{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BD4ON7ZWDAY5B7FJFW5FUSQZAN","short_pith_number":"pith:BD4ON7ZW","canonical_record":{"source":{"id":"1606.00935","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-03T00:10:27Z","cross_cats_sorted":[],"title_canon_sha256":"8810fb8760682641395861a632c40f42ede97017648b42e44ed544bf69ec171e","abstract_canon_sha256":"5cf53a33b8ca39dbe0e77b5a2a67b79d1cca171d4903e3590b7101ff2545b90f"},"schema_version":"1.0"},"canonical_sha256":"08f8e6ff361831d0fca92dba5a4a190354e40deb6b6f939fd2ba2cf1c21c90ef","source":{"kind":"arxiv","id":"1606.00935","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00935","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00935v3","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00935","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"BD4ON7ZWDAY5","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"BD4ON7ZWDAY5B7FJ","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"BD4ON7ZW","created_at":"2026-07-05T01:01:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BD4ON7ZWDAY5B7FJFW5FUSQZAN","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00935","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-03T00:10:27Z","cross_cats_sorted":[],"title_canon_sha256":"8810fb8760682641395861a632c40f42ede97017648b42e44ed544bf69ec171e","abstract_canon_sha256":"5cf53a33b8ca39dbe0e77b5a2a67b79d1cca171d4903e3590b7101ff2545b90f"},"schema_version":"1.0"},"canonical_sha256":"08f8e6ff361831d0fca92dba5a4a190354e40deb6b6f939fd2ba2cf1c21c90ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:01:31.044653Z","signature_b64":"3OvscpSAx6sVT0tywb0zZEzffiS3Xnecz6FJe332MY7o1/RjcM1rou6sDGCvy0VDPk4xehp3sEz/xZC2JdDjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08f8e6ff361831d0fca92dba5a4a190354e40deb6b6f939fd2ba2cf1c21c90ef","last_reissued_at":"2026-07-05T01:01:31.044184Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:01:31.044184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00935","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":"2026-07-05T01:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iul6gvYGeSGKSM+DfACjALQoyRFChgwok/lgT6VBJKn+D0nY0/MVtskvi/L+pdsWcTkFIqeODnBhHTmivBnPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T09:59:56.366108Z"},"content_sha256":"b868fdd3cb529b2992a417b1a4588c1fdb042adf9e77ff47943b5ca0031606e9","schema_version":"1.0","event_id":"sha256:b868fdd3cb529b2992a417b1a4588c1fdb042adf9e77ff47943b5ca0031606e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BD4ON7ZWDAY5B7FJFW5FUSQZAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symbolic powers of codimension two Cohen-Macaulay ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Alexandra Seceleanu, Anna Lorenzini, Elena Guardo, Giuliana Fatabbi, Juan Migliore, Justyna Szpond, Susan Cooper, Uwe Nagel","submitted_at":"2016-06-03T00:10:27Z","abstract_excerpt":"Let $I_X$ be the saturated homogeneous ideal defining a codimension two arithmetically Cohen-Macaulay scheme $X \\subseteq \\mathbb{P}^n$, and let $I_X^{(m)}$ denote its $m$-th symbolic power. We are interested in when $I_X^{(m)} = I_X^m$. We survey what is known about this problem when $X$ is locally a complete intersection, and in particular, we review the classification of when $I_X^{(m)} = I_X^m$ for all $m \\geq 1$. We then discuss how one might weaken these hypotheses, but still obtain equality between the symbolic and ordinary powers. Finally, we show that this classification allows one to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00935","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/1606.00935/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":"2026-07-05T01:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2TjxWP7RHSQ2htWdwLAT0BdYkG+Qsvyyomg07SBrGxgpQTDfvM/31vdHErkXnKuqXxwi5NrXERlBv5yC+gWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T09:59:56.366613Z"},"content_sha256":"3321a7925a774534c88294d7269f04be03f96b09dfeea2516772a4c56bac4d3b","schema_version":"1.0","event_id":"sha256:3321a7925a774534c88294d7269f04be03f96b09dfeea2516772a4c56bac4d3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN/bundle.json","state_url":"https://pith.science/