{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2AXKIYIDPHJGFLTZEKNWV5RMT7","short_pith_number":"pith:2AXKIYID","canonical_record":{"source":{"id":"1104.1842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-11T04:35:03Z","cross_cats_sorted":[],"title_canon_sha256":"69c1dd9374bcedb7f728e1ec7dc337c8eee75038fdf32737c2a00356a1269f6d","abstract_canon_sha256":"00cbda822edaa7ad19bb64398a79cd2836803441a0b36d924c29d3a9f3418a1d"},"schema_version":"1.0"},"canonical_sha256":"d02ea4610379d262ae79229b6af62c9ffdff686e390e83cd4e9c7de4e4c0b85d","source":{"kind":"arxiv","id":"1104.1842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1842","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1842v1","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1842","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"2AXKIYIDPHJG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2AXKIYIDPHJGFLTZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2AXKIYID","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2AXKIYIDPHJGFLTZEKNWV5RMT7","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-11T04:35:03Z","cross_cats_sorted":[],"title_canon_sha256":"69c1dd9374bcedb7f728e1ec7dc337c8eee75038fdf32737c2a00356a1269f6d","abstract_canon_sha256":"00cbda822edaa7ad19bb64398a79cd2836803441a0b36d924c29d3a9f3418a1d"},"schema_version":"1.0"},"canonical_sha256":"d02ea4610379d262ae79229b6af62c9ffdff686e390e83cd4e9c7de4e4c0b85d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:36.987336Z","signature_b64":"FjU0BvdkHeqd39rw97eucQELemE95PmhyJt7HBpWcsR22jK/XX91rxciZyIpOFpkQ5Ta6KRHzQ6b8ChAUQNqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d02ea4610379d262ae79229b6af62c9ffdff686e390e83cd4e9c7de4e4c0b85d","last_reissued_at":"2026-05-18T04:24:36.986928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:36.986928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1842","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":"2026-05-18T04:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RX6H5l67WSL7I2A/j+wDdzfFec+XPWSZfs60EI1wsdp7I57zEw/QQPRrctiXjJCz32M6jFY6RBD4pud2SjknBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:50:00.656599Z"},"content_sha256":"af9a9384374414b5c886a59ddb4fa3fb681f720cb0faf32e076cacdb80803b54","schema_version":"1.0","event_id":"sha256:af9a9384374414b5c886a59ddb4fa3fb681f720cb0faf32e076cacdb80803b54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2AXKIYIDPHJGFLTZEKNWV5RMT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Introducing the hardline in proof theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Toshiyasu Arai","submitted_at":"2011-04-11T04:35:03Z","abstract_excerpt":"In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1842","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":"2026-05-18T04:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1GWLa6X22r0lx/QsMpejEKZr8/S07urkLsw3pRFy7OFspLzYgxvFMlJR1JEwwVoPqtQoDqI+UvhbTNlvcakBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:50:00.656942Z"},"content_sha256":"d5e31cc6135ba2688ba4b1995cc4b8494e700a38e5df923a8db38600f461db57","schema_version":"1.0","event_id":"sha256:d5e31cc6135ba2688ba4b1995cc4b8494e700a38e5df923a8db38600f461db57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7/bundle.json","state_url":"https://pith.science/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7/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":"2026-06-26T05:50:00Z","links":{"resolver":"https://pith.science/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7","bundle":"https://pith.science/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7/bundle.json","state":"https://pith.science/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AXKIYIDPHJGFLTZEKNWV5RMT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2AXKIYIDPHJGFLTZEKNWV5RMT7","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":"00cbda822edaa7ad19bb64398a79cd2836803441a0b36d924c29d3a9f3418a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-11T04:35:03Z","title_canon_sha256":"69c1dd9374bcedb7f728e1ec7dc337c8eee75038fdf32737c2a00356a1269f6d"},"schema_version":"1.0","source":{"id":"1104.1842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1842","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1842v1","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1842","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"2AXKIYIDPHJG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2AXKIYIDPHJGFLTZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2AXKIYID","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:d5e31cc6135ba2688ba4b1995cc4b8494e700a38e5df923a8db38600f461db57","target":"graph","created_at":"2026-05-18T04:24:36Z","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":"In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.","authors_text":"Toshiyasu Arai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-11T04:35:03Z","title":"Introducing the hardline in proof theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1842","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:af9a9384374414b5c886a59ddb4fa3fb681f720cb0faf32e076cacdb80803b54","target":"record","created_at":"2026-05-18T04:24:36Z","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":"00cbda822edaa7ad19bb64398a79cd2836803441a0b36d924c29d3a9f3418a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-11T04:35:03Z","title_canon_sha256":"69c1dd9374bcedb7f728e1ec7dc337c8eee75038fdf32737c2a00356a1269f6d"},"schema_version":"1.0","source":{"id":"1104.1842","kind":"arxiv","version":1}},"canonical_sha256":"d02ea4610379d262ae79229b6af62c9ffdff686e390e83cd4e9c7de4e4c0b85d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d02ea4610379d262ae79229b6af62c9ffdff686e390e83cd4e9c7de4e4c0b85d","first_computed_at":"2026-05-18T04:24:36.986928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:36.986928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FjU0BvdkHeqd39rw97eucQELemE95PmhyJt7HBpWcsR22jK/XX91rxciZyIpOFpkQ5Ta6KRHzQ6b8ChAUQNqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:36.987336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af9a9384374414b5c886a59ddb4fa3fb681f720cb0faf32e076cacdb80803b54","sha256:d5e31cc6135ba2688ba4b1995cc4b8494e700a38e5df923a8db38600f461db57"],"state_sha256":"8dcca46356609cb553352e9b4e7024be69c1dfcaa62853d1f7efb4f638b493d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tj3mQYDBUXqe72CBEGMy4zeZ2h0d/QmGPM4AbQdq380V+ICcDJwa4yH9jzN3NpqjbffHu+oU+unhkwaNXy9XDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T05:50:00.658911Z","bundle_sha256":"ed1224ea469cca036e4fd8e986400787610ecebc85feff1647b37febd14554db"}}