{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TMQHKC54DKNSSB4KZZI6QNUW3T","short_pith_number":"pith:TMQHKC54","canonical_record":{"source":{"id":"1809.00583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-03T12:42:25Z","cross_cats_sorted":[],"title_canon_sha256":"c1ffdf3f7a1a87f4f2aa9e28ed79615aaaf2f8882302bc3b1d2727ce858ec564","abstract_canon_sha256":"861d0d1a00f56d13518ed77c532db04628905dac9eead95d2a59c2d5aa25cacf"},"schema_version":"1.0"},"canonical_sha256":"9b20750bbc1a9b29078ace51e83696dcf695d1bc4492ffda5e243336178637ab","source":{"kind":"arxiv","id":"1809.00583","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00583","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00583v2","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00583","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"pith_short_12","alias_value":"TMQHKC54DKNS","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TMQHKC54DKNSSB4K","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TMQHKC54","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TMQHKC54DKNSSB4KZZI6QNUW3T","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-03T12:42:25Z","cross_cats_sorted":[],"title_canon_sha256":"c1ffdf3f7a1a87f4f2aa9e28ed79615aaaf2f8882302bc3b1d2727ce858ec564","abstract_canon_sha256":"861d0d1a00f56d13518ed77c532db04628905dac9eead95d2a59c2d5aa25cacf"},"schema_version":"1.0"},"canonical_sha256":"9b20750bbc1a9b29078ace51e83696dcf695d1bc4492ffda5e243336178637ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:11.008605Z","signature_b64":"6SKfYfL3V2DNeLGv6Vh1wuXi0ghYicnekb1OAijRCuv4+FeXKjpXZp71UbMSidHOS2NJn8vSUsdFCjGmY97mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b20750bbc1a9b29078ace51e83696dcf695d1bc4492ffda5e243336178637ab","last_reissued_at":"2026-05-18T00:06:11.008044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:11.008044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00583","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3xOHgish+DGg5KVZn/+lws0uwjAG+LDiHoeTYzhzPUBtSqYOiKyrW2g/MHLZWCC8u/KzFAr941UUQjmay2mDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:31:16.881884Z"},"content_sha256":"5ef79178d2f57a719009ec6ec117f436956a9478f145c28f34539947f2c8ea20","schema_version":"1.0","event_id":"sha256:5ef79178d2f57a719009ec6ec117f436956a9478f145c28f34539947f2c8ea20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TMQHKC54DKNSSB4KZZI6QNUW3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincar\\'e series on good semigroup ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Laura Tozzo","submitted_at":"2018-09-03T12:42:25Z","abstract_excerpt":"The Poincar\\'e series of a ring associated to a plane curve was defined by Campillo, Delgado, and Gusein-Zade. This series, defined through the value semigroup of the curve, encodes the topological information of the curve. In this paper we extend the definition of Poincar\\'e series to the class of good semigroup ideals, to which value semigroups of curves belong. Using this definition we generalize a result of Pol: under suitable assumptions, given good semigroup ideals E and K, with K canonical, the Poincar\\'e series of K-E is symmetric to the Poincar\\'e series of E."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00583","kind":"arxiv","version":2},"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":"2026-05-18T00:06:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Az42/nhJWhoWFN7GSTWwWrzOKzrFwRwv6ywnJdFCZSjVFgjF8Ezh01T6bo32c1NklMWGlTnzYUdrWHXXY0FdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:31:16.882233Z"},"content_sha256":"fda742f91bee9938d9d9e5443fba2e5cfb4274503c53b9b6b374209a2ebce363","schema_version":"1.0","event_id":"sha256:fda742f91bee9938d9d9e5443fba2e5cfb4274503c53b9b6b374209a2ebce363"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMQHKC54DKNSSB4KZZI6QNUW3T/bundle.json","state_url":"https://pith.science/pith/TMQHKC54DKNSSB4KZZI6QNUW3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMQHKC54DKNSSB4KZZI6QNUW3T/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":"2026-06-01T08:31:16Z","links":{"resolver":"https://pith.science/pith/TMQHKC54DKNSSB4KZZI6QNUW3T","bundle":"https://pith.science/pith/TMQHKC54DKNSSB4KZZI6QNUW3T/bundle.json","state":"https://pith.science/pith/TMQHKC54DKNSSB4KZZI6QNUW3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMQHKC54DKNSSB4KZZI6QNUW3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TMQHKC54DKNSSB4KZZI6QNUW3T","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":"861d0d1a00f56d13518ed77c532db04628905dac9eead95d2a59c2d5aa25cacf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-03T12:42:25Z","title_canon_sha256":"c1ffdf3f7a1a87f4f2aa9e28ed79615aaaf2f8882302bc3b1d2727ce858ec564"},"schema_version":"1.0","source":{"id":"1809.00583","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00583","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00583v2","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00583","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"pith_short_12","alias_value":"TMQHKC54DKNS","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TMQHKC54DKNSSB4K","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TMQHKC54","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:fda742f91bee9938d9d9e5443fba2e5cfb4274503c53b9b6b374209a2ebce363","target":"graph","created_at":"2026-05-18T00:06:11Z","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":"The Poincar\\'e series of a ring associated to a plane curve was defined by Campillo, Delgado, and Gusein-Zade. This series, defined through the value semigroup of the curve, encodes the topological information of the curve. In this paper we extend the definition of Poincar\\'e series to the class of good semigroup ideals, to which value semigroups of curves belong. Using this definition we generalize a result of Pol: under suitable assumptions, given good semigroup ideals E and K, with K canonical, the Poincar\\'e series of K-E is symmetric to the Poincar\\'e series of E.","authors_text":"Laura Tozzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-03T12:42:25Z","title":"Poincar\\'e series on good semigroup ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00583","kind":"arxiv","version":2},"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":"sha256:5ef79178d2f57a719009ec6ec117f436956a9478f145c28f34539947f2c8ea20","target":"record","created_at":"2026-05-18T00:06:11Z","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":"861d0d1a00f56d13518ed77c532db04628905dac9eead95d2a59c2d5aa25cacf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-03T12:42:25Z","title_canon_sha256":"c1ffdf3f7a1a87f4f2aa9e28ed79615aaaf2f8882302bc3b1d2727ce858ec564"},"schema_version":"1.0","source":{"id":"1809.00583","kind":"arxiv","version":2}},"canonical_sha256":"9b20750bbc1a9b29078ace51e83696dcf695d1bc4492ffda5e243336178637ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b20750bbc1a9b29078ace51e83696dcf695d1bc4492ffda5e243336178637ab","first_computed_at":"2026-05-18T00:06:11.008044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:11.008044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6SKfYfL3V2DNeLGv6Vh1wuXi0ghYicnekb1OAijRCuv4+FeXKjpXZp71UbMSidHOS2NJn8vSUsdFCjGmY97mCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:11.008605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00583","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ef79178d2f57a719009ec6ec117f436956a9478f145c28f34539947f2c8ea20","sha256:fda742f91bee9938d9d9e5443fba2e5cfb4274503c53b9b6b374209a2ebce363"],"state_sha256":"158d2e4e99d2d9654bfdce66fee4858ca9066961680f529205349e1bd47adc20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMROfrvciu8QLu+dQDmkFvRPrb7SKr3TxzufSXp+FF7nrPlSpLIIZjGzZdNrMVRqQpAz2KljxEWh2n1/RicSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:31:16.884160Z","bundle_sha256":"9efc205863c7e2e52345b85f06b594bd02ce09dc67ba632cb0d2764a5164df9d"}}