{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FV5SBHEZ5FMPTYDEUE3YBTTUNQ","short_pith_number":"pith:FV5SBHEZ","canonical_record":{"source":{"id":"1906.01585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-04T16:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"53b6200fd7902ccce58341032b6e59d5372636245e64be11a4abb0a8ccb34e71","abstract_canon_sha256":"fbe5c13cae39a8ea0cfb7e3db9e1b4a6a49277800de71ed5a2fb47e5a645840d"},"schema_version":"1.0"},"canonical_sha256":"2d7b209c99e958f9e064a13780ce746c0e2f93153629e5d6411dad49ae3ca24b","source":{"kind":"arxiv","id":"1906.01585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01585","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01585v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01585","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"FV5SBHEZ5FMP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FV5SBHEZ5FMPTYDE","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FV5SBHEZ","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FV5SBHEZ5FMPTYDEUE3YBTTUNQ","target":"record","payload":{"canonical_record":{"source":{"id":"1906.01585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-04T16:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"53b6200fd7902ccce58341032b6e59d5372636245e64be11a4abb0a8ccb34e71","abstract_canon_sha256":"fbe5c13cae39a8ea0cfb7e3db9e1b4a6a49277800de71ed5a2fb47e5a645840d"},"schema_version":"1.0"},"canonical_sha256":"2d7b209c99e958f9e064a13780ce746c0e2f93153629e5d6411dad49ae3ca24b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:16.050454Z","signature_b64":"7myluauHdubCKqfRl03+PMi9q0bglYbIJPXeZJqUf7KY07RjfjNrHPUWie9WKXZKw2OMxiOSbx16mpzLptH1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d7b209c99e958f9e064a13780ce746c0e2f93153629e5d6411dad49ae3ca24b","last_reissued_at":"2026-05-17T23:44:16.049834Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:16.049834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.01585","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":"2026-05-17T23:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ZNo/QbxESYWsYhp+lJCGpmJGpFeRJX4baX2P4vS3PnFh1Z6IrwFaSfGwiJ5oKeoCbB/ZJgMErcs1P4OhMPiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:31:21.082998Z"},"content_sha256":"ad1fe8eafffe6798d3b83cd074213ce7d4c9ef1a40e66091fc2f05841eebefc5","schema_version":"1.0","event_id":"sha256:ad1fe8eafffe6798d3b83cd074213ce7d4c9ef1a40e66091fc2f05841eebefc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FV5SBHEZ5FMPTYDEUE3YBTTUNQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A geometrical characterization of proportionally modular affine semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A. S\\'anchez-R.-Navarro, A. Vigneron-Tenorio, J. D. D\\'iaz-Ram\\'irez, J. I. Garc\\'ia-Garc\\'ia","submitted_at":"2019-06-04T16:59:46Z","abstract_excerpt":"A proportionally modular affine semigroup is the set of nonnegative integer solutions of a modular Diophantine inequality $f_1x_1+\\cdots +f_nx_n \\mod b \\le g_1x_1+\\cdots +g_nx_n$ where $g_1,\\dots,g_n,$ $f_1,\\ldots ,f_n\\in \\mathbb{Z}$ and $b\\in\\mathbb{N}$. In this work, a geometrical characterization of these semigroups is given. Moreover, some algorithms to check if a semigroup $S$ in $\\mathbb{N}^n$, with $\\mathbb{N}^n\\setminus S$ a finite set, is a proportionally modular affine semigroup are provided by means of that geometrical approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01585","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":"2026-05-17T23:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btnk3jVCFYX9JEGPJ6dfuZ6RvwmRfFHOP8Yy/PK7NGAgXr89rYn42W0GTq80T2AfFQZR2OToJ9f3Fo8eayk6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:31:21.083420Z"},"content_sha256":"744741d108c718a7b53750abe35262f7d9f45be8a9977e040df7a7d2c05faa04","schema_version":"1.0","event_id":"sha256:744741d108c718a7b53750abe35262f7d9f45be8a9977e040df7a7d2c05faa04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ/bundle.json","state_url":"https://pith.science/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ/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":"2026-06-04T15:31:21Z","links":{"resolver":"https://pith.science/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ","bundle":"https://pith.science/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ/bundle.json","state":"https://pith.science/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FV5SBHEZ5FMPTYDEUE3YBTTUNQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FV5SBHEZ5FMPTYDEUE3YBTTUNQ","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":"fbe5c13cae39a8ea0cfb7e3db9e1b4a6a49277800de71ed5a2fb47e5a645840d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-04T16:59:46Z","title_canon_sha256":"53b6200fd7902ccce58341032b6e59d5372636245e64be11a4abb0a8ccb34e71"},"schema_version":"1.0","source":{"id":"1906.01585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01585","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01585v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01585","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"FV5SBHEZ5FMP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FV5SBHEZ5FMPTYDE","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FV5SBHEZ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:744741d108c718a7b53750abe35262f7d9f45be8a9977e040df7a7d2c05faa04","target":"graph","created_at":"2026-05-17T23:44:16Z","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":"A proportionally modular affine semigroup is the set of nonnegative integer solutions of a modular Diophantine inequality $f_1x_1+\\cdots +f_nx_n \\mod b \\le g_1x_1+\\cdots +g_nx_n$ where $g_1,\\dots,g_n,$ $f_1,\\ldots ,f_n\\in \\mathbb{Z}$ and $b\\in\\mathbb{N}$. In this work, a geometrical characterization of these semigroups is given. Moreover, some algorithms to check if a semigroup $S$ in $\\mathbb{N}^n$, with $\\mathbb{N}^n\\setminus S$ a finite set, is a proportionally modular affine semigroup are provided by means of that geometrical approach.","authors_text":"A. S\\'anchez-R.-Navarro, A. Vigneron-Tenorio, J. D. D\\'iaz-Ram\\'irez, J. I. Garc\\'ia-Garc\\'ia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-04T16:59:46Z","title":"A geometrical characterization of proportionally modular affine semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01585","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:ad1fe8eafffe6798d3b83cd074213ce7d4c9ef1a40e66091fc2f05841eebefc5","target":"record","created_at":"2026-05-17T23:44:16Z","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":"fbe5c13cae39a8ea0cfb7e3db9e1b4a6a49277800de71ed5a2fb47e5a645840d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-04T16:59:46Z","title_canon_sha256":"53b6200fd7902ccce58341032b6e59d5372636245e64be11a4abb0a8ccb34e71"},"schema_version":"1.0","source":{"id":"1906.01585","kind":"arxiv","version":1}},"canonical_sha256":"2d7b209c99e958f9e064a13780ce746c0e2f93153629e5d6411dad49ae3ca24b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d7b209c99e958f9e064a13780ce746c0e2f93153629e5d6411dad49ae3ca24b","first_computed_at":"2026-05-17T23:44:16.049834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:16.049834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7myluauHdubCKqfRl03+PMi9q0bglYbIJPXeZJqUf7KY07RjfjNrHPUWie9WKXZKw2OMxiOSbx16mpzLptH1CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:16.050454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad1fe8eafffe6798d3b83cd074213ce7d4c9ef1a40e66091fc2f05841eebefc5","sha256:744741d108c718a7b53750abe35262f7d9f45be8a9977e040df7a7d2c05faa04"],"state_sha256":"fd89da60cfcaa66459c46854d8d578a18957035e27b3eeaa244ed29fdb48e0bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUfiAKsVpUPBjkvi8IZB4X87sf4nzJGoFZbYcOs9LGLfoWOwwwGzsNuCgK+kk1vlqHtE2OjWvcUlnrYbIB40Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:31:21.085930Z","bundle_sha256":"5f7ac4fb69994876d5d877245a51258b17457ce1c41054ba34dd372eb70c7dee"}}