{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:245LSO6DYJV4VGMWPJSCNLQ33R","short_pith_number":"pith:245LSO6D","canonical_record":{"source":{"id":"1807.00134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-06-30T07:43:45Z","cross_cats_sorted":[],"title_canon_sha256":"2a7b1f51cac72b5cbca9039fa70da395cca0b910c9271e710bfac0ff09bc629d","abstract_canon_sha256":"5f8e7e6796e894543939fcb1205dd74537b3f69343c7966bf2507639710518c5"},"schema_version":"1.0"},"canonical_sha256":"d73ab93bc3c26bca99967a6426ae1bdc4f018882d3d3fc98ee1c4133406b09ce","source":{"kind":"arxiv","id":"1807.00134","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00134","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00134v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00134","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"245LSO6DYJV4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"245LSO6DYJV4VGMW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"245LSO6D","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:245LSO6DYJV4VGMWPJSCNLQ33R","target":"record","payload":{"canonical_record":{"source":{"id":"1807.00134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-06-30T07:43:45Z","cross_cats_sorted":[],"title_canon_sha256":"2a7b1f51cac72b5cbca9039fa70da395cca0b910c9271e710bfac0ff09bc629d","abstract_canon_sha256":"5f8e7e6796e894543939fcb1205dd74537b3f69343c7966bf2507639710518c5"},"schema_version":"1.0"},"canonical_sha256":"d73ab93bc3c26bca99967a6426ae1bdc4f018882d3d3fc98ee1c4133406b09ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:55.979117Z","signature_b64":"D9kvkYvOuvAvJfps9XcYmH5u7wANjCUOVJmXNZ0Z9cyMX3O+0bDrVpRTwPxyvuRjZo1Fg0lt0qdB0MSQrYt+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d73ab93bc3c26bca99967a6426ae1bdc4f018882d3d3fc98ee1c4133406b09ce","last_reissued_at":"2026-05-18T00:11:55.978380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:55.978380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.00134","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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ENLTIXOVhvc9SxtNVUqt9A2Qg7782rfCoTjarLANdnNnUle84CA1lAf1vYJNwYSZliHlsugjo2feP/kOzRbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:51:03.641653Z"},"content_sha256":"faaf865b8937e349b267c9a06ea4c3a890b0ec7b177c467a8cef5100e0f3478b","schema_version":"1.0","event_id":"sha256:faaf865b8937e349b267c9a06ea4c3a890b0ec7b177c467a8cef5100e0f3478b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:245LSO6DYJV4VGMWPJSCNLQ33R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost symmetric numerical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"J\\\"urgen Herzog, Kei-ichi Watanabe","submitted_at":"2018-06-30T07:43:45Z","abstract_excerpt":"We study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup.\n  For almost symmetric semigroups generated by $4$ elements we will give a structure theorem by using the \\lq\\lq row-factorization matrices\", introduced by Moscariello. As a result, we give a simpler proof of Komeda's structure theorem of pseudo-symmetric numerical semigroups generated by $4$ elements. Row-factorization matrices are also used to study shifted families of numerical semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00134","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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lb/qBMSSgoORr8afSIC5RJ6wFB79VYH3rZ+TUjfQPLHBrZazzVsO74VGj6sYFcoWvFUO9VXidlEQFAFsm09nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:51:03.641990Z"},"content_sha256":"4e0942d915e29eadba0ab1580c25e2faf2d15e03681247acf4f9fba3774f6709","schema_version":"1.0","event_id":"sha256:4e0942d915e29eadba0ab1580c25e2faf2d15e03681247acf4f9fba3774f6709"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/245LSO6DYJV4VGMWPJSCNLQ33R/bundle.json","state_url":"https://pith.science/pith/245LSO6DYJV4VGMWPJSCNLQ33R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/245LSO6DYJV4VGMWPJSCNLQ33R/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":"2026-06-07T02:51:03Z","links":{"resolver":"https://pith.science/pith/245LSO6DYJV4VGMWPJSCNLQ33R","bundle":"https://pith.science/pith/245LSO6DYJV4VGMWPJSCNLQ33R/bundle.json","state":"https://pith.science/pith/245LSO6DYJV4VGMWPJSCNLQ33R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/245LSO6DYJV4VGMWPJSCNLQ33R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:245LSO6DYJV4VGMWPJSCNLQ33R","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":"5f8e7e6796e894543939fcb1205dd74537b3f69343c7966bf2507639710518c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-06-30T07:43:45Z","title_canon_sha256":"2a7b1f51cac72b5cbca9039fa70da395cca0b910c9271e710bfac0ff09bc629d"},"schema_version":"1.0","source":{"id":"1807.00134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00134","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00134v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00134","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"245LSO6DYJV4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"245LSO6DYJV4VGMW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"245LSO6D","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:4e0942d915e29eadba0ab1580c25e2faf2d15e03681247acf4f9fba3774f6709","target":"graph","created_at":"2026-05-18T00:11:55Z","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 study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup.\n  For almost symmetric semigroups generated by $4$ elements we will give a structure theorem by using the \\lq\\lq row-factorization matrices\", introduced by Moscariello. As a result, we give a simpler proof of Komeda's structure theorem of pseudo-symmetric numerical semigroups generated by $4$ elements. Row-factorization matrices are also used to study shifted families of numerical semigroups.","authors_text":"J\\\"urgen Herzog, Kei-ichi Watanabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-06-30T07:43:45Z","title":"Almost symmetric numerical semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00134","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:faaf865b8937e349b267c9a06ea4c3a890b0ec7b177c467a8cef5100e0f3478b","target":"record","created_at":"2026-05-18T00:11:55Z","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":"5f8e7e6796e894543939fcb1205dd74537b3f69343c7966bf2507639710518c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-06-30T07:43:45Z","title_canon_sha256":"2a7b1f51cac72b5cbca9039fa70da395cca0b910c9271e710bfac0ff09bc629d"},"schema_version":"1.0","source":{"id":"1807.00134","kind":"arxiv","version":1}},"canonical_sha256":"d73ab93bc3c26bca99967a6426ae1bdc4f018882d3d3fc98ee1c4133406b09ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d73ab93bc3c26bca99967a6426ae1bdc4f018882d3d3fc98ee1c4133406b09ce","first_computed_at":"2026-05-18T00:11:55.978380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:55.978380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D9kvkYvOuvAvJfps9XcYmH5u7wANjCUOVJmXNZ0Z9cyMX3O+0bDrVpRTwPxyvuRjZo1Fg0lt0qdB0MSQrYt+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:55.979117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faaf865b8937e349b267c9a06ea4c3a890b0ec7b177c467a8cef5100e0f3478b","sha256:4e0942d915e29eadba0ab1580c25e2faf2d15e03681247acf4f9fba3774f6709"],"state_sha256":"726261f0998424582449bd7672d8cae7837d3b1ecf749793777de355ff232e3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6IMvGSoP1geIy6YWWDfe6MWKIx3Ktods8dM7ZvMO1DEcY/ZsDEEuzHoJOBAqyqqZLKcHndaa/fcC8HtYKcqLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:51:03.644173Z","bundle_sha256":"58f616dc0226af5d2efc1dab77a08313074f2ead70dc56c935e75d22daf08a45"}}