{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LD2S62533IBS5CO7RNIZCBAROP","short_pith_number":"pith:LD2S6253","canonical_record":{"source":{"id":"1605.04372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-14T03:34:56Z","cross_cats_sorted":[],"title_canon_sha256":"00536e211725988b24131b7c946a21b3bf0bd31c5b88fb89154c112f6a250ea0","abstract_canon_sha256":"fa08b9fe9da084ab685ef646c3da140e9b021a39bfddc292ead864a591e1a92d"},"schema_version":"1.0"},"canonical_sha256":"58f52f6bbbda032e89df8b5191041173c759ca071aded8c23175e031a47c9df8","source":{"kind":"arxiv","id":"1605.04372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04372","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04372v1","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04372","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"LD2S62533IBS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LD2S62533IBS5CO7","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LD2S6253","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LD2S62533IBS5CO7RNIZCBAROP","target":"record","payload":{"canonical_record":{"source":{"id":"1605.04372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-14T03:34:56Z","cross_cats_sorted":[],"title_canon_sha256":"00536e211725988b24131b7c946a21b3bf0bd31c5b88fb89154c112f6a250ea0","abstract_canon_sha256":"fa08b9fe9da084ab685ef646c3da140e9b021a39bfddc292ead864a591e1a92d"},"schema_version":"1.0"},"canonical_sha256":"58f52f6bbbda032e89df8b5191041173c759ca071aded8c23175e031a47c9df8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:43.587326Z","signature_b64":"zBPIUF2gIaYIFvCsXtgCwZp4W14/QQ/ToTUtJTfp7fHOV7W1NesV3OXIdSSC2rLlaIAVPyE+UQwT/R1+9K2rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58f52f6bbbda032e89df8b5191041173c759ca071aded8c23175e031a47c9df8","last_reissued_at":"2026-05-17T23:43:43.586719Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:43.586719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.04372","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":"2026-05-17T23:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iaS2vlwqZ4zBge9sTUGbCKNPPpHfFFi3LX92gsTcySj6m5p9aKvcX7YwLGwOca+Mc+iJELkbdHmov1COvywACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:23:34.446848Z"},"content_sha256":"30602f71b57e911ef71818b8c4b87cc4662d6d1393a7ac482fd922bf42690c30","schema_version":"1.0","event_id":"sha256:30602f71b57e911ef71818b8c4b87cc4662d6d1393a7ac482fd922bf42690c30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LD2S62533IBS5CO7RNIZCBAROP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Betti numbers in three dimensional minimal model program","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hsin-Ku Chen","submitted_at":"2016-05-14T03:34:56Z","abstract_excerpt":"Let $X$ be a smooth projective threefold. We prove that, among the process of minimal model program, the variance of the third Betti number can be bounded by some integer depends only on the Picard number of $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04372","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":"2026-05-17T23:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZTxF63iycnD0JWCiol019YT6oChhCU1Rz9e5RY+MxveZ5g+DFJ7nXMsrReqMMZ90DDa5bquK6MHH83yvdMUbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:23:34.447181Z"},"content_sha256":"a7e956fc6253aa45a004f3fdde23951d149fe73f722984f1c96caf107915626a","schema_version":"1.0","event_id":"sha256:a7e956fc6253aa45a004f3fdde23951d149fe73f722984f1c96caf107915626a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LD2S62533IBS5CO7RNIZCBAROP/bundle.json","state_url":"https://pith.science/pith/LD2S62533IBS5CO7RNIZCBAROP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LD2S62533IBS5CO7RNIZCBAROP/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":"2026-06-24T18:23:34Z","links":{"resolver":"https://pith.science/pith/LD2S62533IBS5CO7RNIZCBAROP","bundle":"https://pith.science/pith/LD2S62533IBS5CO7RNIZCBAROP/bundle.json","state":"https://pith.science/pith/LD2S62533IBS5CO7RNIZCBAROP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LD2S62533IBS5CO7RNIZCBAROP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LD2S62533IBS5CO7RNIZCBAROP","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":"fa08b9fe9da084ab685ef646c3da140e9b021a39bfddc292ead864a591e1a92d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-14T03:34:56Z","title_canon_sha256":"00536e211725988b24131b7c946a21b3bf0bd31c5b88fb89154c112f6a250ea0"},"schema_version":"1.0","source":{"id":"1605.04372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04372","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04372v1","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04372","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"LD2S62533IBS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LD2S62533IBS5CO7","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LD2S6253","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:a7e956fc6253aa45a004f3fdde23951d149fe73f722984f1c96caf107915626a","target":"graph","created_at":"2026-05-17T23:43:43Z","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":"Let $X$ be a smooth projective threefold. We prove that, among the process of minimal model program, the variance of the third Betti number can be bounded by some integer depends only on the Picard number of $X$.","authors_text":"Hsin-Ku Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-14T03:34:56Z","title":"Betti numbers in three dimensional minimal model program"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04372","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":"sha256:30602f71b57e911ef71818b8c4b87cc4662d6d1393a7ac482fd922bf42690c30","target":"record","created_at":"2026-05-17T23:43:43Z","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":"fa08b9fe9da084ab685ef646c3da140e9b021a39bfddc292ead864a591e1a92d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-14T03:34:56Z","title_canon_sha256":"00536e211725988b24131b7c946a21b3bf0bd31c5b88fb89154c112f6a250ea0"},"schema_version":"1.0","source":{"id":"1605.04372","kind":"arxiv","version":1}},"canonical_sha256":"58f52f6bbbda032e89df8b5191041173c759ca071aded8c23175e031a47c9df8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58f52f6bbbda032e89df8b5191041173c759ca071aded8c23175e031a47c9df8","first_computed_at":"2026-05-17T23:43:43.586719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:43.586719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zBPIUF2gIaYIFvCsXtgCwZp4W14/QQ/ToTUtJTfp7fHOV7W1NesV3OXIdSSC2rLlaIAVPyE+UQwT/R1+9K2rDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:43.587326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30602f71b57e911ef71818b8c4b87cc4662d6d1393a7ac482fd922bf42690c30","sha256:a7e956fc6253aa45a004f3fdde23951d149fe73f722984f1c96caf107915626a"],"state_sha256":"af59a629e3faff53361586ddff89cff7e40ba5250552f8607ad48080bf9fd714"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pj3P5ODpdqk9ZKjXfs/7jj+6z5IJL/ZSYYESZht5omZgshyLt1bDXo36A7ei4AdyHUeHd7lODTLYJVOwd9jnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:23:34.449109Z","bundle_sha256":"c099ca48725e17c4efbe6977fb8f5e81b83512625348ee929af7e4dfcff582d7"}}