{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XLB3GDIHK4ZGX3J3BLXRBZOGR2","short_pith_number":"pith:XLB3GDIH","canonical_record":{"source":{"id":"2112.06361","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2021-12-13T00:31:14Z","cross_cats_sorted":[],"title_canon_sha256":"022e1d7ae0efc936d5bc38b24e1631ce2bbaa20a78274ff5b43b6b0c09117aee","abstract_canon_sha256":"ff95f51b449528008a3221a56ddab152b08382a626d38a56b2b30ee50bf93b84"},"schema_version":"1.0"},"canonical_sha256":"bac3b30d0757326bed3b0aef10e5c68ea2b66fa2d17b2138259d6ec0ebea870c","source":{"kind":"arxiv","id":"2112.06361","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.06361","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"2112.06361v3","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06361","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"XLB3GDIHK4ZG","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_16","alias_value":"XLB3GDIHK4ZGX3J3","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_8","alias_value":"XLB3GDIH","created_at":"2026-05-20T14:03:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XLB3GDIHK4ZGX3J3BLXRBZOGR2","target":"record","payload":{"canonical_record":{"source":{"id":"2112.06361","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2021-12-13T00:31:14Z","cross_cats_sorted":[],"title_canon_sha256":"022e1d7ae0efc936d5bc38b24e1631ce2bbaa20a78274ff5b43b6b0c09117aee","abstract_canon_sha256":"ff95f51b449528008a3221a56ddab152b08382a626d38a56b2b30ee50bf93b84"},"schema_version":"1.0"},"canonical_sha256":"bac3b30d0757326bed3b0aef10e5c68ea2b66fa2d17b2138259d6ec0ebea870c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:15.488872Z","signature_b64":"dSftKAj27u8F03JIrPSHPNTEP1U/thtA6jq37bjEKNpE8xy00EGD0PxG4FHd88tNtMj6httMGXhuhPiZ5qxfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bac3b30d0757326bed3b0aef10e5c68ea2b66fa2d17b2138259d6ec0ebea870c","last_reissued_at":"2026-05-20T14:03:15.488430Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:15.488430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.06361","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T14:03:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2nfBnWynIbi2LTR7c2mCKhksBIXJsNDdenZQEZKyG4RzswW7dVcQjc+2Jk4ae44RaO6zQfa9kkoVPZaOuZv4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:25:29.710724Z"},"content_sha256":"b86e94daec963c811e43dc39e864ff8166fb6a7b32292d35139a523b14b4e890","schema_version":"1.0","event_id":"sha256:b86e94daec963c811e43dc39e864ff8166fb6a7b32292d35139a523b14b4e890"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XLB3GDIHK4ZGX3J3BLXRBZOGR2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic resolution via multi-weighted blow-ups","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Abramovich, Ming Hao Quek","submitted_at":"2021-12-13T00:31:14Z","abstract_excerpt":"We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka. Specifically, for a singular, reduced closed subscheme $X$ of a smooth scheme $Y$ over a field of characteristic zero, we resolve the singularities of $X$ by taking proper transforms $X_i \\subset Y_i$ along a sequence of multi-weighted blow-ups $Y_N \\to Y_{N-1} \\to \\dotsb \\to Y_0 = Y$ which satisfies the following properties: (i) the $Y_i$ are smooth Artin s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06361","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.06361/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T14:03:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVGsDUFM2hDTXIbk4KBplkOJeugFbDY0YJJ5dltixcaz9v0PQ3pIEbnpJsleRvO8nDF+xfvuOxE9Dt0zMtwoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:25:29.711422Z"},"content_sha256":"3b6fbaa5b21850ef93a3e6c9fcf9cefc67453dedc00755193bb2a13f35bc78ee","schema_version":"1.0","event_id":"sha256:3b6fbaa5b21850ef93a3e6c9fcf9cefc67453dedc00755193bb2a13f35bc78ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2/bundle.json","state_url":"https://pith.science/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2/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":"2026-06-02T05:25:29Z","links":{"resolver":"https://pith.science/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2","bundle":"https://pith.science/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2/bundle.json","state":"https://pith.science/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLB3GDIHK4ZGX3J3BLXRBZOGR2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XLB3GDIHK4ZGX3J3BLXRBZOGR2","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":"ff95f51b449528008a3221a56ddab152b08382a626d38a56b2b30ee50bf93b84","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2021-12-13T00:31:14Z","title_canon_sha256":"022e1d7ae0efc936d5bc38b24e1631ce2bbaa20a78274ff5b43b6b0c09117aee"},"schema_version":"1.0","source":{"id":"2112.06361","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.06361","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"2112.06361v3","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06361","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"XLB3GDIHK4ZG","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_16","alias_value":"XLB3GDIHK4ZGX3J3","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_8","alias_value":"XLB3GDIH","created_at":"2026-05-20T14:03:15Z"}],"graph_snapshots":[{"event_id":"sha256:3b6fbaa5b21850ef93a3e6c9fcf9cefc67453dedc00755193bb2a13f35bc78ee","target":"graph","created_at":"2026-05-20T14:03:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.06361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka. Specifically, for a singular, reduced closed subscheme $X$ of a smooth scheme $Y$ over a field of characteristic zero, we resolve the singularities of $X$ by taking proper transforms $X_i \\subset Y_i$ along a sequence of multi-weighted blow-ups $Y_N \\to Y_{N-1} \\to \\dotsb \\to Y_0 = Y$ which satisfies the following properties: (i) the $Y_i$ are smooth Artin s","authors_text":"Dan Abramovich, Ming Hao Quek","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2021-12-13T00:31:14Z","title":"Logarithmic resolution via multi-weighted blow-ups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06361","kind":"arxiv","version":3},"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:b86e94daec963c811e43dc39e864ff8166fb6a7b32292d35139a523b14b4e890","target":"record","created_at":"2026-05-20T14:03:15Z","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":"ff95f51b449528008a3221a56ddab152b08382a626d38a56b2b30ee50bf93b84","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2021-12-13T00:31:14Z","title_canon_sha256":"022e1d7ae0efc936d5bc38b24e1631ce2bbaa20a78274ff5b43b6b0c09117aee"},"schema_version":"1.0","source":{"id":"2112.06361","kind":"arxiv","version":3}},"canonical_sha256":"bac3b30d0757326bed3b0aef10e5c68ea2b66fa2d17b2138259d6ec0ebea870c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bac3b30d0757326bed3b0aef10e5c68ea2b66fa2d17b2138259d6ec0ebea870c","first_computed_at":"2026-05-20T14:03:15.488430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:15.488430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSftKAj27u8F03JIrPSHPNTEP1U/thtA6jq37bjEKNpE8xy00EGD0PxG4FHd88tNtMj6httMGXhuhPiZ5qxfDQ==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:15.488872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.06361","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b86e94daec963c811e43dc39e864ff8166fb6a7b32292d35139a523b14b4e890","sha256:3b6fbaa5b21850ef93a3e6c9fcf9cefc67453dedc00755193bb2a13f35bc78ee"],"state_sha256":"20673adb27b9904a17014cfc07e927cfeac208b35080282ea716b1f9bb7e46f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1KLsm7b5mMs2zAWsBgfSxpss8WCkfjIGK9FLeVAxWmzASQtQNcU4yXbZPZCs1dB5OHVLEv1oingwd1/MY9+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:25:29.714823Z","bundle_sha256":"339c2447c8d5afc70d23d0f64b3ee1d0b10350d6ced45b9430d762f907c241de"}}