{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TIFMKLRQ3M7GUZOYEBDLNERZBZ","short_pith_number":"pith:TIFMKLRQ","canonical_record":{"source":{"id":"1610.01760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-06T07:28:28Z","cross_cats_sorted":[],"title_canon_sha256":"c28a008d237d6d2718e0e7c02ac9521c1dd56a56919cd083d32cadeaafcfb193","abstract_canon_sha256":"5e16407e2d7afde5cacfc44e1ee60c9cdbf5d3ba9823791308d7fa09784c7ad1"},"schema_version":"1.0"},"canonical_sha256":"9a0ac52e30db3e6a65d82046b692390e62d2d8699d4415e48e796d878a1629ec","source":{"kind":"arxiv","id":"1610.01760","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01760","created_at":"2026-05-18T01:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01760v1","created_at":"2026-05-18T01:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01760","created_at":"2026-05-18T01:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"TIFMKLRQ3M7G","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIFMKLRQ3M7GUZOY","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIFMKLRQ","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TIFMKLRQ3M7GUZOYEBDLNERZBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-06T07:28:28Z","cross_cats_sorted":[],"title_canon_sha256":"c28a008d237d6d2718e0e7c02ac9521c1dd56a56919cd083d32cadeaafcfb193","abstract_canon_sha256":"5e16407e2d7afde5cacfc44e1ee60c9cdbf5d3ba9823791308d7fa09784c7ad1"},"schema_version":"1.0"},"canonical_sha256":"9a0ac52e30db3e6a65d82046b692390e62d2d8699d4415e48e796d878a1629ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:04.947611Z","signature_b64":"6X/moMQ8aNqQvkECdg5xofu4jAWGO18s5qU8WOW/rf+bfRzkbgIurAJWql4QABNuc3+EA0EJNYxrAyTmKfnuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a0ac52e30db3e6a65d82046b692390e62d2d8699d4415e48e796d878a1629ec","last_reissued_at":"2026-05-18T01:03:04.946873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:04.946873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01760","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":"2026-05-18T01:03:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aexK4CMlTgpc5JA+m1GjdoIiOdqO0p2+CQo+3KAPorfYWdZ6mgAXq+5qdyUKwpDgNG0nDjNtlLthIkWB3Q5LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:43:10.773818Z"},"content_sha256":"cbfe124f4b2b92a73702f821000baebef617974abb60bbb399b7b794ae5a4019","schema_version":"1.0","event_id":"sha256:cbfe124f4b2b92a73702f821000baebef617974abb60bbb399b7b794ae5a4019"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TIFMKLRQ3M7GUZOYEBDLNERZBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Problems 85 and 87 of Birkhoff's \"Lattice theory\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dominic van der Zypen, Jonathan David Farley","submitted_at":"2016-10-06T07:28:28Z","abstract_excerpt":"We solve problems 85 a(nd 87 from Birkhoff's book \"Lattice Theory\" (3rd edition)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01760","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":"2026-05-18T01:03:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KmlboQoxv7Sgp920wULh38KYoChtGTF2XVFNBGeOp/sw7bunfsyQCrR9nQgQB1Elspx59YsjE/CVZyx0kKjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:43:10.774155Z"},"content_sha256":"a447e12d333d72e8499db9430d71383a0713a0b96fb32db3e32f4ccef64b9766","schema_version":"1.0","event_id":"sha256:a447e12d333d72e8499db9430d71383a0713a0b96fb32db3e32f4ccef64b9766"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ/bundle.json","state_url":"https://pith.science/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ/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":"2026-06-25T08:43:10Z","links":{"resolver":"https://pith.science/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ","bundle":"https://pith.science/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ/bundle.json","state":"https://pith.science/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIFMKLRQ3M7GUZOYEBDLNERZBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TIFMKLRQ3M7GUZOYEBDLNERZBZ","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":"5e16407e2d7afde5cacfc44e1ee60c9cdbf5d3ba9823791308d7fa09784c7ad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-06T07:28:28Z","title_canon_sha256":"c28a008d237d6d2718e0e7c02ac9521c1dd56a56919cd083d32cadeaafcfb193"},"schema_version":"1.0","source":{"id":"1610.01760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01760","created_at":"2026-05-18T01:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01760v1","created_at":"2026-05-18T01:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01760","created_at":"2026-05-18T01:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"TIFMKLRQ3M7G","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIFMKLRQ3M7GUZOY","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIFMKLRQ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:a447e12d333d72e8499db9430d71383a0713a0b96fb32db3e32f4ccef64b9766","target":"graph","created_at":"2026-05-18T01:03:04Z","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 solve problems 85 a(nd 87 from Birkhoff's book \"Lattice Theory\" (3rd edition)","authors_text":"Dominic van der Zypen, Jonathan David Farley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-06T07:28:28Z","title":"Problems 85 and 87 of Birkhoff's \"Lattice theory\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01760","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:cbfe124f4b2b92a73702f821000baebef617974abb60bbb399b7b794ae5a4019","target":"record","created_at":"2026-05-18T01:03:04Z","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":"5e16407e2d7afde5cacfc44e1ee60c9cdbf5d3ba9823791308d7fa09784c7ad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-06T07:28:28Z","title_canon_sha256":"c28a008d237d6d2718e0e7c02ac9521c1dd56a56919cd083d32cadeaafcfb193"},"schema_version":"1.0","source":{"id":"1610.01760","kind":"arxiv","version":1}},"canonical_sha256":"9a0ac52e30db3e6a65d82046b692390e62d2d8699d4415e48e796d878a1629ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a0ac52e30db3e6a65d82046b692390e62d2d8699d4415e48e796d878a1629ec","first_computed_at":"2026-05-18T01:03:04.946873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:04.946873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6X/moMQ8aNqQvkECdg5xofu4jAWGO18s5qU8WOW/rf+bfRzkbgIurAJWql4QABNuc3+EA0EJNYxrAyTmKfnuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:04.947611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbfe124f4b2b92a73702f821000baebef617974abb60bbb399b7b794ae5a4019","sha256:a447e12d333d72e8499db9430d71383a0713a0b96fb32db3e32f4ccef64b9766"],"state_sha256":"2730890b8959da4f48d5e94d982d0a731ca9ffb6a124c8495431c842fdda82a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AUviMbpYTHXUgVVfEV4J29BvPHdRR7nZffz0tXyVdHvMc3HJOUDkkrXHz1Fd4haaZzjhTyCGThy76W6ZSfoXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:43:10.776149Z","bundle_sha256":"2180a364505888061298b22b532cb71de88660903c4ab055a9d2a310953db7d1"}}