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN/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":"2026-08-16T09:59:56Z","links":{"resolver":"https://pith.science/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN","bundle":"https://pith.science/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN/bundle.json","state":"https://pith.science/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BD4ON7ZWDAY5B7FJFW5FUSQZAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BD4ON7ZWDAY5B7FJFW5FUSQZAN","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":"5cf53a33b8ca39dbe0e77b5a2a67b79d1cca171d4903e3590b7101ff2545b90f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-03T00:10:27Z","title_canon_sha256":"8810fb8760682641395861a632c40f42ede97017648b42e44ed544bf69ec171e"},"schema_version":"1.0","source":{"id":"1606.00935","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00935","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00935v3","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00935","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"BD4ON7ZWDAY5","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"BD4ON7ZWDAY5B7FJ","created_at":"2026-07-05T01:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"BD4ON7ZW","created_at":"2026-07-05T01:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:3321a7925a774534c88294d7269f04be03f96b09dfeea2516772a4c56bac4d3b","target":"graph","created_at":"2026-07-05T01:01:31Z","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/1606.00935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $I_X$ be the saturated homogeneous ideal defining a codimension two arithmetically Cohen-Macaulay scheme $X \\subseteq \\mathbb{P}^n$, and let $I_X^{(m)}$ denote its $m$-th symbolic power. We are interested in when $I_X^{(m)} = I_X^m$. We survey what is known about this problem when $X$ is locally a complete intersection, and in particular, we review the classification of when $I_X^{(m)} = I_X^m$ for all $m \\geq 1$. We then discuss how one might weaken these hypotheses, but still obtain equality between the symbolic and ordinary powers. Finally, we show that this classification allows one to","authors_text":"Adam Van Tuyl, Alexandra Seceleanu, Anna Lorenzini, Elena Guardo, Giuliana Fatabbi, Juan Migliore, Justyna Szpond, Susan Cooper, Uwe Nagel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-03T00:10:27Z","title":"Symbolic powers of codimension two Cohen-Macaulay ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00935","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:b868fdd3cb529b2992a417b1a4588c1fdb042adf9e77ff47943b5ca0031606e9","target":"record","created_at":"2026-07-05T01:01:31Z","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":"5cf53a33b8ca39dbe0e77b5a2a67b79d1cca171d4903e3590b7101ff2545b90f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-03T00:10:27Z","title_canon_sha256":"8810fb8760682641395861a632c40f42ede97017648b42e44ed544bf69ec171e"},"schema_version":"1.0","source":{"id":"1606.00935","kind":"arxiv","version":3}},"canonical_sha256":"08f8e6ff361831d0fca92dba5a4a190354e40deb6b6f939fd2ba2cf1c21c90ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08f8e6ff361831d0fca92dba5a4a190354e40deb6b6f939fd2ba2cf1c21c90ef","first_computed_at":"2026-07-05T01:01:31.044184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:01:31.044184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3OvscpSAx6sVT0tywb0zZEzffiS3Xnecz6FJe332MY7o1/RjcM1rou6sDGCvy0VDPk4xehp3sEz/xZC2JdDjCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:01:31.044653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00935","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b868fdd3cb529b2992a417b1a4588c1fdb042adf9e77ff47943b5ca0031606e9","sha256:3321a7925a774534c88294d7269f04be03f96b09dfeea2516772a4c56bac4d3b"],"state_sha256":"6b49899ccef5b31e44b25a3338c473358b22cef2fc4f6d073c0e430a395868ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p3svhyOi3JhFwC4//01FdxKAFRb+giUBLIknbEJSkVe7iZ6x6rIk1gz13A/IWjLDDDNdheBTGE+nVpQad/OdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T09:59:56.370258Z","bundle_sha256":"2e283a74a0b1f151371a9d60031df3a44b239274143122a8d51e197c71b614fe"}}