{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XL2SPOZ34MWX6LIEI3KZZIJILX","short_pith_number":"pith:XL2SPOZ3","canonical_record":{"source":{"id":"1810.00459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-09-30T20:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"fc05f6baec766f06dca2faf674d8bc1b50643fff4a10b776f754f7b8717dd58a","abstract_canon_sha256":"0ea83d18bd4e4dff47f11ca9d97a7828ee30c6e4f128dd60e02f1fd0e7ccffc0"},"schema_version":"1.0"},"canonical_sha256":"baf527bb3be32d7f2d0446d59ca1285dfc9370fcd9c9e8e45430044b58a271b5","source":{"kind":"arxiv","id":"1810.00459","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00459","created_at":"2026-05-18T00:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00459v1","created_at":"2026-05-18T00:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00459","created_at":"2026-05-18T00:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"XL2SPOZ34MWX","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XL2SPOZ34MWX6LIE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XL2SPOZ3","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XL2SPOZ34MWX6LIEI3KZZIJILX","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-09-30T20:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"fc05f6baec766f06dca2faf674d8bc1b50643fff4a10b776f754f7b8717dd58a","abstract_canon_sha256":"0ea83d18bd4e4dff47f11ca9d97a7828ee30c6e4f128dd60e02f1fd0e7ccffc0"},"schema_version":"1.0"},"canonical_sha256":"baf527bb3be32d7f2d0446d59ca1285dfc9370fcd9c9e8e45430044b58a271b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:26.116593Z","signature_b64":"Rz8U7mVNtypphPmkmTo2eYyYGvkTffCWrriTurc/cYdhGs7okrPGcaJc6FqdhSt/xj0pyMACbKwVqeLAJRtWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baf527bb3be32d7f2d0446d59ca1285dfc9370fcd9c9e8e45430044b58a271b5","last_reissued_at":"2026-05-18T00:04:26.116082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:26.116082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00459","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":"2026-05-18T00:04:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rizS8GDuZrxL/1yUaPXktG8LW/YN/SMT3qr4cMMEcMNRigIq3Ogtt5Tc4OumyJ5Y98y8zFHHIBfEuFEbXYSJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:09:25.222678Z"},"content_sha256":"d9ddaf32432bd87f840a610d6f248b3b77eb8237bbafd1d61efb1a6249e73eaf","schema_version":"1.0","event_id":"sha256:d9ddaf32432bd87f840a610d6f248b3b77eb8237bbafd1d61efb1a6249e73eaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XL2SPOZ34MWX6LIEI3KZZIJILX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-degree Smoothness of Perturbations III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Gang Liu","submitted_at":"2018-09-30T20:33:36Z","abstract_excerpt":"This paper is the continuation of the previous two papers with the same title."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00459","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":"2026-05-18T00:04:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v58MfWC6XiNoi0IOPg2Yda41T1umX3aNF8IeUTfg0CD9uXLkNhXFuZtYPZmHOEKR4dsZfavu8KIxsMcGI67PDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:09:25.223072Z"},"content_sha256":"820ec89679e24d5c382502690e5de079088fe1f847f553f39ece46c8512f032d","schema_version":"1.0","event_id":"sha256:820ec89679e24d5c382502690e5de079088fe1f847f553f39ece46c8512f032d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XL2SPOZ34MWX6LIEI3KZZIJILX/bundle.json","state_url":"https://pith.science/pith/XL2SPOZ34MWX6LIEI3KZZIJILX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XL2SPOZ34MWX6LIEI3KZZIJILX/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":"2026-06-04T15:09:25Z","links":{"resolver":"https://pith.science/pith/XL2SPOZ34MWX6LIEI3KZZIJILX","bundle":"https://pith.science/pith/XL2SPOZ34MWX6LIEI3KZZIJILX/bundle.json","state":"https://pith.science/pith/XL2SPOZ34MWX6LIEI3KZZIJILX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XL2SPOZ34MWX6LIEI3KZZIJILX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XL2SPOZ34MWX6LIEI3KZZIJILX","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":"0ea83d18bd4e4dff47f11ca9d97a7828ee30c6e4f128dd60e02f1fd0e7ccffc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-09-30T20:33:36Z","title_canon_sha256":"fc05f6baec766f06dca2faf674d8bc1b50643fff4a10b776f754f7b8717dd58a"},"schema_version":"1.0","source":{"id":"1810.00459","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00459","created_at":"2026-05-18T00:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00459v1","created_at":"2026-05-18T00:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00459","created_at":"2026-05-18T00:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"XL2SPOZ34MWX","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XL2SPOZ34MWX6LIE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XL2SPOZ3","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:820ec89679e24d5c382502690e5de079088fe1f847f553f39ece46c8512f032d","target":"graph","created_at":"2026-05-18T00:04:26Z","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":"This paper is the continuation of the previous two papers with the same title.","authors_text":"Gang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-09-30T20:33:36Z","title":"Higher-degree Smoothness of Perturbations III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00459","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:d9ddaf32432bd87f840a610d6f248b3b77eb8237bbafd1d61efb1a6249e73eaf","target":"record","created_at":"2026-05-18T00:04:26Z","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":"0ea83d18bd4e4dff47f11ca9d97a7828ee30c6e4f128dd60e02f1fd0e7ccffc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-09-30T20:33:36Z","title_canon_sha256":"fc05f6baec766f06dca2faf674d8bc1b50643fff4a10b776f754f7b8717dd58a"},"schema_version":"1.0","source":{"id":"1810.00459","kind":"arxiv","version":1}},"canonical_sha256":"baf527bb3be32d7f2d0446d59ca1285dfc9370fcd9c9e8e45430044b58a271b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baf527bb3be32d7f2d0446d59ca1285dfc9370fcd9c9e8e45430044b58a271b5","first_computed_at":"2026-05-18T00:04:26.116082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:26.116082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rz8U7mVNtypphPmkmTo2eYyYGvkTffCWrriTurc/cYdhGs7okrPGcaJc6FqdhSt/xj0pyMACbKwVqeLAJRtWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:26.116593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00459","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9ddaf32432bd87f840a610d6f248b3b77eb8237bbafd1d61efb1a6249e73eaf","sha256:820ec89679e24d5c382502690e5de079088fe1f847f553f39ece46c8512f032d"],"state_sha256":"717550b133ebaeb4ae8b107327d5d5d385c0e79b1f251419c27ef7a1bec0e85b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XjgxHq1CVLPMQTDsT2cE7/UvtmbY1wF7zlmEMcV2uY4T5zSj/zmGxlp0+Rh6FjPQTvXOXxqJh2Y9t511+f3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:09:25.226587Z","bundle_sha256":"309977ce8a275fb012093620cb9d951ac65a96f4d26eda757e822e7c7fb00f0b"}}