{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DB4GZUQ2NOY2LX7KFAZYHASOCQ","short_pith_number":"pith:DB4GZUQ2","canonical_record":{"source":{"id":"1803.08752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-23T11:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"dae4cfb9c6115bf16ce1fd89b1da3e5154d83a02778e9c7a15b3ea3e1f4e36cc","abstract_canon_sha256":"639ea2ca2bb8796c18cb2297ba605d24ac90eef9039297be0359bad76a48b694"},"schema_version":"1.0"},"canonical_sha256":"18786cd21a6bb1a5dfea283383824e14104bfa276b658f55ddf74b8d9c9472f2","source":{"kind":"arxiv","id":"1803.08752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08752","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08752v1","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08752","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"DB4GZUQ2NOY2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DB4GZUQ2NOY2LX7K","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DB4GZUQ2","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DB4GZUQ2NOY2LX7KFAZYHASOCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-23T11:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"dae4cfb9c6115bf16ce1fd89b1da3e5154d83a02778e9c7a15b3ea3e1f4e36cc","abstract_canon_sha256":"639ea2ca2bb8796c18cb2297ba605d24ac90eef9039297be0359bad76a48b694"},"schema_version":"1.0"},"canonical_sha256":"18786cd21a6bb1a5dfea283383824e14104bfa276b658f55ddf74b8d9c9472f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:18.634662Z","signature_b64":"F2R5XRduvwejaLqwvB5gz+EE00gwoKJ1rtg16yc2MOJlEj1txrv/MjGZfvTCmpjzC/jz6ubKQnGlH74bZMpiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18786cd21a6bb1a5dfea283383824e14104bfa276b658f55ddf74b8d9c9472f2","last_reissued_at":"2026-05-18T00:20:18.634043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:18.634043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08752","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":"2026-05-18T00:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CyDJAzdCYbwKHhuP9FU+/TKVzb8LEj0a71P7siqQ6FL+fbOb1MeZupKyq4q8ukARl9Jdi2ko3dUDU4aFmqHGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:26:16.489821Z"},"content_sha256":"27f8697d509248486ce4304c2f9025da68ebc4a08d0cb374a59bb4a1c220711a","schema_version":"1.0","event_id":"sha256:27f8697d509248486ce4304c2f9025da68ebc4a08d0cb374a59bb4a1c220711a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DB4GZUQ2NOY2LX7KFAZYHASOCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Weierstrass gaps at several points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guilherme Tizziotti, Wanderson Ten\\'orio","submitted_at":"2018-03-23T11:47:22Z","abstract_excerpt":"We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado \\cite{D}, we present a description of these elements which generalizes the approach of Homma and Kim \\cite{HK} given for pairs. Through this description, we study the gaps and pure gaps at several points on a certain family of curves with separated variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08752","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":"2026-05-18T00:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"po+FEPxI7nMHBk3vI6fcUdb45dZ9GgzH3A5VFT7qjBaY2oqzpG//h8w2+FNni1uQQOW3sEL84fbwp6rbMRHLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:26:16.490161Z"},"content_sha256":"a8b72153ad38eebd0679b3c86ad916ae9007f05bc9dad484e63a28d0193665bb","schema_version":"1.0","event_id":"sha256:a8b72153ad38eebd0679b3c86ad916ae9007f05bc9dad484e63a28d0193665bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ/bundle.json","state_url":"https://pith.science/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ/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":"2026-06-02T17:26:16Z","links":{"resolver":"https://pith.science/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ","bundle":"https://pith.science/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ/bundle.json","state":"https://pith.science/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DB4GZUQ2NOY2LX7KFAZYHASOCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DB4GZUQ2NOY2LX7KFAZYHASOCQ","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":"639ea2ca2bb8796c18cb2297ba605d24ac90eef9039297be0359bad76a48b694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-23T11:47:22Z","title_canon_sha256":"dae4cfb9c6115bf16ce1fd89b1da3e5154d83a02778e9c7a15b3ea3e1f4e36cc"},"schema_version":"1.0","source":{"id":"1803.08752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08752","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08752v1","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08752","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"DB4GZUQ2NOY2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DB4GZUQ2NOY2LX7K","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DB4GZUQ2","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:a8b72153ad38eebd0679b3c86ad916ae9007f05bc9dad484e63a28d0193665bb","target":"graph","created_at":"2026-05-18T00:20:18Z","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":"We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado \\cite{D}, we present a description of these elements which generalizes the approach of Homma and Kim \\cite{HK} given for pairs. Through this description, we study the gaps and pure gaps at several points on a certain family of curves with separated variables.","authors_text":"Guilherme Tizziotti, Wanderson Ten\\'orio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-23T11:47:22Z","title":"On Weierstrass gaps at several points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08752","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":"sha256:27f8697d509248486ce4304c2f9025da68ebc4a08d0cb374a59bb4a1c220711a","target":"record","created_at":"2026-05-18T00:20:18Z","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":"639ea2ca2bb8796c18cb2297ba605d24ac90eef9039297be0359bad76a48b694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-23T11:47:22Z","title_canon_sha256":"dae4cfb9c6115bf16ce1fd89b1da3e5154d83a02778e9c7a15b3ea3e1f4e36cc"},"schema_version":"1.0","source":{"id":"1803.08752","kind":"arxiv","version":1}},"canonical_sha256":"18786cd21a6bb1a5dfea283383824e14104bfa276b658f55ddf74b8d9c9472f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18786cd21a6bb1a5dfea283383824e14104bfa276b658f55ddf74b8d9c9472f2","first_computed_at":"2026-05-18T00:20:18.634043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:18.634043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F2R5XRduvwejaLqwvB5gz+EE00gwoKJ1rtg16yc2MOJlEj1txrv/MjGZfvTCmpjzC/jz6ubKQnGlH74bZMpiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:18.634662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27f8697d509248486ce4304c2f9025da68ebc4a08d0cb374a59bb4a1c220711a","sha256:a8b72153ad38eebd0679b3c86ad916ae9007f05bc9dad484e63a28d0193665bb"],"state_sha256":"580816f3129f4cf069315f98fa9875f3b5d85eb093a72efc12e4cd536a2e2039"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XcbPmWU5ioCyt/UlCBk+B8/oURLVOg4+CIovr6dp1nVozw9K6xnsJU+tngAyz1TOKE6e6e4dlWPDxuKk0+X4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:26:16.492041Z","bundle_sha256":"2ade81a229e8f14fbc9c781ea69cf89ba2ed780bbe97e89a2d9df4c1e7d42130"}}