykVfNYYzSl2Hfu9z1SdHUODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:18:42.146883Z","bundle_sha256":"2d3b2b97ed5bfe4c32f059a6616d389927a49bcf11c84785fd2666e99474bb79"}}