{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NBUEK7PFJ22PQGF6VZFNZWZHQX","short_pith_number":"pith:NBUEK7PF","canonical_record":{"source":{"id":"1903.11028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T17:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"c5f6c913e0e603549c8c3ecbe011deb18e0d1e8eca396acb8381a11d3c66c09e","abstract_canon_sha256":"ace693111caec95c9dcf69cb09a144db69f8e08f9e59919ad76cbfda32be4c2d"},"schema_version":"1.0"},"canonical_sha256":"6868457de54eb4f818beae4adcdb2785ee0807ac0c71617687f10103b7fcfa8e","source":{"kind":"arxiv","id":"1903.11028","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11028","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11028v1","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11028","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"pith_short_12","alias_value":"NBUEK7PFJ22P","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NBUEK7PFJ22PQGF6","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NBUEK7PF","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NBUEK7PFJ22PQGF6VZFNZWZHQX","target":"record","payload":{"canonical_record":{"source":{"id":"1903.11028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T17:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"c5f6c913e0e603549c8c3ecbe011deb18e0d1e8eca396acb8381a11d3c66c09e","abstract_canon_sha256":"ace693111caec95c9dcf69cb09a144db69f8e08f9e59919ad76cbfda32be4c2d"},"schema_version":"1.0"},"canonical_sha256":"6868457de54eb4f818beae4adcdb2785ee0807ac0c71617687f10103b7fcfa8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:16.932848Z","signature_b64":"UqBdsk+uw7bI+s/OuRvkE40dzlPacTwXGQeW80e+GgtOs9Hjil7t+LEmZhUkgJvhY9W8yf6Riy5fVs4LHLr2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6868457de54eb4f818beae4adcdb2785ee0807ac0c71617687f10103b7fcfa8e","last_reissued_at":"2026-05-17T23:50:16.932207Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:16.932207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.11028","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":"2026-05-17T23:50:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5hPVIg8V2stj77NkOvlRj56Z7Df6/k3l7lts+PPc3rRObyOUULLzyuz6OjFK4QhhNzX1tjxcqdaDcvhH2nVNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:35:35.028043Z"},"content_sha256":"4420ed007f43693908d7aa64f5923b049f9debec31e00062bb9e71366b577a76","schema_version":"1.0","event_id":"sha256:4420ed007f43693908d7aa64f5923b049f9debec31e00062bb9e71366b577a76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NBUEK7PFJ22PQGF6VZFNZWZHQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On pseudo-Frobenius elements of submonoids of $\\mathbb{N}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A. Vigneron-Tenorio, I. Ojeda, J.C. Rosales, J.I. Garc\\'ia-Garc\\'ia","submitted_at":"2019-03-26T17:20:28Z","abstract_excerpt":"In this paper we study those submonoids of $\\mathbb{N}^d$ which a non-trivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension possible. We prove that these semigroups are a natural generalization of numerical semigroups and, consequently, most of their invariants can be generalized. In the last section we introduce a new family of submonoids of $\\mathbb{N}^d$ and using its pseudo-Frobenius elements we prove that the elements in the family are direct limits of affine semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11028","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":"2026-05-17T23:50:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWyRrS8cbm5g3xGhE9S/ttNrvBF0d8keuZeDr+vaZBgbcA5OmdXIiwuXOJbQNvsb4M4zEZVEDVO9BMys8wRpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:35:35.028398Z"},"content_sha256":"c6cb1b0803039b12ac73b26deaf0080e0a5a57357cedd716656dbce2eae57176","schema_version":"1.0","event_id":"sha256:c6cb1b0803039b12ac73b26deaf0080e0a5a57357cedd716656dbce2eae57176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX/bundle.json","state_url":"https://pith.science/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX/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":"2026-06-03T21:35:35Z","links":{"resolver":"https://pith.science/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX","bundle":"https://pith.science/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX/bundle.json","state":"https://pith.science/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBUEK7PFJ22PQGF6VZFNZWZHQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NBUEK7PFJ22PQGF6VZFNZWZHQX","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":"ace693111caec95c9dcf69cb09a144db69f8e08f9e59919ad76cbfda32be4c2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T17:20:28Z","title_canon_sha256":"c5f6c913e0e603549c8c3ecbe011deb18e0d1e8eca396acb8381a11d3c66c09e"},"schema_version":"1.0","source":{"id":"1903.11028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11028","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11028v1","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11028","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"pith_short_12","alias_value":"NBUEK7PFJ22P","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NBUEK7PFJ22PQGF6","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NBUEK7PF","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:c6cb1b0803039b12ac73b26deaf0080e0a5a57357cedd716656dbce2eae57176","target":"graph","created_at":"2026-05-17T23:50:16Z","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":"In this paper we study those submonoids of $\\mathbb{N}^d$ which a non-trivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension possible. We prove that these semigroups are a natural generalization of numerical semigroups and, consequently, most of their invariants can be generalized. In the last section we introduce a new family of submonoids of $\\mathbb{N}^d$ and using its pseudo-Frobenius elements we prove that the elements in the family are direct limits of affine semigroups.","authors_text":"A. Vigneron-Tenorio, I. Ojeda, J.C. Rosales, J.I. Garc\\'ia-Garc\\'ia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T17:20:28Z","title":"On pseudo-Frobenius elements of submonoids of $\\mathbb{N}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11028","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":"sha256:4420ed007f43693908d7aa64f5923b049f9debec31e00062bb9e71366b577a76","target":"record","created_at":"2026-05-17T23:50:16Z","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":"ace693111caec95c9dcf69cb09a144db69f8e08f9e59919ad76cbfda32be4c2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-26T17:20:28Z","title_canon_sha256":"c5f6c913e0e603549c8c3ecbe011deb18e0d1e8eca396acb8381a11d3c66c09e"},"schema_version":"1.0","source":{"id":"1903.11028","kind":"arxiv","version":1}},"canonical_sha256":"6868457de54eb4f818beae4adcdb2785ee0807ac0c71617687f10103b7fcfa8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6868457de54eb4f818beae4adcdb2785ee0807ac0c71617687f10103b7fcfa8e","first_computed_at":"2026-05-17T23:50:16.932207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:16.932207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqBdsk+uw7bI+s/OuRvkE40dzlPacTwXGQeW80e+GgtOs9Hjil7t+LEmZhUkgJvhY9W8yf6Riy5fVs4LHLr2AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:16.932848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4420ed007f43693908d7aa64f5923b049f9debec31e00062bb9e71366b577a76","sha256:c6cb1b0803039b12ac73b26deaf0080e0a5a57357cedd716656dbce2eae57176"],"state_sha256":"7c36bd39a603ee5d83391b55ab669626f095bd26ac5d8220f4b9ae12e8b09850"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9xLS0zsH5HjbLTZAexGHOmOmL/jIWMgJ+Irw7rtr6KBNTkPygj+WQZoyf3zUFURSSgRm98DXxRB2a6RTdIxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:35:35.030343Z","bundle_sha256":"f75a5390ccb1b2e11fdd2d6a3c9ab0f34215896554fe5116d302852a8315efaa"}}